LMFDB - Embedded newform 546.2.bi.f.17.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.15
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.67564 - 0.438430i) q^{3} +1.00000 q^{4} +(1.57344 - 0.908426i) q^{5} +(1.67564 - 0.438430i) q^{6} +(-2.47008 - 0.947995i) q^{7} +1.00000 q^{8} +(2.61556 - 1.46930i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.67564 - 0.438430i) q^{3} +1.00000 q^{4} +(1.57344 - 0.908426i) q^{5} +(1.67564 - 0.438430i) q^{6} +(-2.47008 - 0.947995i) q^{7} +1.00000 q^{8} +(2.61556 - 1.46930i) q^{9} +(1.57344 - 0.908426i) q^{10} +(-1.02563 - 1.77645i) q^{11} +(1.67564 - 0.438430i) q^{12} +(-3.57560 - 0.463745i) q^{13} +(-2.47008 - 0.947995i) q^{14} +(2.23824 - 2.21204i) q^{15} +1.00000 q^{16} +5.68717 q^{17} +(2.61556 - 1.46930i) q^{18} +(-0.796762 + 1.38003i) q^{19} +(1.57344 - 0.908426i) q^{20} +(-4.55461 - 0.505542i) q^{21} +(-1.02563 - 1.77645i) q^{22} +8.73960i q^{23} +(1.67564 - 0.438430i) q^{24} +(-0.849523 + 1.47142i) q^{25} +(-3.57560 - 0.463745i) q^{26} +(3.73855 - 3.60877i) q^{27} +(-2.47008 - 0.947995i) q^{28} +(0.724381 + 0.418222i) q^{29} +(2.23824 - 2.21204i) q^{30} +(-3.97501 + 6.88493i) q^{31} +1.00000 q^{32} +(-2.49744 - 2.52703i) q^{33} +5.68717 q^{34} +(-4.74771 + 0.752275i) q^{35} +(2.61556 - 1.46930i) q^{36} -4.21819i q^{37} +(-0.796762 + 1.38003i) q^{38} +(-6.19475 + 0.790580i) q^{39} +(1.57344 - 0.908426i) q^{40} +(0.397180 + 0.229312i) q^{41} +(-4.55461 - 0.505542i) q^{42} +(0.836012 + 1.44802i) q^{43} +(-1.02563 - 1.77645i) q^{44} +(2.78067 - 4.68791i) q^{45} +8.73960i q^{46} +(-1.94760 + 1.12445i) q^{47} +(1.67564 - 0.438430i) q^{48} +(5.20261 + 4.68325i) q^{49} +(-0.849523 + 1.47142i) q^{50} +(9.52967 - 2.49343i) q^{51} +(-3.57560 - 0.463745i) q^{52} +(0.497067 + 0.286982i) q^{53} +(3.73855 - 3.60877i) q^{54} +(-3.22755 - 1.86343i) q^{55} +(-2.47008 - 0.947995i) q^{56} +(-0.730041 + 2.66176i) q^{57} +(0.724381 + 0.418222i) q^{58} -2.19150i q^{59} +(2.23824 - 2.21204i) q^{60} +(-5.97394 - 3.44906i) q^{61} +(-3.97501 + 6.88493i) q^{62} +(-7.85354 + 1.14977i) q^{63} +1.00000 q^{64} +(-6.04728 + 2.51850i) q^{65} +(-2.49744 - 2.52703i) q^{66} +(-4.46448 + 2.57757i) q^{67} +5.68717 q^{68} +(3.83170 + 14.6444i) q^{69} +(-4.74771 + 0.752275i) q^{70} +(4.24250 + 7.34823i) q^{71} +(2.61556 - 1.46930i) q^{72} +(5.11752 - 8.86381i) q^{73} -4.21819i q^{74} +(-0.778384 + 2.83803i) q^{75} +(-0.796762 + 1.38003i) q^{76} +(0.849335 + 5.36027i) q^{77} +(-6.19475 + 0.790580i) q^{78} +(-3.68537 - 6.38325i) q^{79} +(1.57344 - 0.908426i) q^{80} +(4.68229 - 7.68610i) q^{81} +(0.397180 + 0.229312i) q^{82} -15.0678i q^{83} +(-4.55461 - 0.505542i) q^{84} +(8.94843 - 5.16638i) q^{85} +(0.836012 + 1.44802i) q^{86} +(1.39717 + 0.383200i) q^{87} +(-1.02563 - 1.77645i) q^{88} +3.86314i q^{89} +(2.78067 - 4.68791i) q^{90} +(8.39241 + 4.53514i) q^{91} +8.73960i q^{92} +(-3.64215 + 13.2794i) q^{93} +(-1.94760 + 1.12445i) q^{94} +2.89520i q^{95} +(1.67564 - 0.438430i) q^{96} +(-1.72410 - 2.98622i) q^{97} +(5.20261 + 4.68325i) q^{98} +(-5.29275 - 3.13944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.67564	−	0.438430i	0.967433	−	0.253128i
$3$	1.67564	−	0.438430i	0.967433	−	0.253128i
$4$	1.00000			0.500000
$5$	1.57344	−	0.908426i	0.703664	−	0.406261i	−0.105047	−	0.994467i	$-0.533499\pi$
$5$	1.57344	−	0.908426i	0.703664	−	0.406261i	0.808711	+	0.588207i	$0.200166\pi$
$6$	1.67564	−	0.438430i	0.684078	−	0.178988i
$7$	−2.47008	−	0.947995i	−0.933603	−	0.358308i
$7$	−2.47008	−	0.947995i	−0.933603	−	0.358308i
$8$	1.00000			0.353553
$9$	2.61556	−	1.46930i	0.871853	−	0.489768i
$10$	1.57344	−	0.908426i	0.497566	−	0.287270i
$11$	−1.02563	−	1.77645i	−0.309240	−	0.535620i	0.668956	−	0.743302i	$-0.266741\pi$
$11$	−1.02563	−	1.77645i	−0.309240	−	0.535620i	−0.978196	+	0.207682i	$0.933408\pi$
$12$	1.67564	−	0.438430i	0.483716	−	0.126564i
$13$	−3.57560	−	0.463745i	−0.991694	−	0.128620i
$13$	−3.57560	−	0.463745i	−0.991694	−	0.128620i
$14$	−2.47008	−	0.947995i	−0.660157	−	0.253362i
$15$	2.23824	−	2.21204i	0.577912	−	0.571147i
$16$	1.00000			0.250000
$17$	5.68717			1.37934			0.689671	−	0.724123i	$-0.257755\pi$
$17$	5.68717			1.37934			0.689671	+	0.724123i	$0.257755\pi$
$18$	2.61556	−	1.46930i	0.616493	−	0.346318i
$19$	−0.796762	+	1.38003i	−0.182790	+	0.316601i	−0.942829	−	0.333276i	$-0.891846\pi$
$19$	−0.796762	+	1.38003i	−0.182790	+	0.316601i	0.760040	+	0.649876i	$0.225179\pi$
$20$	1.57344	−	0.908426i	0.351832	−	0.203130i
$21$	−4.55461	−	0.505542i	−0.993896	−	0.110318i
$22$	−1.02563	−	1.77645i	−0.218666	−	0.378740i
$23$			8.73960i			1.82233i	0.412039	+	0.911166i	$0.364817\pi$
$23$			8.73960i			1.82233i	−0.412039	+	0.911166i	$0.635183\pi$
$24$	1.67564	−	0.438430i	0.342039	−	0.0894942i
$25$	−0.849523	+	1.47142i	−0.169905	+	0.294283i
$26$	−3.57560	−	0.463745i	−0.701234	−	0.0909480i
$27$	3.73855	−	3.60877i	0.719485	−	0.694508i
$28$	−2.47008	−	0.947995i	−0.466802	−	0.179154i
$29$	0.724381	+	0.418222i	0.134514	+	0.0776618i	0.565747	−	0.824579i	$-0.308588\pi$
$29$	0.724381	+	0.418222i	0.134514	+	0.0776618i	−0.431233	+	0.902241i	$0.641921\pi$
$30$	2.23824	−	2.21204i	0.408645	−	0.403862i
$31$	−3.97501	+	6.88493i	−0.713934	+	1.23657i	0.249436	+	0.968391i	$0.419755\pi$
$31$	−3.97501	+	6.88493i	−0.713934	+	1.23657i	−0.963369	+	0.268178i	$0.913579\pi$
$32$	1.00000			0.176777
$33$	−2.49744	−	2.52703i	−0.434749	−	0.439899i
$34$	5.68717			0.975342
$35$	−4.74771	+	0.752275i	−0.802510	+	0.127158i
$36$	2.61556	−	1.46930i	0.435926	−	0.244884i
$37$		−	4.21819i		−	0.693466i	−0.937964	−	0.346733i	$-0.887291\pi$
$37$		−	4.21819i		−	0.693466i	0.937964	−	0.346733i	$-0.112709\pi$
$38$	−0.796762	+	1.38003i	−0.129252	+	0.223871i
$39$	−6.19475	+	0.790580i	−0.991955	+	0.126594i
$40$	1.57344	−	0.908426i	0.248783	−	0.143635i
$41$	0.397180	+	0.229312i	0.0620290	+	0.0358125i	0.530694	−	0.847564i	$-0.321931\pi$
$41$	0.397180	+	0.229312i	0.0620290	+	0.0358125i	−0.468665	+	0.883376i	$0.655265\pi$
$42$	−4.55461	−	0.505542i	−0.702791	−	0.0780069i
$43$	0.836012	+	1.44802i	0.127491	+	0.220820i	0.922704	−	0.385510i	$-0.125974\pi$
$43$	0.836012	+	1.44802i	0.127491	+	0.220820i	−0.795213	+	0.606330i	$0.792641\pi$
$44$	−1.02563	−	1.77645i	−0.154620	−	0.267810i
$45$	2.78067	−	4.68791i	0.414518	−	0.698832i
$46$			8.73960i			1.28858i
$47$	−1.94760	+	1.12445i	−0.284086	+	0.164017i	−0.635272	−	0.772289i	$-0.719112\pi$
$47$	−1.94760	+	1.12445i	−0.284086	+	0.164017i	0.351186	+	0.936306i	$0.385779\pi$
$48$	1.67564	−	0.438430i	0.241858	−	0.0632819i
$49$	5.20261	+	4.68325i	0.743230	+	0.669036i
$50$	−0.849523	+	1.47142i	−0.120141	+	0.208090i
$51$	9.52967	−	2.49343i	1.33442	−	0.349150i
$52$	−3.57560	−	0.463745i	−0.495847	−	0.0643099i
$53$	0.497067	+	0.286982i	0.0682774	+	0.0394200i	0.533750	−	0.845642i	$-0.320782\pi$
$53$	0.497067	+	0.286982i	0.0682774	+	0.0394200i	−0.465473	+	0.885062i	$0.654116\pi$
$54$	3.73855	−	3.60877i	0.508753	−	0.491091i
$55$	−3.22755	−	1.86343i	−0.435202	−	0.251264i
$56$	−2.47008	−	0.947995i	−0.330079	−	0.126681i
$57$	−0.730041	+	2.66176i	−0.0966962	+	0.352559i
$58$	0.724381	+	0.418222i	0.0951159	+	0.0549152i
$59$		−	2.19150i		−	0.285308i	−0.989773	−	0.142654i	$-0.954436\pi$
$59$		−	2.19150i		−	0.285308i	0.989773	−	0.142654i	$-0.0455637\pi$
$60$	2.23824	−	2.21204i	0.288956	−	0.285573i
$61$	−5.97394	−	3.44906i	−0.764885	−	0.441607i	0.0661618	−	0.997809i	$-0.478925\pi$
$61$	−5.97394	−	3.44906i	−0.764885	−	0.441607i	−0.831047	+	0.556202i	$0.812258\pi$
$62$	−3.97501	+	6.88493i	−0.504827	+	0.874386i
$63$	−7.85354	+	1.14977i	−0.989453	+	0.144857i
$64$	1.00000			0.125000
$65$	−6.04728	+	2.51850i	−0.750073	+	0.312381i
$66$	−2.49744	−	2.52703i	−0.307414	−	0.311055i
$67$	−4.46448	+	2.57757i	−0.545423	+	0.314900i	−0.747274	−	0.664516i	$-0.768638\pi$
$67$	−4.46448	+	2.57757i	−0.545423	+	0.314900i	0.201851	+	0.979416i	$0.435304\pi$
$68$	5.68717			0.689671
$69$	3.83170	+	14.6444i	0.461283	+	1.76298i
$70$	−4.74771	+	0.752275i	−0.567460	+	0.0899140i
$71$	4.24250	+	7.34823i	0.503493	+	0.872075i	0.999992	+	0.00403764i	$0.00128522\pi$
$71$	4.24250	+	7.34823i	0.503493	+	0.872075i	−0.496499	+	0.868037i	$0.665381\pi$
$72$	2.61556	−	1.46930i	0.308246	−	0.173159i
$73$	5.11752	−	8.86381i	0.598961	−	1.03743i	−0.394014	−	0.919104i	$-0.628914\pi$
$73$	5.11752	−	8.86381i	0.598961	−	1.03743i	0.992975	−	0.118326i	$-0.0377528\pi$
$74$		−	4.21819i		−	0.490354i
$75$	−0.778384	+	2.83803i	−0.0898800	+	0.327707i
$76$	−0.796762	+	1.38003i	−0.0913948	+	0.158300i
$77$	0.849335	+	5.36027i	0.0967907	+	0.610860i
$78$	−6.19475	+	0.790580i	−0.701418	+	0.0895156i
$79$	−3.68537	−	6.38325i	−0.414637	−	0.718172i	0.580754	−	0.814079i	$-0.302758\pi$
$79$	−3.68537	−	6.38325i	−0.414637	−	0.718172i	−0.995390	+	0.0959076i	$0.969425\pi$
$80$	1.57344	−	0.908426i	0.175916	−	0.101565i
$81$	4.68229	−	7.68610i	0.520254	−	0.854011i
$82$	0.397180	+	0.229312i	0.0438612	+	0.0253233i
$83$		−	15.0678i		−	1.65391i	−0.562269	−	0.826954i	$-0.690071\pi$
$83$		−	15.0678i		−	1.65391i	0.562269	−	0.826954i	$-0.309929\pi$
$84$	−4.55461	−	0.505542i	−0.496948	−	0.0551592i
$85$	8.94843	−	5.16638i	0.970594	−	0.560373i
$86$	0.836012	+	1.44802i	0.0901495	+	0.156143i
$87$	1.39717	+	0.383200i	0.149792	+	0.0410833i
$88$	−1.02563	−	1.77645i	−0.109333	−	0.189370i
$89$			3.86314i			0.409492i	0.978815	+	0.204746i	$0.0656368\pi$
$89$			3.86314i			0.409492i	−0.978815	+	0.204746i	$0.934363\pi$
$90$	2.78067	−	4.68791i	0.293108	−	0.494149i
$91$	8.39241	+	4.53514i	0.879763	+	0.475412i
$92$			8.73960i			0.911166i
$93$	−3.64215	+	13.2794i	−0.377673	+	1.37701i
$94$	−1.94760	+	1.12445i	−0.200879	+	0.115978i
$95$			2.89520i			0.297041i
$96$	1.67564	−	0.438430i	0.171020	−	0.0447471i
$97$	−1.72410	−	2.98622i	−0.175056	−	0.303205i	0.765125	−	0.643882i	$-0.222677\pi$
$97$	−1.72410	−	2.98622i	−0.175056	−	0.303205i	−0.940180	+	0.340677i	$0.889344\pi$
$98$	5.20261	+	4.68325i	0.525543	+	0.473080i
$99$	−5.29275	−	3.13944i	−0.531941	−	0.315526i
$100$	−0.849523	+	1.47142i	−0.0849523	+	0.147142i
$101$	−4.84811	−	8.39717i	−0.482405	−	0.835550i	0.517391	−	0.855749i	$-0.326903\pi$
$101$	−4.84811	−	8.39717i	−0.482405	−	0.835550i	−0.999796	+	0.0201992i	$0.993570\pi$
$102$	9.52967	−	2.49343i	0.943578	−	0.246886i
$103$	8.08628	−	4.66861i	0.796765	−	0.460012i	−0.0455739	−	0.998961i	$-0.514512\pi$
$103$	8.08628	−	4.66861i	0.796765	−	0.460012i	0.842339	+	0.538949i	$0.181178\pi$
$104$	−3.57560	−	0.463745i	−0.350617	−	0.0454740i
$105$	−7.62565	+	3.34208i	−0.744187	+	0.326154i
$106$	0.497067	+	0.286982i	0.0482794	+	0.0278742i
$107$			10.7060i			1.03499i	0.855687	+	0.517493i	$0.173135\pi$
$107$			10.7060i			1.03499i	−0.855687	+	0.517493i	$0.826865\pi$
$108$	3.73855	−	3.60877i	0.359743	−	0.347254i
$109$	−4.30381	−	2.48481i	−0.412230	−	0.238001i	0.279517	−	0.960141i	$-0.409826\pi$
$109$	−4.30381	−	2.48481i	−0.412230	−	0.238001i	−0.691748	+	0.722139i	$0.743159\pi$
$110$	−3.22755	−	1.86343i	−0.307735	−	0.177671i
$111$	−1.84938	−	7.06818i	−0.175535	−	0.670882i
$112$	−2.47008	−	0.947995i	−0.233401	−	0.0895771i
$113$	−14.4435	+	8.33897i	−1.35873	+	0.784464i	−0.989453	−	0.144855i	$-0.953729\pi$
$113$	−14.4435	+	8.33897i	−1.35873	+	0.784464i	−0.369279	+	0.929319i	$0.620395\pi$
$114$	−0.730041	+	2.66176i	−0.0683746	+	0.249297i
$115$	7.93928	+	13.7512i	0.740342	+	1.28231i
$116$	0.724381	+	0.418222i	0.0672571	+	0.0388309i
$117$	−10.0336	+	4.04070i	−0.927605	+	0.373563i
$118$		−	2.19150i		−	0.201743i
$119$	−14.0478	−	5.39141i	−1.28776	−	0.494230i
$120$	2.23824	−	2.21204i	0.204323	−	0.201931i
$121$	3.39615	−	5.88231i	0.308741	−	0.534755i
$122$	−5.97394	−	3.44906i	−0.540855	−	0.312263i
$123$	0.766068	+	0.210109i	0.0690741	+	0.0189449i
$124$	−3.97501	+	6.88493i	−0.356967	+	0.618285i
$125$			12.1712i			1.08862i
$126$	−7.85354	+	1.14977i	−0.699649	+	0.102429i
$127$	−10.6930	+	18.5208i	−0.948852	+	1.64346i	−0.201003	+	0.979591i	$0.564420\pi$
$127$	−10.6930	+	18.5208i	−0.948852	+	1.64346i	−0.747849	+	0.663869i	$0.768913\pi$
$128$	1.00000			0.0883883
$129$	2.03571	+	2.05982i	0.179234	+	0.181357i
$130$	−6.04728	+	2.51850i	−0.530381	+	0.220887i
$131$	−7.44741	−	12.8993i	−0.650683	−	1.12702i	−0.982957	−	0.183834i	$-0.941149\pi$
$131$	−7.44741	−	12.8993i	−0.650683	−	1.12702i	0.332274	−	0.943183i	$-0.392184\pi$
$132$	−2.49744	−	2.52703i	−0.217375	−	0.219949i
$133$	3.27633	−	2.65347i	0.284094	−	0.230085i
$134$	−4.46448	+	2.57757i	−0.385672	+	0.222668i
$135$	2.60409	−	9.07439i	0.224125	−	0.780999i
$136$	5.68717			0.487671
$137$	−11.6043			−0.991424			−0.495712	−	0.868487i	$-0.665093\pi$
$137$	−11.6043			−0.991424			−0.495712	+	0.868487i	$0.665093\pi$
$138$	3.83170	+	14.6444i	0.326176	+	1.24662i
$139$	13.6556	−	7.88408i	1.15825	−	0.668719i	0.207370	−	0.978263i	$-0.433510\pi$
$139$	13.6556	−	7.88408i	1.15825	−	0.668719i	0.950885	+	0.309544i	$0.100176\pi$
$140$	−4.74771	+	0.752275i	−0.401255	+	0.0635788i
$141$	−2.77049	+	2.73805i	−0.233317	+	0.230586i
$142$	4.24250	+	7.34823i	0.356023	+	0.616650i
$143$	2.84344	+	6.82751i	0.237780	+	0.570945i
$144$	2.61556	−	1.46930i	0.217963	−	0.122442i
$145$	1.51969			0.126204
$146$	5.11752	−	8.86381i	0.423529	−	0.733574i
$147$	10.7710	+	5.56647i	0.888377	+	0.459115i
$148$		−	4.21819i		−	0.346733i
$149$	2.40740	−	4.16974i	0.197222	−	0.341599i	−0.750405	−	0.660979i	$-0.770141\pi$
$149$	2.40740	−	4.16974i	0.197222	−	0.341599i	0.947627	+	0.319380i	$0.103475\pi$
$150$	−0.778384	+	2.83803i	−0.0635548	+	0.231724i
$151$	−1.23569	−	0.713427i	−0.100559	−	0.0580579i	0.448877	−	0.893594i	$-0.351824\pi$
$151$	−1.23569	−	0.713427i	−0.100559	−	0.0580579i	−0.549436	+	0.835536i	$0.685157\pi$
$152$	−0.796762	+	1.38003i	−0.0646259	+	0.111935i
$153$	14.8751	−	8.35619i	1.20258	−	0.675558i
$154$	0.849335	+	5.36027i	0.0684414	+	0.431943i
$155$			14.4440i			1.16017i
$156$	−6.19475	+	0.790580i	−0.495977	+	0.0632971i
$157$	7.14347	+	4.12428i	0.570111	+	0.329154i	0.757194	−	0.653191i	$-0.226570\pi$
$157$	7.14347	+	4.12428i	0.570111	+	0.329154i	−0.187083	+	0.982344i	$0.559903\pi$
$158$	−3.68537	−	6.38325i	−0.293192	−	0.507824i
$159$	0.958729	+	0.262950i	0.0760321	+	0.0208533i
$160$	1.57344	−	0.908426i	0.124391	−	0.0718174i
$161$	8.28509	−	21.5875i	0.652957	−	1.70134i
$162$	4.68229	−	7.68610i	0.367875	−	0.603877i
$163$	−20.7420	−	11.9754i	−1.62464	−	0.937985i	−0.985657	−	0.168762i	$-0.946023\pi$
$163$	−20.7420	−	11.9754i	−1.62464	−	0.937985i	−0.638981	−	0.769223i	$-0.720644\pi$
$164$	0.397180	+	0.229312i	0.0310145	+	0.0179062i
$165$	−6.22520	−	1.70738i	−0.484631	−	0.132920i
$166$		−	15.0678i		−	1.16949i
$167$	20.2949	+	11.7173i	1.57047	+	0.906711i	0.996111	+	0.0881060i	$0.0280814\pi$
$167$	20.2949	+	11.7173i	1.57047	+	0.906711i	0.574358	+	0.818604i	$0.305252\pi$
$168$	−4.55461	−	0.505542i	−0.351395	−	0.0390034i
$169$	12.5699	+	3.31634i	0.966914	+	0.255103i
$170$	8.94843	−	5.16638i	0.686313	−	0.396243i
$171$	−0.0562900	+	4.78024i	−0.00430461	+	0.365554i
$172$	0.836012	+	1.44802i	0.0637453	+	0.110410i
$173$	3.80295	−	6.58691i	0.289133	−	0.500794i	−0.684470	−	0.729041i	$-0.739966\pi$
$173$	3.80295	−	6.58691i	0.289133	−	0.500794i	0.973603	+	0.228248i	$0.0732996\pi$
$174$	1.39717	+	0.383200i	0.105919	+	0.0290503i
$175$	3.49329	−	2.82918i	0.264068	−	0.213866i
$176$	−1.02563	−	1.77645i	−0.0773101	−	0.133905i
$177$	−0.960817	−	3.67216i	−0.0722194	−	0.276017i
$178$			3.86314i			0.289554i
$179$	−15.9356	+	9.20041i	−1.19108	+	0.687671i	−0.958552	−	0.284918i	$-0.908034\pi$
$179$	−15.9356	+	9.20041i	−1.19108	+	0.687671i	−0.232530	+	0.972589i	$0.574700\pi$
$180$	2.78067	−	4.68791i	0.207259	−	0.349416i
$181$			0.190838i			0.0141849i	0.999975	+	0.00709245i	$0.00225762\pi$
$181$			0.190838i			0.0141849i	−0.999975	+	0.00709245i	$0.997742\pi$
$182$	8.39241	+	4.53514i	0.622087	+	0.336167i
$183$	−11.5224	−	3.16023i	−0.851758	−	0.233611i
$184$			8.73960i			0.644292i
$185$	−3.83191	−	6.63707i	−0.281728	−	0.487967i
$186$	−3.64215	+	13.2794i	−0.267055	+	0.973696i
$187$	−5.83296	−	10.1030i	−0.426548	−	0.738803i
$188$	−1.94760	+	1.12445i	−0.142043	+	0.0820086i
$189$	−12.6556	+	5.36983i	−0.920562	+	0.390597i
$190$			2.89520i			0.210040i
$191$	−4.50022	−	2.59820i	−0.325625	−	0.187999i	0.328272	−	0.944583i	$-0.393534\pi$
$191$	−4.50022	−	2.59820i	−0.325625	−	0.187999i	−0.653897	+	0.756584i	$0.726867\pi$
$192$	1.67564	−	0.438430i	0.120929	−	0.0316410i
$193$	9.53669	−	5.50601i	0.686466	−	0.396331i	−0.115821	−	0.993270i	$-0.536950\pi$
$193$	9.53669	−	5.50601i	0.686466	−	0.396331i	0.802287	+	0.596939i	$0.203616\pi$
$194$	−1.72410	−	2.98622i	−0.123783	−	0.214398i
$195$	−9.02890	+	6.87141i	−0.646573	+	0.492072i
$196$	5.20261	+	4.68325i	0.371615	+	0.334518i
$197$	−11.1333	+	19.2835i	−0.793218	+	1.37389i	0.130746	+	0.991416i	$0.458263\pi$
$197$	−11.1333	+	19.2835i	−0.793218	+	1.37389i	−0.923964	+	0.382478i	$0.875071\pi$
$198$	−5.29275	−	3.13944i	−0.376139	−	0.223110i
$199$		−	19.0946i		−	1.35358i	−0.736177	−	0.676789i	$-0.763371\pi$
$199$		−	19.0946i		−	1.35358i	0.736177	−	0.676789i	$-0.236629\pi$
$200$	−0.849523	+	1.47142i	−0.0600703	+	0.104045i
$201$	−6.35079	+	6.27645i	−0.447950	+	0.442706i
$202$	−4.84811	−	8.39717i	−0.341112	−	0.590823i
$203$	−1.39281	−	1.71975i	−0.0977560	−	0.120703i
$204$	9.52967	−	2.49343i	0.667211	−	0.174575i
$205$	0.833252			0.0581968
$206$	8.08628	−	4.66861i	0.563398	−	0.325278i
$207$	12.8411	+	22.8589i	0.892520	+	1.58881i
$208$	−3.57560	−	0.463745i	−0.247923	−	0.0321550i
$209$	3.26874			0.226104
$210$	−7.62565	+	3.34208i	−0.526220	+	0.230626i
$211$	−7.80557	+	13.5196i	−0.537358	+	0.930731i	0.461688	+	0.887043i	$0.347244\pi$
$211$	−7.80557	+	13.5196i	−0.537358	+	0.930731i	−0.999045	+	0.0436882i	$0.986089\pi$
$212$	0.497067	+	0.286982i	0.0341387	+	0.0197100i
$213$	10.3306	+	10.4530i	0.707842	+	0.716226i
$214$			10.7060i			0.731846i
$215$	2.63083	+	1.51891i	0.179421	+	0.103589i
$216$	3.73855	−	3.60877i	0.254376	−	0.245546i
$217$	16.3455	−	13.2380i	1.10960	−	0.898657i
$218$	−4.30381	−	2.48481i	−0.291491	−	0.168292i
$219$	4.68898	−	17.0963i	0.316852	−	1.15526i
$220$	−3.22755	−	1.86343i	−0.217601	−	0.125632i
$221$	−20.3351	−	2.63740i	−1.36789	−	0.177411i
$222$	−1.84938	−	7.06818i	−0.124122	−	0.474385i
$223$	−4.91509	+	8.51319i	−0.329139	+	0.570085i	−0.982341	−	0.187098i	$-0.940092\pi$
$223$	−4.91509	+	8.51319i	−0.329139	+	0.570085i	0.653202	+	0.757183i	$0.273425\pi$
$224$	−2.47008	−	0.947995i	−0.165039	−	0.0633406i
$225$	−0.0600175	+	5.09678i	−0.00400117	+	0.339786i
$226$	−14.4435	+	8.33897i	−0.960768	+	0.554700i
$227$		−	11.3725i		−	0.754821i	−0.926046	−	0.377410i	$-0.876815\pi$
$227$		−	11.3725i		−	0.754821i	0.926046	−	0.377410i	$-0.123185\pi$
$228$	−0.730041	+	2.66176i	−0.0483481	+	0.176280i
$229$	−9.48968	−	16.4366i	−0.627096	−	1.08616i	−0.988132	−	0.153610i	$-0.950910\pi$
$229$	−9.48968	−	16.4366i	−0.627096	−	1.08616i	0.361036	−	0.932552i	$-0.382423\pi$
$230$	7.93928	+	13.7512i	0.523501	+	0.906730i
$231$	3.77329	+	8.60953i	0.248264	+	0.566465i
$232$	0.724381	+	0.418222i	0.0475580	+	0.0274576i
$233$	18.2307	−	10.5255i	1.19433	−	0.689550i	0.235048	−	0.971984i	$-0.424475\pi$
$233$	18.2307	−	10.5255i	1.19433	−	0.689550i	0.959287	+	0.282434i	$0.0911419\pi$
$234$	−10.0336	+	4.04070i	−0.655916	+	0.264149i
$235$	−2.04295	+	3.53850i	−0.133267	+	0.230826i
$236$		−	2.19150i		−	0.142654i
$237$	−8.97398	−	9.08027i	−0.582922	−	0.589827i
$238$	−14.0478	−	5.39141i	−0.910583	−	0.349473i
$239$	16.6885			1.07949			0.539746	−	0.841828i	$-0.318520\pi$
$239$	16.6885			1.07949			0.539746	+	0.841828i	$0.318520\pi$
$240$	2.23824	−	2.21204i	0.144478	−	0.142787i
$241$	15.2747			0.983927			0.491963	−	0.870616i	$-0.336279\pi$
$241$	15.2747			0.983927			0.491963	+	0.870616i	$0.336279\pi$
$242$	3.39615	−	5.88231i	0.218313	−	0.378129i
$243$	4.47603	−	14.9320i	0.287137	−	0.957889i
$244$	−5.97394	−	3.44906i	−0.382443	−	0.220803i
$245$	12.4404	+	2.64262i	0.794787	+	0.168831i
$246$	0.766068	+	0.210109i	0.0488427	+	0.0133961i
$247$	3.48889	−	4.56495i	0.221993	−	0.290461i
$248$	−3.97501	+	6.88493i	−0.252414	+	0.437193i
$249$	−6.60619	−	25.2483i	−0.418650	−	1.60005i
$250$			12.1712i			0.769773i
$251$	4.91975	+	8.52125i	0.310532	+	0.537857i	0.978478	−	0.206353i	$-0.0661596\pi$
$251$	4.91975	+	8.52125i	0.310532	+	0.537857i	−0.667946	+	0.744210i	$0.732826\pi$
$252$	−7.85354	+	1.14977i	−0.494726	+	0.0724285i
$253$	15.5255	−	8.96363i	0.976077	−	0.563538i
$254$	−10.6930	+	18.5208i	−0.670940	+	1.16210i
$255$	12.7293	−	12.5803i	0.797138	−	0.787807i
$256$	1.00000			0.0625000
$257$	1.53233			0.0955843			0.0477921	−	0.998857i	$-0.484781\pi$
$257$	1.53233			0.0955843			0.0477921	+	0.998857i	$0.484781\pi$
$258$	2.03571	+	2.05982i	0.126738	+	0.128239i
$259$	−3.99882	+	10.4193i	−0.248475	+	0.647422i
$260$	−6.04728	+	2.51850i	−0.375036	+	0.156191i
$261$	2.50916	+	0.0295467i	0.155313	+	0.00182890i
$262$	−7.44741	−	12.8993i	−0.460103	−	0.796921i
$263$	16.9520	−	9.78724i	1.04530	−	0.603507i	0.123973	−	0.992286i	$-0.460436\pi$
$263$	16.9520	−	9.78724i	1.04530	−	0.603507i	0.921331	+	0.388779i	$0.127103\pi$
$264$	−2.49744	−	2.52703i	−0.153707	−	0.155528i
$265$	1.04281			0.0640592
$266$	3.27633	−	2.65347i	0.200885	−	0.162694i
$267$	1.69372	+	6.47324i	0.103654	+	0.396156i
$268$	−4.46448	+	2.57757i	−0.272712	+	0.157450i
$269$	13.5580			0.826646			0.413323	−	0.910584i	$-0.364368\pi$
$269$	13.5580			0.826646			0.413323	+	0.910584i	$0.364368\pi$
$270$	2.60409	−	9.07439i	0.158480	−	0.552250i
$271$	−28.0556			−1.70425			−0.852127	−	0.523335i	$-0.824688\pi$
$271$	−28.0556			−1.70425			−0.852127	+	0.523335i	$0.824688\pi$
$272$	5.68717			0.344836
$273$	16.0510	+	3.91980i	0.971452	+	0.237237i
$274$	−11.6043			−0.701042
$275$	3.48520			0.210165
$276$	3.83170	+	14.6444i	0.230641	+	0.881492i
$277$	23.3285			1.40167			0.700836	−	0.713323i	$-0.252811\pi$
$277$	23.3285			1.40167			0.700836	+	0.713323i	$0.252811\pi$
$278$	13.6556	−	7.88408i	0.819010	−	0.472856i
$279$	−0.280829	+	23.8484i	−0.0168128	+	1.42777i
$280$	−4.74771	+	0.752275i	−0.283730	+	0.0449570i
$281$	26.6302			1.58862			0.794311	−	0.607512i	$-0.207832\pi$
$281$	26.6302			1.58862			0.794311	+	0.607512i	$0.207832\pi$
$282$	−2.77049	+	2.73805i	−0.164980	+	0.163049i
$283$	−23.3128	+	13.4597i	−1.38580	+	0.800093i	−0.992839	−	0.119461i	$-0.961884\pi$
$283$	−23.3128	+	13.4597i	−1.38580	+	0.800093i	−0.392964	+	0.919554i	$0.628550\pi$
$284$	4.24250	+	7.34823i	0.251746	+	0.436037i
$285$	1.26934	+	4.85132i	0.0751893	+	0.287367i
$286$	2.84344	+	6.82751i	0.168136	+	0.403719i
$287$	−0.763680	−	0.942943i	−0.0450786	−	0.0556602i
$288$	2.61556	−	1.46930i	0.154123	−	0.0865796i
$289$	15.3439			0.902585
$290$	1.51969			0.0892395
$291$	−4.19822	−	4.24795i	−0.246104	−	0.249019i
$292$	5.11752	−	8.86381i	0.299480	−	0.518715i
$293$	6.97220	−	4.02540i	0.407320	−	0.235167i	−0.282317	−	0.959321i	$-0.591103\pi$
$293$	6.97220	−	4.02540i	0.407320	−	0.235167i	0.689638	+	0.724154i	$0.257770\pi$
$294$	10.7710	+	5.56647i	0.628177	+	0.324643i
$295$	−1.99081	−	3.44819i	−0.115910	−	0.200761i
$296$		−	4.21819i		−	0.245177i
$297$	−10.2452	−	2.94008i	−0.594486	−	0.170601i
$298$	2.40740	−	4.16974i	0.139457	−	0.241547i
$299$	4.05295	−	31.2493i	0.234388	−	1.80720i
$300$	−0.778384	+	2.83803i	−0.0449400	+	0.163853i
$301$	−0.692308	−	4.36925i	−0.0399039	−	0.251839i
$302$	−1.23569	−	0.713427i	−0.0711061	−	0.0410531i
$303$	−11.8053	−	11.9451i	−0.678195	−	0.686228i
$304$	−0.796762	+	1.38003i	−0.0456974	+	0.0791502i
$305$	−12.5329			−0.717630
$306$	14.8751	−	8.35619i	0.850355	−	0.477692i
$307$	13.6194			0.777300			0.388650	−	0.921385i	$-0.372942\pi$
$307$	13.6194			0.777300			0.388650	+	0.921385i	$0.372942\pi$
$308$	0.849335	+	5.36027i	0.0483953	+	0.305430i
$309$	11.5029	−	11.3682i	0.654374	−	0.646714i
$310$			14.4440i			0.820366i
$311$	12.6742	−	21.9523i	0.718685	−	1.24480i	−0.242835	−	0.970068i	$-0.578077\pi$
$311$	12.6742	−	21.9523i	0.718685	−	1.24480i	0.961521	−	0.274732i	$-0.0885892\pi$
$312$	−6.19475	+	0.790580i	−0.350709	+	0.0447578i
$313$	−7.41295	+	4.27987i	−0.419005	+	0.241913i	−0.694651	−	0.719347i	$-0.744441\pi$
$313$	−7.41295	+	4.27987i	−0.419005	+	0.241913i	0.275647	+	0.961259i	$0.411108\pi$
$314$	7.14347	+	4.12428i	0.403129	+	0.232747i
$315$	−11.3126	+	8.94345i	−0.637393	+	0.503906i
$316$	−3.68537	−	6.38325i	−0.207318	−	0.359086i
$317$	−11.7752	−	20.3952i	−0.661360	−	1.14551i	−0.980258	−	0.197721i	$-0.936646\pi$
$317$	−11.7752	−	20.3952i	−0.661360	−	1.14551i	0.318898	−	0.947789i	$-0.396687\pi$
$318$	0.958729	+	0.262950i	0.0537628	+	0.0147455i
$319$		−	1.71577i		−	0.0960646i
$320$	1.57344	−	0.908426i	0.0879580	−	0.0507826i
$321$	4.69382	+	17.9394i	0.261984	+	1.00128i
$322$	8.28509	−	21.5875i	0.461710	−	1.20303i
$323$	−4.53132	+	7.84848i	−0.252129	+	0.436701i
$324$	4.68229	−	7.68610i	0.260127	−	0.427006i
$325$	3.71992	−	4.86724i	0.206344	−	0.269986i
$326$	−20.7420	−	11.9754i	−1.14879	−	0.663256i
$327$	−8.30107	−	2.27673i	−0.459050	−	0.125903i
$328$	0.397180	+	0.229312i	0.0219306	+	0.0126616i
$329$	5.87669	−	0.931162i	0.323992	−	0.0513366i
$330$	−6.22520	−	1.70738i	−0.342686	−	0.0939883i
$331$	6.15849	+	3.55561i	0.338501	+	0.195434i	0.659609	−	0.751609i	$-0.270722\pi$
$331$	6.15849	+	3.55561i	0.338501	+	0.195434i	−0.321108	+	0.947043i	$0.604055\pi$
$332$		−	15.0678i		−	0.826954i
$333$	−6.19780	−	11.0329i	−0.339638	−	0.604600i
$334$	20.2949	+	11.7173i	1.11049	+	0.641141i
$335$	−4.68306	+	8.11130i	−0.255863	+	0.443168i
$336$	−4.55461	−	0.505542i	−0.248474	−	0.0275796i
$337$	19.1187			1.04146			0.520730	−	0.853722i	$-0.325660\pi$
$337$	19.1187			1.04146			0.520730	+	0.853722i	$0.325660\pi$
$338$	12.5699	+	3.31634i	0.683711	+	0.180385i
$339$	−20.5461	+	20.3056i	−1.11591	+	1.10285i
$340$	8.94843	−	5.16638i	0.485297	−	0.280186i
$341$	16.3076			0.883108
$342$	−0.0562900	+	4.78024i	−0.00304382	+	0.258486i
$343$	−8.41119	−	16.5001i	−0.454161	−	0.890919i
$344$	0.836012	+	1.44802i	0.0450747	+	0.0780717i
$345$	19.3324	+	19.5613i	1.04082	+	1.05315i
$346$	3.80295	−	6.58691i	0.204448	−	0.354114i
$347$			23.0701i			1.23847i	0.785207	+	0.619233i	$0.212556\pi$
$347$			23.0701i			1.23847i	−0.785207	+	0.619233i	$0.787444\pi$
$348$	1.39717	+	0.383200i	0.0748959	+	0.0205417i
$349$	2.11359	−	3.66085i	0.113138	−	0.195961i	−0.803896	−	0.594770i	$-0.797243\pi$
$349$	2.11359	−	3.66085i	0.113138	−	0.195961i	0.917034	+	0.398809i	$0.130576\pi$
$350$	3.49329	−	2.82918i	0.186724	−	0.151226i
$351$	−15.0411	+	11.1698i	−0.802837	+	0.596199i
$352$	−1.02563	−	1.77645i	−0.0546665	−	0.0946851i
$353$	27.6603	−	15.9697i	1.47221	−	0.849981i	0.472699	−	0.881224i	$-0.343280\pi$
$353$	27.6603	−	15.9697i	1.47221	−	0.849981i	0.999512	+	0.0312428i	$0.00994650\pi$
$354$	−0.960817	−	3.67216i	−0.0510669	−	0.195173i
$355$	13.3507	+	7.70801i	0.708579	+	0.409098i
$356$			3.86314i			0.204746i
$357$	−25.9028	−	2.87511i	−1.37092	−	0.152167i
$358$	−15.9356	+	9.20041i	−0.842222	+	0.486257i
$359$	−12.2496	−	21.2169i	−0.646509	−	1.11979i	−0.983951	−	0.178440i	$-0.942895\pi$
$359$	−12.2496	−	21.2169i	−0.646509	−	1.11979i	0.337442	−	0.941346i	$-0.390438\pi$
$360$	2.78067	−	4.68791i	0.146554	−	0.247074i
$361$	8.23034	+	14.2554i	0.433176	+	0.750283i
$362$			0.190838i			0.0100302i
$363$	3.11176	−	11.3456i	0.163325	−	0.595491i
$364$	8.39241	+	4.53514i	0.439882	+	0.237706i
$365$		−	18.5956i		−	0.973337i
$366$	−11.5224	−	3.16023i	−0.602284	−	0.165188i
$367$	−28.7618	+	16.6056i	−1.50135	+	0.866807i	−0.501355	+	0.865241i	$0.667165\pi$
$367$	−28.7618	+	16.6056i	−1.50135	+	0.866807i	−0.999999	+	0.00156589i	$0.999502\pi$
$368$			8.73960i			0.455583i
$369$	1.37578	+	0.0162005i	0.0716200	+	0.000843366i
$370$	−3.83191	−	6.63707i	−0.199212	−	0.345045i
$371$	−0.955740	−	1.18009i	−0.0496195	−	0.0612670i
$372$	−3.64215	+	13.2794i	−0.188836	+	0.688507i
$373$	2.06003	−	3.56807i	0.106664	−	0.184748i	−0.807753	−	0.589521i	$-0.799316\pi$
$373$	2.06003	−	3.56807i	0.106664	−	0.184748i	0.914417	+	0.404774i	$0.132650\pi$
$374$	−5.83296	−	10.1030i	−0.301615	−	0.522413i
$375$	5.33621	+	20.3946i	0.275561	+	1.05317i
$376$	−1.94760	+	1.12445i	−0.100440	+	0.0579888i
$377$	−2.39615	−	1.83132i	−0.123408	−	0.0943179i
$378$	−12.6556	+	5.36983i	−0.650935	+	0.276194i
$379$	−2.80001	−	1.61659i	−0.143827	−	0.0830385i	0.426360	−	0.904554i	$-0.359796\pi$
$379$	−2.80001	−	1.61659i	−0.143827	−	0.0830385i	−0.570187	+	0.821515i	$0.693129\pi$
$380$			2.89520i			0.148520i
$381$	−9.79758	+	35.7225i	−0.501945	+	1.83012i
$382$	−4.50022	−	2.59820i	−0.230251	−	0.132936i
$383$	−3.61672	−	2.08811i	−0.184806	−	0.106698i	0.404743	−	0.914430i	$-0.367361\pi$
$383$	−3.61672	−	2.08811i	−0.184806	−	0.106698i	−0.589549	+	0.807733i	$0.700694\pi$
$384$	1.67564	−	0.438430i	0.0855098	−	0.0223735i
$385$	6.20579	+	7.66251i	0.316276	+	0.390518i
$386$	9.53669	−	5.50601i	0.485405	−	0.280249i
$387$	4.31421	+	2.55901i	0.219304	+	0.130082i
$388$	−1.72410	−	2.98622i	−0.0875278	−	0.151603i
$389$	−3.57665	−	2.06498i	−0.181343	−	0.104699i	0.406580	−	0.913615i	$-0.366721\pi$
$389$	−3.57665	−	2.06498i	−0.181343	−	0.104699i	−0.587924	+	0.808916i	$0.700054\pi$
$390$	−9.02890	+	6.87141i	−0.457196	+	0.347947i
$391$			49.7036i			2.51362i
$392$	5.20261	+	4.68325i	0.262772	+	0.236540i
$393$	−18.1346	−	18.3494i	−0.914772	−	0.925607i
$394$	−11.1333	+	19.2835i	−0.560890	+	0.971490i
$395$	−11.5974	−	6.69578i	−0.583530	−	0.336901i
$396$	−5.29275	−	3.13944i	−0.265971	−	0.157763i
$397$	2.38133	−	4.12458i	0.119515	−	0.207007i	−0.800060	−	0.599920i	$-0.795199\pi$
$397$	2.38133	−	4.12458i	0.119515	−	0.207007i	0.919576	+	0.392913i	$0.128533\pi$
$398$		−	19.0946i		−	0.957124i
$399$	4.32660	−	5.88270i	0.216601	−	0.294503i
$400$	−0.849523	+	1.47142i	−0.0424761	+	0.0735708i
$401$	15.4809			0.773080			0.386540	−	0.922273i	$-0.373670\pi$
$401$	15.4809			0.773080			0.386540	+	0.922273i	$0.373670\pi$
$402$	−6.35079	+	6.27645i	−0.316749	+	0.313041i
$403$	17.4059	−	22.7744i	0.867051	−	1.13447i
$404$	−4.84811	−	8.39717i	−0.241202	−	0.417775i
$405$	0.385047	−	16.3471i	0.0191331	−	0.812296i
$406$	−1.39281	−	1.71975i	−0.0691240	−	0.0853498i
$407$	−7.49340	+	4.32632i	−0.371434	+	0.214448i
$408$	9.52967	−	2.49343i	0.471789	−	0.123443i
$409$	−39.7884			−1.96741			−0.983706	−	0.179784i	$-0.942460\pi$
$409$	−39.7884			−1.96741			−0.983706	+	0.179784i	$0.942460\pi$
$410$	0.833252			0.0411514
$411$	−19.4447	+	5.08768i	−0.959136	+	0.250957i
$412$	8.08628	−	4.66861i	0.398382	−	0.230006i
$413$	−2.07753	+	5.41317i	−0.102228	+	0.266365i
$414$	12.8411	+	22.8589i	0.631107	+	1.12345i
$415$	−13.6880	−	23.7083i	−0.671918	−	1.16380i
$416$	−3.57560	−	0.463745i	−0.175308	−	0.0227370i
$417$	19.4253	−	19.1979i	0.951263	−	0.940127i
$418$	3.26874			0.159879
$419$	13.1146	−	22.7152i	0.640690	−	1.10971i	−0.344589	−	0.938754i	$-0.611982\pi$
$419$	13.1146	−	22.7152i	0.640690	−	1.10971i	0.985279	−	0.170954i	$-0.0546850\pi$
$420$	−7.62565	+	3.34208i	−0.372094	+	0.163077i
$421$		−	14.0343i		−	0.683989i	−0.939702	−	0.341994i	$-0.888898\pi$
$421$		−	14.0343i		−	0.683989i	0.939702	−	0.341994i	$-0.111102\pi$
$422$	−7.80557	+	13.5196i	−0.379969	+	0.658126i
$423$	−3.44190	+	5.80266i	−0.167351	+	0.282135i
$424$	0.497067	+	0.286982i	0.0241397	+	0.0139371i
$425$	−4.83138	+	8.36820i	−0.234357	+	0.405917i
$426$	10.3306	+	10.4530i	0.500520	+	0.506448i
$427$	11.4864	+	14.1827i	0.555868	+	0.686350i
$428$			10.7060i			0.517493i
$429$	7.75798	+	10.1938i	0.374559	+	0.492162i
$430$	2.63083	+	1.51891i	0.126870	+	0.0732484i
$431$	8.06272	+	13.9650i	0.388368	+	0.672673i	0.992230	−	0.124416i	$-0.0397057\pi$
$431$	8.06272	+	13.9650i	0.388368	+	0.672673i	−0.603862	+	0.797089i	$0.706372\pi$
$432$	3.73855	−	3.60877i	0.179871	−	0.173627i
$433$	−13.9038	+	8.02734i	−0.668172	+	0.385769i	−0.795384	−	0.606106i	$-0.792731\pi$
$433$	−13.9038	+	8.02734i	−0.668172	+	0.385769i	0.127211	+	0.991876i	$0.459397\pi$
$434$	16.3455	−	13.2380i	0.784608	−	0.635446i
$435$	2.54647	−	0.666280i	0.122094	−	0.0319457i
$436$	−4.30381	−	2.48481i	−0.206115	−	0.119001i
$437$	−12.0609	−	6.96338i	−0.576952	−	0.333103i
$438$	4.68898	−	17.0963i	0.224048	−	0.816891i
$439$		−	16.1774i		−	0.772104i	−0.922477	−	0.386052i	$-0.873838\pi$
$439$		−	16.1774i		−	0.772104i	0.922477	−	0.386052i	$-0.126162\pi$
$440$	−3.22755	−	1.86343i	−0.153867	−	0.0888353i
$441$	20.4889	+	4.60509i	0.975660	+	0.219290i
$442$	−20.3351	−	2.63740i	−0.967241	−	0.125448i
$443$	−10.8594	+	6.26970i	−0.515948	+	0.297883i	−0.735275	−	0.677769i	$-0.762947\pi$
$443$	−10.8594	+	6.26970i	−0.515948	+	0.297883i	0.219327	+	0.975651i	$0.429614\pi$
$444$	−1.84938	−	7.06818i	−0.0877677	−	0.335441i
$445$	3.50938	+	6.07842i	0.166360	+	0.288145i
$446$	−4.91509	+	8.51319i	−0.232736	+	0.403111i
$447$	2.20581	−	8.04248i	0.104331	−	0.380396i
$448$	−2.47008	−	0.947995i	−0.116700	−	0.0447885i
$449$	−8.48307	−	14.6931i	−0.400341	−	0.693411i	0.593426	−	0.804888i	$-0.297775\pi$
$449$	−8.48307	−	14.6931i	−0.400341	−	0.693411i	−0.993767	+	0.111478i	$0.964442\pi$
$450$	−0.0600175	+	5.09678i	−0.00282925	+	0.240265i
$451$		−	0.940760i		−	0.0442986i
$452$	−14.4435	+	8.33897i	−0.679366	+	0.392232i
$453$	−2.38337	−	0.653685i	−0.111980	−	0.0307128i
$454$		−	11.3725i		−	0.533739i
$455$	17.3248	−	0.488106i	0.812199	−	0.0228828i
$456$	−0.730041	+	2.66176i	−0.0341873	+	0.124649i
$457$		−	9.47441i		−	0.443194i	−0.975138	−	0.221597i	$-0.928873\pi$
$457$		−	9.47441i		−	0.443194i	0.975138	−	0.221597i	$-0.0711270\pi$
$458$	−9.48968	−	16.4366i	−0.443424	−	0.768032i
$459$	21.2618	−	20.5237i	0.992416	−	0.957964i
$460$	7.93928	+	13.7512i	0.370171	+	0.641155i
$461$	−31.5250	+	18.2010i	−1.46827	+	0.847703i	−0.999368	−	0.0355490i	$-0.988682\pi$
$461$	−31.5250	+	18.2010i	−1.46827	+	0.847703i	−0.468898	+	0.883253i	$0.655349\pi$
$462$	3.77329	+	8.60953i	0.175549	+	0.400551i
$463$			17.8517i			0.829638i	0.909904	+	0.414819i	$0.136155\pi$
$463$			17.8517i			0.829638i	−0.909904	+	0.414819i	$0.863845\pi$
$464$	0.724381	+	0.418222i	0.0336286	+	0.0194155i
$465$	6.33270	+	24.2030i	0.293672	+	1.12239i
$466$	18.2307	−	10.5255i	0.844522	−	0.487585i
$467$	15.1928	+	26.3147i	0.703039	+	1.21770i	0.967394	+	0.253274i	$0.0815075\pi$
$467$	15.1928	+	26.3147i	0.703039	+	1.21770i	−0.264355	+	0.964425i	$0.585159\pi$
$468$	−10.0336	+	4.04070i	−0.463803	+	0.186781i
$469$	13.4712	−	2.13450i	0.622040	−	0.0985622i
$470$	−2.04295	+	3.53850i	−0.0942343	+	0.163219i
$471$	13.7781	+	3.77892i	0.634862	+	0.174123i
$472$		−	2.19150i		−	0.100872i
$473$	1.71488	−	2.97027i	0.0788505	−	0.136573i
$474$	−8.97398	−	9.08027i	−0.412188	−	0.417071i
$475$	−1.35373	−	2.34474i	−0.0621136	−	0.107584i
$476$	−14.0478	−	5.39141i	−0.643879	−	0.247115i
$477$	1.72177	+	0.0202748i	0.0788345	+	0.000928322i
$478$	16.6885			0.763316
$479$	−19.9492	+	11.5177i	−0.911504	+	0.526257i	−0.880915	−	0.473275i	$-0.843072\pi$
$479$	−19.9492	+	11.5177i	−0.911504	+	0.526257i	−0.0305891	+	0.999532i	$0.509738\pi$
$480$	2.23824	−	2.21204i	0.102161	−	0.100965i
$481$	−1.95617	+	15.0826i	−0.0891935	+	0.687706i
$482$	15.2747			0.695741
$483$	4.41824	−	39.8054i	0.201037	−	1.81121i
$484$	3.39615	−	5.88231i	0.154370	−	0.267378i
$485$	−5.42553	−	3.13243i	−0.246361	−	0.142236i
$486$	4.47603	−	14.9320i	0.203037	−	0.677330i
$487$			14.2075i			0.643804i	0.946773	+	0.321902i	$0.104322\pi$
$487$			14.2075i			0.643804i	−0.946773	+	0.321902i	$0.895678\pi$
$488$	−5.97394	−	3.44906i	−0.270428	−	0.156132i
$489$	−40.0065	−	10.9726i	−1.80916	−	0.496197i
$490$	12.4404	+	2.64262i	0.562000	+	0.119382i
$491$	2.47085	+	1.42654i	0.111508	+	0.0643790i	0.554717	−	0.832039i	$-0.312827\pi$
$491$	2.47085	+	1.42654i	0.111508	+	0.0643790i	−0.443209	+	0.896418i	$0.646160\pi$
$492$	0.766068	+	0.210109i	0.0345370	+	0.00947245i
$493$	4.11968	+	2.37850i	0.185541	+	0.107122i
$494$	3.48889	−	4.56495i	0.156972	−	0.205387i
$495$	−11.1798	−	0.131648i	−0.502494	−	0.00591715i
$496$	−3.97501	+	6.88493i	−0.178483	+	0.309142i
$497$	−3.51325	−	22.1726i	−0.157591	−	0.994578i
$498$	−6.60619	−	25.2483i	−0.296030	−	1.13140i
$499$	−15.9720	+	9.22146i	−0.715007	+	0.412809i	−0.812912	−	0.582386i	$-0.802119\pi$
$499$	−15.9720	+	9.22146i	−0.715007	+	0.412809i	0.0979055	+	0.995196i	$0.468786\pi$
$500$			12.1712i			0.544312i
$501$	39.1443	+	10.7361i	1.74884	+	0.479652i
$502$	4.91975	+	8.52125i	0.219579	+	0.380322i
$503$	6.05432	+	10.4864i	0.269949	+	0.467565i	0.968848	−	0.247655i	$-0.0796599\pi$
$503$	6.05432	+	10.4864i	0.269949	+	0.467565i	−0.698900	+	0.715220i	$0.746327\pi$
$504$	−7.85354	+	1.14977i	−0.349824	+	0.0512147i
$505$	−15.2564	−	8.80830i	−0.678902	−	0.391964i
$506$	15.5255	−	8.96363i	0.690191	−	0.398482i
$507$	22.5166	+	0.0459880i	0.999998	+	0.00204240i
$508$	−10.6930	+	18.5208i	−0.474426	+	0.821730i
$509$			36.9477i			1.63768i	0.574023	+	0.818839i	$0.305382\pi$
$509$			36.9477i			1.63768i	−0.574023	+	0.818839i	$0.694618\pi$
$510$	12.7293	−	12.5803i	0.563662	−	0.557064i
$511$	−21.0435	+	17.0430i	−0.930912	+	0.753936i
$512$	1.00000			0.0441942
$513$	2.00148	+	8.03465i	0.0883674	+	0.354739i
$514$	1.53233			0.0675883
$515$	8.48219	−	14.6916i	0.373770	−	0.647388i
$516$	2.03571	+	2.05982i	0.0896172	+	0.0906787i
$517$	3.99504	+	2.30654i	0.175702	+	0.101441i
$518$	−3.99882	+	10.4193i	−0.175698	+	0.457797i
$519$	3.48449	−	12.7046i	0.152952	−	0.557672i
$520$	−6.04728	+	2.51850i	−0.265191	+	0.110443i
$521$	−9.03063	+	15.6415i	−0.395639	+	0.685267i	−0.993183	−	0.116569i	$-0.962810\pi$
$521$	−9.03063	+	15.6415i	−0.395639	+	0.685267i	0.597543	+	0.801837i	$0.296144\pi$
$522$	2.50916	+	0.0295467i	0.109823	+	0.00129323i
$523$		−	39.5905i		−	1.73117i	−0.500762	−	0.865585i	$-0.666947\pi$
$523$		−	39.5905i		−	1.73117i	0.500762	−	0.865585i	$-0.333053\pi$
$524$	−7.44741	−	12.8993i	−0.325342	−	0.563508i
$525$	4.61310	−	6.27225i	0.201332	−	0.273744i
$526$	16.9520	−	9.78724i	0.739142	−	0.426744i
$527$	−22.6066	+	39.1558i	−0.984759	+	1.70565i
$528$	−2.49744	−	2.52703i	−0.108687	−	0.109975i
$529$	−53.3806			−2.32089
$530$	1.04281			0.0452967
$531$	−3.21997	−	5.73198i	−0.139735	−	0.248747i
$532$	3.27633	−	2.65347i	0.142047	−	0.115042i
$533$	−1.31381	−	1.00412i	−0.0569076	−	0.0434932i
$534$	1.69372	+	6.47324i	0.0732943	+	0.280125i
$535$	9.72559	+	16.8452i	0.420474	+	0.728283i
$536$	−4.46448	+	2.57757i	−0.192836	+	0.111334i
$537$	−22.6686	+	22.4032i	−0.978223	+	0.966771i
$538$	13.5580			0.584527
$539$	2.98358	−	14.0455i	0.128512	−	0.604982i
$540$	2.60409	−	9.07439i	0.112062	−	0.390499i
$541$	−21.7849	+	12.5775i	−0.936606	+	0.540750i	−0.888895	−	0.458111i	$-0.848526\pi$
$541$	−21.7849	+	12.5775i	−0.936606	+	0.540750i	−0.0477116	+	0.998861i	$0.515193\pi$
$542$	−28.0556			−1.20509
$543$	0.0836693	+	0.319777i	0.00359059	+	0.0137229i
$544$	5.68717			0.243836
$545$	−9.02906			−0.386762
$546$	16.0510	+	3.91980i	0.686920	+	0.167752i
$547$	9.83208			0.420389			0.210195	−	0.977660i	$-0.432590\pi$
$547$	9.83208			0.420389			0.210195	+	0.977660i	$0.432590\pi$
$548$	−11.6043			−0.495712
$549$	−20.6929	−	0.243671i	−0.883152	−	0.0103996i
$550$	3.48520			0.148609
$551$	−1.15432	+	0.666446i	−0.0491756	+	0.0283916i
$552$	3.83170	+	14.6444i	0.163088	+	0.623309i
$553$	3.05188	+	19.2609i	0.129779	+	0.819055i
$554$	23.3285			0.991131
$555$	−9.33081	−	9.44133i	−0.396071	−	0.400762i
$556$	13.6556	−	7.88408i	0.579127	−	0.334359i
$557$	2.73252	+	4.73287i	0.115781	+	0.200538i	0.918092	−	0.396368i	$-0.129730\pi$
$557$	2.73252	+	4.73287i	0.115781	+	0.200538i	−0.802311	+	0.596906i	$0.796396\pi$
$558$	−0.280829	+	23.8484i	−0.0118884	+	1.00958i
$559$	−2.31774	−	5.56522i	−0.0980298	−	0.235384i
$560$	−4.74771	+	0.752275i	−0.200627	+	0.0317894i
$561$	−14.2034	−	14.3716i	−0.599668	−	0.606771i
$562$	26.6302			1.12333
$563$	25.5357			1.07620			0.538101	−	0.842880i	$-0.319142\pi$
$563$	25.5357			1.07620			0.538101	+	0.842880i	$0.319142\pi$
$564$	−2.77049	+	2.73805i	−0.116658	+	0.115293i
$565$	−15.1507	+	26.2417i	−0.637394	+	1.10400i
$566$	−23.3128	+	13.4597i	−0.979910	+	0.565752i
$567$	−18.8520	+	14.5465i	−0.791711	+	0.610896i
$568$	4.24250	+	7.34823i	0.178012	+	0.308325i
$569$			16.5159i			0.692384i	0.938164	+	0.346192i	$0.112525\pi$
$569$			16.5159i			0.692384i	−0.938164	+	0.346192i	$0.887475\pi$
$570$	1.26934	+	4.85132i	0.0531669	+	0.203199i
$571$	−1.84946	+	3.20337i	−0.0773977	+	0.134057i	−0.902126	−	0.431472i	$-0.857994\pi$
$571$	−1.84946	+	3.20337i	−0.0773977	+	0.134057i	0.824729	+	0.565529i	$0.191328\pi$
$572$	2.84344	+	6.82751i	0.118890	+	0.285473i
$573$	−8.67989	−	2.38063i	−0.362608	−	0.0994522i
$574$	−0.763680	−	0.942943i	−0.0318754	−	0.0393577i
$575$	−12.8596	−	7.42449i	−0.536282	−	0.309623i
$576$	2.61556	−	1.46930i	0.108982	−	0.0612210i
$577$	−4.25571	+	7.37111i	−0.177168	+	0.306863i	−0.940909	−	0.338659i	$-0.890027\pi$
$577$	−4.25571	+	7.37111i	−0.177168	+	0.306863i	0.763742	+	0.645522i	$0.223360\pi$
$578$	15.3439			0.638224
$579$	13.5661	−	13.4073i	0.563787	−	0.557188i
$580$	1.51969			0.0631019
$581$	−14.2842	+	37.2188i	−0.592609	+	1.54409i
$582$	−4.19822	−	4.24795i	−0.174022	−	0.176083i
$583$		−	1.17735i		−	0.0487610i
$584$	5.11752	−	8.86381i	0.211765	−	0.366787i
$585$	−12.1166	+	15.4726i	−0.500959	+	0.639712i
$586$	6.97220	−	4.02540i	0.288019	−	0.166288i
$587$	−5.89064	−	3.40096i	−0.243133	−	0.140373i	0.373483	−	0.927637i	$-0.378163\pi$
$587$	−5.89064	−	3.40096i	−0.243133	−	0.140373i	−0.616616	+	0.787264i	$0.711497\pi$
$588$	10.7710	+	5.56647i	0.444188	+	0.229557i
$589$	−6.33428	−	10.9713i	−0.260999	−	0.452064i
$590$	−1.99081	−	3.44819i	−0.0819604	−	0.141960i
$591$	−10.2010	+	37.1935i	−0.419615	+	1.52994i
$592$		−	4.21819i		−	0.173366i
$593$	−6.06317	+	3.50057i	−0.248984	+	0.143751i	−0.619299	−	0.785155i	$-0.712583\pi$
$593$	−6.06317	+	3.50057i	−0.248984	+	0.143751i	0.370315	+	0.928906i	$0.379250\pi$
$594$	−10.2452	−	2.94008i	−0.420365	−	0.120633i
$595$	−27.0011	+	4.27832i	−1.10694	+	0.175394i
$596$	2.40740	−	4.16974i	0.0986111	−	0.170799i
$597$	−8.37163	−	31.9957i	−0.342628	−	1.30950i
$598$	4.05295	−	31.2493i	0.165737	−	1.27788i
$599$	−36.0831	−	20.8326i	−1.47432	−	0.851197i	−0.474735	−	0.880129i	$-0.657456\pi$
$599$	−36.0831	−	20.8326i	−1.47432	−	0.851197i	−0.999581	+	0.0289321i	$0.990789\pi$
$600$	−0.778384	+	2.83803i	−0.0317774	+	0.115862i
$601$	1.93484	+	1.11708i	0.0789239	+	0.0455668i	0.538943	−	0.842342i	$-0.318824\pi$
$601$	1.93484	+	1.11708i	0.0789239	+	0.0455668i	−0.460019	+	0.887909i	$0.652157\pi$
$602$	−0.692308	−	4.36925i	−0.0282164	−	0.178077i
$603$	−7.88987	+	13.3015i	−0.321301	+	0.541677i
$604$	−1.23569	−	0.713427i	−0.0502796	−	0.0290289i
$605$		−	12.3406i		−	0.501717i
$606$	−11.8053	−	11.9451i	−0.479556	−	0.485237i
$607$	−0.586288	−	0.338493i	−0.0237967	−	0.0137390i	0.488054	−	0.872813i	$-0.337707\pi$
$607$	−0.586288	−	0.338493i	−0.0237967	−	0.0137390i	−0.511851	+	0.859074i	$0.671040\pi$
$608$	−0.796762	+	1.38003i	−0.0323129	+	0.0559677i
$609$	−3.08784	−	2.27104i	−0.125126	−	0.0920272i
$610$	−12.5329			−0.507441
$611$	7.48529	−	3.11738i	0.302822	−	0.126116i
$612$	14.8751	−	8.35619i	0.601292	−	0.337779i
$613$	6.34919	−	3.66571i	0.256441	−	0.148057i	−0.366269	−	0.930509i	$-0.619365\pi$
$613$	6.34919	−	3.66571i	0.256441	−	0.148057i	0.622710	+	0.782453i	$0.286032\pi$
$614$	13.6194			0.549634
$615$	1.39623	−	0.365323i	0.0563015	−	0.0147312i
$616$	0.849335	+	5.36027i	0.0342207	+	0.215972i
$617$	22.6183	+	39.1761i	0.910579	+	1.57717i	0.813248	+	0.581917i	$0.197697\pi$
$617$	22.6183	+	39.1761i	0.910579	+	1.57717i	0.0973311	+	0.995252i	$0.468969\pi$
$618$	11.5029	−	11.3682i	0.462713	−	0.457296i
$619$	5.37271	−	9.30581i	0.215948	−	0.374032i	−0.737618	−	0.675219i	$-0.764049\pi$
$619$	5.37271	−	9.30581i	0.215948	−	0.374032i	0.953565	+	0.301186i	$0.0973826\pi$
$620$			14.4440i			0.580086i
$621$	31.5392	+	32.6735i	1.26562	+	1.31114i
$622$	12.6742	−	21.9523i	0.508187	−	0.880206i
$623$	3.66223	−	9.54227i	0.146724	−	0.382303i
$624$	−6.19475	+	0.790580i	−0.247989	+	0.0316485i
$625$	6.80901	+	11.7935i	0.272360	+	0.471742i
$626$	−7.41295	+	4.27987i	−0.296281	+	0.171058i
$627$	5.47724	−	1.43311i	0.218740	−	0.0572331i
$628$	7.14347	+	4.12428i	0.285055	+	0.164577i
$629$		−	23.9896i		−	0.956527i
$630$	−11.3126	+	8.94345i	−0.450705	+	0.356316i
$631$	15.7277	−	9.08038i	0.626109	−	0.361484i	−0.153135	−	0.988205i	$-0.548937\pi$
$631$	15.7277	−	9.08038i	0.626109	−	0.361484i	0.779244	+	0.626721i	$0.215603\pi$
$632$	−3.68537	−	6.38325i	−0.146596	−	0.253912i
$633$	−7.15193	+	26.0763i	−0.284264	+	1.03644i
$634$	−11.7752	−	20.3952i	−0.467652	−	0.809998i
$635$			38.8553i			1.54192i
$636$	0.958729	+	0.262950i	0.0380161	+	0.0104266i
$637$	−16.4306	−	19.1581i	−0.651006	−	0.759073i
$638$		−	1.71577i		−	0.0679279i
$639$	21.8933	+	12.9862i	0.866086	+	0.513726i
$640$	1.57344	−	0.908426i	0.0621957	−	0.0359087i
$641$		−	14.4746i		−	0.571714i	−0.958272	−	0.285857i	$-0.907722\pi$
$641$		−	14.4746i		−	0.571714i	0.958272	−	0.285857i	$-0.0922782\pi$
$642$	4.69382	+	17.9394i	0.185250	+	0.708012i
$643$	6.24408	+	10.8151i	0.246243	+	0.426505i	0.962480	−	0.271352i	$-0.0874707\pi$
$643$	6.24408	+	10.8151i	0.246243	+	0.426505i	−0.716238	+	0.697856i	$0.754137\pi$
$644$	8.28509	−	21.5875i	0.326478	−	0.850668i
$645$	5.07427	+	1.39172i	0.199799	+	0.0547988i
$646$	−4.53132	+	7.84848i	−0.178282	+	0.308794i
$647$	−16.1151	−	27.9122i	−0.633550	−	1.09734i	−0.986820	−	0.161819i	$-0.948264\pi$
$647$	−16.1151	−	27.9122i	−0.633550	−	1.09734i	0.353271	−	0.935521i	$-0.385069\pi$
$648$	4.68229	−	7.68610i	0.183938	−	0.301939i
$649$	−3.89308	+	2.24767i	−0.152817	+	0.0882288i
$650$	3.71992	−	4.86724i	0.145907	−	0.190909i
$651$	21.5852	−	29.3486i	0.845992	−	1.15026i
$652$	−20.7420	−	11.9754i	−0.812319	−	0.468992i
$653$			36.7354i			1.43757i	0.695234	+	0.718783i	$0.255301\pi$
$653$			36.7354i			1.43757i	−0.695234	+	0.718783i	$0.744699\pi$
$654$	−8.30107	−	2.27673i	−0.324597	−	0.0890271i
$655$	−23.4361	−	13.5309i	−0.915725	−	0.528694i
$656$	0.397180	+	0.229312i	0.0155073	+	0.00895312i
$657$	0.361545	−	30.7030i	0.0141052	−	1.19784i
$658$	5.87669	−	0.931162i	0.229097	−	0.0363005i
$659$	39.7060	−	22.9243i	1.54673	−	0.893003i	0.548338	−	0.836257i	$-0.315261\pi$
$659$	39.7060	−	22.9243i	1.54673	−	0.893003i	0.998389	−	0.0567462i	$-0.0180726\pi$
$660$	−6.22520	−	1.70738i	−0.242316	−	0.0664598i
$661$	−7.51367	−	13.0141i	−0.292248	−	0.506188i	0.682093	−	0.731265i	$-0.261070\pi$
$661$	−7.51367	−	13.0141i	−0.292248	−	0.506188i	−0.974341	+	0.225077i	$0.927737\pi$
$662$	6.15849	+	3.55561i	0.239356	+	0.138193i
$663$	−35.2306	+	4.49617i	−1.36824	+	0.174617i
$664$		−	15.0678i		−	0.584745i
$665$	2.74463	−	7.15138i	0.106432	−	0.277318i
$666$	−6.19780	−	11.0329i	−0.240160	−	0.427517i
$667$	−3.65509	+	6.33080i	−0.141526	+	0.245130i
$668$	20.2949	+	11.7173i	0.785234	+	0.453355i
$669$	−4.50350	+	16.4200i	−0.174115	+	0.634833i
$670$	−4.68306	+	8.11130i	−0.180923	+	0.313367i
$671$			14.1499i			0.546250i
$672$	−4.55461	−	0.505542i	−0.175698	−	0.0195017i
$673$	−13.8713	+	24.0258i	−0.534700	+	0.926127i	0.464478	+	0.885585i	$0.346242\pi$
$673$	−13.8713	+	24.0258i	−0.534700	+	0.926127i	−0.999178	+	0.0405428i	$0.987091\pi$
$674$	19.1187			0.736423
$675$	2.13401	+	8.56670i	0.0821383	+	0.329733i
$676$	12.5699	+	3.31634i	0.483457	+	0.127552i
$677$	−0.275329	−	0.476883i	−0.0105817	−	0.0183281i	0.860686	−	0.509136i	$-0.170035\pi$
$677$	−0.275329	−	0.476883i	−0.0105817	−	0.0183281i	−0.871268	+	0.490808i	$0.836702\pi$
$678$	−20.5461	+	20.3056i	−0.789069	+	0.779832i
$679$	1.42774	+	9.01065i	0.0547915	+	0.345797i
$680$	8.94843	−	5.16638i	0.343157	−	0.198122i
$681$	−4.98606	−	19.0563i	−0.191066	−	0.730239i
$682$	16.3076			0.624452
$683$	−36.3756			−1.39188			−0.695938	−	0.718102i	$-0.745011\pi$
$683$	−36.3756			−1.39188			−0.695938	+	0.718102i	$0.745011\pi$
$684$	−0.0562900	+	4.78024i	−0.00215230	+	0.182777i
$685$	−18.2587	+	10.5417i	−0.697629	+	0.402776i
$686$	−8.41119	−	16.5001i	−0.321141	−	0.629975i
$687$	−23.1076	−	23.3813i	−0.881610	−	0.892053i
$688$	0.836012	+	1.44802i	0.0318727	+	0.0552051i
$689$	−1.64423	−	1.25665i	−0.0626401	−	0.0478744i
$690$	19.3324	+	19.5613i	0.735970	+	0.744688i
$691$	32.3519			1.23073			0.615363	−	0.788244i	$-0.289010\pi$
$691$	32.3519			1.23073			0.615363	+	0.788244i	$0.289010\pi$
$692$	3.80295	−	6.58691i	0.144567	−	0.250397i
$693$	10.0974	+	12.7722i	0.383567	+	0.485175i
$694$			23.0701i			0.875728i
$695$	14.3242	−	24.8103i	0.543348	−	0.941107i
$696$	1.39717	+	0.383200i	0.0529594	+	0.0145251i
$697$	2.25883	+	1.30414i	0.0855593	+	0.0493977i
$698$	2.11359	−	3.66085i	0.0800007	−	0.138565i
$699$	25.9335	−	25.6299i	0.980895	−	0.969412i
$700$	3.49329	−	2.82918i	0.132034	−	0.106933i
$701$		−	13.2279i		−	0.499612i	−0.968296	−	0.249806i	$-0.919633\pi$
$701$		−	13.2279i		−	0.499612i	0.968296	−	0.249806i	$-0.0803669\pi$
$702$	−15.0411	+	11.1698i	−0.567691	+	0.421576i
$703$	5.82123	+	3.36089i	0.219552	+	0.126758i
$704$	−1.02563	−	1.77645i	−0.0386550	−	0.0669525i
$705$	−1.87187	+	6.82495i	−0.0704989	+	0.257042i
$706$	27.6603	−	15.9697i	1.04101	−	0.601028i
$707$	4.01476	+	25.3377i	0.150990	+	0.952922i
$708$	−0.960817	−	3.67216i	−0.0361097	−	0.138008i
$709$	23.6162	+	13.6348i	0.886926	+	0.512067i	0.872936	−	0.487835i	$-0.162213\pi$
$709$	23.6162	+	13.6348i	0.886926	+	0.512067i	0.0139902	+	0.999902i	$0.495547\pi$
$710$	13.3507	+	7.70801i	0.501041	+	0.289276i
$711$	−19.0182	−	11.2808i	−0.713240	−	0.423064i
$712$			3.86314i			0.144777i
$713$	−60.1715	−	34.7400i	−2.25344	−	1.30102i
$714$	−25.9028	−	2.87511i	−0.969389	−	0.107598i
$715$	10.6763	+	8.15963i	0.399270	+	0.305153i
$716$	−15.9356	+	9.20041i	−0.595541	+	0.343836i
$717$	27.9640	−	7.31676i	1.04434	−	0.273249i
$718$	−12.2496	−	21.2169i	−0.457151	−	0.791808i
$719$	−7.69041	+	13.3202i	−0.286804	+	0.496759i	−0.973045	−	0.230615i	$-0.925926\pi$
$719$	−7.69041	+	13.3202i	−0.286804	+	0.496759i	0.686241	+	0.727374i	$0.259259\pi$
$720$	2.78067	−	4.68791i	0.103629	−	0.174708i
$721$	−24.3996	+	3.86611i	−0.908688	+	0.143982i
$722$	8.23034	+	14.2554i	0.306302	+	0.530530i
$723$	25.5949	−	6.69687i	0.951883	−	0.249059i
$724$			0.190838i			0.00709245i
$725$	−1.23076	+	0.710578i	−0.0457092	+	0.0263902i
$726$	3.11176	−	11.3456i	0.115488	−	0.421075i
$727$			34.8309i			1.29181i	0.763420	+	0.645903i	$0.223519\pi$
$727$			34.8309i			1.29181i	−0.763420	+	0.645903i	$0.776481\pi$
$728$	8.39241	+	4.53514i	0.311043	+	0.168084i
$729$	0.953579	−	26.9832i	0.0353177	−	0.999376i
$730$		−	18.5956i		−	0.688253i
$731$	4.75455	+	8.23511i	0.175853	+	0.304587i
$732$	−11.5224	−	3.16023i	−0.425879	−	0.116806i
$733$	9.43951	+	16.3497i	0.348656	+	0.603890i	0.986011	−	0.166680i	$-0.0533048\pi$
$733$	9.43951	+	16.3497i	0.348656	+	0.603890i	−0.637355	+	0.770570i	$0.719971\pi$
$734$	−28.7618	+	16.6056i	−1.06162	+	0.612925i
$735$	22.0043	−	1.02615i	0.811639	−	0.0378500i
$736$			8.73960i			0.322146i
$737$	9.15784	+	5.28728i	0.337333	+	0.194760i
$738$	1.37578	+	0.0162005i	0.0506430	+	0.000596350i
$739$	6.89197	−	3.97908i	0.253525	−	0.146373i	−0.367852	−	0.929884i	$-0.619907\pi$
$739$	6.89197	−	3.97908i	0.253525	−	0.146373i	0.621377	+	0.783511i	$0.286573\pi$
$740$	−3.83191	−	6.63707i	−0.140864	−	0.243984i
$741$	3.84472	−	9.17886i	0.141239	−	0.337194i
$742$	−0.955740	−	1.18009i	−0.0350863	−	0.0433223i
$743$	9.17025	−	15.8833i	0.336424	−	0.582703i	−0.647334	−	0.762207i	$-0.724116\pi$
$743$	9.17025	−	15.8833i	0.336424	−	0.582703i	0.983757	+	0.179504i	$0.0574492\pi$
$744$	−3.64215	+	13.2794i	−0.133528	+	0.486848i
$745$		−	8.74779i		−	0.320494i
$746$	2.06003	−	3.56807i	0.0754230	−	0.130636i
$747$	−22.1392	−	39.4108i	−0.810032	−	1.44196i
$748$	−5.83296	−	10.1030i	−0.213274	−	0.369401i
$749$	10.1492	−	26.4446i	0.370844	−	0.966266i
$750$	5.33621	+	20.3946i	0.194851	+	0.744704i
$751$	−13.7928			−0.503307			−0.251654	−	0.967817i	$-0.580974\pi$
$751$	−13.7928			−0.503307			−0.251654	+	0.967817i	$0.580974\pi$
$752$	−1.94760	+	1.12445i	−0.0710215	+	0.0410043i
$753$	11.9797	+	12.1216i	0.436565	+	0.441736i
$754$	−2.39615	−	1.83132i	−0.0872627	−	0.0666929i
$755$	−2.59238			−0.0943465
$756$	−12.6556	+	5.36983i	−0.460281	+	0.195299i
$757$	21.2683	−	36.8378i	0.773010	−	1.33889i	−0.162896	−	0.986643i	$-0.552084\pi$
$757$	21.2683	−	36.8378i	0.773010	−	1.33889i	0.935906	−	0.352249i	$-0.114583\pi$
$758$	−2.80001	−	1.61659i	−0.101701	−	0.0587171i
$759$	22.0852	−	21.8267i	0.801642	−	0.792258i
$760$			2.89520i			0.105020i
$761$	−27.9822	−	16.1555i	−1.01435	−	0.585638i	−0.101891	−	0.994796i	$-0.532489\pi$
$761$	−27.9822	−	16.1555i	−1.01435	−	0.585638i	−0.912464	+	0.409157i	$0.865823\pi$
$762$	−9.79758	+	35.7225i	−0.354929	+	1.29409i
$763$	8.27519	+	10.2177i	0.299582	+	0.369904i
$764$	−4.50022	−	2.59820i	−0.162812	−	0.0939997i
$765$	15.8142	−	26.6609i	0.571762	−	0.963928i
$766$	−3.61672	−	2.08811i	−0.130677	−	0.0754465i
$767$	−1.01630	+	7.83592i	−0.0366963	+	0.282939i
$768$	1.67564	−	0.438430i	0.0604646	−	0.0158205i
$769$	6.20736	−	10.7515i	0.223843	−	0.387707i	−0.732129	−	0.681166i	$-0.761473\pi$
$769$	6.20736	−	10.7515i	0.223843	−	0.387707i	0.955972	+	0.293459i	$0.0948064\pi$
$770$	6.20579	+	7.66251i	0.223641	+	0.276138i
$771$	2.56764	−	0.671821i	0.0924714	−	0.0241950i
$772$	9.53669	−	5.50601i	0.343233	−	0.198166i
$773$			12.5201i			0.450318i	0.974322	+	0.225159i	$0.0722901\pi$
$773$			12.5201i			0.450318i	−0.974322	+	0.225159i	$0.927710\pi$
$774$	4.31421	+	2.55901i	0.155071	+	0.0919818i
$775$	−6.75373	−	11.6978i	−0.242601	−	0.420197i
$776$	−1.72410	−	2.98622i	−0.0618915	−	0.107199i
$777$	−2.13247	+	19.2122i	−0.0765020	+	0.689233i
$778$	−3.57665	−	2.06498i	−0.128229	−	0.0740331i
$779$	−0.632915	+	0.365414i	−0.0226765	+	0.0130923i
$780$	−9.02890	+	6.87141i	−0.323286	+	0.246036i
$781$	8.70251	−	15.0732i	0.311400	−	0.539361i
$782$			49.7036i			1.77740i
$783$	4.21740	−	1.05058i	0.150718	−	0.0375447i
$784$	5.20261	+	4.68325i	0.185808	+	0.167259i
$785$	14.9864			0.534889
$786$	−18.1346	−	18.3494i	−0.646841	−	0.654503i
$787$	39.3805			1.40376			0.701882	−	0.712294i	$-0.252344\pi$
$787$	39.3805			1.40376			0.701882	+	0.712294i	$0.252344\pi$
$788$	−11.1333	+	19.2835i	−0.396609	+	0.686947i
$789$	24.1145	−	23.8322i	0.858498	−	0.848448i
$790$	−11.5974	−	6.69578i	−0.412618	−	0.238225i
$791$	43.5820	−	6.90556i	1.54960	−	0.245533i
$792$	−5.29275	−	3.13944i	−0.188070	−	0.111555i
$793$	19.7610	+	15.1029i	0.701733	+	0.536318i
$794$	2.38133	−	4.12458i	0.0845101	−	0.146376i
$795$	1.74737	−	0.457198i	0.0619730	−	0.0162152i
$796$		−	19.0946i		−	0.676789i
$797$	15.1983	+	26.3242i	0.538350	+	0.932449i	0.998993	+	0.0448640i	$0.0142855\pi$
$797$	15.1983	+	26.3242i	0.538350	+	0.932449i	−0.460643	+	0.887585i	$0.652381\pi$
$798$	4.32660	−	5.88270i	0.153160	−	0.208245i
$799$	−11.0763	+	6.39492i	−0.391852	+	0.226236i
$800$	−0.849523	+	1.47142i	−0.0300352	+	0.0520224i
$801$	5.67613	+	10.1043i	0.200556	+	0.357017i
$802$	15.4809			0.546650
$803$	−20.9948			−0.740891
$804$	−6.35079	+	6.27645i	−0.223975	+	0.221353i
$805$	−6.57458	−	41.4931i	−0.231723	−	1.46244i
$806$	17.4059	−	22.7744i	0.613098	−	0.802193i
$807$	22.7184	−	5.94424i	0.799725	−	0.209247i
$808$	−4.84811	−	8.39717i	−0.170556	−	0.295412i
$809$	14.1316	−	8.15889i	0.496841	−	0.286851i	−0.230567	−	0.973056i	$-0.574058\pi$
$809$	14.1316	−	8.15889i	0.496841	−	0.286851i	0.727408	+	0.686205i	$0.240725\pi$
$810$	0.385047	−	16.3471i	0.0135292	−	0.574380i
$811$	−5.92788			−0.208156			−0.104078	−	0.994569i	$-0.533189\pi$
$811$	−5.92788			−0.208156			−0.104078	+	0.994569i	$0.533189\pi$
$812$	−1.39281	−	1.71975i	−0.0488780	−	0.0603514i
$813$	−47.0111	+	12.3004i	−1.64875	+	0.431394i
$814$	−7.49340	+	4.32632i	−0.262644	+	0.151637i
$815$	−43.5150			−1.52427
$816$	9.52967	−	2.49343i	0.333605	−	0.0872874i
$817$	−2.66441			−0.0932159
$818$	−39.7884			−1.39117
$819$	28.6143	−	0.469071i	0.999866	−	0.0163907i
$820$	0.833252			0.0290984
$821$	−33.2585			−1.16073			−0.580364	−	0.814357i	$-0.697090\pi$
$821$	−33.2585			−1.16073			−0.580364	+	0.814357i	$0.697090\pi$
$822$	−19.4447	+	5.08768i	−0.678211	+	0.177453i
$823$	3.16826			0.110439			0.0552193	−	0.998474i	$-0.482414\pi$
$823$	3.16826			0.110439			0.0552193	+	0.998474i	$0.482414\pi$
$824$	8.08628	−	4.66861i	0.281699	−	0.162639i
$825$	5.83995	−	1.52801i	0.203321	−	0.0531987i
$826$	−2.07753	+	5.41317i	−0.0722864	+	0.188348i
$827$	24.0773			0.837250			0.418625	−	0.908159i	$-0.362512\pi$
$827$	24.0773			0.837250			0.418625	+	0.908159i	$0.362512\pi$
$828$	12.8411	+	22.8589i	0.446260	+	0.794403i
$829$	30.2946	−	17.4906i	1.05218	−	0.607474i	0.128918	−	0.991655i	$-0.458850\pi$
$829$	30.2946	−	17.4906i	1.05218	−	0.607474i	0.923258	+	0.384182i	$0.125516\pi$
$830$	−13.6880	−	23.7083i	−0.475118	−	0.822928i
$831$	39.0902	−	10.2279i	1.35602	−	0.354802i
$832$	−3.57560	−	0.463745i	−0.123962	−	0.0160775i
$833$	29.5882	+	26.6345i	1.02517	+	0.922829i
$834$	19.4253	−	19.1979i	0.672644	−	0.664770i
$835$	42.5772			1.47344
$836$	3.26874			0.113052
$837$	9.98530	+	40.0846i	0.345142	+	1.38553i
$838$	13.1146	−	22.7152i	0.453036	−	0.784682i
$839$	1.10165	−	0.636039i	0.0380332	−	0.0219585i	−0.480863	−	0.876796i	$-0.659676\pi$
$839$	1.10165	−	0.636039i	0.0380332	−	0.0219585i	0.518896	+	0.854837i	$0.326343\pi$
$840$	−7.62565	+	3.34208i	−0.263110	+	0.115313i
$841$	−14.1502	−	24.5088i	−0.487937	−	0.845132i
$842$		−	14.0343i		−	0.483653i
$843$	44.6226	−	11.6755i	1.53688	−	0.402124i
$844$	−7.80557	+	13.5196i	−0.268679	+	0.465365i
$845$	22.7906	−	6.20075i	0.784021	−	0.213312i
$846$	−3.44190	+	5.80266i	−0.118335	+	0.199500i
$847$	−13.9652	+	11.3102i	−0.479849	+	0.388625i
$848$	0.497067	+	0.286982i	0.0170694	+	0.00985500i
$849$	−33.1628	+	32.7746i	−1.13815	+	1.12482i
$850$	−4.83138	+	8.36820i	−0.165715	+	0.287027i
$851$	36.8653			1.26373
$852$	10.3306	+	10.4530i	0.353921	+	0.358113i
$853$	−8.88125			−0.304088			−0.152044	−	0.988374i	$-0.548586\pi$
$853$	−8.88125			−0.304088			−0.152044	+	0.988374i	$0.548586\pi$
$854$	11.4864	+	14.1827i	0.393058	+	0.485323i
$855$	4.25393	+	7.57256i	0.145481	+	0.258976i
$856$			10.7060i			0.365923i
$857$	−14.1680	+	24.5397i	−0.483969	+	0.838259i	−0.999830	−	0.0184131i	$-0.994139\pi$
$857$	−14.1680	+	24.5397i	−0.483969	+	0.838259i	0.515861	+	0.856672i	$0.327472\pi$
$858$	7.75798	+	10.1938i	0.264853	+	0.348011i
$859$	15.6163	−	9.01607i	0.532821	−	0.307624i	−0.209343	−	0.977842i	$-0.567133\pi$
$859$	15.6163	−	9.01607i	0.532821	−	0.307624i	0.742164	+	0.670218i	$0.233799\pi$
$860$	2.63083	+	1.51891i	0.0897106	+	0.0517944i
$861$	−1.69307	−	1.24522i	−0.0576997	−	0.0424368i
$862$	8.06272	+	13.9650i	0.274617	+	0.475651i
$863$	20.8330	+	36.0838i	0.709163	+	1.22831i	0.965168	+	0.261631i	$0.0842603\pi$
$863$	20.8330	+	36.0838i	0.709163	+	1.22831i	−0.256005	+	0.966675i	$0.582406\pi$
$864$	3.73855	−	3.60877i	0.127188	−	0.122773i
$865$		−	13.8188i		−	0.469854i
$866$	−13.9038	+	8.02734i	−0.472469	+	0.272780i
$867$	25.7110	−	6.72725i	0.873191	−	0.228469i
$868$	16.3455	−	13.2380i	0.554802	−	0.449328i
$869$	−7.55968	+	13.0938i	−0.256445	+	0.444175i
$870$	2.54647	−	0.666280i	0.0863333	−	0.0225890i
$871$	17.1585	−	7.14598i	0.581395	−	0.242132i
$872$	−4.30381	−	2.48481i	−0.145745	−	0.0841462i
$873$	−8.89715	−	5.27742i	−0.301123	−	0.178614i
$874$	−12.0609	−	6.96338i	−0.407967	−	0.235540i
$875$	11.5382	−	30.0638i	0.390063	−	1.01634i
$876$	4.68898	−	17.0963i	0.158426	−	0.577629i
$877$	−32.0440	−	18.5006i	−1.08205	−	0.624722i	−0.150601	−	0.988595i	$-0.548121\pi$
$877$	−32.0440	−	18.5006i	−1.08205	−	0.624722i	−0.931449	+	0.363873i	$0.881454\pi$
$878$		−	16.1774i		−	0.545960i
$879$	9.91807	−	9.80196i	0.334528	−	0.330612i
$880$	−3.22755	−	1.86343i	−0.108801	−	0.0628161i
$881$	−12.5417	+	21.7228i	−0.422540	+	0.731861i	−0.996187	−	0.0872416i	$-0.972195\pi$
$881$	−12.5417	+	21.7228i	−0.422540	+	0.731861i	0.573647	+	0.819103i	$0.305528\pi$
$882$	20.4889	+	4.60509i	0.689896	+	0.155061i
$883$	23.5431			0.792287			0.396144	−	0.918189i	$-0.370348\pi$
$883$	23.5431			0.792287			0.396144	+	0.918189i	$0.370348\pi$
$884$	−20.3351	−	2.63740i	−0.683943	−	0.0887054i
$885$	−4.84768	−	4.90510i	−0.162953	−	0.164883i
$886$	−10.8594	+	6.26970i	−0.364830	+	0.210635i
$887$	29.4455			0.988682			0.494341	−	0.869268i	$-0.335409\pi$
$887$	29.4455			0.988682			0.494341	+	0.869268i	$0.335409\pi$
$888$	−1.84938	−	7.06818i	−0.0620611	−	0.237193i
$889$	43.9703	−	35.6111i	1.47472	−	1.19436i
$890$	3.50938	+	6.07842i	0.117635	+	0.203749i
$891$	−18.4563	−	0.434727i	−0.618309	−	0.0145639i
$892$	−4.91509	+	8.51319i	−0.164569	+	0.285043i
$893$		−	3.58366i		−	0.119923i
$894$	2.20581	−	8.04248i	0.0737732	−	0.268981i
$895$	−16.7158	+	28.9526i	−0.558748	+	0.967779i
$896$	−2.47008	−	0.947995i	−0.0825197	−	0.0316703i
$897$	−6.90935	−	54.1397i	−0.230697	−	1.80767i
$898$	−8.48307	−	14.6931i	−0.283084	−	0.490315i
$899$	−5.75885	+	3.32487i	−0.192068	+	0.110891i
$900$	−0.0600175	+	5.09678i	−0.00200058	+	0.169893i
$901$	2.82691	+	1.63212i	0.0941780	+	0.0543737i
$902$		−	0.940760i		−	0.0313239i
$903$	−3.07567	−	7.01778i	−0.102352	−	0.233537i
$904$	−14.4435	+	8.33897i	−0.480384	+	0.277350i
$905$	0.173363	+	0.300273i	0.00576277	+	0.00998141i
$906$	−2.38337	−	0.653685i	−0.0791821	−	0.0217172i
$907$	−6.92697	−	11.9979i	−0.230006	−	0.398383i	0.727803	−	0.685786i	$-0.240541\pi$
$907$	−6.92697	−	11.9979i	−0.230006	−	0.398383i	−0.957810	+	0.287403i	$0.907208\pi$
$908$		−	11.3725i		−	0.377410i
$909$	−25.0185	−	14.8399i	−0.829812	−	0.492210i
$910$	17.3248	−	0.488106i	0.574311	−	0.0161806i
$911$		−	27.4426i		−	0.909213i	−0.890692	−	0.454607i	$-0.849780\pi$
$911$		−	27.4426i		−	0.909213i	0.890692	−	0.454607i	$-0.150220\pi$
$912$	−0.730041	+	2.66176i	−0.0241741	+	0.0881398i
$913$	−26.7672	+	15.4541i	−0.885866	+	0.511455i
$914$		−	9.47441i		−	0.313386i
$915$	−21.0006	+	5.49478i	−0.694259	+	0.181652i
$916$	−9.48968	−	16.4366i	−0.313548	−	0.543081i
$917$	6.16726	+	38.9224i	0.203661	+	1.28533i
$918$	21.2618	−	20.5237i	0.701744	−	0.677383i
$919$	22.0343	−	38.1646i	0.726845	−	1.25893i	−0.231365	−	0.972867i	$-0.574319\pi$
$919$	22.0343	−	38.1646i	0.726845	−	1.25893i	0.958210	−	0.286066i	$-0.0923476\pi$
$920$	7.93928	+	13.7512i	0.261750	+	0.453365i
$921$	22.8212	−	5.97115i	0.751986	−	0.196756i
$922$	−31.5250	+	18.2010i	−1.03822	+	0.599417i
$923$	−11.7618	−	28.2418i	−0.387144	−	0.929590i
$924$	3.77329	+	8.60953i	0.124132	+	0.283233i
$925$	6.20671	+	3.58345i	0.204075	+	0.117823i
$926$			17.8517i			0.586643i
$927$	14.2905	−	24.0922i	0.469362	−	0.791293i
$928$	0.724381	+	0.418222i	0.0237790	+	0.0137288i
$929$	36.2869	+	20.9503i	1.19053	+	0.687356i	0.958428	−	0.285335i	$-0.0921047\pi$
$929$	36.2869	+	20.9503i	1.19053	+	0.687356i	0.232107	+	0.972690i	$0.425438\pi$
$930$	6.33270	+	24.2030i	0.207657	+	0.793649i
$931$	−10.6083	+	3.44834i	−0.347672	+	0.113015i
$932$	18.2307	−	10.5255i	0.597167	−	0.344775i
$933$	11.6128	−	42.3409i	0.380187	−	1.38618i
$934$	15.1928	+	26.3147i	0.497124	+	0.861044i
$935$	−18.3556	−	10.5976i	−0.600293	−	0.346579i
$936$	−10.0336	+	4.04070i	−0.327958	+	0.132074i
$937$		−	1.71598i		−	0.0560586i	−0.999607	−	0.0280293i	$-0.991077\pi$
$937$		−	1.71598i		−	0.0560586i	0.999607	−	0.0280293i	$-0.00892317\pi$
$938$	13.4712	−	2.13450i	0.439849	−	0.0696940i
$939$	−10.5450	+	10.4216i	−0.344124	+	0.340096i
$940$	−2.04295	+	3.53850i	−0.0666337	+	0.115413i
$941$	−1.26611	−	0.730989i	−0.0412740	−	0.0238296i	0.479221	−	0.877694i	$-0.340919\pi$
$941$	−1.26611	−	0.730989i	−0.0412740	−	0.0238296i	−0.520495	+	0.853865i	$0.674253\pi$
$942$	13.7781	+	3.77892i	0.448915	+	0.123124i
$943$	−2.00409	+	3.47119i	−0.0652622	+	0.113038i
$944$		−	2.19150i		−	0.0713271i
$945$	−15.0348	+	19.9458i	−0.489082	+	0.648837i
$946$	1.71488	−	2.97027i	0.0557557	−	0.0965717i
$947$	−15.2680			−0.496145			−0.248072	−	0.968742i	$-0.579797\pi$
$947$	−15.2680			−0.496145			−0.248072	+	0.968742i	$0.579797\pi$
$948$	−8.97398	−	9.08027i	−0.291461	−	0.294914i
$949$	−22.4088	+	29.3202i	−0.727420	+	0.951775i
$950$	−1.35373	−	2.34474i	−0.0439209	−	0.0760733i
$951$	−28.6729	−	29.0125i	−0.929782	−	0.940795i
$952$	−14.0478	−	5.39141i	−0.455291	−	0.174737i
$953$	20.0074	−	11.5513i	0.648104	−	0.374183i	−0.139625	−	0.990204i	$-0.544590\pi$
$953$	20.0074	−	11.5513i	0.648104	−	0.374183i	0.787729	+	0.616021i	$0.211257\pi$
$954$	1.72177	+	0.0202748i	0.0557444	+	0.000656422i
$955$	−9.44111			−0.305507
$956$	16.6885			0.539746
$957$	−0.752245	−	2.87502i	−0.0243166	−	0.0929361i
$958$	−19.9492	+	11.5177i	−0.644530	+	0.372120i
$959$	28.6636	+	11.0008i	0.925596	+	0.355235i
$960$	2.23824	−	2.21204i	0.0722390	−	0.0713933i
$961$	−16.1015	−	27.8886i	−0.519402	−	0.899631i
$962$	−1.95617	+	15.0826i	−0.0630693	+	0.486282i
$963$	15.7303	+	28.0021i	0.506903	+	0.902355i
$964$	15.2747			0.491963
$965$	10.0036	−	17.3268i	0.322028	−	0.557768i
$966$	4.41824	−	39.8054i	0.142154	−	1.28072i
$967$			14.3674i			0.462026i	0.972951	+	0.231013i	$0.0742040\pi$
$967$			14.3674i			0.462026i	−0.972951	+	0.231013i	$0.925796\pi$
$968$	3.39615	−	5.88231i	0.109156	−	0.189064i
$969$	−4.15187	+	15.1379i	−0.133377	+	0.486300i
$970$	−5.42553	−	3.13243i	−0.174203	−	0.100576i
$971$	15.6985	−	27.1905i	0.503788	−	0.872586i	−0.496203	−	0.868207i	$-0.665273\pi$
$971$	15.6985	−	27.1905i	0.503788	−	0.872586i	0.999990	−	0.00437930i	$-0.00139398\pi$
$972$	4.47603	−	14.9320i	0.143569	−	0.478945i
$973$	−41.2046	+	6.52886i	−1.32096	+	0.209306i
$974$			14.2075i			0.455238i
$975$	4.09931	−	9.78668i	0.131283	−	0.313425i
$976$	−5.97394	−	3.44906i	−0.191221	−	0.110402i
$977$	21.8776	+	37.8931i	0.699926	+	1.21231i	0.968492	+	0.249046i	$0.0801171\pi$
$977$	21.8776	+	37.8931i	0.699926	+	1.21231i	−0.268566	+	0.963261i	$0.586550\pi$
$978$	−40.0065	−	10.9726i	−1.27927	−	0.350864i
$979$	6.86267	−	3.96217i	0.219332	−	0.126631i
$980$	12.4404	+	2.64262i	0.397394	+	0.0844155i
$981$	−14.9078	−	0.175548i	−0.475970	−	0.00560481i
$982$	2.47085	+	1.42654i	0.0788479	+	0.0455228i
$983$	−3.21594	−	1.85672i	−0.102572	−	0.0592202i	0.447836	−	0.894116i	$-0.352195\pi$
$983$	−3.21594	−	1.85672i	−0.102572	−	0.0592202i	−0.550409	+	0.834895i	$0.685528\pi$
$984$	0.766068	+	0.210109i	0.0244214	+	0.00669804i
$985$			40.4553i			1.28901i
$986$	4.11968	+	2.37850i	0.131197	+	0.0757469i
$987$	9.43899	−	4.13681i	0.300446	−	0.131676i
$988$	3.48889	−	4.56495i	0.110996	−	0.145230i
$989$	−12.6551	+	7.30641i	−0.402408	+	0.232330i
$990$	−11.1798	−	0.131648i	−0.355317	−	0.00418406i
$991$	21.0267	+	36.4192i	0.667934	+	1.15690i	0.978481	+	0.206337i	$0.0661544\pi$
$991$	21.0267	+	36.4192i	0.667934	+	1.15690i	−0.310547	+	0.950558i	$0.600512\pi$
$992$	−3.97501	+	6.88493i	−0.126207	+	0.218597i
$993$	11.8783	+	3.25786i	0.376947	+	0.103385i
$994$	−3.51325	−	22.1726i	−0.111434	−	0.703273i
$995$	−17.3460	−	30.0442i	−0.549905	−	0.952464i
$996$	−6.60619	−	25.2483i	−0.209325	−	0.800023i
$997$			45.1553i			1.43008i	0.699083	+	0.715041i	$0.253592\pi$
$997$			45.1553i			1.43008i	−0.699083	+	0.715041i	$0.746408\pi$
$998$	−15.9720	+	9.22146i	−0.505586	+	0.291900i
$999$	−15.2225	−	15.7699i	−0.481618	−	0.498938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.f.17.15	yes	34
3.2	odd	2		546.2.bi.e.17.14	✓	34
7.5	odd	6		546.2.bn.e.173.10	yes	34
13.10	even	6		546.2.bn.f.101.8	yes	34
21.5	even	6		546.2.bn.f.173.8	yes	34
39.23	odd	6		546.2.bn.e.101.10	yes	34
91.75	odd	6		546.2.bi.e.257.14	yes	34
273.257	even	6	inner	546.2.bi.f.257.15	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.14	✓	34	3.2	odd	2
546.2.bi.e.257.14	yes	34	91.75	odd	6
546.2.bi.f.17.15	yes	34	1.1	even	1	trivial
546.2.bi.f.257.15	yes	34	273.257	even	6	inner
546.2.bn.e.101.10	yes	34	39.23	odd	6
546.2.bn.e.173.10	yes	34	7.5	odd	6
546.2.bn.f.101.8	yes	34	13.10	even	6
546.2.bn.f.173.8	yes	34	21.5	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.67564 - 0.438430i) q^{3} +1.00000 q^{4} +(1.57344 - 0.908426i) q^{5} +(1.67564 - 0.438430i) q^{6} +(-2.47008 - 0.947995i) q^{7} +1.00000 q^{8} +(2.61556 - 1.46930i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.67564 - 0.438430i) q^{3} +1.00000 q^{4} +(1.57344 - 0.908426i) q^{5} +(1.67564 - 0.438430i) q^{6} +(-2.47008 - 0.947995i) q^{7} +1.00000 q^{8} +(2.61556 - 1.46930i) q^{9} +(1.57344 - 0.908426i) q^{10} +(-1.02563 - 1.77645i) q^{11} +(1.67564 - 0.438430i) q^{12} +(-3.57560 - 0.463745i) q^{13} +(-2.47008 - 0.947995i) q^{14} +(2.23824 - 2.21204i) q^{15} +1.00000 q^{16} +5.68717 q^{17} +(2.61556 - 1.46930i) q^{18} +(-0.796762 + 1.38003i) q^{19} +(1.57344 - 0.908426i) q^{20} +(-4.55461 - 0.505542i) q^{21} +(-1.02563 - 1.77645i) q^{22} +8.73960i q^{23} +(1.67564 - 0.438430i) q^{24} +(-0.849523 + 1.47142i) q^{25} +(-3.57560 - 0.463745i) q^{26} +(3.73855 - 3.60877i) q^{27} +(-2.47008 - 0.947995i) q^{28} +(0.724381 + 0.418222i) q^{29} +(2.23824 - 2.21204i) q^{30} +(-3.97501 + 6.88493i) q^{31} +1.00000 q^{32} +(-2.49744 - 2.52703i) q^{33} +5.68717 q^{34} +(-4.74771 + 0.752275i) q^{35} +(2.61556 - 1.46930i) q^{36} -4.21819i q^{37} +(-0.796762 + 1.38003i) q^{38} +(-6.19475 + 0.790580i) q^{39} +(1.57344 - 0.908426i) q^{40} +(0.397180 + 0.229312i) q^{41} +(-4.55461 - 0.505542i) q^{42} +(0.836012 + 1.44802i) q^{43} +(-1.02563 - 1.77645i) q^{44} +(2.78067 - 4.68791i) q^{45} +8.73960i q^{46} +(-1.94760 + 1.12445i) q^{47} +(1.67564 - 0.438430i) q^{48} +(5.20261 + 4.68325i) q^{49} +(-0.849523 + 1.47142i) q^{50} +(9.52967 - 2.49343i) q^{51} +(-3.57560 - 0.463745i) q^{52} +(0.497067 + 0.286982i) q^{53} +(3.73855 - 3.60877i) q^{54} +(-3.22755 - 1.86343i) q^{55} +(-2.47008 - 0.947995i) q^{56} +(-0.730041 + 2.66176i) q^{57} +(0.724381 + 0.418222i) q^{58} -2.19150i q^{59} +(2.23824 - 2.21204i) q^{60} +(-5.97394 - 3.44906i) q^{61} +(-3.97501 + 6.88493i) q^{62} +(-7.85354 + 1.14977i) q^{63} +1.00000 q^{64} +(-6.04728 + 2.51850i) q^{65} +(-2.49744 - 2.52703i) q^{66} +(-4.46448 + 2.57757i) q^{67} +5.68717 q^{68} +(3.83170 + 14.6444i) q^{69} +(-4.74771 + 0.752275i) q^{70} +(4.24250 + 7.34823i) q^{71} +(2.61556 - 1.46930i) q^{72} +(5.11752 - 8.86381i) q^{73} -4.21819i q^{74} +(-0.778384 + 2.83803i) q^{75} +(-0.796762 + 1.38003i) q^{76} +(0.849335 + 5.36027i) q^{77} +(-6.19475 + 0.790580i) q^{78} +(-3.68537 - 6.38325i) q^{79} +(1.57344 - 0.908426i) q^{80} +(4.68229 - 7.68610i) q^{81} +(0.397180 + 0.229312i) q^{82} -15.0678i q^{83} +(-4.55461 - 0.505542i) q^{84} +(8.94843 - 5.16638i) q^{85} +(0.836012 + 1.44802i) q^{86} +(1.39717 + 0.383200i) q^{87} +(-1.02563 - 1.77645i) q^{88} +3.86314i q^{89} +(2.78067 - 4.68791i) q^{90} +(8.39241 + 4.53514i) q^{91} +8.73960i q^{92} +(-3.64215 + 13.2794i) q^{93} +(-1.94760 + 1.12445i) q^{94} +2.89520i q^{95} +(1.67564 - 0.438430i) q^{96} +(-1.72410 - 2.98622i) q^{97} +(5.20261 + 4.68325i) q^{98} +(-5.29275 - 3.13944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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