LMFDB - Embedded newform 546.2.q.i.251.6

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			251.6
Character	$\chi$	$=$	546.251
Dual form			546.2.q.i.335.6

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	−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	$-0.953186\pi$
$5$		−	0.655349i		−	0.293081i	0.989205	−	0.146541i	$-0.0468139\pi$
$6$	−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	−0.916016	−	0.401142i	$-0.868613\pi$
$11$	−0.366849	+	0.635401i	−0.110609	+	0.191580i	0.805407	+	0.592722i	$0.201947\pi$
$12$	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	0.786804	−	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	$-0.970501\pi$
$19$	−2.51943	−	4.36378i	−0.577996	−	1.00112i	0.417713	−	0.908579i	$-0.362832\pi$
$20$	−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	−0.207496	−	0.978236i	$-0.566531\pi$
$23$	−5.55559	−	3.20752i	−1.15842	−	0.668815i	−0.950925	+	0.309421i	$0.899865\pi$
$24$	−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	0.575873	−	0.817539i	$-0.304662\pi$
$29$	0.839009	+	0.484402i	0.155800	+	0.0899512i	−0.420073	+	0.907490i	$0.637996\pi$
$30$	−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	0.765809	−	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
$39$	6.21218	−	0.639432i	0.994744	−	0.102391i
$40$		−	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	$0.791169\pi$
$42$	1.59417	+	4.29635i	0.245986	+	0.662941i
$43$	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
$45$	−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	$-0.843261\pi$
$47$		−	6.48204i		−	0.945503i	0.881196	−	0.472752i	$-0.156739\pi$
$48$	−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	$-0.971635\pi$
$53$		−	1.29577i		−	0.177987i	0.996032	−	0.0889937i	$-0.0283651\pi$
$54$	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	−0.352902	−	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	−0.558527	−	0.829486i	$-0.688633\pi$
$61$	−0.932808	+	0.538557i	−0.119434	+	0.0689551i	0.439093	+	0.898442i	$0.355300\pi$
$62$	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	0.156584	−	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
$69$	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	0.513326	−	0.858194i	$-0.328413\pi$
$71$	−4.09978	−	7.10103i	−0.486555	−	0.842738i	−0.999881	+	0.0154562i	$0.995080\pi$
$72$	−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	$0.240664\pi$
$83$			12.5007i			1.37213i	−0.727539	+	0.686066i	$0.759336\pi$
$84$	−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	−0.356650	−	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
$91$	−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	0.642685	−	0.766131i	$-0.277820\pi$
$97$	−3.36975	−	5.83658i	−0.342146	−	0.592615i	−0.984831	+	0.173516i	$0.944487\pi$
$98$	−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	−0.802681	−	0.596409i	$-0.796594\pi$
$101$	1.15739	−	2.00466i	0.115165	−	0.199471i	0.917846	+	0.396938i	$0.129927\pi$
$102$	−0.0310783	+	2.01523i	−0.00307721	+	0.199537i
$103$			11.2924i			1.11268i	0.830956	+	0.556338i	$0.187794\pi$
$103$			11.2924i			1.11268i	−0.830956	+	0.556338i	$0.812206\pi$
$104$	−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	0.218286	−	0.975885i	$-0.429954\pi$
$107$	−5.35526	−	3.09186i	−0.517713	−	0.298901i	−0.735998	+	0.676983i	$0.763287\pi$
$108$	−4.61533	+	2.38719i	−0.444111	+	0.229708i
$109$		−	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
$111$	−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	−0.714820	−	0.699308i	$-0.753492\pi$
$113$	−4.96016	+	2.86375i	−0.466612	+	0.269399i	0.248208	+	0.968707i	$0.420158\pi$
$114$	−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	−0.650673	−	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	$0.685482\pi$
$132$	−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	0.742824	+	0.669487i	$0.233486\pi$
$137$	11.1336	+	19.2839i	0.951205	+	1.64753i	0.208381	+	0.978048i	$0.433181\pi$
$138$	5.40655	+	9.70709i	0.460236	+	0.826322i
$139$	−3.15133	+	1.81942i	−0.267293	+	0.154321i	−0.627657	−	0.778490i	$-0.715986\pi$
$139$	−3.15133	+	1.81942i	−0.267293	+	0.154321i	0.360364	+	0.932812i	$0.382652\pi$
$140$	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	−0.835378	−	0.549675i	$-0.814751\pi$
$149$	−10.9093	−	18.8954i	−0.893722	−	1.54797i	−0.0583437	−	0.998297i	$-0.518582\pi$
$150$	−6.79393	−	4.06343i	−0.554722	−	0.331778i
$151$		−	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
$153$	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	$-0.921965\pi$
$157$		−	6.08218i		−	0.485411i	0.970100	−	0.242705i	$-0.0780349\pi$
$158$	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	−0.803090	−	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
$165$	−0.427481	+	0.714735i	−0.0332794	+	0.0556421i
$166$	−10.8259	−	6.25036i	−0.840256	−	0.485122i
$167$	18.4911	+	10.6759i	1.43089	+	0.826122i	0.997188	−	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
$171$	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	0.692140	−	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
$175$	−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	0.417169	−	0.908829i	$-0.363022\pi$
$179$	−2.15825	−	1.24607i	−0.161315	−	0.0931353i	−0.578484	+	0.815694i	$0.696356\pi$
$180$	1.73215	−	0.930053i	0.129107	−	0.0693221i
$181$			19.3857i			1.44092i	0.693494	+	0.720462i	$0.256070\pi$
$181$			19.3857i			1.44092i	−0.693494	+	0.720462i	$0.743930\pi$
$182$	−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	−0.863206	−	0.504852i	$-0.831547\pi$
$191$	−11.8522	+	6.84286i	−0.857594	+	0.495132i	0.00561166	+	0.999984i	$0.498214\pi$
$192$	−0.0267080	+	1.73184i	−0.00192749	+	0.124985i
$193$	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
$195$	−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	−0.189741	−	0.981834i	$-0.560765\pi$
$197$	10.6029	−	18.3647i	0.755423	−	1.30843i	0.945164	−	0.326596i	$-0.105902\pi$
$198$	1.04124	+	1.93923i	0.0739979	+	0.137815i
$199$	2.97067	−	1.71512i	0.210585	−	0.121581i	−0.390998	−	0.920391i	$-0.627870\pi$
$199$	2.97067	−	1.71512i	0.210585	−	0.121581i	0.601583	+	0.798810i	$0.294537\pi$
$200$	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	−0.0198516	−	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
$217$	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	−0.972825	−	0.231540i	$-0.925624\pi$
$223$	−4.26929	+	7.39463i	−0.285893	+	0.495181i	0.686932	+	0.726721i	$0.258957\pi$
$224$	−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	−0.287589	−	0.957754i	$-0.592854\pi$
$227$	5.99732	−	3.46256i	0.398056	−	0.229818i	0.685645	+	0.727936i	$0.259520\pi$
$228$	−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	$0.0910499\pi$
$233$			8.61388i			0.564314i	−0.959368	+	0.282157i	$0.908950\pi$
$234$	−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	−0.999762	−	0.0218264i	$-0.993052\pi$
$241$	−8.05368	−	13.9494i	−0.518783	−	0.898559i	0.480979	−	0.876732i	$-0.340281\pi$
$242$	−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	0.980497	+	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	$-0.161656\pi$
$258$	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	0.969434	+	0.245352i	$0.0789036\pi$
$263$	27.0282	+	15.6048i	1.66663	+	0.962231i	0.697198	+	0.716878i	$0.254430\pi$
$264$	−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	0.866967	−	0.498365i	$-0.166066\pi$
$269$	0.0309493	+	0.0536058i	0.00188701	+	0.00326841i	−0.865080	+	0.501633i	$0.832733\pi$
$270$	1.83721	−	2.86718i	0.111809	−	0.174491i
$271$	2.55715	−	4.42912i	0.155336	−	0.269050i	−0.777845	−	0.628456i	$-0.783687\pi$
$271$	2.55715	−	4.42912i	0.155336	−	0.269050i	0.933181	+	0.359406i	$0.117021\pi$
$272$	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	0.570833	−	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
$279$	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	−0.170631	−	0.985335i	$-0.554580\pi$
$283$	−18.6608	−	10.7738i	−1.10927	−	0.640438i	−0.938640	+	0.344897i	$0.887914\pi$
$284$	−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	0.178615	−	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
$297$	3.20995	+	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	$0.160883\pi$
$313$			17.1322i			0.968368i	−0.874966	+	0.484184i	$0.839117\pi$
$314$	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	−0.746128	−	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
$336$	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	0.0390595	−	0.999237i	$-0.487564\pi$
$347$	17.2114	−	9.93698i	0.923954	−	0.533445i	0.884894	+	0.465792i	$0.154230\pi$
$348$	1.67782	+	0.0258749i	0.0899405	+	0.00138704i
$349$	−8.02933	+	13.9072i	−0.429800	+	0.744436i	−0.996855	−	0.0792439i	$-0.974749\pi$
$349$	−8.02933	+	13.9072i	−0.429800	+	0.744436i	0.567055	+	0.823680i	$0.308083\pi$
$350$	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	−0.267794	−	0.963476i	$-0.586295\pi$
$353$	−23.2239	−	13.4084i	−1.23609	−	0.713655i	−0.968292	+	0.249822i	$0.919628\pi$
$354$	−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	0.451528	−	0.892257i	$-0.350879\pi$
$367$	−1.82808	−	1.05544i	−0.0954251	−	0.0550937i	−0.546953	+	0.837163i	$0.684212\pi$
$368$	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	0.987869	+	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
$375$	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	0.699938	−	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
$381$	11.1327	+	6.65843i	0.570345	+	0.341122i
$382$		−	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	$0.0881979\pi$
$384$	−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	$0.135373\pi$
$389$			16.2748i			0.825166i	−0.910920	+	0.412583i	$0.864627\pi$
$390$	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	−0.999963	−	0.00855427i	$-0.997277\pi$
$397$	−10.1097	−	17.5105i	−0.507390	−	0.878825i	0.492573	−	0.870271i	$-0.336056\pi$
$398$			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	−0.0736358	−	0.997285i	$-0.523460\pi$
$401$	16.5578	−	28.6789i	0.826856	−	1.43216i	0.900492	−	0.434872i	$-0.143206\pi$
$402$	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	0.782388	+	0.622791i	$0.214001\pi$
$409$	18.8192	+	32.5957i	0.930547	+	1.61175i	0.148159	+	0.988964i	$0.452665\pi$
$410$	−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	0.162146	+	0.986767i	$0.448158\pi$
$419$	−15.8330	+	27.4235i	−0.773492	+	1.33973i	−0.935638	+	0.352961i	$0.885175\pi$
$420$	−0.503035	+	2.96076i	−0.0245456	+	0.144470i
$421$		−	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
$423$	−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	−0.828310	−	0.560270i	$-0.810697\pi$
$431$	1.47511	−	2.55497i	0.0710536	−	0.123068i	0.899363	+	0.437202i	$0.144031\pi$
$432$	4.37504	+	2.80340i	0.210494	+	0.134879i
$433$	−20.2415	+	11.6864i	−0.972742	+	0.561613i	−0.900071	−	0.435743i	$-0.856486\pi$
$433$	−20.2415	+	11.6864i	−0.972742	+	0.561613i	−0.0726709	+	0.997356i	$0.523152\pi$
$434$	−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	0.818695	−	0.574228i	$-0.194698\pi$
$439$	15.3108	+	8.83972i	0.730747	+	0.421897i	−0.0879485	+	0.996125i	$0.528031\pi$
$440$	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	$0.0437640\pi$
$443$			5.76939i			0.274112i	−0.990563	+	0.137056i	$0.956236\pi$
$444$	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	0.657779	−	0.753211i	$-0.271496\pi$
$449$	−6.85295	−	11.8697i	−0.323411	−	0.560164i	−0.981189	+	0.193047i	$0.938163\pi$
$450$	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	0.664474	−	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
$459$	−5.37054	+	2.77781i	−0.250675	+	0.129657i
$460$	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	$0.612516\pi$
$462$	−3.31472	−	0.563174i	−0.154215	−	0.0262012i
$463$			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
$465$	−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	−0.271989	−	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
$483$	−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	−0.711646	−	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
$490$	−1.38084	+	4.37469i	−0.0623802	+	0.197628i
$491$	−35.7809	−	20.6581i	−1.61477	−	0.932287i	−0.988244	−	0.152886i	$-0.951143\pi$
$491$	−35.7809	−	20.6581i	−1.61477	−	0.932287i	−0.626525	−	0.779401i	$-0.715524\pi$
$492$	−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	$-0.804356\pi$
$499$		−	25.7632i		−	1.15332i	0.816985	−	0.576660i	$-0.195644\pi$
$500$	−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	0.705026	−	0.709181i	$-0.250935\pi$
$503$	−5.86833	−	10.1642i	−0.261656	−	0.453201i	−0.966682	+	0.255980i	$0.917602\pi$
$504$	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	−0.479059	−	0.877783i	$-0.659022\pi$
$509$	−33.3626	−	19.2619i	−1.47877	−	0.853768i	−0.999712	+	0.0240145i	$0.992355\pi$
$510$	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	0.980076	−	0.198625i	$-0.0636474\pi$
$523$	29.6865	+	17.1395i	1.29810	+	0.749458i	0.318024	+	0.948083i	$0.396981\pi$
$524$	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	$-0.853834\pi$
$541$		−	20.6184i		−	0.886454i	0.896410	−	0.443227i	$-0.146166\pi$
$542$	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	−0.943173	−	0.332302i	$-0.892175\pi$
$557$	−4.33794	+	7.51353i	−0.183804	+	0.318358i	0.759369	+	0.650661i	$0.225508\pi$
$558$	−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	0.685659	−	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	0.887887	−	0.460062i	$-0.152173\pi$
$569$	22.2652	+	12.8548i	0.933404	+	0.538901i	0.0455175	+	0.998964i	$0.485506\pi$
$570$	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	0.106854	−	0.994275i	$-0.465922\pi$
$587$	−16.9787	−	9.80266i	−0.700786	−	0.404599i	−0.807640	+	0.589676i	$0.799256\pi$
$588$	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	$0.0522261\pi$
$593$			7.95508i			0.326676i	−0.986570	+	0.163338i	$0.947774\pi$
$594$	−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	$-0.844675\pi$
$599$		−	22.9488i		−	0.937662i	0.883288	−	0.468831i	$-0.155325\pi$
$600$	−0.122070	+	7.91543i	−0.00498347	+	0.323146i
$601$	−6.23997	−	3.60265i	−0.254534	−	0.146955i	0.367305	−	0.930101i	$-0.380281\pi$
$601$	−6.23997	−	3.60265i	−0.254534	−	0.146955i	−0.621839	+	0.783145i	$0.713614\pi$
$602$	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	−0.501350	−	0.865245i	$-0.667163\pi$
$607$	−0.0665333	+	0.0384130i	−0.00270050	+	0.00155914i	0.498649	+	0.866804i	$0.333830\pi$
$608$	−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	−0.341718	−	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
$615$	−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	0.896334	−	0.443379i	$-0.146221\pi$
$617$	1.59443	+	2.76163i	0.0641892	+	0.111179i	−0.832145	+	0.554558i	$0.812887\pi$
$618$	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	−0.454849	−	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
$633$	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	−0.861824	−	0.507207i	$-0.830678\pi$
$641$	−21.6084	+	12.4756i	−0.853482	+	0.492758i	0.00834190	+	0.999965i	$0.497345\pi$
$642$	5.21160	+	9.35706i	0.205685	+	0.369294i
$643$	−2.49176	−	4.31585i	−0.0982653	−	0.170200i	0.812701	−	0.582680i	$-0.197996\pi$
$643$	−2.49176	−	4.31585i	−0.0982653	−	0.170200i	−0.910967	+	0.412480i	$0.864663\pi$
$644$	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	−0.382288	−	0.924043i	$-0.624864\pi$
$647$	15.4932	−	26.8350i	0.609101	−	1.05499i	0.991389	−	0.130951i	$-0.0418030\pi$
$648$	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	−0.00686241	−	0.999976i	$-0.502184\pi$
$653$	−22.3928	−	12.9285i	−0.876299	−	0.505931i	−0.869436	+	0.494045i	$0.835518\pi$
$654$	−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	0.475136	−	0.879912i	$-0.342399\pi$
$659$	37.8578	−	21.8572i	1.47473	−	0.851436i	0.999594	+	0.0284766i	$0.00906561\pi$
$660$	0.832719	+	0.0128420i	0.0324136	+	0.000499873i
$661$	−16.3148	+	28.2581i	−0.634573	+	1.09911i	0.352032	+	0.935988i	$0.385491\pi$
$661$	−16.3148	+	28.2581i	−0.634573	+	1.09911i	−0.986605	+	0.163125i	$0.947842\pi$
$662$		−	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	−0.640292	−	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	$0.372132\pi$
$678$	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	0.601620	−	0.798783i	$-0.294522\pi$
$683$	−10.2174	−	17.6970i	−0.390956	−	0.677156i	−0.992576	+	0.121627i	$0.961189\pi$
$684$	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	0.338573	−	0.940940i	$-0.390056\pi$
$691$	25.8706	−	44.8092i	0.984165	−	1.70462i	0.645591	−	0.763683i	$-0.276611\pi$
$692$	−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	$0.0781820\pi$
$701$			12.8757i			0.486308i	−0.969988	+	0.243154i	$0.921818\pi$
$702$	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	−0.214702	−	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
$711$	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	0.510768	−	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
$721$	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	$-0.900648\pi$
$727$		−	16.5596i		−	0.614161i	0.951683	−	0.307081i	$-0.0993521\pi$
$728$	−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	0.615676	−	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
$741$	−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	−0.460545	−	0.887636i	$-0.652346\pi$
$743$	14.6769	−	25.4211i	0.538443	−	0.932610i	0.998988	−	0.0449741i	$-0.0143205\pi$
$744$	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	−0.0544211	−	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
$756$	13.4760	+	2.71959i	0.490119	+	0.0989107i
$757$	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
$763$	−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	−0.899848	−	0.436203i	$-0.856323\pi$
$769$	−2.00109	+	3.46599i	−0.0721612	+	0.124987i	0.827687	+	0.561190i	$0.189656\pi$
$770$	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	−0.883535	−	0.468365i	$-0.844843\pi$
$773$	−25.5699	+	14.7628i	−0.919686	+	0.530981i	−0.0361510	+	0.999346i	$0.511510\pi$
$774$	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	−0.953865	−	0.300236i	$-0.902934\pi$
$787$	−20.6739	−	35.8082i	−0.736945	−	1.27643i	0.216920	−	0.976189i	$-0.430399\pi$
$788$	−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	0.995914	−	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
$804$	−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	−0.0908575	−	0.995864i	$-0.528961\pi$
$809$	−28.4068	−	16.4007i	−0.998730	−	0.576617i	−0.907872	+	0.419247i	$0.862294\pi$
$810$	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	−0.998388	−	0.0567514i	$-0.981926\pi$
$821$	−12.8952	+	22.3352i	−0.450046	+	0.779503i	0.548342	+	0.836254i	$0.315259\pi$
$822$	0.594711	−	38.5632i	0.0207429	−	1.34505i
$823$	−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
$825$	−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	0.272693	−	0.962101i	$-0.412086\pi$
$829$	−12.2127	−	7.05100i	−0.424164	−	0.244891i	−0.696857	+	0.717210i	$0.745419\pi$
$830$	−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	−0.346604	−	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
$843$	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	$0.0235556\pi$
$859$			4.33385i			0.147869i	−0.997263	+	0.0739346i	$0.976444\pi$
$860$	−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	−0.293046	−	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	$-0.0954298\pi$
$882$	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	−0.377102	−	0.926172i	$-0.623079\pi$
$887$	18.2727	−	31.6493i	0.613537	−	1.06268i	0.990639	−	0.136506i	$-0.0435874\pi$
$888$	−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	−0.825399	−	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
$910$	−5.51979	+	2.93510i	−0.182979	+	0.0972976i
$911$			60.0679i			1.99014i	0.0991827	+	0.995069i	$0.468377\pi$
$911$			60.0679i			1.99014i	−0.0991827	+	0.995069i	$0.531623\pi$
$912$	−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	0.553179	−	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
$921$	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	−0.688314	−	0.725413i	$-0.741649\pi$
$929$	−12.3212	+	7.11365i	−0.404246	+	0.233391i	0.284069	+	0.958804i	$0.408316\pi$
$930$	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	$-0.977595\pi$
$937$		−	4.30558i		−	0.140657i	0.997524	−	0.0703287i	$-0.0224048\pi$
$938$	−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	$0.0569095\pi$
$941$			10.9105i			0.355671i	−0.984060	+	0.177835i	$0.943091\pi$
$942$	−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	−0.905960	−	0.423362i	$-0.860850\pi$
$947$	−2.65690	+	4.60188i	−0.0863376	+	0.149541i	0.819623	+	0.572904i	$0.194183\pi$
$948$	−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	−0.572508	−	0.819899i	$-0.694029\pi$
$953$	−4.59073	+	2.65046i	−0.148708	+	0.0858569i	0.423800	+	0.905756i	$0.360696\pi$
$954$	−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	$0.0277754\pi$
$967$			5.42003i			0.174296i	−0.996195	+	0.0871482i	$0.972225\pi$
$968$	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	−0.716493	−	0.697594i	$-0.754254\pi$
$971$	−29.9886	−	51.9418i	−0.962381	−	1.66689i	−0.245888	−	0.969298i	$-0.579079\pi$
$972$	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	0.486175	+	0.873862i	$0.338392\pi$
$977$	−16.0567	+	27.8110i	−0.513699	+	0.889753i	−0.999874	+	0.0158911i	$0.994941\pi$
$978$	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	$0.0246258\pi$
$983$			4.84635i			0.154574i	−0.997009	+	0.0772872i	$0.975374\pi$
$984$	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	0.176108	+	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
$994$	−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	0.366089	−	0.930580i	$-0.380697\pi$
$997$	42.7858	−	24.7024i	1.35504	−	0.782332i	0.988950	+	0.148248i	$0.0473632\pi$
$998$	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.251.6	✓	24
3.2	odd	2		546.2.q.j.251.10	yes	24
7.6	odd	2	inner	546.2.q.i.251.7	yes	24
13.10	even	6		546.2.q.j.335.3	yes	24
21.20	even	2		546.2.q.j.251.3	yes	24
39.23	odd	6	inner	546.2.q.i.335.7	yes	24
91.62	odd	6		546.2.q.j.335.10	yes	24
273.62	even	6	inner	546.2.q.i.335.6	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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