LMFDB - Embedded newform 546.2.q.i.251.7

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			251.7
Character	$\chi$	$=$	546.251
Dual form			546.2.q.i.335.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.0267080 - 1.73184i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.655349i q^{5} +(1.48647 + 0.889052i) q^{6} +(0.402891 + 2.61490i) q^{7} +1.00000 q^{8} +(-2.99857 - 0.0925084i) q^{9} +O(q^{10})$	\(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} +(0.402891 + 2.61490i) 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} +(4.53935 - 0.627906i) 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} +(2.06312 - 1.65636i) 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} +(-1.71367 + 0.264034i) 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} +(-1.72589 + 4.24515i) 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} +(-6.67536 + 2.10704i) q^{49} +(-2.28526 + 3.95818i) q^{50} +(1.76078 - 0.980698i) q^{51} +(2.88857 - 2.15781i) q^{52} -1.29577i q^{53} +(-4.37504 - 2.80340i) q^{54} +(-0.416409 - 0.240414i) q^{55} +(0.402891 + 2.61490i) q^{56} +(7.62467 - 4.24671i) q^{57} +(-0.839009 + 0.484402i) q^{58} +(-2.15803 + 1.24594i) q^{59} +(-0.552323 - 0.991658i) q^{60} +(0.932808 - 0.538557i) q^{61} +(-2.10220 + 3.64112i) q^{62} +(-0.966199 - 7.87823i) 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} +(-2.81346 - 3.61724i) 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} +(-9.19158 + 2.55240i) 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} +(1.51293 - 6.83455i) q^{98} +(1.15880 - 1.87136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 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	$0.0468139\pi$
$5$			0.655349i			0.293081i	−0.989205	+	0.146541i	$0.953186\pi$
$6$	1.48647	+	0.889052i	0.606848	+	0.362954i
$7$	0.402891	+	2.61490i	0.152279	+	0.988338i
$7$	0.402891	+	2.61490i	0.152279	+	0.988338i
$8$	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	0.927915	−	0.372791i	$-0.121599\pi$
$17$	0.581815	+	1.00773i	0.141111	+	0.244411i	−0.786804	+	0.617202i	$0.788266\pi$
$18$	1.57940	−	2.55059i	0.372268	−	0.601179i
$19$	2.51943	+	4.36378i	0.577996	+	1.00112i	0.995709	+	0.0925398i	$0.0294986\pi$
$19$	2.51943	+	4.36378i	0.577996	+	1.00112i	−0.417713	+	0.908579i	$0.637168\pi$
$20$	0.567549	−	0.327675i	0.126908	−	0.0732703i
$21$	4.53935	−	0.627906i	0.990568	−	0.137020i
$22$	−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
$28$	2.06312	−	1.65636i	0.389893	−	0.313023i
$29$	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	$-0.376761\pi$
$31$	4.20440			0.755132			0.377566	+	0.925983i	$0.376761\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.09062	+	0.652295i	0.189852	+	0.113550i
$34$	−1.16363			−0.199561
$35$	−1.71367	+	0.264034i	−0.289663	+	0.0446300i
$36$	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	0.792401	−	0.610001i	$-0.208831\pi$
$41$	4.22814	+	2.44112i	0.660324	+	0.381238i	−0.132076	+	0.991240i	$0.542164\pi$
$42$	−1.72589	+	4.24515i	−0.266311	+	0.655041i
$43$	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	$0.156739\pi$
$47$			6.48204i			0.945503i	−0.881196	+	0.472752i	$0.843261\pi$
$48$	1.48647	+	0.889052i	0.214553	+	0.128324i
$49$	−6.67536	+	2.10704i	−0.953622	+	0.301005i
$50$	−2.28526	+	3.95818i	−0.323184	+	0.559772i
$51$	1.76078	−	0.980698i	0.246558	−	0.137325i
$52$	2.88857	−	2.15781i	0.400573	−	0.299235i
$53$		−	1.29577i		−	0.177987i	−0.996032	−	0.0889937i	$-0.971635\pi$
$53$		−	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
$56$	0.402891	+	2.61490i	0.0538386	+	0.349430i
$57$	7.62467	−	4.24671i	1.00991	−	0.562490i
$58$	−0.839009	+	0.484402i	−0.110167	+	0.0636051i
$59$	−2.15803	+	1.24594i	−0.280952	+	0.162208i	−0.633854	−	0.773452i	$-0.718528\pi$
$59$	−2.15803	+	1.24594i	−0.280952	+	0.162208i	0.352902	+	0.935660i	$0.385195\pi$
$60$	−0.552323	−	0.991658i	−0.0713046	−	0.128023i
$61$	0.932808	−	0.538557i	0.119434	−	0.0689551i	−0.439093	−	0.898442i	$-0.644700\pi$
$61$	0.932808	−	0.538557i	0.119434	−	0.0689551i	0.558527	+	0.829486i	$0.311367\pi$
$62$	−2.10220	+	3.64112i	−0.266980	+	0.462422i
$63$	−0.966199	−	7.87823i	−0.121730	−	0.992563i
$64$	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	$-0.632921\pi$
$73$	−6.93011			−0.811108			−0.405554	+	0.914071i	$0.632921\pi$
$74$	−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	$-0.240664\pi$
$84$	−2.81346	−	3.61724i	−0.306974	−	0.394674i
$85$	−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	$-0.0505856\pi$
$89$	12.6797	+	7.32065i	1.34405	+	0.775987i	0.356650	+	0.934238i	$0.383919\pi$
$90$	1.67152	+	1.03506i	0.176194	+	0.109105i
$91$	−9.19158	+	2.55240i	−0.963540	+	0.267565i
$92$			6.41504i			0.668815i
$93$	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	$-0.0555129\pi$
$97$	3.36975	+	5.83658i	0.342146	+	0.592615i	−0.642685	+	0.766131i	$0.722180\pi$
$98$	1.51293	−	6.83455i	0.152829	−	0.690394i
$99$	1.15880	−	1.87136i	0.116464	−	0.188079i
$100$	−2.28526	−	3.95818i	−0.228526	−	0.395818i
$101$	−1.15739	+	2.00466i	−0.115165	+	0.199471i	−0.917846	−	0.396938i	$-0.870073\pi$
$101$	−1.15739	+	2.00466i	−0.115165	+	0.199471i	0.802681	+	0.596409i	$0.203406\pi$
$102$	−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
$105$	0.411498	+	2.97486i	0.0401581	+	0.290317i
$106$	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
$119$	−2.40071	+	1.92739i	−0.220072	+	0.176684i
$120$	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
$126$	7.30584	+	3.10236i	0.650856	+	0.276380i
$127$	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	$-0.314518\pi$
$131$	12.5967			1.10058			0.550288	+	0.834975i	$0.314518\pi$
$132$	0.0195956	−	1.27065i	0.00170558	−	0.110596i
$133$	−10.3958	+	8.34617i	−0.901427	+	0.723704i
$134$	5.07874	−	2.93221i	0.438736	−	0.253304i
$135$	−3.40165	−	0.157478i	−0.292767	−	0.0135535i
$136$	0.581815	+	1.00773i	0.0498902	+	0.0864123i
$137$	11.1336	+	19.2839i	0.951205	+	1.64753i	0.742824	+	0.669487i	$0.233486\pi$
$137$	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	−0.360364	−	0.932812i	$-0.617348\pi$
$139$	3.15133	−	1.81942i	0.267293	−	0.154321i	0.627657	+	0.778490i	$0.284014\pi$
$140$	1.08550	+	1.35206i	0.0917411	+	0.114270i
$141$	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
$147$	3.47078	+	11.6170i	0.286265	+	0.958151i
$148$		−	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
$154$	1.51371	−	1.21527i	0.121978	−	0.0979291i
$155$			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	−0.803090	−	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	−0.433698	−	0.901058i	$-0.642791\pi$
$167$	−18.4911	−	10.6759i	−1.43089	−	0.826122i	−0.997188	+	0.0749359i	$0.976125\pi$
$168$	4.53935	−	0.627906i	0.350219	−	0.0484440i
$169$	−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	$-0.0766653\pi$
$173$	3.66961	+	6.35595i	0.278995	+	0.483234i	−0.692140	+	0.721763i	$0.743332\pi$
$174$	0.816501	+	1.46597i	0.0618988	+	0.111135i
$175$	1.84142	+	11.9514i	0.139198	+	0.903443i
$176$	−0.366849	−	0.635401i	−0.0276523	−	0.0478951i
$177$	2.10014	+	3.77066i	0.157856	+	0.283420i
$178$	−12.6797	+	7.32065i	−0.950386	+	0.548706i
$179$	−2.15825	−	1.24607i	−0.161315	−	0.0931353i	0.417169	−	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	$-0.743930\pi$
$181$		−	19.3857i		−	1.44092i	0.693494	−	0.720462i	$-0.256070\pi$
$182$	2.38535	−	9.23635i	0.176814	−	0.684644i
$183$	−0.907783	−	1.62986i	−0.0671053	−	0.120483i
$184$	−5.55559	−	3.20752i	−0.409564	−	0.236462i
$185$	−1.36204	+	2.35912i	−0.100139	+	0.173446i
$186$	6.24970	+	3.73793i	0.458250	+	0.274078i
$187$	−0.853752			−0.0624325
$188$	5.61361	−	3.24102i	0.409415	−	0.236376i
$189$	−13.6697	+	1.46289i	−0.994322	+	0.106410i
$190$		−	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	−0.601583	−	0.798810i	$-0.705463\pi$
$199$	−2.97067	+	1.71512i	−0.210585	+	0.121581i	0.390998	+	0.920391i	$0.372130\pi$
$200$	4.57052			0.323184
$201$	−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
$210$	−2.78205	−	1.13106i	−0.191980	−	0.0780508i
$211$	12.4331	−	21.5347i	0.855929	−	1.48251i	−0.0198516	−	0.999803i	$-0.506319\pi$
$211$	12.4331	−	21.5347i	0.855929	−	1.48251i	0.875781	−	0.482710i	$-0.160347\pi$
$212$	−1.12217	+	0.647884i	−0.0770708	+	0.0444969i
$213$	−12.4074	+	6.91054i	−0.850140	+	0.473502i
$214$	5.35526	−	3.09186i	0.366078	−	0.211355i
$215$	−4.32576	+	2.49748i	−0.295014	+	0.170326i
$216$	−0.240296	+	5.19059i	−0.0163501	+	0.353175i
$217$	1.69392	+	10.9941i	0.114990	+	0.746326i
$218$	14.0505	+	8.11209i	0.951623	+	0.549420i
$219$	−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	$-0.741043\pi$
$223$	4.26929	−	7.39463i	0.285893	−	0.495181i	0.972825	+	0.231540i	$0.0743764\pi$
$224$	2.06312	−	1.65636i	0.137848	−	0.110670i
$225$	−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	$-0.740480\pi$
$227$	−5.99732	+	3.46256i	−0.398056	+	0.229818i	0.287589	+	0.957754i	$0.407146\pi$
$228$	−7.49010	−	4.47981i	−0.496044	−	0.296682i
$229$	−4.68499			−0.309593			−0.154796	−	0.987946i	$-0.549472\pi$
$229$	−4.68499			−0.309593			−0.154796	+	0.987946i	$0.549472\pi$
$230$	2.10205	+	3.64085i	0.138605	+	0.240071i
$231$	−1.26628	+	3.11465i	−0.0833154	+	0.204929i
$232$	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
$238$	−0.468816	−	3.04277i	−0.0303888	−	0.197233i
$239$	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	$0.00694812\pi$
$241$	8.05368	+	13.9494i	0.518783	+	0.898559i	−0.480979	+	0.876732i	$0.659719\pi$
$242$	−10.4617			−0.672503
$243$	1.20072	−	15.5421i	0.0770262	−	0.997029i
$244$	−0.932808	−	0.538557i	−0.0597169	−	0.0344776i
$245$	−1.38084	−	4.37469i	−0.0882189	−	0.279489i
$246$	4.11471	+	7.38768i	0.262344	+	0.471021i
$247$	−14.5551	+	10.8729i	−0.926118	+	0.691827i
$248$	4.20440			0.266980
$249$	−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	$-0.937031\pi$
$251$	−10.4635	−	18.1234i	−0.660453	−	1.14394i	0.320044	−	0.947403i	$-0.396302\pi$
$252$	−6.33965	+	4.77587i	−0.399360	+	0.300851i
$253$	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	$0.494989\pi$
$257$	−13.7555	+	23.8253i	−0.858047	+	1.48618i	−0.873789	+	0.486305i	$0.838344\pi$
$258$	−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
$266$	−2.03011	−	13.1761i	−0.124474	−	0.807877i
$267$	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	$-0.167267\pi$
$269$	−0.0309493	−	0.0536058i	−0.00188701	−	0.00326841i	−0.866967	+	0.498365i	$0.833934\pi$
$270$	1.83721	−	2.86718i	0.111809	−	0.174491i
$271$	−2.55715	+	4.42912i	−0.155336	+	0.269050i	−0.933181	−	0.359406i	$-0.882979\pi$
$271$	−2.55715	+	4.42912i	−0.155336	+	0.269050i	0.777845	+	0.628456i	$0.216313\pi$
$272$	−1.16363			−0.0705554
$273$	4.17488	+	15.9866i	0.252675	+	0.967551i
$274$	−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
$280$	−1.71367	+	0.264034i	−0.102411	+	0.0157791i
$281$	−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	$-0.112086\pi$
$283$	18.6608	+	10.7738i	1.10927	+	0.640438i	0.170631	+	0.985335i	$0.445420\pi$
$284$	−4.09978	+	7.10103i	−0.243277	+	0.421369i
$285$	2.78308	+	4.99682i	0.164855	+	0.295986i
$286$	2.11934	−	1.58318i	0.125319	−	0.0936156i
$287$	−4.67979	+	12.0396i	−0.276239	+	0.710678i
$288$	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	$-0.890495\pi$
$293$	−19.1717	+	11.0688i	−1.12002	+	0.646645i	−0.178615	+	0.983919i	$0.557162\pi$
$294$	−11.7960	−	2.80270i	−0.687955	−	0.163457i
$295$	−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
$301$	−15.7247	+	12.6245i	−0.906358	+	0.727664i
$302$	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	$-0.480218\pi$
$307$	2.17640			0.124214			0.0621068	+	0.998070i	$0.480218\pi$
$308$	0.295600	+	1.91854i	0.0168434	+	0.109319i
$309$	−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	$-0.435456\pi$
$311$	7.10285			0.402766			0.201383	+	0.979513i	$0.435456\pi$
$312$	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
$315$	5.16299	−	0.633198i	0.290901	−	0.0356766i
$316$	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
$322$	10.6256	+	13.2350i	0.592143	+	0.737558i
$323$	−2.93168	+	5.07782i	−0.163123	+	0.282537i
$324$	−4.01098	−	8.05680i	−0.222832	−	0.447600i
$325$	1.93990	+	16.3647i	0.107606	+	0.907748i
$326$		−	10.1516i		−	0.562246i
$327$	−28.0978	−	0.433316i	−1.55381	−	0.0239624i
$328$	4.22814	+	2.44112i	0.233460	+	0.134788i
$329$	−16.9499	+	2.61156i	−0.934476	+	0.143980i
$330$	−0.405238	−	0.727577i	−0.0223076	−	0.0400518i
$331$	−9.87158	+	5.69936i	−0.542591	+	0.313265i	−0.746128	−	0.665802i	$-0.768090\pi$
$331$	−9.87158	+	5.69936i	−0.542591	+	0.313265i	0.203537	+	0.979067i	$0.434756\pi$
$332$	−10.8259	+	6.25036i	−0.594151	+	0.343033i
$333$	−10.6020	−	6.56505i	−0.580983	−	0.359763i
$334$	18.4911	−	10.6759i	1.01179	−	0.584157i
$335$	1.92162	−	3.32835i	0.104989	−	0.181847i
$336$	−1.72589	+	4.24515i	−0.0941552	+	0.231592i
$337$	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	−0.567055	−	0.823680i	$-0.691917\pi$
$349$	8.02933	−	13.9072i	0.429800	−	0.744436i	0.996855	+	0.0792439i	$0.0252506\pi$
$350$	−11.2709	−	4.38100i	−0.602458	−	0.234174i
$351$	−18.6868	+	1.34271i	−0.997429	+	0.0716683i
$352$	0.733697			0.0391062
$353$	23.2239	+	13.4084i	1.23609	+	0.713655i	0.968292	−	0.249822i	$-0.0803720\pi$
$353$	23.2239	+	13.4084i	1.23609	+	0.713655i	0.267794	+	0.963476i	$0.413705\pi$
$354$	−4.31555	−	0.0665533i	−0.229369	−	0.00353727i
$355$	4.65366	−	2.68679i	0.246990	−	0.142600i
$356$		−	14.6413i		−	0.775987i
$357$	3.27382	+	4.20913i	0.173269	+	0.222771i
$358$	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
$364$	6.80624	+	6.68394i	0.356744	+	0.350334i
$365$		−	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	$-0.315788\pi$
$367$	1.82808	+	1.05544i	0.0954251	+	0.0550937i	−0.451528	+	0.892257i	$0.649121\pi$
$368$	5.55559	−	3.20752i	0.289605	−	0.167204i
$369$	−12.4526	−	7.71101i	−0.648254	−	0.401419i
$370$	−1.36204	−	2.35912i	−0.0708089	−	0.122645i
$371$	3.38830	−	0.522054i	0.175912	−	0.0271037i
$372$	−6.36199	+	3.54344i	−0.329854	+	0.183719i
$373$	12.1368	+	21.0216i	0.628421	+	1.08846i	0.987869	+	0.155292i	$0.0496318\pi$
$373$	12.1368	+	21.0216i	0.628421	+	1.08846i	−0.359448	+	0.933165i	$0.617035\pi$
$374$	0.426876	−	0.739371i	0.0220732	−	0.0382319i
$375$	10.8622	+	0.167514i	0.560921	+	0.00865037i
$376$			6.48204i			0.334286i
$377$	−1.37829	+	3.20965i	−0.0709853	+	0.165306i
$378$	5.56793	−	12.5697i	0.286384	−	0.646517i
$379$	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	−0.961858	−	0.273550i	$-0.911802\pi$
$383$	−23.5996	+	13.6253i	−1.20589	+	0.696218i	−0.244028	+	0.969768i	$0.578469\pi$
$384$	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
$392$	−6.67536	+	2.10704i	−0.337156	+	0.106421i
$393$	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	$0.00272294\pi$
$397$	10.1097	+	17.5105i	0.507390	+	0.878825i	−0.492573	+	0.870271i	$0.663944\pi$
$398$		−	3.43023i		−	0.171942i
$399$	14.1766	+	18.2268i	0.709719	+	0.912479i
$400$	−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
$406$	−1.60469	−	1.99876i	−0.0796394	−	0.0991967i
$407$	−2.64115	+	1.52487i	−0.130917	+	0.0755850i
$408$	1.76078	−	0.980698i	0.0871714	−	0.0485518i
$409$	−18.8192	−	32.5957i	−0.930547	−	1.61175i	−0.782388	−	0.622791i	$-0.785999\pi$
$409$	−18.8192	−	32.5957i	−0.930547	−	1.61175i	−0.148159	−	0.988964i	$-0.547335\pi$
$410$	−1.59978	−	2.77091i	−0.0790077	−	0.136845i
$411$	33.6941	−	18.7666i	1.66201	−	0.925687i
$412$	−9.77953	+	5.64621i	−0.481803	+	0.278169i
$413$	−4.12746	−	5.14105i	−0.203099	−	0.252975i
$414$	−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	$-0.551842\pi$
$419$	15.8330	−	27.4235i	0.773492	−	1.33973i	0.935638	−	0.352961i	$-0.114825\pi$
$420$	2.37056	−	1.84380i	0.115671	−	0.0899682i
$421$		−	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
$427$	1.78409	+	2.22221i	0.0863381	+	0.107540i
$428$			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	0.0726709	−	0.997356i	$-0.476848\pi$
$433$	20.2415	−	11.6864i	0.972742	−	0.561613i	0.900071	+	0.435743i	$0.143514\pi$
$434$	−10.3681	−	4.03006i	−0.497685	−	0.193449i
$435$	0.943765	+	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	$-0.471969\pi$
$439$	−15.3108	−	8.83972i	−0.730747	−	0.421897i	−0.818695	+	0.574228i	$0.805302\pi$
$440$	−0.416409	−	0.240414i	−0.0198515	−	0.0114613i
$441$	20.2115	−	5.70058i	0.962451	−	0.271456i
$442$	−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
$448$	0.402891	+	2.61490i	0.0190348	+	0.123542i
$449$	−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
$455$	−1.67272	−	6.02370i	−0.0784181	−	0.282395i
$456$	7.62467	−	4.24671i	0.357058	−	0.198870i
$457$	7.47187	+	4.31389i	0.349519	+	0.201795i	0.664474	−	0.747312i	$-0.268656\pi$
$457$	7.47187	+	4.31389i	0.349519	+	0.201795i	−0.314954	+	0.949107i	$0.601989\pi$
$458$	2.34250	−	4.05732i	0.109458	−	0.189586i
$459$	−5.37054	+	2.77781i	−0.250675	+	0.129657i
$460$	−4.20409			−0.196017
$461$	28.5935	−	16.5084i	1.33173	−	0.768875i	0.346165	−	0.938173i	$-0.387484\pi$
$461$	28.5935	−	16.5084i	1.33173	−	0.768875i	0.985565	+	0.169299i	$0.0541502\pi$
$462$	−2.06423	−	2.65396i	−0.0960366	−	0.123473i
$463$			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	$-0.482007\pi$
$467$	2.44186			0.112996			0.0564978	+	0.998403i	$0.482007\pi$
$468$	−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	$-0.0789853\pi$
$479$	27.1685	+	15.6857i	1.24136	+	0.716699i	0.271989	+	0.962300i	$0.412319\pi$
$480$	−0.552323	−	0.991658i	−0.0252100	−	0.0452628i
$481$	−5.91356	+	13.7711i	−0.269635	+	0.627907i
$482$	−16.1074			−0.733670
$483$	−27.2328	−	11.0717i	−1.23914	−	0.503779i
$484$	5.23084	−	9.06009i	0.237766	−	0.411822i
$485$	−3.82500	+	2.20836i	−0.173684	+	0.100277i
$486$	12.8595	+	8.81093i	0.583320	+	0.399672i
$487$	−10.1304	+	5.84880i	−0.459053	+	0.265035i	−0.711646	−	0.702538i	$-0.752050\pi$
$487$	−10.1304	+	5.84880i	−0.459053	+	0.265035i	0.252593	+	0.967573i	$0.418717\pi$
$488$	0.932808	−	0.538557i	0.0422262	−	0.0243793i
$489$	8.55571	+	15.3612i	0.386902	+	0.694656i
$490$	4.47901	+	0.991498i	0.202341	+	0.0447913i
$491$	−35.7809	−	20.6581i	−1.61477	−	0.932287i	−0.988244	−	0.152886i	$-0.951143\pi$
$491$	−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
$497$	16.9167	−	13.5815i	0.758818	−	0.609211i
$498$	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	0.966682	−	0.255980i	$-0.0823981\pi$
$503$	5.86833	+	10.1642i	0.261656	+	0.453201i	−0.705026	+	0.709181i	$0.749065\pi$
$504$	−0.966199	−	7.87823i	−0.0430379	−	0.350924i
$505$	−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	$-0.00764479\pi$
$509$	33.3626	+	19.2619i	1.47877	+	0.853768i	0.479059	+	0.877783i	$0.340978\pi$
$510$	−1.32068	−	0.0203671i	−0.0584805	−	0.000901871i
$511$	−2.79208	−	18.1215i	−0.123514	−	0.801648i
$512$	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
$518$	−6.88495	−	8.57572i	−0.302507	−	0.376795i
$519$	11.1055	−	6.18544i	0.487479	−	0.271511i
$520$	−2.34647	+	0.278155i	−0.102899	+	0.0121979i
$521$	−38.0123			−1.66535			−0.832674	−	0.553763i	$-0.813191\pi$
$521$	−38.0123			−1.66535			−0.832674	+	0.553763i	$0.813191\pi$
$522$	2.56064	−	1.37490i	0.112076	−	0.0601777i
$523$	−29.6865	−	17.1395i	−1.29810	−	0.749458i	−0.318024	−	0.948083i	$-0.603019\pi$
$523$	−29.6865	−	17.1395i	−1.29810	−	0.749458i	−0.980076	+	0.198625i	$0.936353\pi$
$524$	−6.29833	−	10.9090i	−0.275144	−	0.476563i
$525$	20.7472	−	2.86986i	0.905482	−	0.125251i
$526$	−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
$539$	1.11003	−	5.01449i	0.0478125	−	0.215989i
$540$	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
$546$	−15.9322	−	4.37773i	−0.681836	−	0.187350i
$547$	−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
$553$	−5.31623	−	34.5040i	−0.226069	−	1.46726i
$554$	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	0.973229	−	0.229836i	$-0.0738191\pi$
$563$	6.82336	+	11.8184i	0.287570	+	0.498087i	−0.685659	+	0.727923i	$0.740486\pi$
$564$	−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
$567$	2.16842	+	23.7128i	0.0910649	+	0.995845i
$568$	−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
$574$	−8.08675	−	10.0726i	−0.337534	−	0.420424i
$575$	−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	$-0.331834\pi$
$577$	24.2166			1.00815			0.504075	+	0.863660i	$0.331834\pi$
$578$	7.82298	+	13.5498i	0.325393	+	0.563598i
$579$	19.2088	−	32.1165i	0.798291	−	1.33472i
$580$	0.634905			0.0263630
$581$	32.6881	−	5.03643i	1.35613	−	0.208946i
$582$	−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	$-0.200744\pi$
$587$	16.9787	+	9.80266i	0.700786	+	0.404599i	−0.106854	+	0.994275i	$0.534078\pi$
$588$	8.32519	−	8.81426i	0.343325	−	0.363494i
$589$	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
$595$	−1.26311	−	1.57330i	−0.0517826	−	0.0644991i
$596$	−10.9093	+	18.8954i	−0.446861	+	0.773986i
$597$	2.89098	+	5.19055i	0.118320	+	0.212435i
$598$	13.8425	+	18.5303i	0.566061	+	0.757760i
$599$		−	22.9488i		−	0.937662i	−0.883288	−	0.468831i	$-0.844675\pi$
$599$		−	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	0.621839	−	0.783145i	$-0.286386\pi$
$601$	6.23997	+	3.60265i	0.254534	+	0.146955i	−0.367305	+	0.930101i	$0.619719\pi$
$602$	−3.07076	−	19.9303i	−0.125155	−	0.812297i
$603$	14.9577	+	9.26227i	0.609125	+	0.377189i
$604$	−5.49769	+	3.17409i	−0.223698	+	0.129152i
$605$	−5.93752	+	3.42803i	−0.241395	+	0.139369i
$606$	−3.50267	+	1.95088i	−0.142286	+	0.0792492i
$607$	0.0665333	−	0.0384130i	0.00270050	−	0.00155914i	−0.498649	−	0.866804i	$-0.666170\pi$
$607$	0.0665333	−	0.0384130i	0.00270050	−	0.00155914i	0.501350	+	0.865245i	$0.332837\pi$
$608$	2.51943	−	4.36378i	0.102176	−	0.176975i
$609$	4.11272	+	1.67205i	0.166656	+	0.0677550i
$610$	−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	$-0.570812\pi$
$619$	−10.9786			−0.441267			−0.220634	+	0.975357i	$0.570812\pi$
$620$	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
$630$	−2.03313	+	4.78788i	−0.0810018	+	0.190754i
$631$	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
$637$	−10.3775	−	23.0067i	−0.411171	−	0.911558i
$638$		−	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	0.910967	−	0.412480i	$-0.135337\pi$
$643$	2.49176	+	4.31585i	0.0982653	+	0.170200i	−0.812701	+	0.582680i	$0.802004\pi$
$644$	−16.7747	+	2.58456i	−0.661015	+	0.101846i
$645$	4.20971	+	7.55824i	0.165757	+	0.297605i
$646$	−2.93168	−	5.07782i	−0.115345	−	0.199784i
$647$	−15.4932	+	26.8350i	−0.609101	+	1.05499i	0.382288	+	0.924043i	$0.375136\pi$
$647$	−15.4932	+	26.8350i	−0.609101	+	1.05499i	−0.991389	+	0.130951i	$0.958197\pi$
$648$	8.98288	+	0.554786i	0.352881	+	0.0217941i
$649$		−	1.82829i		−	0.0717666i
$650$	−15.1422	−	6.50233i	−0.593924	−	0.255042i
$651$	19.0853	−	2.63997i	0.748010	−	0.103469i
$652$	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	$-0.614509\pi$
$661$	16.3148	−	28.2581i	0.634573	−	1.09911i	0.986605	−	0.163125i	$-0.0521575\pi$
$662$		−	11.3987i		−	0.443024i
$663$	4.25871	+	5.88818i	0.165395	+	0.228678i
$664$		−	12.5007i		−	0.485122i
$665$	−5.46965	−	6.81286i	−0.212104	−	0.264191i
$666$	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
$672$	−2.81346	−	3.61724i	−0.108532	−	0.139538i
$673$	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	$-0.627868\pi$
$677$	−20.3466			−0.781983			−0.390992	+	0.920394i	$0.627868\pi$
$678$	−9.91913	−	0.152970i	−0.380942	−	0.00587478i
$679$	−13.9044	+	11.1630i	−0.533602	+	0.428398i
$680$	−0.660417	+	0.381292i	−0.0253258	+	0.0146219i
$681$	5.83643	+	10.4789i	0.223653	+	0.401553i
$682$	−1.54238	−	2.67148i	−0.0590607	−	0.102296i
$683$	−10.2174	−	17.6970i	−0.390956	−	0.677156i	0.601620	−	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
$686$	18.4812	+	1.20258i	0.705615	+	0.0459147i
$687$	−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	$0.609944\pi$
$691$	−25.8706	+	44.8092i	−0.984165	+	1.70462i	−0.645591	+	0.763683i	$0.723389\pi$
$692$	3.66961	−	6.35595i	0.139498	−	0.241617i
$693$	5.36028	+	2.27619i	0.203620	+	0.0864655i
$694$			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
$700$	9.42953	−	7.57043i	0.356403	−	0.286135i
$701$			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
$714$	−5.28212	+	0.730650i	−0.197679	+	0.0273439i
$715$	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	$-0.00397208\pi$
$719$	13.1163	+	22.7181i	0.489155	+	0.847241i	−0.510768	+	0.859719i	$0.670639\pi$
$720$	1.67152	+	1.03506i	0.0622940	+	0.0385744i
$721$	29.5285	−	4.54962i	1.09970	−	0.169437i
$722$	−3.19503	−	5.53396i	−0.118907	−	0.205953i
$723$	24.3733	−	13.5752i	0.906451	−	0.504866i
$724$	−16.7885	+	9.69283i	−0.623939	+	0.360231i
$725$	3.83470	+	2.21397i	0.142417	+	0.0822247i
$726$	−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	$0.900648\pi$
$728$	−9.19158	+	2.55240i	−0.340663	+	0.0945984i
$729$	−26.8845	−	2.49456i	−0.995723	−	0.0923911i
$730$	3.93318	+	2.27082i	0.145573	+	0.0840468i
$731$	−4.43449	+	7.68075i	−0.164015	+	0.284083i
$732$	−0.957610	+	1.60109i	−0.0353943	+	0.0591781i
$733$	6.98748			0.258088			0.129044	−	0.991639i	$-0.458809\pi$
$733$	6.98748			0.258088			0.129044	+	0.991639i	$0.458809\pi$
$734$	−1.82808	+	1.05544i	−0.0674758	+	0.0389572i
$735$	−7.61316	+	2.27457i	−0.280816	+	0.0838988i
$736$			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
$756$	8.10174	+	11.1068i	0.294657	+	0.403952i
$757$	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	−0.582674	−	0.812706i	$-0.697993\pi$
$761$	−4.69480	+	2.71054i	−0.170186	+	0.0982571i	0.412487	+	0.910963i	$0.364660\pi$
$762$	11.3327	−	6.31198i	0.410541	−	0.228659i
$763$	42.4245	−	6.53658i	1.53587	−	0.236640i
$764$	11.8522	+	6.84286i	0.428797	+	0.247566i
$765$	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	$-0.810344\pi$
$769$	2.00109	−	3.46599i	0.0721612	−	0.124987i	0.899848	+	0.436203i	$0.143677\pi$
$770$	0.796425	+	0.992006i	0.0287012	+	0.0357494i
$771$	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	$-0.488490\pi$
$773$	25.5699	−	14.7628i	0.919686	−	0.530981i	0.883535	+	0.468365i	$0.155157\pi$
$774$	22.8546	+	0.705082i	0.821491	+	0.0253437i
$775$	19.2163			0.690269
$776$	3.36975	+	5.83658i	0.120967	+	0.209521i
$777$	17.6457	+	7.17398i	0.633036	+	0.257365i
$778$	−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
$784$	1.51293	−	6.83455i	0.0540333	−	0.244091i
$785$	−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	$0.0970655\pi$
$787$	20.6739	+	35.8082i	0.736945	+	1.27643i	−0.216920	+	0.976189i	$0.569601\pi$
$788$	−21.2057			−0.755423
$789$	27.7469	−	46.3919i	0.987816	−	1.65160i
$790$	7.48892	+	4.32373i	0.266444	+	0.153831i
$791$	−9.48680	−	11.8165i	−0.337312	−	0.420147i
$792$	1.15880	−	1.87136i	0.0411763	−	0.0664958i
$793$	2.32421	+	3.11132i	0.0825352	+	0.110486i
$794$	−20.2193			−0.717558
$795$	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	$-0.304550\pi$
$797$	−11.8501	−	20.5250i	−0.419753	−	0.727034i	−0.995914	+	0.0903022i	$0.971217\pi$
$798$	−22.8731	+	3.16393i	−0.809701	+	0.112002i
$799$	−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	$-0.548498\pi$
$811$	−8.64443			−0.303547			−0.151774	+	0.988415i	$0.548498\pi$
$812$	2.53332	−	0.390323i	0.0889021	−	0.0136976i
$813$	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
$819$	27.7978	−	6.80327i	0.971332	−	0.237726i
$820$	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
$826$	6.51601	−	1.00396i	0.226721	−	0.0349322i
$827$	−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	$-0.254581\pi$
$829$	12.2127	+	7.05100i	0.424164	+	0.244891i	−0.272693	+	0.962101i	$0.587914\pi$
$830$	−4.09617	+	7.09477i	−0.142180	+	0.246263i
$831$	−21.4393	+	11.9410i	−0.743720	+	0.414229i
$832$	0.424437	+	3.58048i	0.0147147	+	0.124131i
$833$	−6.00715	−	5.50107i	−0.208135	−	0.190601i
$834$	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	$-0.720668\pi$
$839$	−8.47056	+	4.89048i	−0.292436	+	0.168838i	0.346604	+	0.938012i	$0.387335\pi$
$840$	0.411498	+	2.97486i	0.0141980	+	0.102642i
$841$	−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
$847$	−21.5837	+	17.3283i	−0.741625	+	0.595409i
$848$	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	$-0.529912\pi$
$853$	−5.48095			−0.187664			−0.0938321	+	0.995588i	$0.529912\pi$
$854$	−2.81654	+	0.433959i	−0.0963800	+	0.0148498i
$855$	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	$-0.450602\pi$
$857$	9.04966			0.309130			0.154565	+	0.987983i	$0.450602\pi$
$858$	−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
$861$	20.7258	+	8.42622i	0.706334	+	0.287165i
$862$	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
$868$	8.67418	−	6.96401i	0.294421	−	0.236374i
$869$	4.84064	−	8.38423i	0.164207	−	0.284416i
$870$	−0.960723	+	0.535093i	−0.0325715	+	0.0181414i
$871$	8.34312	−	19.4289i	0.282696	−	0.658322i
$872$		−	16.2242i		−	0.549420i
$873$	−9.56451	−	17.8131i	−0.323710	−	0.602883i
$874$	27.9938	+	16.1622i	0.946905	+	0.546696i
$875$	−16.4007	+	2.52695i	−0.554445	+	0.0854264i
$876$	10.4865	−	5.84064i	0.354305	−	0.197337i
$877$	11.5032	−	6.64138i	0.388436	−	0.224264i	−0.293046	−	0.956098i	$-0.594669\pi$
$877$	11.5032	−	6.64138i	0.388436	−	0.224264i	0.681482	+	0.731835i	$0.261336\pi$
$878$	15.3108	−	8.83972i	0.516716	−	0.298326i
$879$	18.6574	+	33.4980i	0.629297	+	1.12986i
$880$	0.416409	−	0.240414i	0.0140372	−	0.00810435i
$881$	−21.7703	+	37.7073i	−0.733461	+	1.27039i	0.221934	+	0.975062i	$0.428763\pi$
$881$	−21.7703	+	37.7073i	−0.733461	+	1.27039i	−0.955395	+	0.295331i	$0.904570\pi$
$882$	−5.16889	+	20.3539i	−0.174046	+	0.685353i
$883$	−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	$0.376921\pi$
$887$	−18.2727	+	31.6493i	−0.613537	+	1.06268i	−0.990639	+	0.136506i	$0.956413\pi$
$888$	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
$903$	21.4437	+	27.5700i	0.713601	+	0.917471i
$904$	−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
$910$	6.05303	+	1.56323i	0.200656	+	0.0518207i
$911$			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
$917$	5.07508	+	32.9389i	0.167594	+	1.08774i
$918$	0.279616	−	6.03993i	0.00922869	−	0.199347i
$919$	−13.4861	−	23.3585i	−0.444864	−	0.770527i	0.553179	−	0.833063i	$-0.313415\pi$
$919$	−13.4861	−	23.3585i	−0.444864	−	0.770527i	−0.998043	+	0.0625354i	$0.980081\pi$
$920$	2.10205	−	3.64085i	0.0693024	−	0.120035i
$921$	0.0581273	−	3.76918i	0.00191536	−	0.124199i
$922$			33.0169i			1.08735i
$923$	23.6850	−	17.6931i	0.779602	−	0.582377i
$924$	3.33051	−	0.460693i	0.109566	−	0.0151557i
$925$	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	$-0.591684\pi$
$929$	12.3212	−	7.11365i	0.404246	−	0.233391i	0.688314	+	0.725413i	$0.258351\pi$
$930$	−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	$0.977595\pi$
$938$	9.71360	+	12.0990i	0.317160	+	0.395046i
$939$	−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
$945$	−0.958707	−	8.95841i	−0.0311867	−	0.291417i
$946$	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
$952$	−2.40071	+	1.92739i	−0.0778074	+	0.0624671i
$953$	−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
$959$	−45.9398	+	36.8824i	−1.48347	+	1.19100i
$960$	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
$966$	23.2048	−	18.0485i	0.746601	−	0.580700i
$967$			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	$0.245746\pi$
$971$	29.9886	+	51.9418i	0.962381	+	1.66689i	0.245888	+	0.969298i	$0.420921\pi$
$972$	−14.0603	+	6.73122i	−0.450983	+	0.215904i
$973$	6.02724	+	7.50738i	0.193225	+	0.240675i
$974$		−	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	$-0.975374\pi$
$983$		−	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
$987$	4.07012	+	29.4243i	0.129553	+	0.936585i
$988$	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
$994$	3.30353	+	21.4410i	0.104782	+	0.680068i
$995$	−1.12400	−	1.94683i	−0.0356332	−	0.0617185i
$996$	10.5355	+	18.9158i	0.333831	+	0.599370i
$997$	−42.7858	+	24.7024i	−1.35504	+	0.782332i	−0.988950	−	0.148248i	$-0.952637\pi$
$997$	−42.7858	+	24.7024i	−1.35504	+	0.782332i	−0.366089	+	0.930580i	$0.619303\pi$
$998$	22.3116	+	12.8816i	0.706261	+	0.407760i
$999$	−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.251.7	yes	24
3.2	odd	2		546.2.q.j.251.3	yes	24
7.6	odd	2	inner	546.2.q.i.251.6	✓	24
13.10	even	6		546.2.q.j.335.10	yes	24
21.20	even	2		546.2.q.j.251.10	yes	24
39.23	odd	6	inner	546.2.q.i.335.6	yes	24
91.62	odd	6		546.2.q.j.335.3	yes	24
273.62	even	6	inner	546.2.q.i.335.7	yes	24

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.0267080 - 1.73184i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.655349i q^{5} +(1.48647 + 0.889052i) q^{6} +(0.402891 + 2.61490i) q^{7} +1.00000 q^{8} +(-2.99857 - 0.0925084i) q^{9} +O(q^{10})\)	\(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} +(0.402891 + 2.61490i) 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} +(4.53935 - 0.627906i) 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} +(2.06312 - 1.65636i) 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} +(-1.71367 + 0.264034i) 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} +(-1.72589 + 4.24515i) 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} +(-6.67536 + 2.10704i) q^{49} +(-2.28526 + 3.95818i) q^{50} +(1.76078 - 0.980698i) q^{51} +(2.88857 - 2.15781i) q^{52} -1.29577i q^{53} +(-4.37504 - 2.80340i) q^{54} +(-0.416409 - 0.240414i) q^{55} +(0.402891 + 2.61490i) q^{56} +(7.62467 - 4.24671i) q^{57} +(-0.839009 + 0.484402i) q^{58} +(-2.15803 + 1.24594i) q^{59} +(-0.552323 - 0.991658i) q^{60} +(0.932808 - 0.538557i) q^{61} +(-2.10220 + 3.64112i) q^{62} +(-0.966199 - 7.87823i) 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} +(-2.81346 - 3.61724i) 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} +(-9.19158 + 2.55240i) 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} +(1.51293 - 6.83455i) q^{98} +(1.15880 - 1.87136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9}+O(q^{10}) \) 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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