LMFDB - Embedded newform 546.2.u.a.185.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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, 1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (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:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.13
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.804592 - 1.53383i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.14723 + 3.71911i) q^{5} +(-1.46371 + 0.926039i) q^{6} +(2.58099 - 0.581819i) q^{7} -1.00000i q^{8} +(-1.70526 - 2.46821i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.804592 - 1.53383i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.14723 + 3.71911i) q^{5} +(-1.46371 + 0.926039i) q^{6} +(2.58099 - 0.581819i) q^{7} -1.00000i q^{8} +(-1.70526 - 2.46821i) q^{9} -4.29446i q^{10} +1.08598i q^{11} +(1.73063 - 0.0701179i) q^{12} +(-2.47541 + 2.62151i) q^{13} +(-2.52611 - 0.786623i) q^{14} +(7.43212 - 0.301118i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.95808 + 3.39149i) q^{17} +(0.242696 + 2.99017i) q^{18} -4.05717i q^{19} +(-2.14723 + 3.71911i) q^{20} +(1.18423 - 4.42692i) q^{21} +(0.542991 - 0.940488i) q^{22} +(6.61595 + 3.81972i) q^{23} +(-1.53383 - 0.804592i) q^{24} +(-6.72118 + 11.6414i) q^{25} +(3.45453 - 1.03259i) q^{26} +(-5.15786 + 0.629682i) q^{27} +(1.79436 + 1.94429i) q^{28} +(-1.84864 + 1.06731i) q^{29} +(-6.58696 - 3.45528i) q^{30} +(-1.04968 - 0.606034i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.66571 + 0.873772i) q^{33} -3.91616i q^{34} +(7.70581 + 8.34967i) q^{35} +(1.28490 - 2.71091i) q^{36} +(3.03928 - 5.26419i) q^{37} +(-2.02858 + 3.51361i) q^{38} +(2.02926 + 5.90611i) q^{39} +(3.71911 - 2.14723i) q^{40} +(-1.00855 - 1.74686i) q^{41} +(-3.23903 + 3.24171i) q^{42} +(1.69618 - 2.93788i) q^{43} +(-0.940488 + 0.542991i) q^{44} +(5.51796 - 11.6419i) q^{45} +(-3.81972 - 6.61595i) q^{46} +(-4.97996 - 8.62555i) q^{47} +(0.926039 + 1.46371i) q^{48} +(6.32297 - 3.00333i) q^{49} +(11.6414 - 6.72118i) q^{50} +(6.77743 - 0.274593i) q^{51} +(-3.50800 - 0.833013i) q^{52} +(-2.81574 - 1.62567i) q^{53} +(4.78168 + 2.03361i) q^{54} +(-4.03889 + 2.33185i) q^{55} +(-0.581819 - 2.58099i) q^{56} +(-6.22300 - 3.26436i) q^{57} +2.13462 q^{58} +(-0.822371 - 1.42439i) q^{59} +(3.97684 + 6.28585i) q^{60} -13.9381i q^{61} +(0.606034 + 1.04968i) q^{62} +(-5.83732 - 5.37827i) q^{63} -1.00000 q^{64} +(-15.0650 - 3.57734i) q^{65} +(-1.00566 - 1.58956i) q^{66} +8.03769 q^{67} +(-1.95808 + 3.39149i) q^{68} +(11.1819 - 7.07443i) q^{69} +(-2.49860 - 11.0839i) q^{70} +(-2.68997 - 1.55305i) q^{71} +(-2.46821 + 1.70526i) q^{72} +(3.86528 + 2.23162i) q^{73} +(-5.26419 + 3.03928i) q^{74} +(12.4482 + 19.6757i) q^{75} +(3.51361 - 2.02858i) q^{76} +(0.631845 + 2.80290i) q^{77} +(1.19566 - 6.12947i) q^{78} +(2.33626 + 4.04652i) q^{79} -4.29446 q^{80} +(-3.18414 + 8.41791i) q^{81} +2.01710i q^{82} +4.52632 q^{83} +(4.42594 - 1.18789i) q^{84} +(-8.40889 + 14.5646i) q^{85} +(-2.93788 + 1.69618i) q^{86} +(0.149675 + 3.69424i) q^{87} +1.08598 q^{88} +(-8.48968 + 14.7046i) q^{89} +(-10.5996 + 7.32319i) q^{90} +(-4.86376 + 8.20633i) q^{91} +7.63945i q^{92} +(-1.77412 + 1.12242i) q^{93} +9.95993i q^{94} +(15.0891 - 8.71167i) q^{95} +(-0.0701179 - 1.73063i) q^{96} +(-10.7814 - 6.22463i) q^{97} +(-6.97752 - 0.560526i) q^{98} +(2.68043 - 1.85189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.804592	−	1.53383i	0.464531	−	0.885557i
$3$	0.804592	−	1.53383i	0.464531	−	0.885557i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.14723	+	3.71911i	0.960270	+	1.66324i	0.721819	+	0.692082i	$0.243306\pi$
$5$	2.14723	+	3.71911i	0.960270	+	1.66324i	0.238451	+	0.971155i	$0.423361\pi$
$6$	−1.46371	+	0.926039i	−0.597558	+	0.378054i
$7$	2.58099	−	0.581819i	0.975521	−	0.219907i
$7$	2.58099	−	0.581819i	0.975521	−	0.219907i
$8$		−	1.00000i		−	0.353553i
$9$	−1.70526	−	2.46821i	−0.568422	−	0.822737i
$10$		−	4.29446i		−	1.35803i
$11$			1.08598i			0.327436i	0.986507	+	0.163718i	$0.0523487\pi$
$11$			1.08598i			0.327436i	−0.986507	+	0.163718i	$0.947651\pi$
$12$	1.73063	−	0.0701179i	0.499590	−	0.0202413i
$13$	−2.47541	+	2.62151i	−0.686556	+	0.727077i
$13$	−2.47541	+	2.62151i	−0.686556	+	0.727077i
$14$	−2.52611	−	0.786623i	−0.675131	−	0.210234i
$15$	7.43212	−	0.301118i	1.91897	−	0.0777484i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.95808	+	3.39149i	0.474904	+	0.822558i	0.999587	−	0.0287399i	$-0.00914944\pi$
$17$	1.95808	+	3.39149i	0.474904	+	0.822558i	−0.524683	+	0.851298i	$0.675816\pi$
$18$	0.242696	+	2.99017i	0.0572041	+	0.704789i
$19$		−	4.05717i		−	0.930778i	−0.885106	−	0.465389i	$-0.845914\pi$
$19$		−	4.05717i		−	0.930778i	0.885106	−	0.465389i	$-0.154086\pi$
$20$	−2.14723	+	3.71911i	−0.480135	+	0.831618i
$21$	1.18423	−	4.42692i	0.258420	−	0.966033i
$22$	0.542991	−	0.940488i	0.115766	−	0.200513i
$23$	6.61595	+	3.81972i	1.37952	+	0.796467i	0.992102	−	0.125436i	$-0.0400330\pi$
$23$	6.61595	+	3.81972i	1.37952	+	0.796467i	0.387420	+	0.921903i	$0.373366\pi$
$24$	−1.53383	−	0.804592i	−0.313092	−	0.164237i
$25$	−6.72118	+	11.6414i	−1.34424	+	2.32829i
$26$	3.45453	−	1.03259i	0.677488	−	0.202508i
$27$	−5.15786	+	0.629682i	−0.992630	+	0.121182i
$28$	1.79436	+	1.94429i	0.339103	+	0.367436i
$29$	−1.84864	+	1.06731i	−0.343283	+	0.198195i	−0.661723	−	0.749748i	$-0.730174\pi$
$29$	−1.84864	+	1.06731i	−0.343283	+	0.198195i	0.318440	+	0.947943i	$0.396841\pi$
$30$	−6.58696	−	3.45528i	−1.20261	−	0.630846i
$31$	−1.04968	−	0.606034i	−0.188528	−	0.108847i	0.402765	−	0.915303i	$-0.368049\pi$
$31$	−1.04968	−	0.606034i	−0.188528	−	0.108847i	−0.591293	+	0.806457i	$0.701382\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.66571	+	0.873772i	0.289963	+	0.152104i
$34$		−	3.91616i		−	0.671616i
$35$	7.70581	+	8.34967i	1.30252	+	1.41135i
$36$	1.28490	−	2.71091i	0.214150	−	0.451818i
$37$	3.03928	−	5.26419i	0.499654	−	0.865427i	−0.500345	−	0.865826i	$-0.666794\pi$
$37$	3.03928	−	5.26419i	0.499654	−	0.865427i	1.00000		0.000398985i	$0.000127001\pi$
$38$	−2.02858	+	3.51361i	−0.329080	+	0.569983i
$39$	2.02926	+	5.90611i	0.324941	+	0.945734i
$40$	3.71911	−	2.14723i	0.588043	−	0.339507i
$41$	−1.00855	−	1.74686i	−0.157509	−	0.272814i	0.776461	−	0.630166i	$-0.217013\pi$
$41$	−1.00855	−	1.74686i	−0.157509	−	0.272814i	−0.933970	+	0.357352i	$0.883680\pi$
$42$	−3.23903	+	3.24171i	−0.499793	+	0.500207i
$43$	1.69618	−	2.93788i	0.258666	−	0.448022i	−0.707219	−	0.706995i	$-0.750051\pi$
$43$	1.69618	−	2.93788i	0.258666	−	0.448022i	0.965885	+	0.258972i	$0.0833838\pi$
$44$	−0.940488	+	0.542991i	−0.141784	+	0.0818590i
$45$	5.51796	−	11.6419i	0.822569	−	1.73547i
$46$	−3.81972	−	6.61595i	−0.563187	−	0.975469i
$47$	−4.97996	−	8.62555i	−0.726402	−	1.25817i	−0.958394	−	0.285448i	$-0.907858\pi$
$47$	−4.97996	−	8.62555i	−0.726402	−	1.25817i	0.231992	−	0.972718i	$-0.425476\pi$
$48$	0.926039	+	1.46371i	0.133662	+	0.211269i
$49$	6.32297	−	3.00333i	0.903282	−	0.429047i
$50$	11.6414	−	6.72118i	1.64635	−	0.950519i
$51$	6.77743	−	0.274593i	0.949029	−	0.0384507i
$52$	−3.50800	−	0.833013i	−0.486473	−	0.115518i
$53$	−2.81574	−	1.62567i	−0.386772	−	0.223303i	0.293989	−	0.955809i	$-0.405017\pi$
$53$	−2.81574	−	1.62567i	−0.386772	−	0.223303i	−0.680761	+	0.732506i	$0.738351\pi$
$54$	4.78168	+	2.03361i	0.650704	+	0.276739i
$55$	−4.03889	+	2.33185i	−0.544603	+	0.314427i
$56$	−0.581819	−	2.58099i	−0.0777488	−	0.344899i
$57$	−6.22300	−	3.26436i	−0.824257	−	0.432375i
$58$	2.13462			0.280290
$59$	−0.822371	−	1.42439i	−0.107064	−	0.185440i	0.807516	−	0.589846i	$-0.200812\pi$
$59$	−0.822371	−	1.42439i	−0.107064	−	0.185440i	−0.914579	+	0.404406i	$0.867478\pi$
$60$	3.97684	+	6.28585i	0.513407	+	0.811499i
$61$		−	13.9381i		−	1.78460i	−0.451446	−	0.892298i	$-0.649092\pi$
$61$		−	13.9381i		−	1.78460i	0.451446	−	0.892298i	$-0.350908\pi$
$62$	0.606034	+	1.04968i	0.0769664	+	0.133310i
$63$	−5.83732	−	5.37827i	−0.735433	−	0.677598i
$64$	−1.00000			−0.125000
$65$	−15.0650	−	3.57734i	−1.86858	−	0.443714i
$66$	−1.00566	−	1.58956i	−0.123788	−	0.195662i
$67$	8.03769			0.981960			0.490980	−	0.871171i	$-0.336639\pi$
$67$	8.03769			0.981960			0.490980	+	0.871171i	$0.336639\pi$
$68$	−1.95808	+	3.39149i	−0.237452	+	0.411279i
$69$	11.1819	−	7.07443i	1.34615	−	0.851661i
$70$	−2.49860	−	11.0839i	−0.298639	−	1.32478i
$71$	−2.68997	−	1.55305i	−0.319241	−	0.184314i	0.331813	−	0.943345i	$-0.392340\pi$
$71$	−2.68997	−	1.55305i	−0.319241	−	0.184314i	−0.651054	+	0.759031i	$0.725673\pi$
$72$	−2.46821	+	1.70526i	−0.290882	+	0.200967i
$73$	3.86528	+	2.23162i	0.452397	+	0.261191i	0.708842	−	0.705367i	$-0.249218\pi$
$73$	3.86528	+	2.23162i	0.452397	+	0.261191i	−0.256445	+	0.966559i	$0.582551\pi$
$74$	−5.26419	+	3.03928i	−0.611949	+	0.353309i
$75$	12.4482	+	19.6757i	1.43739	+	2.27196i
$76$	3.51361	−	2.02858i	0.403039	−	0.232695i
$77$	0.631845	+	2.80290i	0.0720054	+	0.319421i
$78$	1.19566	−	6.12947i	0.135382	−	0.694026i
$79$	2.33626	+	4.04652i	0.262850	+	0.455269i	0.966998	−	0.254784i	$-0.0820043\pi$
$79$	2.33626	+	4.04652i	0.262850	+	0.455269i	−0.704148	+	0.710053i	$0.748671\pi$
$80$	−4.29446			−0.480135
$81$	−3.18414	+	8.41791i	−0.353794	+	0.935323i
$82$			2.01710i			0.222751i
$83$	4.52632			0.496828			0.248414	−	0.968654i	$-0.420091\pi$
$83$	4.52632			0.496828			0.248414	+	0.968654i	$0.420091\pi$
$84$	4.42594	−	1.18789i	0.482909	−	0.129609i
$85$	−8.40889	+	14.5646i	−0.912072	+	1.57976i
$86$	−2.93788	+	1.69618i	−0.316800	+	0.182904i
$87$	0.149675	+	3.69424i	0.0160469	+	0.396064i
$88$	1.08598			0.115766
$89$	−8.48968	+	14.7046i	−0.899905	+	1.55868i	−0.0722904	+	0.997384i	$0.523031\pi$
$89$	−8.48968	+	14.7046i	−0.899905	+	1.55868i	−0.827614	+	0.561297i	$0.810302\pi$
$90$	−10.5996	+	7.32319i	−1.11730	+	0.771932i
$91$	−4.86376	+	8.20633i	−0.509860	+	0.860257i
$92$			7.63945i			0.796467i
$93$	−1.77412	+	1.12242i	−0.183967	+	0.116390i
$94$			9.95993i			1.02729i
$95$	15.0891	−	8.71167i	1.54810	−	0.893798i
$96$	−0.0701179	−	1.73063i	−0.00715638	−	0.176632i
$97$	−10.7814	−	6.22463i	−1.09468	−	0.632015i	−0.159863	−	0.987139i	$-0.551105\pi$
$97$	−10.7814	−	6.22463i	−1.09468	−	0.632015i	−0.934819	+	0.355124i	$0.884439\pi$
$98$	−6.97752	−	0.560526i	−0.704836	−	0.0566217i
$99$	2.68043	−	1.85189i	0.269394	−	0.186122i
$100$	−13.4424			−1.34424
$101$	5.20857			0.518272			0.259136	−	0.965841i	$-0.416562\pi$
$101$	5.20857			0.518272			0.259136	+	0.965841i	$0.416562\pi$
$102$	−6.00672	−	3.15091i	−0.594754	−	0.311986i
$103$	−5.74356	+	3.31605i	−0.565930	+	0.326740i	−0.755522	−	0.655123i	$-0.772617\pi$
$103$	−5.74356	+	3.31605i	−0.565930	+	0.326740i	0.189592	+	0.981863i	$0.439283\pi$
$104$	2.62151	+	2.47541i	0.257061	+	0.242734i
$105$	19.0070	−	5.10133i	1.85489	−	0.497839i
$106$	1.62567	+	2.81574i	0.157899	+	0.273489i
$107$	−4.85098	−	2.80071i	−0.468962	−	0.270755i	0.246843	−	0.969055i	$-0.420607\pi$
$107$	−4.85098	−	2.80071i	−0.468962	−	0.270755i	−0.715805	+	0.698300i	$0.753940\pi$
$108$	−3.12425	−	4.15200i	−0.300631	−	0.399526i
$109$	6.04035	−	10.4622i	0.578561	−	1.00210i	−0.417084	−	0.908868i	$-0.636948\pi$
$109$	6.04035	−	10.4622i	0.578561	−	1.00210i	0.995645	−	0.0932289i	$-0.0297188\pi$
$110$	4.66370			0.444667
$111$	−5.62898	−	8.89726i	−0.534280	−	0.844490i
$112$	−0.786623	+	2.52611i	−0.0743289	+	0.238695i
$113$	−11.8295	−	6.82976i	−1.11283	−	0.642490i	−0.173266	−	0.984875i	$-0.555432\pi$
$113$	−11.8295	−	6.82976i	−1.11283	−	0.642490i	−0.939560	+	0.342385i	$0.888765\pi$
$114$	3.75710	+	5.93852i	0.351884	+	0.556194i
$115$			32.8073i			3.05929i
$116$	−1.84864	−	1.06731i	−0.171642	−	0.0990973i
$117$	10.6917	+	1.63947i	0.988447	+	0.151569i
$118$			1.64474i			0.151411i
$119$	7.02701	+	7.61415i	0.644165	+	0.697988i
$120$	−0.301118	−	7.43212i	−0.0274882	−	0.678457i
$121$	9.82064			0.892786
$122$	−6.96907	+	12.0708i	−0.630950	+	1.09284i
$123$	−3.49086	+	0.141435i	−0.314760	+	0.0127528i
$124$		−	1.21207i		−	0.108847i
$125$	−36.2554			−3.24278
$126$	2.36613	+	7.57637i	0.210792	+	0.674957i
$127$	−8.72940	−	15.1198i	−0.774609	−	1.34166i	−0.935014	−	0.354611i	$-0.884613\pi$
$127$	−8.72940	−	15.1198i	−0.774609	−	1.34166i	0.160405	−	0.987051i	$-0.448720\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.14147	−	4.96545i	−0.276591	−	0.437183i
$130$	11.2580	+	10.6306i	0.987390	+	0.932361i
$131$	4.80013	+	8.31407i	0.419389	+	0.726404i	0.995878	−	0.0907014i	$-0.0289109\pi$
$131$	4.80013	+	8.31407i	0.419389	+	0.726404i	−0.576489	+	0.817105i	$0.695578\pi$
$132$	0.0761468	+	1.87943i	0.00662773	+	0.163584i
$133$	−2.36054	−	10.4715i	−0.204684	−	0.907994i
$134$	−6.96084	−	4.01884i	−0.601325	−	0.347175i
$135$	−13.4170	−	17.8306i	−1.15475	−	1.53461i
$136$	3.39149	−	1.95808i	0.290818	−	0.167904i
$137$	−0.845527	+	0.488165i	−0.0722383	+	0.0417068i	−0.535684	−	0.844418i	$-0.679946\pi$
$137$	−0.845527	+	0.488165i	−0.0722383	+	0.0417068i	0.463446	+	0.886125i	$0.346613\pi$
$138$	−13.2211	+	0.535662i	−1.12545	+	0.0455986i
$139$	4.16317	+	2.40361i	0.353116	+	0.203871i	0.666057	−	0.745901i	$-0.267981\pi$
$139$	4.16317	+	2.40361i	0.353116	+	0.203871i	−0.312941	+	0.949773i	$0.601314\pi$
$140$	−3.37812	+	10.8483i	−0.285503	+	0.916846i
$141$	−17.2370	+	0.698369i	−1.45161	+	0.0588133i
$142$	1.55305	+	2.68997i	0.130329	+	0.225737i
$143$	−2.84692	−	2.68825i	−0.238071	−	0.224803i
$144$	2.99017	−	0.242696i	0.249181	−	0.0202247i
$145$	−7.93889	−	4.58352i	−0.659289	−	0.380641i
$146$	−2.23162	−	3.86528i	−0.184690	−	0.319893i
$147$	0.480815	−	12.1148i	0.0396569	−	0.999213i
$148$	6.07856			0.499654
$149$			4.19428i			0.343609i	0.985131	+	0.171805i	$0.0549598\pi$
$149$			4.19428i			0.343609i	−0.985131	+	0.171805i	$0.945040\pi$
$150$	−0.942551	−	23.2638i	−0.0769589	−	1.89948i
$151$	−4.52705	+	7.84109i	−0.368406	+	0.638099i	−0.989317	−	0.145783i	$-0.953430\pi$
$151$	−4.52705	+	7.84109i	−0.368406	+	0.638099i	0.620910	+	0.783882i	$0.286763\pi$
$152$	−4.05717			−0.329080
$153$	5.03188	−	10.6163i	0.406803	−	0.858281i
$154$	0.854259	−	2.74331i	0.0688381	−	0.221062i
$155$		−	5.20517i		−	0.418089i
$156$	−4.10021	+	4.71044i	−0.328280	+	0.377137i
$157$	5.51607	+	3.18471i	0.440230	+	0.254167i	0.703695	−	0.710502i	$-0.251532\pi$
$157$	5.51607	+	3.18471i	0.440230	+	0.254167i	−0.263465	+	0.964669i	$0.584865\pi$
$158$		−	4.67252i		−	0.371726i
$159$	−4.75902	+	3.01087i	−0.377415	+	0.238777i
$160$	3.71911	+	2.14723i	0.294021	+	0.169753i
$161$	19.2981	+	6.00936i	1.52090	+	0.473604i
$162$	6.96651	−	5.69805i	0.547340	−	0.447681i
$163$	−2.65466			−0.207929			−0.103964	−	0.994581i	$-0.533153\pi$
$163$	−2.65466			−0.207929			−0.103964	+	0.994581i	$0.533153\pi$
$164$	1.00855	−	1.74686i	0.0787545	−	0.136407i
$165$	0.327009	+	8.07115i	0.0254576	+	0.628338i
$166$	−3.91991	−	2.26316i	−0.304244	−	0.175655i
$167$	−12.3076	−	21.3175i	−0.952394	−	1.64959i	−0.740222	−	0.672363i	$-0.765280\pi$
$167$	−12.3076	−	21.3175i	−0.952394	−	1.64959i	−0.212172	−	0.977232i	$-0.568054\pi$
$168$	−4.42692	−	1.18423i	−0.341544	−	0.0913652i
$169$	−0.744666	−	12.9787i	−0.0572820	−	0.998358i
$170$	14.5646	−	8.40889i	1.11706	−	0.644932i
$171$	−10.0140	+	6.91855i	−0.765786	+	0.529074i
$172$	3.39237			0.258666
$173$	−11.3270			−0.861176			−0.430588	−	0.902549i	$-0.641694\pi$
$173$	−11.3270			−0.861176			−0.430588	+	0.902549i	$0.641694\pi$
$174$	1.71750	−	3.27414i	0.130203	−	0.248212i
$175$	−10.5741	+	33.9569i	−0.799325	+	2.56690i
$176$	−0.940488	−	0.542991i	−0.0708920	−	0.0409295i
$177$	−2.84644	+	0.115326i	−0.213952	+	0.00866843i
$178$	14.7046	−	8.48968i	1.10215	−	0.636329i
$179$			4.16273i			0.311137i	0.987825	+	0.155569i	$0.0497209\pi$
$179$			4.16273i			0.311137i	−0.987825	+	0.155569i	$0.950279\pi$
$180$	12.8411	−	1.04225i	0.957122	−	0.0776847i
$181$			15.2174i			1.13110i	0.824715	+	0.565549i	$0.191336\pi$
$181$			15.2174i			1.13110i	−0.824715	+	0.565549i	$0.808664\pi$
$182$	8.31530	−	4.67501i	0.616371	−	0.346535i
$183$	−21.3787	−	11.2145i	−1.58036	−	0.829001i
$184$	3.81972	−	6.61595i	0.281594	−	0.487735i
$185$	26.1041			1.91921
$186$	2.09764	−	0.0849876i	0.153807	−	0.00623160i
$187$	−3.68310	+	2.12644i	−0.269335	+	0.155501i
$188$	4.97996	−	8.62555i	0.363201	−	0.629083i
$189$	−12.9460	+	4.62614i	−0.941683	+	0.336502i
$190$	−17.4233			−1.26402
$191$			2.93980i			0.212717i	0.994328	+	0.106358i	$0.0339191\pi$
$191$			2.93980i			0.212717i	−0.994328	+	0.106358i	$0.966081\pi$
$192$	−0.804592	+	1.53383i	−0.0580664	+	0.110695i
$193$	−0.475216			−0.0342068			−0.0171034	−	0.999854i	$-0.505444\pi$
$193$	−0.475216			−0.0342068			−0.0171034	+	0.999854i	$0.505444\pi$
$194$	6.22463	+	10.7814i	0.446902	+	0.774057i
$195$	−17.6082	+	20.2288i	−1.26095	+	1.44861i
$196$	5.76245	+	3.97419i	0.411603	+	0.283871i
$197$	15.1888	−	8.76926i	1.08216	−	0.624784i	0.150680	−	0.988583i	$-0.451854\pi$
$197$	15.1888	−	8.76926i	1.08216	−	0.624784i	0.931478	+	0.363799i	$0.118520\pi$
$198$	−3.24727	+	0.263564i	−0.230773	+	0.0187307i
$199$	−0.645978	+	0.372956i	−0.0457922	+	0.0264381i	−0.522721	−	0.852504i	$-0.675083\pi$
$199$	−0.645978	+	0.372956i	−0.0457922	+	0.0264381i	0.476929	+	0.878942i	$0.341750\pi$
$200$	11.6414	+	6.72118i	0.823173	+	0.475259i
$201$	6.46706	−	12.3284i	0.456151	−	0.869581i
$202$	−4.51075	−	2.60428i	−0.317375	−	0.183237i
$203$	−4.15032	+	3.83028i	−0.291296	+	0.268833i
$204$	3.62652	+	5.73213i	0.253907	+	0.401329i
$205$	4.33118	−	7.50182i	0.302502	−	0.523950i
$206$	6.63210			0.462080
$207$	−1.85407	−	22.8432i	−0.128867	−	1.58771i
$208$	−1.03259	−	3.45453i	−0.0715973	−	0.239528i
$209$	4.40601			0.304770
$210$	−19.0112	−	5.08562i	−1.31190	−	0.350941i
$211$	8.40841	+	14.5638i	0.578859	+	1.00261i	0.995611	+	0.0935929i	$0.0298352\pi$
$211$	8.40841	+	14.5638i	0.578859	+	1.00261i	−0.416751	+	0.909020i	$0.636831\pi$
$212$		−	3.25134i		−	0.223303i
$213$	−4.54645	+	2.87638i	−0.311517	+	0.197086i
$214$	2.80071	+	4.85098i	0.191453	+	0.331606i
$215$	14.5684			0.993556
$216$	0.629682	+	5.15786i	0.0428445	+	0.350948i
$217$	−3.06181	−	0.953440i	−0.207849	−	0.0647237i
$218$	−10.4622	+	6.04035i	−0.708590	+	0.409104i
$219$	6.53290	−	4.13314i	0.441452	−	0.279292i
$220$	−4.03889	−	2.33185i	−0.272302	−	0.157213i
$221$	−13.7379	−	3.26221i	−0.924111	−	0.219440i
$222$	0.426216	+	10.5197i	0.0286057	+	0.706039i
$223$	−19.8957	+	11.4868i	−1.33232	+	0.769213i	−0.985654	−	0.168777i	$-0.946018\pi$
$223$	−19.8957	+	11.4868i	−1.33232	+	0.769213i	−0.346662	+	0.937990i	$0.612685\pi$
$224$	1.94429	−	1.79436i	0.129908	−	0.119891i
$225$	40.1949	−	3.26241i	2.67966	−	0.217494i
$226$	6.82976	+	11.8295i	0.454309	+	0.786886i
$227$	−4.79429	−	8.30396i	−0.318208	−	0.551153i	0.661906	−	0.749587i	$-0.269748\pi$
$227$	−4.79429	−	8.30396i	−0.318208	−	0.551153i	−0.980114	+	0.198434i	$0.936415\pi$
$228$	−0.284480	−	7.02146i	−0.0188402	−	0.465008i
$229$	5.98689	−	3.45653i	0.395625	−	0.228414i	−0.288970	−	0.957338i	$-0.593313\pi$
$229$	5.98689	−	3.45653i	0.395625	−	0.228414i	0.684594	+	0.728924i	$0.259979\pi$
$230$	16.4036	−	28.4119i	1.08162	−	1.87343i
$231$	4.80755	+	1.28605i	0.316314	+	0.0846160i
$232$	1.06731	+	1.84864i	0.0700724	+	0.121369i
$233$	−13.8432	+	7.99238i	−0.906899	+	0.523599i	−0.879432	−	0.476024i	$-0.842077\pi$
$233$	−13.8432	+	7.99238i	−0.906899	+	0.523599i	−0.0274670	+	0.999623i	$0.508744\pi$
$234$	−8.43954	−	6.76566i	−0.551710	−	0.442285i
$235$	21.3862	−	37.0421i	1.39508	−	2.41636i
$236$	0.822371	−	1.42439i	0.0535318	−	0.0927198i
$237$	8.08641	−	0.327627i	0.525268	−	0.0212817i
$238$	−2.27849	−	10.1076i	−0.147693	−	0.655175i
$239$		−	15.7358i		−	1.01786i	−0.860807	−	0.508931i	$-0.830041\pi$
$239$		−	15.7358i		−	1.01786i	0.860807	−	0.508931i	$-0.169959\pi$
$240$	−3.45528	+	6.58696i	−0.223038	+	0.425187i
$241$	−15.8715	+	9.16342i	−1.02237	+	0.590268i	−0.914791	−	0.403928i	$-0.867644\pi$
$241$	−15.8715	+	9.16342i	−1.02237	+	0.590268i	−0.107583	+	0.994196i	$0.534311\pi$
$242$	−8.50493	−	4.91032i	−0.546717	−	0.315647i
$243$	10.3497	+	11.6569i	0.663934	+	0.747791i
$244$	12.0708	−	6.96907i	0.772753	−	0.446149i
$245$	24.7466	+	17.0670i	1.58100	+	1.09037i
$246$	3.09389	+	1.62294i	0.197259	+	0.103475i
$247$	10.6359	+	10.0432i	0.676747	+	0.639031i
$248$	−0.606034	+	1.04968i	−0.0384832	+	0.0666548i
$249$	3.64184	−	6.94260i	0.230792	−	0.439969i
$250$	31.3981	+	18.1277i	1.98579	+	1.14650i
$251$	−4.55211	+	7.88449i	−0.287327	+	0.497665i	−0.973171	−	0.230084i	$-0.926100\pi$
$251$	−4.55211	+	7.88449i	−0.287327	+	0.497665i	0.685844	+	0.727749i	$0.259433\pi$
$252$	1.73906	−	7.74440i	0.109550	−	0.487851i
$253$	−4.14815	+	7.18481i	−0.260792	+	0.451705i
$254$			17.4588i			1.09546i
$255$	15.5739	+	24.6164i	0.975277	+	1.54154i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.47385	+	7.74893i	−0.279071	+	0.483365i	−0.971154	−	0.238453i	$-0.923360\pi$
$257$	−4.47385	+	7.74893i	−0.279071	+	0.483365i	0.692083	+	0.721818i	$0.256693\pi$
$258$	0.237866	+	5.87094i	0.0148089	+	0.365509i
$259$	4.78153	−	15.3551i	0.297110	−	0.954119i
$260$	−4.43442	−	14.8353i	−0.275011	−	0.920047i
$261$	5.78676	+	2.74278i	0.358192	+	0.169774i
$262$		−	9.60026i		−	0.593106i
$263$			21.2499i			1.31033i	0.755487	+	0.655164i	$0.227400\pi$
$263$			21.2499i			1.31033i	−0.755487	+	0.655164i	$0.772600\pi$
$264$	0.873772	−	1.66571i	0.0537770	−	0.102517i
$265$		−	13.9627i		−	0.857724i
$266$	−3.19146	+	10.2488i	−0.195681	+	0.628397i
$267$	15.7236	+	24.8529i	0.962267	+	1.52097i
$268$	4.01884	+	6.96084i	0.245490	+	0.425201i
$269$	4.55699	+	7.89294i	0.277845	+	0.481241i	0.970849	−	0.239692i	$-0.0770466\pi$
$269$	4.55699	+	7.89294i	0.277845	+	0.481241i	−0.693004	+	0.720934i	$0.743713\pi$
$270$	2.70414	+	22.1502i	0.164569	+	1.34802i
$271$	−20.6044	−	11.8959i	−1.25163	−	0.722627i	−0.280194	−	0.959943i	$-0.590399\pi$
$271$	−20.6044	−	11.8959i	−1.25163	−	0.722627i	−0.971432	+	0.237316i	$0.923732\pi$
$272$	−3.91616			−0.237452
$273$	8.67377	+	14.0629i	0.524960	+	0.851127i
$274$	0.976331			0.0589823
$275$	−12.6424	−	7.29908i	−0.762365	−	0.440151i
$276$	11.7176	+	6.14663i	0.705317	+	0.369984i
$277$	−8.04262	−	13.9302i	−0.483234	−	0.836986i	0.516581	−	0.856239i	$-0.327205\pi$
$277$	−8.04262	−	13.9302i	−0.483234	−	0.836986i	−0.999815	+	0.0192526i	$0.993871\pi$
$278$	−2.40361	−	4.16317i	−0.144159	−	0.249690i
$279$	0.294164	+	3.62428i	0.0176112	+	0.216980i
$280$	8.34967	−	7.70581i	0.498988	−	0.460510i
$281$		−	4.07708i		−	0.243218i	−0.992578	−	0.121609i	$-0.961195\pi$
$281$		−	4.07708i		−	0.243218i	0.992578	−	0.121609i	$-0.0388055\pi$
$282$	15.2768	+	8.01367i	0.909722	+	0.477207i
$283$			9.30729i			0.553261i	0.960976	+	0.276630i	$0.0892178\pi$
$283$			9.30729i			0.553261i	−0.960976	+	0.276630i	$0.910782\pi$
$284$		−	3.10611i		−	0.184314i
$285$	−1.22169	−	30.1534i	−0.0723665	−	1.78613i
$286$	1.12138	+	3.75156i	0.0663083	+	0.221834i
$287$	−3.61941	−	3.92183i	−0.213647	−	0.231498i
$288$	−2.71091	−	1.28490i	−0.159742	−	0.0757136i
$289$	0.831850	−	1.44081i	0.0489323	−	0.0847533i
$290$	4.58352	+	7.93889i	0.269154	+	0.466188i
$291$	−18.2221	+	11.5285i	−1.06820	+	0.675813i
$292$			4.46324i			0.261191i
$293$	5.17715	−	8.96708i	0.302452	−	0.523862i	−0.674239	−	0.738513i	$-0.735528\pi$
$293$	5.17715	−	8.96708i	0.302452	−	0.523862i	0.976691	+	0.214651i	$0.0688614\pi$
$294$	−6.47381	+	10.2513i	−0.377560	+	0.597870i
$295$	3.53164	−	6.11698i	0.205620	−	0.356144i
$296$	−5.26419	−	3.03928i	−0.305975	−	0.176655i
$297$	−0.683824	−	5.60134i	−0.0396795	−	0.325023i
$298$	2.09714	−	3.63236i	0.121484	−	0.210417i
$299$	−26.3907	+	7.88842i	−1.52621	+	0.456199i
$300$	−10.8156	+	20.6183i	−0.624440	+	1.19040i
$301$	2.66852	−	8.56949i	0.153811	−	0.493937i
$302$	7.84109	−	4.52705i	0.451204	−	0.260503i
$303$	4.19077	−	7.98905i	0.240753	−	0.458959i
$304$	3.51361	+	2.02858i	0.201519	+	0.116347i
$305$	51.8375	−	29.9284i	2.96821	−	1.71369i
$306$	−9.66591	+	6.67809i	−0.552563	+	0.381761i
$307$		−	3.63183i		−	0.207280i	−0.994615	−	0.103640i	$-0.966951\pi$
$307$		−	3.63183i		−	0.207280i	0.994615	−	0.103640i	$-0.0330489\pi$
$308$	−2.11146	+	1.94865i	−0.120312	+	0.111034i
$309$	0.465029	+	11.4777i	0.0264546	+	0.652944i
$310$	−2.60259	+	4.50781i	−0.147817	+	0.256026i
$311$	−7.55359	+	13.0832i	−0.428325	+	0.741881i	−0.996724	−	0.0808721i	$-0.974229\pi$
$311$	−7.55359	+	13.0832i	−0.428325	+	0.741881i	0.568400	+	0.822753i	$0.307563\pi$
$312$	5.90611	−	2.02926i	0.334368	−	0.114884i
$313$	−21.7519	+	12.5585i	−1.22949	+	0.709848i	−0.966924	−	0.255066i	$-0.917903\pi$
$313$	−21.7519	+	12.5585i	−1.22949	+	0.709848i	−0.262568	+	0.964913i	$0.584569\pi$
$314$	−3.18471	−	5.51607i	−0.179723	−	0.311290i
$315$	7.46831	−	33.2580i	0.420791	−	1.87387i
$316$	−2.33626	+	4.04652i	−0.131425	+	0.227635i
$317$	9.48911	−	5.47854i	0.532962	−	0.307706i	−0.209260	−	0.977860i	$-0.567105\pi$
$317$	9.48911	−	5.47854i	0.532962	−	0.307706i	0.742222	+	0.670154i	$0.233772\pi$
$318$	5.62687	−	0.227977i	0.315539	−	0.0127843i
$319$	−1.15908	−	2.00759i	−0.0648960	−	0.112403i
$320$	−2.14723	−	3.71911i	−0.120034	−	0.207905i
$321$	−8.19887	+	5.18714i	−0.457617	+	0.289518i
$322$	−13.7079	−	14.8533i	−0.763913	−	0.827742i
$323$	13.7599	−	7.94426i	0.765619	−	0.442030i
$324$	−8.88220	+	1.45141i	−0.493455	+	0.0806337i
$325$	−13.8805	−	46.4370i	−0.769950	−	2.57586i
$326$	2.29900	+	1.32733i	0.127330	+	0.0735140i
$327$	−11.1872	−	17.6827i	−0.618654	−	0.977854i
$328$	−1.74686	+	1.00855i	−0.0964542	+	0.0556879i
$329$	−17.8717	−	19.3650i	−0.985300	−	1.06763i
$330$	3.75238	−	7.15333i	0.206562	−	0.393778i
$331$	5.01376			0.275581			0.137791	−	0.990461i	$-0.456000\pi$
$331$	5.01376			0.275581			0.137791	+	0.990461i	$0.456000\pi$
$332$	2.26316	+	3.91991i	0.124207	+	0.215133i
$333$	−18.1759	+	1.47524i	−0.996033	+	0.0808429i
$334$			24.6153i			1.34689i
$335$	17.2588	+	29.8930i	0.942946	+	1.63323i
$336$	3.24171	+	3.23903i	0.176850	+	0.176704i
$337$	27.4419			1.49486			0.747428	−	0.664343i	$-0.231288\pi$
$337$	27.4419			1.49486			0.747428	+	0.664343i	$0.231288\pi$
$338$	−5.84443	+	11.6122i	−0.317895	+	0.631619i
$339$	−19.9936	+	12.6493i	−1.08590	+	0.687013i
$340$	−16.8178			−0.912072
$341$	0.658142	−	1.13994i	0.0356404	−	0.0617310i
$342$	12.1316	−	0.984660i	0.656002	−	0.0532443i
$343$	14.5721	−	11.4304i	0.786820	−	0.617182i
$344$	−2.93788	−	1.69618i	−0.158400	−	0.0914522i
$345$	50.3208	+	26.3965i	2.70918	+	1.42114i
$346$	9.80947	+	5.66350i	0.527360	+	0.304472i
$347$	25.3779	−	14.6519i	1.36236	−	0.786558i	0.372420	−	0.928064i	$-0.378528\pi$
$347$	25.3779	−	14.6519i	1.36236	−	0.786558i	0.989937	+	0.141507i	$0.0451946\pi$
$348$	−3.12447	+	1.97674i	−0.167489	+	0.105965i
$349$	20.5600	−	11.8703i	1.10055	−	0.635402i	0.164184	−	0.986430i	$-0.447501\pi$
$349$	20.5600	−	11.8703i	1.10055	−	0.635402i	0.936365	+	0.351027i	$0.114168\pi$
$350$	26.1359	−	24.1205i	1.39702	−	1.28929i
$351$	11.1171	−	15.0801i	0.593387	−	0.804917i
$352$	0.542991	+	0.940488i	0.0289415	+	0.0501282i
$353$	−7.60250			−0.404640			−0.202320	−	0.979319i	$-0.564848\pi$
$353$	−7.60250			−0.404640			−0.202320	+	0.979319i	$0.564848\pi$
$354$	2.52275	+	1.32335i	0.134083	+	0.0703351i
$355$		−	13.3391i		−	0.707963i
$356$	−16.9794			−0.899905
$357$	17.3327	−	4.65195i	0.917342	−	0.246207i
$358$	2.08136	−	3.60503i	0.110004	−	0.190532i
$359$	19.1204	−	11.0392i	1.00914	−	0.582626i	0.0981985	−	0.995167i	$-0.468692\pi$
$359$	19.1204	−	11.0392i	1.00914	−	0.582626i	0.910939	+	0.412541i	$0.135359\pi$
$360$	−11.6419	−	5.51796i	−0.613581	−	0.290822i
$361$	2.53939			0.133652
$362$	7.60868	−	13.1786i	0.399903	−	0.692653i
$363$	7.90161	−	15.0632i	0.414727	−	0.790612i
$364$	−9.53877	−	0.108974i	−0.499967	−	0.00571178i
$365$			19.1672i			1.00326i
$366$	12.9073	+	20.4014i	0.674674	+	1.06640i
$367$		−	7.20404i		−	0.376048i	−0.982164	−	0.188024i	$-0.939792\pi$
$367$		−	7.20404i		−	0.376048i	0.982164	−	0.188024i	$-0.0602083\pi$
$368$	−6.61595	+	3.81972i	−0.344880	+	0.199117i
$369$	−2.59178	+	5.46817i	−0.134922	+	0.284662i
$370$	−22.6068	−	13.0521i	−1.17527	−	0.678544i
$371$	−8.21324	−	2.55758i	−0.426410	−	0.132783i
$372$	−1.85910	−	0.975219i	−0.0963901	−	0.0505628i
$373$	−26.6689			−1.38086			−0.690432	−	0.723397i	$-0.742580\pi$
$373$	−26.6689			−1.38086			−0.690432	+	0.723397i	$0.742580\pi$
$374$	4.25288			0.219911
$375$	−29.1708	+	55.6096i	−1.50637	+	2.87167i
$376$	−8.62555	+	4.97996i	−0.444829	+	0.256822i
$377$	1.77817	−	7.48826i	0.0915803	−	0.385665i
$378$	13.5246	+	2.46664i	0.695632	+	0.126871i
$379$	−9.47287	−	16.4075i	−0.486589	−	0.842796i	0.513292	−	0.858214i	$-0.328426\pi$
$379$	−9.47287	−	16.4075i	−0.486589	−	0.842796i	−0.999881	+	0.0154174i	$0.995092\pi$
$380$	15.0891	+	8.71167i	0.774052	+	0.446899i
$381$	−30.2147	+	1.22417i	−1.54795	+	0.0627163i
$382$	1.46990	−	2.54594i	0.0752067	−	0.130262i
$383$	29.9109			1.52838			0.764188	−	0.644994i	$-0.223140\pi$
$383$	29.9109			1.52838			0.764188	+	0.644994i	$0.223140\pi$
$384$	1.46371	−	0.926039i	0.0746947	−	0.0472567i
$385$	−9.06759	+	8.36838i	−0.462127	+	0.426492i
$386$	0.411549	+	0.237608i	0.0209473	+	0.0120939i
$387$	−10.1438	+	0.823316i	−0.515636	+	0.0418515i
$388$		−	12.4493i		−	0.632015i
$389$	−0.821075	−	0.474048i	−0.0416301	−	0.0240352i	0.479040	−	0.877793i	$-0.340985\pi$
$389$	−0.821075	−	0.474048i	−0.0416301	−	0.0240352i	−0.520671	+	0.853758i	$0.674318\pi$
$390$	25.3635	−	8.71456i	1.28433	−	0.441279i
$391$			29.9173i			1.51298i
$392$	−3.00333	−	6.32297i	−0.151691	−	0.319358i
$393$	16.6145	−	0.673150i	0.838091	−	0.0339559i
$394$	−17.5385			−0.883578
$395$	−10.0330	+	17.3776i	−0.504813	+	0.874362i
$396$	2.94400	+	1.39538i	0.147942	+	0.0701205i
$397$			13.9746i			0.701363i	0.936495	+	0.350682i	$0.114050\pi$
$397$			13.9746i			0.701363i	−0.936495	+	0.350682i	$0.885950\pi$
$398$	0.745911			0.0373891
$399$	−17.9608	−	4.80462i	−0.899162	−	0.240532i
$400$	−6.72118	−	11.6414i	−0.336059	−	0.582071i
$401$	−32.3390	−	18.6709i	−1.61493	−	0.932381i	−0.988204	−	0.153143i	$-0.951060\pi$
$401$	−32.3390	−	18.6709i	−1.61493	−	0.932381i	−0.626728	−	0.779238i	$-0.715606\pi$
$402$	−11.7649	+	7.44321i	−0.586778	+	0.371234i
$403$	4.18712	−	1.25157i	0.208575	−	0.0623451i
$404$	2.60428	+	4.51075i	0.129568	+	0.224418i
$405$	−38.1442	+	6.23300i	−1.89540	+	0.309720i
$406$	5.50943	−	1.24196i	0.273428	−	0.0616376i
$407$	5.71681	+	3.30060i	0.283372	+	0.163605i
$408$	−0.274593	−	6.77743i	−0.0135944	−	0.335533i
$409$	−7.02063	+	4.05336i	−0.347148	+	0.200426i	−0.663428	−	0.748240i	$-0.730899\pi$
$409$	−7.02063	+	4.05336i	−0.347148	+	0.200426i	0.316281	+	0.948666i	$0.397566\pi$
$410$	−7.50182	+	4.33118i	−0.370488	+	0.213902i
$411$	0.0684583	+	1.68967i	0.00337680	+	0.0833452i
$412$	−5.74356	−	3.31605i	−0.282965	−	0.163370i
$413$	−2.95127	−	3.19786i	−0.145222	−	0.157356i
$414$	−9.81594	+	20.7098i	−0.482427	+	1.01783i
$415$	9.71904	+	16.8339i	0.477089	+	0.826342i
$416$	−0.833013	+	3.50800i	−0.0408418	+	0.171994i
$417$	7.03638	−	4.45167i	0.344573	−	0.217999i
$418$	−3.81572	−	2.20301i	−0.186633	−	0.107753i
$419$	6.79325	+	11.7663i	0.331872	+	0.574819i	0.982879	−	0.184253i	$-0.0589864\pi$
$419$	6.79325	+	11.7663i	0.331872	+	0.574819i	−0.651007	+	0.759072i	$0.725653\pi$
$420$	13.9214	+	13.9099i	0.679294	+	0.678733i
$421$	28.4439			1.38627			0.693136	−	0.720807i	$-0.256229\pi$
$421$	28.4439			1.38627			0.693136	+	0.720807i	$0.256229\pi$
$422$		−	16.8168i		−	0.818630i
$423$	−12.7975	+	27.0005i	−0.622237	+	1.31281i
$424$	−1.62567	+	2.81574i	−0.0789495	+	0.136745i
$425$	−52.6424			−2.55353
$426$	5.37553	−	0.217794i	0.260445	−	0.0105521i
$427$	−8.10947	−	35.9741i	−0.392445	−	1.74091i
$428$		−	5.60143i		−	0.270755i
$429$	−6.41393	+	2.20374i	−0.309667	+	0.106397i
$430$	−12.6166	−	7.28419i	−0.608426	−	0.351275i
$431$			12.1183i			0.583717i	0.956461	+	0.291859i	$0.0942737\pi$
$431$			12.1183i			0.583717i	−0.956461	+	0.291859i	$0.905726\pi$
$432$	2.03361	−	4.78168i	0.0978420	−	0.230059i
$433$	5.42399	+	3.13154i	0.260661	+	0.150492i	0.624636	−	0.780916i	$-0.285247\pi$
$433$	5.42399	+	3.13154i	0.260661	+	0.150492i	−0.363975	+	0.931409i	$0.618581\pi$
$434$	2.17489	+	2.35661i	0.104398	+	0.113121i
$435$	−13.4179	+	8.48904i	−0.643339	+	0.407018i
$436$	12.0807			0.578561
$437$	15.4973	−	26.8420i	0.741334	−	1.28403i
$438$	−7.72422	+	0.312953i	−0.369078	+	0.0149535i
$439$	28.4056	+	16.4000i	1.35573	+	0.782729i	0.989044	−	0.147618i	$-0.0471606\pi$
$439$	28.4056	+	16.4000i	1.35573	+	0.782729i	0.366681	+	0.930347i	$0.380494\pi$
$440$	2.33185	+	4.03889i	0.111167	+	0.192546i
$441$	−18.1952	−	10.4850i	−0.866438	−	0.499284i
$442$	10.2663	+	9.69411i	0.488316	+	0.461102i
$443$	15.8838	−	9.17053i	0.754663	−	0.435705i	−0.0727133	−	0.997353i	$-0.523166\pi$
$443$	15.8838	−	9.17053i	0.754663	−	0.435705i	0.827376	+	0.561648i	$0.189832\pi$
$444$	4.89076	−	9.32347i	0.232105	−	0.442472i
$445$	−72.9172			−3.45661
$446$	22.9736			1.08783
$447$	6.43332	+	3.37469i	0.304285	+	0.159617i
$448$	−2.58099	+	0.581819i	−0.121940	+	0.0274883i
$449$	−14.5674	−	8.41050i	−0.687478	−	0.396916i	0.115188	−	0.993344i	$-0.463253\pi$
$449$	−14.5674	−	8.41050i	−0.687478	−	0.396916i	−0.802667	+	0.596428i	$0.796586\pi$
$450$	−36.4410	−	17.2721i	−1.71785	−	0.814216i
$451$	1.89706	−	1.09527i	0.0893290	−	0.0515741i
$452$		−	13.6595i		−	0.642490i
$453$	8.38446	+	13.2526i	0.393936	+	0.622661i
$454$			9.58859i			0.450015i
$455$	−40.9638	−	0.467984i	−1.92041	−	0.0219394i
$456$	−3.26436	+	6.22300i	−0.152868	+	0.291419i
$457$	−18.3813	+	31.8373i	−0.859840	+	1.48929i	0.0122413	+	0.999925i	$0.496103\pi$
$457$	−18.3813	+	31.8373i	−0.859840	+	1.48929i	−0.872081	+	0.489361i	$0.837230\pi$
$458$	−6.91307			−0.323026
$459$	−12.2351	−	16.2599i	−0.571084	−	0.758946i
$460$	−28.4119	+	16.4036i	−1.32471	+	0.764824i
$461$	−7.08949	+	12.2793i	−0.330190	+	0.571906i	−0.982549	−	0.186004i	$-0.940446\pi$
$461$	−7.08949	+	12.2793i	−0.330190	+	0.571906i	0.652359	+	0.757910i	$0.273780\pi$
$462$	−3.52044	−	3.51753i	−0.163786	−	0.163650i
$463$	−23.7992			−1.10604			−0.553022	−	0.833167i	$-0.686525\pi$
$463$	−23.7992			−1.10604			−0.553022	+	0.833167i	$0.686525\pi$
$464$		−	2.13462i		−	0.0990973i
$465$	−7.98385	−	4.18804i	−0.370242	−	0.194216i
$466$	15.9848			0.740480
$467$	−2.73830	−	4.74288i	−0.126713	−	0.219474i	0.795688	−	0.605707i	$-0.207110\pi$
$467$	−2.73830	−	4.74288i	−0.126713	−	0.219474i	−0.922401	+	0.386233i	$0.873776\pi$
$468$	3.92602	+	10.0790i	0.181480	+	0.465902i
$469$	20.7452	−	4.67648i	0.957922	−	0.215940i
$470$	−37.0421	+	21.3862i	−1.70862	+	0.986474i
$471$	9.32298	−	5.89833i	0.429580	−	0.271781i
$472$	−1.42439	+	0.822371i	−0.0655628	+	0.0378527i
$473$	3.19048	+	1.84203i	0.146699	+	0.0846965i
$474$	−7.16685	−	3.75947i	−0.329184	−	0.172678i
$475$	47.2312	+	27.2690i	2.16712	+	1.25119i
$476$	−3.08054	+	9.89264i	−0.141196	+	0.453429i
$477$	0.789089	+	9.72205i	0.0361299	+	0.445142i
$478$	−7.86788	+	13.6276i	−0.359869	+	0.623311i
$479$	12.9339			0.590963			0.295482	−	0.955348i	$-0.404520\pi$
$479$	12.9339			0.590963			0.295482	+	0.955348i	$0.404520\pi$
$480$	6.28585	−	3.97684i	0.286908	−	0.181517i
$481$	6.27666	+	20.9985i	0.286191	+	0.957451i
$482$	18.3268			0.834765
$483$	24.7444	−	24.7649i	1.12591	−	1.12684i
$484$	4.91032	+	8.50493i	0.223196	+	0.386588i
$485$		−	53.4628i		−	2.42762i
$486$	−3.13465	−	15.2700i	−0.142191	−	0.692663i
$487$	5.77625	+	10.0048i	0.261747	+	0.453359i	0.966706	−	0.255889i	$-0.0823681\pi$
$487$	5.77625	+	10.0048i	0.261747	+	0.453359i	−0.704959	+	0.709248i	$0.749035\pi$
$488$	−13.9381			−0.630950
$489$	−2.13592	+	4.07179i	−0.0965895	+	0.184133i
$490$	−12.8977	−	27.1537i	−0.582658	−	1.22668i
$491$	18.2188	−	10.5186i	0.822202	−	0.474698i	−0.0289733	−	0.999580i	$-0.509224\pi$
$491$	18.2188	−	10.5186i	0.822202	−	0.474698i	0.851175	+	0.524882i	$0.175890\pi$
$492$	−1.86791	−	2.95245i	−0.0842121	−	0.133107i
$493$	−7.23955	−	4.17976i	−0.326053	−	0.188247i
$494$	−4.18940	−	14.0156i	−0.188490	−	0.630592i
$495$	12.6429	+	5.99240i	0.568255	+	0.269339i
$496$	1.04968	−	0.606034i	0.0471321	−	0.0272117i
$497$	−7.84637	−	2.44334i	−0.351958	−	0.109599i
$498$	−6.62522	+	4.19155i	−0.296883	+	0.187828i
$499$	12.4392	+	21.5453i	0.556855	+	0.964502i	0.997757	+	0.0669462i	$0.0213256\pi$
$499$	12.4392	+	21.5453i	0.556855	+	0.964502i	−0.440901	+	0.897556i	$0.645341\pi$
$500$	−18.1277	−	31.3981i	−0.810695	−	1.40416i
$501$	−42.6000	+	1.72597i	−1.90323	+	0.0771108i
$502$	7.88449	−	4.55211i	0.351902	−	0.203171i
$503$	−0.553605	+	0.958873i	−0.0246840	+	0.0427540i	−0.878104	−	0.478471i	$-0.841191\pi$
$503$	−0.553605	+	0.958873i	−0.0246840	+	0.0427540i	0.853420	+	0.521225i	$0.174525\pi$
$504$	−5.37827	+	5.83732i	−0.239567	+	0.260015i
$505$	11.1840	+	19.3712i	0.497681	+	0.862008i
$506$	7.18481	−	4.14815i	0.319404	−	0.184408i
$507$	−20.5062	−	9.30033i	−0.910712	−	0.413042i
$508$	8.72940	−	15.1198i	0.387304	−	0.670831i
$509$	−4.65580	+	8.06408i	−0.206365	+	0.357434i	−0.950567	−	0.310521i	$-0.899497\pi$
$509$	−4.65580	+	8.06408i	−0.206365	+	0.357434i	0.744202	+	0.667955i	$0.232830\pi$
$510$	−1.17923	−	29.1054i	−0.0522171	−	1.28881i
$511$	11.2746	+	3.51089i	0.498760	+	0.155313i
$512$			1.00000i			0.0441942i
$513$	2.55473	+	20.9263i	0.112794	+	0.923919i
$514$	7.74893	−	4.47385i	0.341791	−	0.197333i
$515$	−24.6655	−	14.2406i	−1.08689	−	0.627517i
$516$	2.72947	−	5.20332i	0.120158	−	0.229063i
$517$	9.36720	−	5.40815i	0.411969	−	0.237850i
$518$	−11.8185	+	10.9071i	−0.519274	+	0.479232i
$519$	−9.11361	+	17.3737i	−0.400043	+	0.762620i
$520$	−3.57734	+	15.0650i	−0.156877	+	0.660643i
$521$	−1.07206	+	1.85687i	−0.0469680	+	0.0813510i	−0.888554	−	0.458773i	$-0.848289\pi$
$521$	−1.07206	+	1.85687i	−0.0469680	+	0.0813510i	0.841586	+	0.540124i	$0.181623\pi$
$522$	−3.64009	−	5.26870i	−0.159323	−	0.230605i
$523$	19.6892	+	11.3676i	0.860949	+	0.497069i	0.864330	−	0.502925i	$-0.167743\pi$
$523$	19.6892	+	11.3676i	0.860949	+	0.497069i	−0.00338098	+	0.999994i	$0.501076\pi$
$524$	−4.80013	+	8.31407i	−0.209695	+	0.363202i
$525$	43.5762	+	43.5402i	1.90182	+	1.90025i
$526$	10.6250	−	18.4030i	0.463271	−	0.802409i
$527$		−	4.74665i		−	0.206767i
$528$	−1.58956	+	1.00566i	−0.0691769	+	0.0437658i
$529$	17.6806	+	30.6236i	0.768720	+	1.33146i
$530$	−6.98137	+	12.0921i	−0.303251	+	0.525247i
$531$	−2.11333	+	4.45875i	−0.0917109	+	0.193493i
$532$	7.88831	−	7.28003i	0.342002	−	0.315629i
$533$	7.07600	+	1.68027i	0.306495	+	0.0727806i
$534$	−1.19056	−	29.3850i	−0.0515205	−	1.27161i
$535$		−	24.0551i		−	1.03999i
$536$		−	8.03769i		−	0.347175i
$537$	6.38492	+	3.34930i	0.275529	+	0.144533i
$538$		−	9.11399i		−	0.392932i
$539$	3.26156	+	6.86664i	0.140486	+	0.295767i
$540$	8.73324	−	20.5347i	0.375819	−	0.883673i
$541$	−12.4149	−	21.5032i	−0.533756	−	0.924493i	−0.999222	−	0.0394274i	$-0.987447\pi$
$541$	−12.4149	−	21.5032i	−0.533756	−	0.924493i	0.465466	−	0.885066i	$-0.345887\pi$
$542$	11.8959	+	20.6044i	0.510975	+	0.885034i
$543$	23.3408	+	12.2438i	1.00165	+	0.525430i
$544$	3.39149	+	1.95808i	0.145409	+	0.0839520i
$545$	51.8801			2.22230
$546$	−0.480245	−	16.5157i	−0.0205526	−	0.706808i
$547$	12.4908			0.534066			0.267033	−	0.963687i	$-0.413957\pi$
$547$	12.4908			0.534066			0.267033	+	0.963687i	$0.413957\pi$
$548$	−0.845527	−	0.488165i	−0.0361191	−	0.0208534i
$549$	−34.4023	+	23.7682i	−1.46825	+	1.01440i
$550$	7.29908	+	12.6424i	0.311234	+	0.539073i
$551$	4.33026	+	7.50023i	0.184475	+	0.319520i
$552$	−7.07443	−	11.1819i	−0.301108	−	0.475935i
$553$	8.38419	+	9.08473i	0.356532	+	0.386322i
$554$			16.0852i			0.683396i
$555$	21.0031	−	40.0392i	0.891534	−	1.69957i
$556$			4.80722i			0.203871i
$557$		−	7.02871i		−	0.297816i	−0.988851	−	0.148908i	$-0.952424\pi$
$557$		−	7.02871i		−	0.297816i	0.988851	−	0.148908i	$-0.0475758\pi$
$558$	1.55739	−	3.28580i	0.0659295	−	0.139099i
$559$	3.50293	+	11.7190i	0.148158	+	0.495662i
$560$	−11.0839	+	2.49860i	−0.468382	+	0.105585i
$561$	0.298203	+	7.36016i	0.0125901	+	0.310746i
$562$	−2.03854	+	3.53086i	−0.0859907	+	0.148940i
$563$	0.887780	+	1.53768i	0.0374155	+	0.0648055i	0.884127	−	0.467247i	$-0.154754\pi$
$563$	0.887780	+	1.53768i	0.0374155	+	0.0648055i	−0.846711	+	0.532053i	$0.821421\pi$
$564$	−9.22329	−	14.5785i	−0.388370	−	0.613864i
$565$		−	58.6602i		−	2.46785i
$566$	4.65364	−	8.06035i	0.195607	−	0.338802i
$567$	−3.32053	+	23.5791i	−0.139449	+	0.990229i
$568$	−1.55305	+	2.68997i	−0.0651647	+	0.112869i
$569$	−4.46613	−	2.57852i	−0.187230	−	0.108097i	0.403455	−	0.914999i	$-0.367809\pi$
$569$	−4.46613	−	2.57852i	−0.187230	−	0.108097i	−0.590685	+	0.806902i	$0.701142\pi$
$570$	−14.0187	+	26.7244i	−0.587177	+	1.11936i
$571$	12.8678	−	22.2876i	0.538499	−	0.932707i	−0.460486	−	0.887667i	$-0.652325\pi$
$571$	12.8678	−	22.2876i	0.538499	−	0.932707i	0.998985	−	0.0450405i	$-0.0143417\pi$
$572$	0.904638	−	3.80963i	0.0378248	−	0.159289i
$573$	4.50916	+	2.36534i	0.188373	+	0.0988136i
$574$	1.17359	+	5.20611i	0.0489846	+	0.217299i
$575$	−88.9341	+	51.3461i	−3.70881	+	2.14128i
$576$	1.70526	+	2.46821i	0.0710527	+	0.102842i
$577$	−5.09936	−	2.94412i	−0.212289	−	0.122565i	0.390086	−	0.920779i	$-0.372445\pi$
$577$	−5.09936	−	2.94412i	−0.212289	−	0.122565i	−0.602375	+	0.798213i	$0.705779\pi$
$578$	−1.44081	+	0.831850i	−0.0599296	+	0.0346004i
$579$	−0.382355	+	0.728901i	−0.0158901	+	0.0302921i
$580$		−	9.16704i		−	0.380641i
$581$	11.6824	−	2.63350i	0.484666	−	0.109256i
$582$	21.5451	−	0.872916i	0.893072	−	0.0361835i
$583$	1.76545	−	3.05785i	0.0731174	−	0.126643i
$584$	2.23162	−	3.86528i	0.0923451	−	0.159946i
$585$	16.8601	+	43.2839i	0.697081	+	1.78957i
$586$	−8.96708	+	5.17715i	−0.370427	+	0.213866i
$587$	−19.3999	−	33.6017i	−0.800721	−	1.38689i	−0.919142	−	0.393926i	$-0.871117\pi$
$587$	−19.3999	−	33.6017i	−0.800721	−	1.38689i	0.118421	−	0.992963i	$-0.462217\pi$
$588$	10.7321	−	5.64101i	0.442586	−	0.232631i
$589$	−2.45878	+	4.25873i	−0.101312	+	0.175478i
$590$	−6.11698	+	3.53164i	−0.251832	+	0.145395i
$591$	−1.22976	−	30.3527i	−0.0505858	−	1.24854i
$592$	3.03928	+	5.26419i	0.124914	+	0.216357i
$593$	−8.45753	−	14.6489i	−0.347309	−	0.601557i	0.638461	−	0.769654i	$-0.279571\pi$
$593$	−8.45753	−	14.6489i	−0.347309	−	0.601557i	−0.985770	+	0.168097i	$0.946238\pi$
$594$	−2.20846	+	5.19282i	−0.0906143	+	0.213064i
$595$	−13.2293	+	42.4835i	−0.542346	+	1.74165i
$596$	−3.63236	+	2.09714i	−0.148787	+	0.0859023i
$597$	0.0523017	+	1.29090i	0.00214057	+	0.0528329i
$598$	26.7992	+	6.36376i	1.09590	+	0.260234i
$599$	−27.3660	−	15.7998i	−1.11814	−	0.645561i	−0.177217	−	0.984172i	$-0.556710\pi$
$599$	−27.3660	−	15.7998i	−1.11814	−	0.645561i	−0.940926	+	0.338611i	$0.890043\pi$
$600$	19.6757	−	12.4482i	0.803259	−	0.508194i
$601$	5.98901	−	3.45775i	0.244297	−	0.141045i	−0.372853	−	0.927890i	$-0.621621\pi$
$601$	5.98901	−	3.45775i	0.244297	−	0.141045i	0.617150	+	0.786846i	$0.288287\pi$
$602$	−6.59575	+	6.08714i	−0.268823	+	0.248093i
$603$	−13.7064	−	19.8387i	−0.558167	−	0.807895i
$604$	−9.05411			−0.368406
$605$	21.0872	+	36.5240i	0.857315	+	1.48491i
$606$	−7.62384	+	4.82334i	−0.309697	+	0.195935i
$607$		−	28.1401i		−	1.14217i	−0.820890	−	0.571086i	$-0.806522\pi$
$607$		−	28.1401i		−	1.14217i	0.820890	−	0.571086i	$-0.193478\pi$
$608$	−2.02858	−	3.51361i	−0.0822699	−	0.142496i
$609$	2.53569	+	9.44770i	0.102751	+	0.382840i
$610$	−59.8568			−2.42353
$611$	34.9395	+	8.29675i	1.41350	+	0.335651i
$612$	11.7100	−	0.950438i	0.473347	−	0.0384192i
$613$	45.8879			1.85340			0.926698	−	0.375807i	$-0.122634\pi$
$613$	45.8879			1.85340			0.926698	+	0.375807i	$0.122634\pi$
$614$	−1.81592	+	3.14526i	−0.0732844	+	0.126932i
$615$	−8.02168	−	12.6792i	−0.323465	−	0.511274i
$616$	2.80290	−	0.631845i	0.112932	−	0.0254577i
$617$	−13.1635	−	7.59995i	−0.529942	−	0.305962i	0.211051	−	0.977475i	$-0.432312\pi$
$617$	−13.1635	−	7.59995i	−0.529942	−	0.305962i	−0.740993	+	0.671513i	$0.765645\pi$
$618$	5.33613	−	10.1725i	0.214651	−	0.409198i
$619$	42.0050	+	24.2516i	1.68832	+	0.974753i	0.955804	+	0.294005i	$0.0949882\pi$
$619$	42.0050	+	24.2516i	1.68832	+	0.974753i	0.732518	+	0.680748i	$0.238345\pi$
$620$	4.50781	−	2.60259i	0.181038	−	0.104522i
$621$	−36.5294	−	15.5356i	−1.46587	−	0.623424i
$622$	13.0832	−	7.55359i	0.524589	−	0.302871i
$623$	−13.3564	+	42.8917i	−0.535111	+	1.71842i
$624$	−6.12947	−	1.19566i	−0.245375	−	0.0478649i
$625$	−44.2427	−	76.6305i	−1.76971	−	3.06522i
$626$	25.1170			1.00388
$627$	3.54504	−	6.75807i	0.141575	−	0.269891i
$628$			6.36941i			0.254167i
$629$	23.8046			0.949152
$630$	−23.0967	+	25.0681i	−0.920196	+	0.998737i
$631$	−6.26200	+	10.8461i	−0.249286	+	0.431776i	−0.963328	−	0.268327i	$-0.913529\pi$
$631$	−6.26200	+	10.8461i	−0.249286	+	0.431776i	0.714042	+	0.700103i	$0.246863\pi$
$632$	4.04652	−	2.33626i	0.160962	−	0.0929314i
$633$	29.1037	−	1.17916i	1.15677	−	0.0468674i
$634$	−10.9571			−0.435161
$635$	37.4880	−	64.9312i	1.48767	−	2.57671i
$636$	−4.98700	−	2.61600i	−0.197747	−	0.103731i
$637$	−7.77870	+	24.0102i	−0.308203	+	0.951321i
$638$			2.31816i			0.0917769i
$639$	0.753842	+	9.28778i	0.0298215	+	0.367419i
$640$			4.29446i			0.169753i
$641$	−0.626662	+	0.361803i	−0.0247517	+	0.0142904i	−0.512325	−	0.858792i	$-0.671216\pi$
$641$	−0.626662	+	0.361803i	−0.0247517	+	0.0142904i	0.487573	+	0.873082i	$0.337882\pi$
$642$	9.69401	−	0.392760i	0.382592	−	0.0155010i
$643$	−32.0601	−	18.5099i	−1.26433	−	0.729959i	−0.290418	−	0.956900i	$-0.593794\pi$
$643$	−32.0601	−	18.5099i	−1.26433	−	0.729959i	−0.973909	+	0.226940i	$0.927128\pi$
$644$	4.44477	+	19.7173i	0.175149	+	0.776970i
$645$	11.7216	−	22.3454i	0.461538	−	0.879850i
$646$	−15.8885			−0.625125
$647$	28.5617			1.12288			0.561439	−	0.827518i	$-0.310248\pi$
$647$	28.5617			1.12288			0.561439	+	0.827518i	$0.310248\pi$
$648$	8.41791	+	3.18414i	0.330687	+	0.125085i
$649$	1.54686	−	0.893081i	0.0607196	−	0.0350565i
$650$	−11.1977	+	47.1559i	−0.439209	+	1.84961i
$651$	−3.92592	+	3.92917i	−0.153869	+	0.153996i
$652$	−1.32733	−	2.29900i	−0.0519822	−	0.0900359i
$653$	12.5433	+	7.24187i	0.490856	+	0.283396i	0.724930	−	0.688823i	$-0.241872\pi$
$653$	12.5433	+	7.24187i	0.490856	+	0.283396i	−0.234073	+	0.972219i	$0.575206\pi$
$654$	0.847074	+	20.9072i	0.0331232	+	0.817538i
$655$	−20.6140	+	35.7044i	−0.805454	+	1.39509i
$656$	2.01710			0.0787545
$657$	−1.08321	−	13.3458i	−0.0422602	−	0.520671i
$658$	5.79487	+	25.7064i	0.225908	+	1.00214i
$659$	−10.1298	−	5.84845i	−0.394601	−	0.227823i	0.289551	−	0.957163i	$-0.406494\pi$
$659$	−10.1298	−	5.84845i	−0.394601	−	0.227823i	−0.684152	+	0.729340i	$0.739827\pi$
$660$	−6.82632	+	4.31877i	−0.265714	+	0.168108i
$661$			11.2378i			0.437100i	0.975826	+	0.218550i	$0.0701327\pi$
$661$			11.2378i			0.437100i	−0.975826	+	0.218550i	$0.929867\pi$
$662$	−4.34205	−	2.50688i	−0.168758	−	0.0974327i
$663$	−16.0571	+	18.4468i	−0.623605	+	0.716416i
$664$		−	4.52632i		−	0.175655i
$665$	33.8760	−	31.2638i	1.31366	−	1.21236i
$666$	16.4784	+	7.81035i	0.638526	+	0.302645i
$667$	−16.3073			−0.631422
$668$	12.3076	−	21.3175i	0.476197	−	0.824797i
$669$	1.61086	+	39.7588i	0.0622795	+	1.53716i
$670$		−	34.5175i		−	1.33353i
$671$	15.1366			0.584341
$672$	−1.18789	−	4.42594i	−0.0458237	−	0.170734i
$673$	10.0141	+	17.3450i	0.386016	+	0.668600i	0.991910	−	0.126946i	$-0.0405176\pi$
$673$	10.0141	+	17.3450i	0.386016	+	0.668600i	−0.605893	+	0.795546i	$0.707184\pi$
$674$	−23.7654	−	13.7210i	−0.915409	−	0.528512i
$675$	27.3365	−	64.2770i	1.05218	−	2.47402i
$676$	10.8675	−	7.13423i	0.417981	−	0.274393i
$677$	21.3263	+	36.9382i	0.819635	+	1.41965i	0.905952	+	0.423381i	$0.139157\pi$
$677$	21.3263	+	36.9382i	0.819635	+	1.41965i	−0.0863170	+	0.996268i	$0.527510\pi$
$678$	23.6396	−	0.957777i	0.907873	−	0.0367832i
$679$	−31.4482	−	9.79287i	−1.20687	−	0.375816i
$680$	14.5646	+	8.40889i	0.558528	+	0.322466i
$681$	−16.5943	+	0.672332i	−0.635895	+	0.0257638i
$682$	−1.13994	+	0.658142i	−0.0436504	+	0.0252016i
$683$	−12.0857	+	6.97765i	−0.462445	+	0.266993i	−0.713072	−	0.701091i	$-0.752697\pi$
$683$	−12.0857	+	6.97765i	−0.462445	+	0.266993i	0.250627	+	0.968084i	$0.419363\pi$
$684$	−10.9986	−	5.21306i	−0.420542	−	0.199326i
$685$	−3.63108	−	2.09641i	−0.138736	−	0.0800996i
$686$	−18.3350	+	2.61294i	−0.700034	+	0.0997626i
$687$	−0.484730	−	11.9640i	−0.0184936	−	0.456454i
$688$	1.69618	+	2.93788i	0.0646664	+	0.112006i
$689$	11.2318	−	3.35730i	0.427899	−	0.127903i
$690$	−30.3808	−	48.0204i	−1.15658	−	1.82810i
$691$	32.4226	+	18.7192i	1.23341	+	0.712112i	0.967740	−	0.251952i	$-0.0810724\pi$
$691$	32.4226	+	18.7192i	1.23341	+	0.712112i	0.265673	+	0.964063i	$0.414406\pi$
$692$	−5.66350	−	9.80947i	−0.215294	−	0.372900i
$693$	5.84070	−	6.33922i	0.221870	−	0.240807i
$694$	−29.3039			−1.11236
$695$			20.6444i			0.783086i
$696$	3.69424	−	0.149675i	0.140030	−	0.00567342i
$697$	3.94964	−	6.84098i	0.149603	−	0.259121i
$698$	−23.7406			−0.898595
$699$	1.12082	+	27.6637i	0.0423933	+	1.04634i
$700$	−34.6945	+	7.82102i	−1.31133	+	0.295607i
$701$			20.0942i			0.758948i	0.925202	+	0.379474i	$0.123895\pi$
$701$			20.0942i			0.758948i	−0.925202	+	0.379474i	$0.876105\pi$
$702$	−17.1678	+	7.50121i	−0.647955	+	0.283115i
$703$	−21.3577	−	12.3309i	−0.805520	−	0.465067i
$704$		−	1.08598i		−	0.0409295i
$705$	−39.6090	−	62.6066i	−1.49176	−	2.35790i
$706$	6.58396	+	3.80125i	0.247791	+	0.143062i
$707$	13.4432	−	3.03044i	0.505585	−	0.113971i
$708$	−1.52310	−	2.40743i	−0.0572415	−	0.0904767i
$709$	−16.6858			−0.626649			−0.313325	−	0.949646i	$-0.601443\pi$
$709$	−16.6858			−0.626649			−0.313325	+	0.949646i	$0.601443\pi$
$710$	−6.66953	+	11.5520i	−0.250303	+	0.433537i
$711$	6.00373	−	12.6668i	0.225157	−	0.475041i
$712$	14.7046	+	8.48968i	0.551077	+	0.318164i
$713$	−4.62976	−	8.01898i	−0.173386	−	0.300313i
$714$	−17.3365	−	4.63763i	−0.648803	−	0.173559i
$715$	3.88493	−	16.3603i	0.145288	−	0.611840i
$716$	−3.60503	+	2.08136i	−0.134726	+	0.0777843i
$717$	−24.1360	−	12.6609i	−0.901375	−	0.472829i
$718$	−22.0784			−0.823957
$719$	−16.3460			−0.609602			−0.304801	−	0.952416i	$-0.598590\pi$
$719$	−16.3460			−0.609602			−0.304801	+	0.952416i	$0.598590\pi$
$720$	7.32319	+	10.5996i	0.272919	+	0.395025i
$721$	−12.8947	+	11.9004i	−0.480224	+	0.443193i
$722$	−2.19917	−	1.26969i	−0.0818447	−	0.0472531i
$723$	1.28504	+	31.7170i	0.0477911	+	1.17957i
$724$	−13.1786	+	7.60868i	−0.489779	+	0.282774i
$725$		−	28.6944i		−	1.06568i
$726$	−14.3746	+	9.09430i	−0.533491	+	0.337521i
$727$		−	20.7212i		−	0.768508i	−0.923227	−	0.384254i	$-0.874459\pi$
$727$		−	20.7212i		−	0.768508i	0.923227	−	0.384254i	$-0.125541\pi$
$728$	8.20633	+	4.86376i	0.304147	+	0.180263i
$729$	26.2070	−	6.49562i	0.970630	−	0.240579i
$730$	9.58360	−	16.5993i	0.354705	−	0.614367i
$731$	13.2851			0.491366
$732$	−0.977314	−	24.1218i	−0.0361225	−	0.891567i
$733$	−34.6007	+	19.9767i	−1.27801	+	0.737857i	−0.976482	−	0.215601i	$-0.930829\pi$
$733$	−34.6007	+	19.9767i	−1.27801	+	0.737857i	−0.301525	+	0.953458i	$0.597496\pi$
$734$	−3.60202	+	6.23889i	−0.132953	+	0.230281i
$735$	46.0888	−	24.2251i	1.70001	−	0.893556i
$736$	7.63945			0.281594
$737$			8.72879i			0.321529i
$738$	4.97863	−	3.43969i	0.183266	−	0.126617i
$739$	39.9486			1.46953			0.734766	−	0.678321i	$-0.237292\pi$
$739$	39.9486			1.46953			0.734766	+	0.678321i	$0.237292\pi$
$740$	13.0521	+	22.6068i	0.479803	+	0.831043i
$741$	23.9621	−	8.23304i	0.880269	−	0.302448i
$742$	5.83408	+	6.32155i	0.214176	+	0.232071i
$743$	−25.4018	+	14.6657i	−0.931900	+	0.538033i	−0.887412	−	0.460977i	$-0.847499\pi$
$743$	−25.4018	+	14.6657i	−0.931900	+	0.538033i	−0.0444880	+	0.999010i	$0.514166\pi$
$744$	1.12242	+	1.77412i	0.0411500	+	0.0650423i
$745$	−15.5990	+	9.00609i	−0.571503	+	0.329958i
$746$	23.0960	+	13.3345i	0.845603	+	0.488209i
$747$	−7.71857	−	11.1719i	−0.282408	−	0.408759i
$748$	−3.68310	−	2.12644i	−0.134668	−	0.0777503i
$749$	−14.1498	−	4.40621i	−0.517023	−	0.161000i
$750$	53.0674	−	33.5739i	1.93775	−	1.22595i
$751$	−2.16303	+	3.74647i	−0.0789299	+	0.136711i	−0.902789	−	0.430085i	$-0.858484\pi$
$751$	−2.16303	+	3.74647i	−0.0789299	+	0.136711i	0.823859	+	0.566795i	$0.191817\pi$
$752$	9.95993			0.363201
$753$	8.43087	+	13.3260i	0.307238	+	0.485625i
$754$	−5.28407	+	5.59594i	−0.192434	+	0.203792i
$755$	−38.8825			−1.41508
$756$	−10.4794	−	8.89849i	−0.381130	−	0.323635i
$757$	−22.0785	−	38.2410i	−0.802456	−	1.38989i	−0.917995	−	0.396591i	$-0.870193\pi$
$757$	−22.0785	−	38.2410i	−0.802456	−	1.38989i	0.115540	−	0.993303i	$-0.463140\pi$
$758$			18.9457i			0.688140i
$759$	7.68270	+	12.1434i	0.278864	+	0.440777i
$760$	−8.71167	−	15.0891i	−0.316005	−	0.547337i
$761$	−25.2109			−0.913893			−0.456947	−	0.889494i	$-0.651057\pi$
$761$	−25.2109			−0.913893			−0.456947	+	0.889494i	$0.651057\pi$
$762$	26.7788	+	14.0472i	0.970094	+	0.508876i
$763$	9.50296	−	30.5172i	0.344030	−	1.10480i
$764$	−2.54594	+	1.46990i	−0.0921090	+	0.0531792i
$765$	50.2880	−	4.08162i	1.81817	−	0.147571i
$766$	−25.9036	−	14.9555i	−0.935935	−	0.540362i
$767$	5.76976	+	1.37009i	0.208334	+	0.0494712i
$768$	−1.73063	+	0.0701179i	−0.0624488	+	0.00253016i
$769$	34.7089	−	20.0392i	1.25164	−	0.722633i	0.280202	−	0.959941i	$-0.409599\pi$
$769$	34.7089	−	20.0392i	1.25164	−	0.722633i	0.971434	+	0.237308i	$0.0762652\pi$
$770$	12.0370	−	2.71343i	0.433782	−	0.0977852i
$771$	8.28592	+	13.0968i	0.298410	+	0.471671i
$772$	−0.237608	−	0.411549i	−0.00855171	−	0.0148120i
$773$	21.8101	+	37.7763i	0.784456	+	1.35872i	0.929323	+	0.369267i	$0.120391\pi$
$773$	21.8101	+	37.7763i	0.784456	+	1.35872i	−0.144867	+	0.989451i	$0.546276\pi$
$774$	9.19640	+	4.35886i	0.330558	+	0.156676i
$775$	14.1102	−	8.14653i	0.506853	−	0.292632i
$776$	−6.22463	+	10.7814i	−0.223451	+	0.387029i
$777$	−19.7049	−	19.6886i	−0.706910	−	0.706326i
$778$	0.474048	+	0.821075i	0.0169954	+	0.0294369i
$779$	−7.08731	+	4.09186i	−0.253929	+	0.146606i
$780$	−26.3227	−	5.13473i	−0.942505	−	0.183853i
$781$	1.68659	−	2.92126i	0.0603509	−	0.104531i
$782$	14.9586	−	25.9091i	0.534920	−	0.926508i
$783$	8.86294	−	6.66909i	0.316736	−	0.238334i
$784$	−0.560526	+	6.97752i	−0.0200188	+	0.249197i
$785$			27.3532i			0.976276i
$786$	−14.7252	−	7.72429i	−0.525229	−	0.275516i
$787$	21.0980	−	12.1809i	0.752063	−	0.434204i	−0.0743758	−	0.997230i	$-0.523696\pi$
$787$	21.0980	−	12.1809i	0.752063	−	0.434204i	0.826439	+	0.563026i	$0.190363\pi$
$788$	15.1888	+	8.76926i	0.541079	+	0.312392i
$789$	32.5938	+	17.0975i	1.16037	+	0.608688i
$790$	17.3776	−	10.0330i	0.618268	−	0.356957i
$791$	−34.5054	−	10.7449i	−1.22687	−	0.382045i
$792$	−1.85189	−	2.68043i	−0.0658040	−	0.0952451i
$793$	36.5390	+	34.5027i	1.29754	+	1.22523i
$794$	6.98728	−	12.1023i	0.247969	−	0.429496i
$795$	−21.4165	−	11.2343i	−0.759564	−	0.398440i
$796$	−0.645978	−	0.372956i	−0.0228961	−	0.0132191i
$797$	−20.9559	+	36.2967i	−0.742297	+	1.28570i	0.209150	+	0.977884i	$0.432930\pi$
$797$	−20.9559	+	36.2967i	−0.742297	+	1.28570i	−0.951447	+	0.307812i	$0.900403\pi$
$798$	13.1522	+	13.1413i	0.465581	+	0.465197i
$799$	19.5023	−	33.7790i	0.689943	−	1.19502i
$800$			13.4424i			0.475259i
$801$	50.7711	−	4.12083i	1.79391	−	0.145602i
$802$	18.6709	+	32.3390i	0.659293	+	1.14193i
$803$	−2.42350	+	4.19763i	−0.0855235	+	0.148131i
$804$	13.9103	−	0.563586i	0.490577	−	0.0198761i
$805$	19.0879	+	84.6751i	0.672759	+	2.98441i
$806$	−4.25194	−	1.00967i	−0.149768	−	0.0355641i
$807$	15.7729	−	0.639054i	0.555234	−	0.0224958i
$808$		−	5.20857i		−	0.183237i
$809$			3.55503i			0.124988i	0.998045	+	0.0624942i	$0.0199055\pi$
$809$			3.55503i			0.124988i	−0.998045	+	0.0624942i	$0.980095\pi$
$810$	36.1504	+	13.6742i	1.27019	+	0.480461i
$811$			12.7250i			0.446836i	0.974723	+	0.223418i	$0.0717215\pi$
$811$			12.7250i			0.446836i	−0.974723	+	0.223418i	$0.928279\pi$
$812$	−5.39228	−	1.67914i	−0.189232	−	0.0589264i
$813$	−34.8245	+	22.0322i	−1.22135	+	0.772704i
$814$	−3.30060	−	5.71681i	−0.115686	−	0.200374i
$815$	−5.70016	−	9.87297i	−0.199668	−	0.345835i
$816$	−3.15091	+	6.00672i	−0.110304	+	0.210277i
$817$	−11.9195	−	6.88171i	−0.417009	−	0.240760i
$818$	8.10672			0.283445
$819$	28.5490	−	1.98918i	0.997581	−	0.0695074i
$820$	8.66235			0.302502
$821$	25.4487	+	14.6928i	0.888165	+	0.512782i	0.873342	−	0.487108i	$-0.161948\pi$
$821$	25.4487	+	14.6928i	0.888165	+	0.512782i	0.0148229	+	0.999890i	$0.495282\pi$
$822$	0.785548	−	1.49753i	0.0273991	−	0.0522322i
$823$	−0.850962	−	1.47391i	−0.0296627	−	0.0513772i	0.850813	−	0.525469i	$-0.176110\pi$
$823$	−0.850962	−	1.47391i	−0.0296627	−	0.0513772i	−0.880476	+	0.474091i	$0.842777\pi$
$824$	3.31605	+	5.74356i	0.115520	+	0.200087i
$825$	−21.3675	+	13.5185i	−0.743921	+	0.470653i
$826$	0.956942	+	4.24506i	0.0332963	+	0.147704i
$827$		−	11.9648i		−	0.416057i	−0.978123	−	0.208029i	$-0.933295\pi$
$827$		−	11.9648i		−	0.416057i	0.978123	−	0.208029i	$-0.0667047\pi$
$828$	18.8558	−	13.0273i	0.655283	−	0.452729i
$829$			11.6607i			0.404994i	0.979283	+	0.202497i	$0.0649057\pi$
$829$			11.6607i			0.404994i	−0.979283	+	0.202497i	$0.935094\pi$
$830$		−	19.4381i		−	0.674706i
$831$	−27.8376	+	1.12786i	−0.965676	+	0.0391251i
$832$	2.47541	−	2.62151i	0.0858195	−	0.0908846i
$833$	22.5667	+	15.5636i	0.781888	+	0.539245i
$834$	−8.31952	+	0.337072i	−0.288081	+	0.0116718i
$835$	52.8547	−	91.5469i	1.82911	−	3.16811i
$836$	2.20301	+	3.81572i	0.0761926	+	0.131969i
$837$	5.79572	+	2.46487i	0.200329	+	0.0851984i
$838$		−	13.5865i		−	0.469338i
$839$	15.1044	−	26.1616i	0.521461	−	0.903197i	−0.478227	−	0.878236i	$-0.658720\pi$
$839$	15.1044	−	26.1616i	0.521461	−	0.903197i	0.999688	−	0.0249613i	$-0.00794625\pi$
$840$	−5.10133	−	19.0070i	−0.176013	−	0.655804i
$841$	−12.2217	+	21.1686i	−0.421438	+	0.729952i
$842$	−24.6331	−	14.2220i	−0.848914	−	0.490121i
$843$	−6.25355	−	3.28039i	−0.215384	−	0.112983i
$844$	−8.40841	+	14.5638i	−0.289430	+	0.501307i
$845$	46.6701	−	30.6376i	1.60550	−	1.05397i
$846$	24.5832	−	16.9843i	0.845188	−	0.583933i
$847$	25.3469	−	5.71383i	0.870931	−	0.196330i
$848$	2.81574	−	1.62567i	0.0966930	−	0.0558257i
$849$	14.2758	+	7.48856i	0.489944	+	0.257007i
$850$	45.5897	+	26.3212i	1.56371	+	0.902810i
$851$	40.2155	−	23.2184i	1.37857	−	0.795917i
$852$	−4.76424	−	2.49915i	−0.163220	−	0.0856194i
$853$		−	24.1160i		−	0.825715i	−0.910796	−	0.412858i	$-0.864531\pi$
$853$		−	24.1160i		−	0.825715i	0.910796	−	0.412858i	$-0.135469\pi$
$854$	−10.9641	+	35.2093i	−0.375183	+	1.20484i
$855$	−47.2331	−	22.3873i	−1.61534	−	0.765629i
$856$	−2.80071	+	4.85098i	−0.0957264	+	0.165803i
$857$	−10.2452	+	17.7452i	−0.349970	+	0.606166i	−0.986244	−	0.165297i	$-0.947142\pi$
$857$	−10.2452	+	17.7452i	−0.349970	+	0.606166i	0.636274	+	0.771463i	$0.280475\pi$
$858$	6.65649	+	1.29847i	0.227249	+	0.0443291i
$859$	−48.7579	+	28.1504i	−1.66360	+	0.960479i	−0.692623	+	0.721300i	$0.743545\pi$
$859$	−48.7579	+	28.1504i	−1.66360	+	0.960479i	−0.970975	+	0.239179i	$0.923122\pi$
$860$	7.28419	+	12.6166i	0.248389	+	0.430222i
$861$	−8.92756	+	2.39609i	−0.304250	+	0.0816584i
$862$	6.05914	−	10.4947i	0.206375	−	0.357452i
$863$	−3.63343	+	2.09776i	−0.123683	+	0.0714087i	−0.560565	−	0.828110i	$-0.689416\pi$
$863$	−3.63343	+	2.09776i	−0.123683	+	0.0714087i	0.436882	+	0.899519i	$0.356083\pi$
$864$	−4.15200	+	3.12425i	−0.141254	+	0.106289i
$865$	−24.3217	−	42.1263i	−0.826961	−	1.43234i
$866$	−3.13154	−	5.42399i	−0.106414	−	0.184315i
$867$	−1.54065	−	2.43518i	−0.0523233	−	0.0827029i
$868$	−0.705203	−	3.12833i	−0.0239362	−	0.106182i
$869$	−4.39445	+	2.53714i	−0.149071	+	0.0860665i
$870$	15.8648	−	0.642774i	0.537866	−	0.0217921i
$871$	−19.8966	+	21.0709i	−0.674170	+	0.713960i
$872$	−10.4622	−	6.04035i	−0.354295	−	0.204552i
$873$	3.02139	+	37.2254i	0.102259	+	1.25989i
$874$	−26.8420	+	15.4973i	−0.907945	+	0.524203i
$875$	−93.5746	+	21.0941i	−3.16340	+	0.713109i
$876$	6.84585	+	3.59109i	0.231300	+	0.121332i
$877$	3.97262			0.134146			0.0670730	−	0.997748i	$-0.478634\pi$
$877$	3.97262			0.134146			0.0670730	+	0.997748i	$0.478634\pi$
$878$	−16.4000	−	28.4056i	−0.553473	−	0.958643i
$879$	−9.58848	−	15.1557i	−0.323411	−	0.511189i
$880$		−	4.66370i		−	0.157213i
$881$	6.30198	+	10.9153i	0.212319	+	0.367747i	0.952440	−	0.304727i	$-0.0985651\pi$
$881$	6.30198	+	10.9153i	0.212319	+	0.367747i	−0.740121	+	0.672474i	$0.765232\pi$
$882$	10.5150	+	18.1779i	0.354059	+	0.612080i
$883$	25.7438			0.866349			0.433175	−	0.901310i	$-0.357393\pi$
$883$	25.7438			0.866349			0.433175	+	0.901310i	$0.357393\pi$
$884$	−4.04379	−	13.5285i	−0.136007	−	0.455012i
$885$	−6.54087	−	10.3386i	−0.219869	−	0.347528i
$886$	−18.3411			−0.616180
$887$	15.4952	−	26.8384i	0.520277	−	0.901145i	−0.479446	−	0.877572i	$-0.659162\pi$
$887$	15.4952	−	26.8384i	0.520277	−	0.901145i	0.999722	−	0.0235738i	$-0.00750447\pi$
$888$	−8.89726	+	5.62898i	−0.298572	+	0.188896i
$889$	−31.3274	−	33.9450i	−1.05069	−	1.13848i
$890$	63.1481	+	36.4586i	2.11673	+	1.22209i
$891$	−9.14170	−	3.45792i	−0.306259	−	0.115845i
$892$	−19.8957	−	11.4868i	−0.666158	−	0.384606i
$893$	−34.9953	+	20.2046i	−1.17107	+	0.676120i
$894$	−3.88407	−	6.13922i	−0.129903	−	0.205326i
$895$	−15.4816	+	8.93833i	−0.517494	+	0.298775i
$896$	2.52611	+	0.786623i	0.0843914	+	0.0262792i
$897$	−9.13422	+	46.8257i	−0.304983	+	1.56347i
$898$	8.41050	+	14.5674i	0.280662	+	0.486121i
$899$	2.58731			0.0862915
$900$	22.9228	+	33.1786i	0.764093	+	1.10595i
$901$		−	12.7328i		−	0.424190i
$902$	−2.19054			−0.0729368
$903$	−10.9971	−	10.9880i	−0.365960	−	0.365657i
$904$	−6.82976	+	11.8295i	−0.227154	+	0.393443i
$905$	−56.5950	+	32.6751i	−1.88128	+	1.08616i
$906$	−0.634855	−	15.6693i	−0.0210916	−	0.520578i
$907$	−22.7692			−0.756040			−0.378020	−	0.925798i	$-0.623395\pi$
$907$	−22.7692			−0.756040			−0.378020	+	0.925798i	$0.623395\pi$
$908$	4.79429	−	8.30396i	0.159104	−	0.275577i
$909$	−8.88199	−	12.8558i	−0.294597	−	0.426402i
$910$	35.2417	+	20.8872i	1.16825	+	0.692404i
$911$			30.1970i			1.00047i	0.865889	+	0.500236i	$0.166753\pi$
$911$			30.1970i			1.00047i	−0.865889	+	0.500236i	$0.833247\pi$
$912$	5.93852	−	3.75710i	0.196644	−	0.124410i
$913$			4.91550i			0.162679i
$914$	31.8373	−	18.3813i	1.05308	−	0.607999i
$915$	−4.19703	−	103.590i	−0.138750	−	3.42458i
$916$	5.98689	+	3.45653i	0.197812	+	0.114207i
$917$	17.2263	+	18.6657i	0.568864	+	0.616395i
$918$	2.46594	+	20.1990i	0.0813880	+	0.666666i
$919$	8.48809			0.279996			0.139998	−	0.990152i	$-0.455290\pi$
$919$	8.48809			0.279996			0.139998	+	0.990152i	$0.455290\pi$
$920$	32.8073			1.08162
$921$	−5.57061	−	2.92214i	−0.183558	−	0.0962878i
$922$	12.2793	−	7.08949i	0.404399	−	0.233480i
$923$	10.7301	−	3.20734i	0.353187	−	0.105571i
$924$	1.29002	+	4.80649i	0.0424387	+	0.158122i
$925$	40.8551	+	70.7631i	1.34331	+	2.32668i
$926$	20.6107	+	11.8996i	0.677310	+	0.391045i
$927$	17.9790	+	8.52159i	0.590508	+	0.279886i
$928$	−1.06731	+	1.84864i	−0.0350362	+	0.0606845i
$929$	−23.6462			−0.775806			−0.387903	−	0.921700i	$-0.626800\pi$
$929$	−23.6462			−0.775806			−0.387903	+	0.921700i	$0.626800\pi$
$930$	4.82019	+	7.61887i	0.158060	+	0.249833i
$931$	−12.1850	−	25.6534i	−0.399348	−	0.840755i
$932$	−13.8432	−	7.99238i	−0.453450	−	0.261799i
$933$	13.9898	+	22.1126i	0.458007	+	0.723933i
$934$			5.47660i			0.179200i
$935$	−15.8169	−	9.13190i	−0.517269	−	0.298645i
$936$	1.63947	−	10.6917i	0.0535877	−	0.349469i
$937$			40.7293i			1.33057i	0.746591	+	0.665284i	$0.231689\pi$
$937$			40.7293i			1.33057i	−0.746591	+	0.665284i	$0.768311\pi$
$938$	−20.3041	−	6.32263i	−0.662951	−	0.206441i
$939$	1.76115	+	43.4682i	0.0574729	+	1.41853i
$940$	42.7725			1.39508
$941$	−18.6395	+	32.2845i	−0.607629	+	1.05244i	0.384001	+	0.923333i	$0.374546\pi$
$941$	−18.6395	+	32.2845i	−0.607629	+	1.05244i	−0.991630	+	0.129111i	$0.958788\pi$
$942$	−11.0231	+	0.446610i	−0.359152	+	0.0145513i
$943$		−	15.4095i		−	0.501803i
$944$	1.64474			0.0535318
$945$	−45.0031	−	38.2142i	−1.46395	−	1.24311i
$946$	−1.84203	−	3.19048i	−0.0598895	−	0.103732i
$947$	32.7009	+	18.8799i	1.06264	+	0.613513i	0.926160	−	0.377130i	$-0.123089\pi$
$947$	32.7009	+	18.8799i	1.06264	+	0.613513i	0.136476	+	0.990643i	$0.456422\pi$
$948$	4.32694	+	6.83922i	0.140532	+	0.222127i
$949$	−15.4184	+	4.60870i	−0.500502	+	0.149605i
$950$	−27.2690	−	47.2312i	−0.884722	−	1.53238i
$951$	−0.768288	−	18.9627i	−0.0249134	−	0.614907i
$952$	7.61415	−	7.02701i	0.246776	−	0.227747i
$953$	30.1541	+	17.4095i	0.976786	+	0.563948i	0.901298	−	0.433199i	$-0.142615\pi$
$953$	30.1541	+	17.4095i	0.976786	+	0.563948i	0.0754876	+	0.997147i	$0.475949\pi$
$954$	4.17765	−	8.81409i	0.135257	−	0.285367i
$955$	−10.9335	+	6.31243i	−0.353798	+	0.204265i
$956$	13.6276	−	7.86788i	0.440747	−	0.254465i
$957$	−4.01188	+	0.162545i	−0.129686	+	0.00525432i
$958$	−11.2010	−	6.46693i	−0.361889	−	0.208937i
$959$	−1.89827	+	1.75189i	−0.0612984	+	0.0565715i
$960$	−7.43212	+	0.301118i	−0.239871	+	0.00971855i
$961$	−14.7654	−	25.5745i	−0.476305	−	0.824984i
$962$	5.06352	−	21.3236i	0.163254	−	0.687501i
$963$	1.35945	+	16.7492i	0.0438076	+	0.539736i
$964$	−15.8715	−	9.16342i	−0.511187	−	0.295134i
$965$	−1.02040	−	1.76738i	−0.0328478	−	0.0568940i
$966$	−33.8117	+	9.07480i	−1.08787	+	0.291977i
$967$	20.8316			0.669898			0.334949	−	0.942236i	$-0.391281\pi$
$967$	20.8316			0.669898			0.334949	+	0.942236i	$0.391281\pi$
$968$		−	9.82064i		−	0.315647i
$969$	−1.11407	−	27.4972i	−0.0357891	−	0.883336i
$970$	−26.7314	+	46.3001i	−0.858294	+	1.48661i
$971$	51.4557			1.65129			0.825645	−	0.564189i	$-0.190811\pi$
$971$	51.4557			1.65129			0.825645	+	0.564189i	$0.190811\pi$
$972$	−4.92033	+	14.7916i	−0.157820	+	0.474440i
$973$	12.1436	+	3.78147i	0.389304	+	0.121228i
$974$		−	11.5525i		−	0.370166i
$975$	−82.3945	−	16.0726i	−2.63874	−	0.514734i
$976$	12.0708	+	6.96907i	0.386376	+	0.223075i
$977$			31.7396i			1.01544i	0.861522	+	0.507720i	$0.169512\pi$
$977$			31.7396i			1.01544i	−0.861522	+	0.507720i	$0.830488\pi$
$978$	3.88565	−	2.45832i	0.124250	−	0.0786084i
$979$	−15.9689	−	9.21965i	−0.510368	−	0.294661i
$980$	−2.40716	+	29.9647i	−0.0768938	+	0.957186i
$981$	−36.1233	+	2.93195i	−1.15333	+	0.0936098i
$982$	−21.0372			−0.671325
$983$	5.74547	−	9.95145i	0.183252	−	0.317402i	−0.759734	−	0.650234i	$-0.774671\pi$
$983$	5.74547	−	9.95145i	0.183252	−	0.317402i	0.942986	+	0.332832i	$0.108004\pi$
$984$	0.141435	+	3.49086i	0.00450878	+	0.111284i
$985$	65.2277	+	37.6592i	2.07833	+	1.19992i
$986$	4.17976	+	7.23955i	0.133111	+	0.230554i
$987$	−44.0820	+	11.8313i	−1.40315	+	0.376593i
$988$	−3.37968	+	14.2326i	−0.107522	+	0.452798i
$989$	22.4438	−	12.9579i	0.713670	−	0.412038i
$990$	−7.95285	−	11.5110i	−0.252758	−	0.365844i
$991$	21.8884			0.695308			0.347654	−	0.937623i	$-0.386978\pi$
$991$	21.8884			0.695308			0.347654	+	0.937623i	$0.386978\pi$
$992$	−1.21207			−0.0384832
$993$	4.03403	−	7.69025i	0.128016	−	0.244043i
$994$	5.57349	+	6.03918i	0.176780	+	0.191551i
$995$	−2.77412	−	1.60164i	−0.0879457	−	0.0507754i
$996$	7.83339	−	0.317376i	0.248210	−	0.0100564i
$997$	−10.5871	+	6.11244i	−0.335295	+	0.193583i	−0.658190	−	0.752852i	$-0.728678\pi$
$997$	−10.5871	+	6.11244i	−0.335295	+	0.193583i	0.322894	+	0.946435i	$0.395344\pi$
$998$		−	24.8784i		−	0.787512i
$999$	−12.3614	+	29.0657i	−0.391098	+	0.919598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.185.13	✓	76
3.2	odd	2	inner	546.2.u.a.185.26	yes	76
7.5	odd	6		546.2.bb.a.341.25	yes	76
13.9	even	3		546.2.bb.a.269.21	yes	76
21.5	even	6		546.2.bb.a.341.2	yes	76
39.35	odd	6		546.2.bb.a.269.6	yes	76
91.61	odd	6	inner	546.2.u.a.425.26	yes	76
273.152	even	6	inner	546.2.u.a.425.13	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.13	✓	76	1.1	even	1	trivial
546.2.u.a.185.26	yes	76	3.2	odd	2	inner
546.2.u.a.425.13	yes	76	273.152	even	6	inner
546.2.u.a.425.26	yes	76	91.61	odd	6	inner
546.2.bb.a.269.6	yes	76	39.35	odd	6
546.2.bb.a.269.21	yes	76	13.9	even	3
546.2.bb.a.341.2	yes	76	21.5	even	6
546.2.bb.a.341.25	yes	76	7.5	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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.804592 - 1.53383i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.14723 + 3.71911i) q^{5} +(-1.46371 + 0.926039i) q^{6} +(2.58099 - 0.581819i) q^{7} -1.00000i q^{8} +(-1.70526 - 2.46821i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.804592 - 1.53383i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.14723 + 3.71911i) q^{5} +(-1.46371 + 0.926039i) q^{6} +(2.58099 - 0.581819i) q^{7} -1.00000i q^{8} +(-1.70526 - 2.46821i) q^{9} -4.29446i q^{10} +1.08598i q^{11} +(1.73063 - 0.0701179i) q^{12} +(-2.47541 + 2.62151i) q^{13} +(-2.52611 - 0.786623i) q^{14} +(7.43212 - 0.301118i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.95808 + 3.39149i) q^{17} +(0.242696 + 2.99017i) q^{18} -4.05717i q^{19} +(-2.14723 + 3.71911i) q^{20} +(1.18423 - 4.42692i) q^{21} +(0.542991 - 0.940488i) q^{22} +(6.61595 + 3.81972i) q^{23} +(-1.53383 - 0.804592i) q^{24} +(-6.72118 + 11.6414i) q^{25} +(3.45453 - 1.03259i) q^{26} +(-5.15786 + 0.629682i) q^{27} +(1.79436 + 1.94429i) q^{28} +(-1.84864 + 1.06731i) q^{29} +(-6.58696 - 3.45528i) q^{30} +(-1.04968 - 0.606034i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.66571 + 0.873772i) q^{33} -3.91616i q^{34} +(7.70581 + 8.34967i) q^{35} +(1.28490 - 2.71091i) q^{36} +(3.03928 - 5.26419i) q^{37} +(-2.02858 + 3.51361i) q^{38} +(2.02926 + 5.90611i) q^{39} +(3.71911 - 2.14723i) q^{40} +(-1.00855 - 1.74686i) q^{41} +(-3.23903 + 3.24171i) q^{42} +(1.69618 - 2.93788i) q^{43} +(-0.940488 + 0.542991i) q^{44} +(5.51796 - 11.6419i) q^{45} +(-3.81972 - 6.61595i) q^{46} +(-4.97996 - 8.62555i) q^{47} +(0.926039 + 1.46371i) q^{48} +(6.32297 - 3.00333i) q^{49} +(11.6414 - 6.72118i) q^{50} +(6.77743 - 0.274593i) q^{51} +(-3.50800 - 0.833013i) q^{52} +(-2.81574 - 1.62567i) q^{53} +(4.78168 + 2.03361i) q^{54} +(-4.03889 + 2.33185i) q^{55} +(-0.581819 - 2.58099i) q^{56} +(-6.22300 - 3.26436i) q^{57} +2.13462 q^{58} +(-0.822371 - 1.42439i) q^{59} +(3.97684 + 6.28585i) q^{60} -13.9381i q^{61} +(0.606034 + 1.04968i) q^{62} +(-5.83732 - 5.37827i) q^{63} -1.00000 q^{64} +(-15.0650 - 3.57734i) q^{65} +(-1.00566 - 1.58956i) q^{66} +8.03769 q^{67} +(-1.95808 + 3.39149i) q^{68} +(11.1819 - 7.07443i) q^{69} +(-2.49860 - 11.0839i) q^{70} +(-2.68997 - 1.55305i) q^{71} +(-2.46821 + 1.70526i) q^{72} +(3.86528 + 2.23162i) q^{73} +(-5.26419 + 3.03928i) q^{74} +(12.4482 + 19.6757i) q^{75} +(3.51361 - 2.02858i) q^{76} +(0.631845 + 2.80290i) q^{77} +(1.19566 - 6.12947i) q^{78} +(2.33626 + 4.04652i) q^{79} -4.29446 q^{80} +(-3.18414 + 8.41791i) q^{81} +2.01710i q^{82} +4.52632 q^{83} +(4.42594 - 1.18789i) q^{84} +(-8.40889 + 14.5646i) q^{85} +(-2.93788 + 1.69618i) q^{86} +(0.149675 + 3.69424i) q^{87} +1.08598 q^{88} +(-8.48968 + 14.7046i) q^{89} +(-10.5996 + 7.32319i) q^{90} +(-4.86376 + 8.20633i) q^{91} +7.63945i q^{92} +(-1.77412 + 1.12242i) q^{93} +9.95993i q^{94} +(15.0891 - 8.71167i) q^{95} +(-0.0701179 - 1.73063i) q^{96} +(-10.7814 - 6.22463i) q^{97} +(-6.97752 - 0.560526i) q^{98} +(2.68043 - 1.85189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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