LMFDB - Embedded newform 546.2.bw.a.11.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (of order $12$, degree $4$, 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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	546.11
Dual form			546.2.bw.a.149.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(1.63257 - 0.578534i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.965749 - 0.258772i) q^{5} +(-0.981362 - 1.42721i) q^{6} +(1.68839 + 2.03700i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.33060 - 1.88900i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(1.63257 - 0.578534i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.965749 - 0.258772i) q^{5} +(-0.981362 - 1.42721i) q^{6} +(1.68839 + 2.03700i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.33060 - 1.88900i) q^{9} +0.999817i q^{10} +(1.92357 + 1.92357i) q^{11} +(-1.12458 + 1.31731i) q^{12} +(3.59766 + 0.238399i) q^{13} +(1.53060 - 2.15807i) q^{14} +(-1.72636 + 0.136254i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.19596 + 2.07146i) q^{17} +(-2.42784 - 1.76228i) q^{18} +(-2.20581 - 2.20581i) q^{19} +(0.965749 - 0.258772i) q^{20} +(3.93489 + 2.34876i) q^{21} +(1.36017 - 2.35588i) q^{22} +(3.01026 - 5.21393i) q^{23} +(1.56349 + 0.745319i) q^{24} +(-3.46442 - 2.00018i) q^{25} +(-0.700868 - 3.53678i) q^{26} +(2.71202 - 4.43226i) q^{27} +(-2.48068 - 0.919898i) q^{28} +(-2.49077 + 1.43804i) q^{29} +(0.578428 + 1.63228i) q^{30} +(1.32280 - 0.354443i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(4.25321 + 2.02752i) q^{33} +(1.69134 - 1.69134i) q^{34} +(-1.10344 - 2.40413i) q^{35} +(-1.07386 + 2.80122i) q^{36} +(0.281908 + 1.05209i) q^{37} +(-1.55974 + 2.70155i) q^{38} +(6.01137 - 1.69216i) q^{39} +(-0.499908 - 0.865867i) q^{40} +(0.406096 + 0.108813i) q^{41} +(1.25030 - 4.40871i) q^{42} +(-3.05357 - 1.76298i) q^{43} +(-2.62764 - 0.704074i) q^{44} +(-2.73959 + 1.22121i) q^{45} +(-5.81538 - 1.55823i) q^{46} +(0.192204 - 0.717315i) q^{47} +(0.315262 - 1.70312i) q^{48} +(-1.29871 + 6.87847i) q^{49} +(-1.03537 + 3.86406i) q^{50} +(3.15090 + 2.68991i) q^{51} +(-3.23487 + 1.59237i) q^{52} +(-2.12547 - 1.22714i) q^{53} +(-4.98316 - 1.47246i) q^{54} +(-1.35992 - 2.35545i) q^{55} +(-0.246505 + 2.63424i) q^{56} +(-4.87728 - 2.32501i) q^{57} +(2.03370 + 2.03370i) q^{58} +(-2.81769 + 10.5158i) q^{59} +(1.42695 - 0.981182i) q^{60} +1.80704 q^{61} +(-0.684731 - 1.18599i) q^{62} +(7.78283 + 1.55806i) q^{63} +1.00000i q^{64} +(-3.41275 - 1.16121i) q^{65} +(0.857618 - 4.63305i) q^{66} +(0.0850834 + 0.0850834i) q^{67} +(-2.07146 - 1.19596i) q^{68} +(1.89804 - 10.2537i) q^{69} +(-2.03662 + 1.68808i) q^{70} +(3.68364 + 13.7475i) q^{71} +(2.98370 + 0.312257i) q^{72} +(-1.12279 - 4.19031i) q^{73} +(0.943282 - 0.544604i) q^{74} +(-6.81309 - 1.26116i) q^{75} +(3.01319 + 0.807382i) q^{76} +(-0.670575 + 7.16601i) q^{77} +(-3.19036 - 5.36857i) q^{78} +(-5.71760 - 9.90318i) q^{79} +(-0.706977 + 0.706977i) q^{80} +(1.86337 - 8.80499i) q^{81} -0.420422i q^{82} +(7.50388 - 7.50388i) q^{83} +(-4.58209 - 0.0666422i) q^{84} +(-0.618961 - 2.30999i) q^{85} +(-0.912585 + 3.40581i) q^{86} +(-3.23440 + 3.78871i) q^{87} +2.72033i q^{88} +(-9.86938 + 2.64449i) q^{89} +(1.88865 + 2.33017i) q^{90} +(5.58862 + 7.73093i) q^{91} +6.02053i q^{92} +(1.95451 - 1.34394i) q^{93} -0.742619 q^{94} +(1.55946 + 2.70106i) q^{95} +(-1.72668 + 0.136279i) q^{96} +(-4.73874 + 1.26974i) q^{97} +(6.98022 - 0.525824i) q^{98} +(8.11667 + 0.849444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	1.63257	−	0.578534i	0.942567	−	0.334017i
$3$	1.63257	−	0.578534i	0.942567	−	0.334017i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.965749	−	0.258772i	−0.431896	−	0.115726i	0.0363200	−	0.999340i	$-0.488436\pi$
$5$	−0.965749	−	0.258772i	−0.431896	−	0.115726i	−0.468216	+	0.883614i	$0.655103\pi$
$6$	−0.981362	−	1.42721i	−0.400639	−	0.582656i
$7$	1.68839	+	2.03700i	0.638150	+	0.769912i
$7$	1.68839	+	2.03700i	0.638150	+	0.769912i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.33060	−	1.88900i	0.776866	−	0.629666i
$10$			0.999817i			0.316170i
$11$	1.92357	+	1.92357i	0.579977	+	0.579977i	0.934897	−	0.354920i	$-0.115492\pi$
$11$	1.92357	+	1.92357i	0.579977	+	0.579977i	−0.354920	+	0.934897i	$0.615492\pi$
$12$	−1.12458	+	1.31731i	−0.324639	+	0.380275i
$13$	3.59766	+	0.238399i	0.997812	+	0.0661200i
$13$	3.59766	+	0.238399i	0.997812	+	0.0661200i
$14$	1.53060	−	2.15807i	0.409070	−	0.576768i
$15$	−1.72636	+	0.136254i	−0.445746	+	0.0351808i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.19596	+	2.07146i	0.290063	+	0.502404i	0.973824	−	0.227302i	$-0.0729905\pi$
$17$	1.19596	+	2.07146i	0.290063	+	0.502404i	−0.683761	+	0.729706i	$0.739657\pi$
$18$	−2.42784	−	1.76228i	−0.572246	−	0.415372i
$19$	−2.20581	−	2.20581i	−0.506047	−	0.506047i	0.407263	−	0.913311i	$-0.366483\pi$
$19$	−2.20581	−	2.20581i	−0.506047	−	0.506047i	−0.913311	+	0.407263i	$0.866483\pi$
$20$	0.965749	−	0.258772i	0.215948	−	0.0578631i
$21$	3.93489	+	2.34876i	0.858663	+	0.512541i
$22$	1.36017	−	2.35588i	0.289988	−	0.502275i
$23$	3.01026	−	5.21393i	0.627683	−	1.08718i	−0.360332	−	0.932824i	$-0.617337\pi$
$23$	3.01026	−	5.21393i	0.627683	−	1.08718i	0.988015	−	0.154355i	$-0.0493301\pi$
$24$	1.56349	+	0.745319i	0.319146	+	0.152138i
$25$	−3.46442	−	2.00018i	−0.692884	−	0.400037i
$26$	−0.700868	−	3.53678i	−0.137451	−	0.693619i
$27$	2.71202	−	4.43226i	0.521929	−	0.852989i
$28$	−2.48068	−	0.919898i	−0.468805	−	0.173844i
$29$	−2.49077	+	1.43804i	−0.462524	+	0.267038i	−0.713105	−	0.701057i	$-0.752712\pi$
$29$	−2.49077	+	1.43804i	−0.462524	+	0.267038i	0.250581	+	0.968096i	$0.419378\pi$
$30$	0.578428	+	1.63228i	0.105606	+	0.298011i
$31$	1.32280	−	0.354443i	0.237582	−	0.0636598i	−0.138064	−	0.990423i	$-0.544088\pi$
$31$	1.32280	−	0.354443i	0.237582	−	0.0636598i	0.375645	+	0.926764i	$0.377421\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	4.25321	+	2.02752i	0.740389	+	0.352945i
$34$	1.69134	−	1.69134i	0.290063	−	0.290063i
$35$	−1.10344	−	2.40413i	−0.186515	−	0.406373i
$36$	−1.07386	+	2.80122i	−0.178976	+	0.466870i
$37$	0.281908	+	1.05209i	0.0463454	+	0.172963i	0.985219	−	0.171298i	$-0.0547961\pi$
$37$	0.281908	+	1.05209i	0.0463454	+	0.172963i	−0.938874	+	0.344261i	$0.888129\pi$
$38$	−1.55974	+	2.70155i	−0.253024	+	0.438250i
$39$	6.01137	−	1.69216i	0.962590	−	0.270963i
$40$	−0.499908	−	0.865867i	−0.0790425	−	0.136906i
$41$	0.406096	+	0.108813i	0.0634216	+	0.0169938i	0.290390	−	0.956908i	$-0.406215\pi$
$41$	0.406096	+	0.108813i	0.0634216	+	0.0169938i	−0.226969	+	0.973902i	$0.572882\pi$
$42$	1.25030	−	4.40871i	0.192926	−	0.680279i
$43$	−3.05357	−	1.76298i	−0.465665	−	0.268852i	0.248758	−	0.968566i	$-0.419978\pi$
$43$	−3.05357	−	1.76298i	−0.465665	−	0.268852i	−0.714423	+	0.699714i	$0.753311\pi$
$44$	−2.62764	−	0.704074i	−0.396131	−	0.106143i
$45$	−2.73959	+	1.22121i	−0.408394	+	0.182047i
$46$	−5.81538	−	1.55823i	−0.857431	−	0.229748i
$47$	0.192204	−	0.717315i	0.0280358	−	0.104631i	−0.950490	−	0.310755i	$-0.899418\pi$
$47$	0.192204	−	0.717315i	0.0280358	−	0.104631i	0.978526	+	0.206124i	$0.0660849\pi$
$48$	0.315262	−	1.70312i	0.0455042	−	0.245824i
$49$	−1.29871	+	6.87847i	−0.185530	+	0.982639i
$50$	−1.03537	+	3.86406i	−0.146424	+	0.546460i
$51$	3.15090	+	2.68991i	0.441215	+	0.376663i
$52$	−3.23487	+	1.59237i	−0.448595	+	0.220822i
$53$	−2.12547	−	1.22714i	−0.291956	−	0.168561i	0.346867	−	0.937914i	$-0.387245\pi$
$53$	−2.12547	−	1.22714i	−0.291956	−	0.168561i	−0.638824	+	0.769353i	$0.720579\pi$
$54$	−4.98316	−	1.47246i	−0.678122	−	0.200376i
$55$	−1.35992	−	2.35545i	−0.183371	−	0.317608i
$56$	−0.246505	+	2.63424i	−0.0329406	+	0.352016i
$57$	−4.87728	−	2.32501i	−0.646012	−	0.307955i
$58$	2.03370	+	2.03370i	0.267038	+	0.267038i
$59$	−2.81769	+	10.5158i	−0.366832	+	1.36903i	0.498089	+	0.867126i	$0.334035\pi$
$59$	−2.81769	+	10.5158i	−0.366832	+	1.36903i	−0.864921	+	0.501909i	$0.832631\pi$
$60$	1.42695	−	0.981182i	0.184218	−	0.126670i
$61$	1.80704			0.231368			0.115684	−	0.993286i	$-0.463094\pi$
$61$	1.80704			0.231368			0.115684	+	0.993286i	$0.463094\pi$
$62$	−0.684731	−	1.18599i	−0.0869609	−	0.150621i
$63$	7.78283	+	1.55806i	0.980544	+	0.196297i
$64$			1.00000i			0.125000i
$65$	−3.41275	−	1.16121i	−0.423299	−	0.144030i
$66$	0.857618	−	4.63305i	0.105565	−	0.570288i
$67$	0.0850834	+	0.0850834i	0.0103946	+	0.0103946i	0.712285	−	0.701890i	$-0.247660\pi$
$67$	0.0850834	+	0.0850834i	0.0103946	+	0.0103946i	−0.701890	+	0.712285i	$0.747660\pi$
$68$	−2.07146	−	1.19596i	−0.251202	−	0.145031i
$69$	1.89804	−	10.2537i	0.228498	−	1.23440i
$70$	−2.03662	+	1.68808i	−0.243423	+	0.201764i
$71$	3.68364	+	13.7475i	0.437168	+	1.63153i	0.735825	+	0.677172i	$0.236795\pi$
$71$	3.68364	+	13.7475i	0.437168	+	1.63153i	−0.298657	+	0.954361i	$0.596539\pi$
$72$	2.98370	+	0.312257i	0.351633	+	0.0367999i
$73$	−1.12279	−	4.19031i	−0.131413	−	0.490439i	0.868574	−	0.495559i	$-0.165037\pi$
$73$	−1.12279	−	4.19031i	−0.131413	−	0.490439i	−0.999987	+	0.00512035i	$0.998370\pi$
$74$	0.943282	−	0.544604i	0.109654	−	0.0633090i
$75$	−6.81309	−	1.26116i	−0.786708	−	0.145627i
$76$	3.01319	+	0.807382i	0.345637	+	0.0926131i
$77$	−0.670575	+	7.16601i	−0.0764191	+	0.816643i
$78$	−3.19036	−	5.36857i	−0.361237	−	0.607871i
$79$	−5.71760	−	9.90318i	−0.643281	−	1.11419i	−0.984696	−	0.174282i	$-0.944240\pi$
$79$	−5.71760	−	9.90318i	−0.643281	−	1.11419i	0.341415	−	0.939913i	$-0.389094\pi$
$80$	−0.706977	+	0.706977i	−0.0790425	+	0.0790425i
$81$	1.86337	−	8.80499i	0.207041	−	0.978332i
$82$		−	0.420422i		−	0.0464278i
$83$	7.50388	−	7.50388i	0.823658	−	0.823658i	−0.162972	−	0.986631i	$-0.552108\pi$
$83$	7.50388	−	7.50388i	0.823658	−	0.823658i	0.986631	+	0.162972i	$0.0521081\pi$
$84$	−4.58209	−	0.0666422i	−0.499947	−	0.00727126i
$85$	−0.618961	−	2.30999i	−0.0671357	−	0.250554i
$86$	−0.912585	+	3.40581i	−0.0984066	+	0.367258i
$87$	−3.23440	+	3.78871i	−0.346764	+	0.406192i
$88$			2.72033i			0.289988i
$89$	−9.86938	+	2.64449i	−1.04615	+	0.280316i	−0.740661	−	0.671879i	$-0.765487\pi$
$89$	−9.86938	+	2.64449i	−1.04615	+	0.280316i	−0.305491	+	0.952195i	$0.598821\pi$
$90$	1.88865	+	2.33017i	0.199081	+	0.245622i
$91$	5.58862	+	7.73093i	0.585847	+	0.810422i
$92$			6.02053i			0.627683i
$93$	1.95451	−	1.34394i	0.202673	−	0.139360i
$94$	−0.742619			−0.0765953
$95$	1.55946	+	2.70106i	0.159997	+	0.277123i
$96$	−1.72668	+	0.136279i	−0.176229	+	0.0139090i
$97$	−4.73874	+	1.26974i	−0.481146	+	0.128923i	−0.491236	−	0.871026i	$-0.663455\pi$
$97$	−4.73874	+	1.26974i	−0.481146	+	0.128923i	0.0100903	+	0.999949i	$0.496788\pi$
$98$	6.98022	−	0.525824i	0.705109	−	0.0531163i
$99$	8.11667	+	0.849444i	0.815756	+	0.0853723i
$100$	4.00037			0.400037
$101$	4.43607			0.441405			0.220703	−	0.975341i	$-0.429165\pi$
$101$	4.43607			0.441405			0.220703	+	0.975341i	$0.429165\pi$
$102$	1.78274	−	3.73974i	0.176518	−	0.370290i
$103$	−6.30061	+	3.63766i	−0.620817	+	0.358429i	−0.777187	−	0.629270i	$-0.783354\pi$
$103$	−6.30061	+	3.63766i	−0.620817	+	0.358429i	0.156370	+	0.987699i	$0.450021\pi$
$104$	2.37536	+	2.71250i	0.232923	+	0.265983i
$105$	−3.19232	−	3.28655i	−0.311539	−	0.320734i
$106$	−0.635216	+	2.37066i	−0.0616976	+	0.230259i
$107$	−17.1722	−	9.91438i	−1.66010	−	0.958459i	−0.972665	−	0.232213i	$-0.925403\pi$
$107$	−17.1722	−	9.91438i	−1.66010	−	0.958459i	−0.687435	−	0.726246i	$-0.741263\pi$
$108$	−0.132551	+	5.19446i	−0.0127548	+	0.499837i
$109$	14.3267	−	3.83882i	1.37225	−	0.367693i	0.503948	−	0.863734i	$-0.331880\pi$
$109$	14.3267	−	3.83882i	1.37225	−	0.367693i	0.868299	+	0.496041i	$0.165214\pi$
$110$	−1.92321	+	1.92321i	−0.183371	+	0.183371i
$111$	1.06891	+	1.55453i	0.101456	+	0.147549i
$112$	2.60828	−	0.443687i	0.246460	−	0.0419245i
$113$	3.61436	+	2.08675i	0.340010	+	0.196305i	0.660277	−	0.751022i	$-0.270439\pi$
$113$	3.61436	+	2.08675i	0.340010	+	0.196305i	−0.320266	+	0.947328i	$0.603772\pi$
$114$	−0.983455	+	5.31285i	−0.0921090	+	0.497594i
$115$	−4.25638	+	4.25638i	−0.396909	+	0.396909i
$116$	1.43804	−	2.49077i	0.133519	−	0.231262i
$117$	8.83503	−	6.24037i	0.816799	−	0.576922i
$118$	10.8867			1.00220
$119$	−2.20032	+	5.93359i	−0.201703	+	0.543932i
$120$	−1.31707	−	1.12438i	−0.120232	−	0.102641i
$121$		−	3.59979i		−	0.327254i
$122$	−0.467697	−	1.74547i	−0.0423433	−	0.158027i
$123$	0.725934	−	0.0572948i	0.0654553	−	0.00516610i
$124$	−0.968356	+	0.968356i	−0.0869609	+	0.0869609i
$125$	6.36305	+	6.36305i	0.569129	+	0.569129i
$126$	−0.509375	−	7.92089i	−0.0453787	−	0.705649i
$127$	2.36521	−	1.36556i	0.209879	−	0.121173i	−0.391376	−	0.920231i	$-0.628001\pi$
$127$	2.36521	−	1.36556i	0.209879	−	0.121173i	0.601255	+	0.799057i	$0.294668\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−6.00512	−	1.11160i	−0.528721	−	0.0978710i
$130$	−0.238355	+	3.59700i	−0.0209051	+	0.315478i
$131$	−12.6239	+	7.28842i	−1.10296	+	0.636793i	−0.936996	−	0.349340i	$-0.886406\pi$
$131$	−12.6239	+	7.28842i	−1.10296	+	0.636793i	−0.165961	+	0.986132i	$0.553073\pi$
$132$	−4.69715	+	0.370725i	−0.408834	+	0.0322675i
$133$	0.768968	−	8.21748i	0.0666780	−	0.712546i
$134$	0.0601631	−	0.104205i	0.00519730	−	0.00900198i
$135$	−3.76608	+	3.57866i	−0.324132	+	0.308002i
$136$	−0.619074	+	2.31042i	−0.0530852	+	0.198117i
$137$	−2.29170	+	8.55275i	−0.195793	+	0.730711i	0.796267	+	0.604946i	$0.206805\pi$
$137$	−2.29170	+	8.55275i	−0.195793	+	0.730711i	−0.992060	+	0.125765i	$0.959861\pi$
$138$	−10.3955	+	0.820474i	−0.884926	+	0.0698434i
$139$	−11.2557	+	19.4954i	−0.954695	+	1.65358i	−0.219629	+	0.975583i	$0.570485\pi$
$139$	−11.2557	+	19.4954i	−0.954695	+	1.65358i	−0.735065	+	0.677996i	$0.762849\pi$
$140$	2.15767	+	1.53032i	0.182357	+	0.129336i
$141$	−0.101204	−	1.28227i	−0.00852289	−	0.107986i
$142$	12.3257	−	7.11625i	1.03435	−	0.597182i
$143$	6.46176	+	7.37891i	0.540360	+	0.617056i
$144$	−0.470622	−	2.96286i	−0.0392185	−	0.246905i
$145$	2.77758	−	0.744250i	0.230665	−	0.0618066i
$146$	−3.75693	+	2.16906i	−0.310926	+	0.179513i
$147$	1.85919	+	11.9810i	0.153344	+	0.988173i
$148$	−0.770187	−	0.770187i	−0.0633090	−	0.0633090i
$149$	−15.8682	+	15.8682i	−1.29997	+	1.29997i	−0.371565	+	0.928407i	$0.621179\pi$
$149$	−15.8682	+	15.8682i	−1.29997	+	1.29997i	−0.928407	+	0.371565i	$0.878821\pi$
$150$	0.545168	+	6.90736i	0.0445127	+	0.563983i
$151$	−3.20779	−	11.9716i	−0.261046	−	0.974237i	−0.964626	−	0.263621i	$-0.915083\pi$
$151$	−3.20779	−	11.9716i	−0.261046	−	0.974237i	0.703580	−	0.710616i	$-0.251584\pi$
$152$		−	3.11948i		−	0.253024i
$153$	6.70029	+	2.56858i	0.541686	+	0.207657i
$154$	7.09540	−	1.20698i	0.571763	−	0.0972609i
$155$	−1.36921			−0.109978
$156$	−4.35992	+	4.47114i	−0.349073	+	0.357978i
$157$	−2.86148	+	4.95622i	−0.228371	+	0.395550i	−0.957325	−	0.289012i	$-0.906673\pi$
$157$	−2.86148	+	4.95622i	−0.228371	+	0.395550i	0.728955	+	0.684562i	$0.240007\pi$
$158$	−8.08591	+	8.08591i	−0.643281	+	0.643281i
$159$	−4.17994	−	0.773744i	−0.331491	−	0.0613619i
$160$	0.865867	+	0.499908i	0.0684528	+	0.0395212i
$161$	15.7032	−	2.67123i	1.23759	−	0.210522i
$162$	−8.98724	+	0.479024i	−0.706104	+	0.0376357i
$163$	−16.4888	+	16.4888i	−1.29150	+	1.29150i	−0.357644	+	0.933858i	$0.616420\pi$
$163$	−16.4888	+	16.4888i	−1.29150	+	1.29150i	−0.933858	+	0.357644i	$0.883580\pi$
$164$	−0.406096	+	0.108813i	−0.0317108	+	0.00849688i
$165$	−3.58287	−	3.05868i	−0.278926	−	0.238118i
$166$	−9.19034	−	5.30605i	−0.713309	−	0.411829i
$167$	−1.91833	+	7.15930i	−0.148445	+	0.554003i	0.851133	+	0.524950i	$0.175916\pi$
$167$	−1.91833	+	7.15930i	−0.148445	+	0.554003i	−0.999578	+	0.0290533i	$0.990751\pi$
$168$	1.12156	+	4.44321i	0.0865303	+	0.342801i
$169$	12.8863	+	1.71536i	0.991256	+	0.131951i
$170$	−2.07108	+	1.19574i	−0.158845	+	0.0917091i
$171$	−9.30762	−	0.974082i	−0.711772	−	0.0744899i
$172$	3.52596			0.268852
$173$	17.6726			1.34362			0.671812	−	0.740721i	$-0.265516\pi$
$173$	17.6726			1.34362			0.671812	+	0.740721i	$0.265516\pi$
$174$	4.49673	+	2.14360i	0.340897	+	0.162506i
$175$	−1.77491	−	10.4341i	−0.134171	−	0.788743i
$176$	2.62764	−	0.704074i	0.198066	−	0.0530716i
$177$	1.48363	+	18.7979i	0.111517	+	1.41293i
$178$	5.10877	+	8.84864i	0.382918	+	0.663234i
$179$	−9.66983			−0.722757			−0.361379	−	0.932419i	$-0.617694\pi$
$179$	−9.66983			−0.722757			−0.361379	+	0.932419i	$0.617694\pi$
$180$	1.76195	−	2.42739i	0.131328	−	0.180927i
$181$		−	5.02844i		−	0.373761i	−0.982383	−	0.186880i	$-0.940162\pi$
$181$		−	5.02844i		−	0.373761i	0.982383	−	0.186880i	$-0.0598377\pi$
$182$	6.02106	−	7.39911i	0.446311	−	0.548458i
$183$	2.95013	−	1.04544i	0.218080	−	0.0772808i
$184$	5.81538	−	1.55823i	0.428716	−	0.114874i
$185$		−	1.08901i		−	0.0800655i
$186$	−1.80401	−	1.54007i	−0.132276	−	0.112924i
$187$	−1.68409	+	6.28510i	−0.123153	+	0.459612i
$188$	0.192204	+	0.717315i	0.0140179	+	0.0523156i
$189$	13.6074	−	1.95898i	0.989796	−	0.142495i
$190$	2.20540	−	2.20540i	0.159997	−	0.159997i
$191$		−	23.0728i		−	1.66949i	−0.550636	−	0.834745i	$-0.685615\pi$
$191$		−	23.0728i		−	1.66949i	0.550636	−	0.834745i	$-0.314385\pi$
$192$	0.578534	+	1.63257i	0.0417521	+	0.117821i
$193$	−0.515937	+	0.515937i	−0.0371380	+	0.0371380i	−0.725432	−	0.688294i	$-0.758360\pi$
$193$	−0.515937	+	0.515937i	−0.0371380	+	0.0371380i	0.688294	+	0.725432i	$0.258360\pi$
$194$	2.45295	+	4.24863i	0.176112	+	0.305034i
$195$	−6.24336	+	0.0786339i	−0.447096	+	0.00563109i
$196$	−2.31452	−	6.60628i	−0.165323	−	0.471877i
$197$	−12.8434	−	3.44137i	−0.915051	−	0.245187i	−0.229582	−	0.973289i	$-0.573736\pi$
$197$	−12.8434	−	3.44137i	−0.915051	−	0.245187i	−0.685469	+	0.728102i	$0.740403\pi$
$198$	−1.28025	−	8.05995i	−0.0909833	−	0.572796i
$199$	−7.57282	+	4.37217i	−0.536823	+	0.309935i	−0.743790	−	0.668413i	$-0.766974\pi$
$199$	−7.57282	+	4.37217i	−0.536823	+	0.309935i	0.206967	+	0.978348i	$0.433641\pi$
$200$	−1.03537	−	3.86406i	−0.0732118	−	0.273230i
$201$	0.188129	+	0.0896814i	0.0132696	+	0.00632564i
$202$	−1.14814	−	4.28491i	−0.0807828	−	0.301485i
$203$	−7.13467	−	2.64571i	−0.500755	−	0.185692i
$204$	−4.07372	−	0.754082i	−0.285217	−	0.0527963i
$205$	−0.364029	−	0.210172i	−0.0254249	−	0.0146791i
$206$	5.14443	+	5.14443i	0.358429	+	0.358429i
$207$	−2.83339	−	17.8380i	−0.196935	−	1.23982i
$208$	2.00529	−	2.99647i	0.139042	−	0.207768i
$209$		−	8.48603i		−	0.586991i
$210$	−2.34833	+	3.93417i	−0.162050	+	0.271483i
$211$	−8.87901	−	15.3789i	−0.611256	−	1.05873i	−0.991029	−	0.133647i	$-0.957331\pi$
$211$	−8.87901	−	15.3789i	−0.611256	−	1.05873i	0.379773	−	0.925080i	$-0.376002\pi$
$212$	2.45429			0.168561
$213$	13.9672	+	20.3128i	0.957019	+	1.39181i
$214$	−5.13206	+	19.1531i	−0.350820	+	1.30928i
$215$	2.49277	+	2.49277i	0.170006	+	0.170006i
$216$	5.05177	−	1.21639i	0.343730	−	0.0827649i
$217$	2.95539	+	2.09610i	0.200625	+	0.142293i
$218$	−7.41604	−	12.8450i	−0.502277	−	0.869970i
$219$	−4.25727	−	6.19142i	−0.287680	−	0.418377i
$220$	2.35545	+	1.35992i	0.158804	+	0.0916856i
$221$	3.80882	+	7.73754i	0.256209	+	0.520483i
$222$	1.22491	−	1.43483i	0.0822103	−	0.0962993i
$223$	0.888970	−	3.31768i	0.0595299	−	0.222168i	−0.929752	−	0.368186i	$-0.879979\pi$
$223$	0.888970	−	3.31768i	0.0595299	−	0.222168i	0.989282	+	0.146018i	$0.0466456\pi$
$224$	−1.10364	−	2.40457i	−0.0737402	−	0.160662i
$225$	−11.8525	+	1.88266i	−0.790167	+	0.125511i
$226$	1.08018	−	4.03129i	0.0718526	−	0.268158i
$227$	16.8946	+	4.52689i	1.12133	+	0.300460i	0.771423	−	0.636323i	$-0.219545\pi$
$227$	16.8946	+	4.52689i	1.12133	+	0.300460i	0.349910	+	0.936783i	$0.386212\pi$
$228$	5.38636	−	0.425122i	0.356720	−	0.0281544i
$229$	4.89806	+	1.31243i	0.323673	+	0.0867279i	0.416997	−	0.908908i	$-0.363083\pi$
$229$	4.89806	+	1.31243i	0.323673	+	0.0867279i	−0.0933240	+	0.995636i	$0.529749\pi$
$230$	5.21298	+	3.00971i	0.343733	+	0.198455i
$231$	3.05102	+	12.0870i	0.200742	+	0.795266i
$232$	−2.77809	−	0.744387i	−0.182390	−	0.0488714i
$233$	−12.0628	−	20.8933i	−0.790258	−	1.36877i	−0.925807	−	0.377996i	$-0.876613\pi$
$233$	−12.0628	−	20.8933i	−0.790258	−	1.36877i	0.135549	−	0.990771i	$-0.456720\pi$
$234$	−8.31441	−	6.91886i	−0.543530	−	0.452300i
$235$	−0.371241	+	0.643009i	−0.0242171	+	0.0419453i
$236$	−2.81769	−	10.5158i	−0.183416	−	0.684517i
$237$	−15.0637	−	12.8598i	−0.978495	−	0.835337i
$238$	6.30090	+	0.589620i	0.408426	+	0.0382194i
$239$	13.7771	−	13.7771i	0.891170	−	0.891170i	−0.103464	−	0.994633i	$-0.532993\pi$
$239$	13.7771	−	13.7771i	0.891170	−	0.891170i	0.994633	+	0.103464i	$0.0329925\pi$
$240$	−0.745183	+	1.56320i	−0.0481013	+	0.100904i
$241$	−9.13026	−	2.44645i	−0.588132	−	0.157589i	−0.0475326	−	0.998870i	$-0.515136\pi$
$241$	−9.13026	−	2.44645i	−0.588132	−	0.157589i	−0.540599	+	0.841280i	$0.681802\pi$
$242$	−3.47713	+	0.931695i	−0.223519	+	0.0598916i
$243$	−2.05190	−	15.4528i	−0.131629	−	0.991299i
$244$	−1.56494	+	0.903521i	−0.100185	+	0.0578420i
$245$	3.03418	−	6.30681i	0.193847	−	0.402927i
$246$	−0.243228	−	0.686370i	−0.0155077	−	0.0437613i
$247$	−7.40989	−	8.46161i	−0.471480	−	0.538400i
$248$	1.18599	+	0.684731i	0.0753104	+	0.0434805i
$249$	7.90940	−	16.5919i	0.501238	−	1.05147i
$250$	4.49936	−	7.79312i	0.284564	−	0.492880i
$251$	11.7459	−	20.3444i	0.741393	−	1.28413i	−0.210468	−	0.977601i	$-0.567499\pi$
$251$	11.7459	−	20.3444i	0.741393	−	1.28413i	0.951861	−	0.306529i	$-0.0991678\pi$
$252$	−7.51916	+	2.54210i	−0.473662	+	0.160137i
$253$	15.8198	−	4.23890i	0.994581	−	0.266497i
$254$	−1.93119	−	1.93119i	−0.121173	−	0.121173i
$255$	−2.34691	−	3.41315i	−0.146969	−	0.213740i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.35777	+	2.35172i	−0.0846952	+	0.146696i	−0.905261	−	0.424855i	$-0.860325\pi$
$257$	−1.35777	+	2.35172i	−0.0846952	+	0.146696i	0.820566	+	0.571552i	$0.193658\pi$
$258$	0.480515	+	6.08820i	0.0299156	+	0.379035i
$259$	−1.66714	+	2.35059i	−0.103591	+	0.146058i
$260$	3.53613	−	0.700739i	0.219301	−	0.0434580i
$261$	−3.08851	+	8.05656i	−0.191174	+	0.498688i
$262$	10.3074	+	10.3074i	0.636793	+	0.636793i
$263$		−	26.8299i		−	1.65440i	−0.561904	−	0.827202i	$-0.689931\pi$
$263$		−	26.8299i		−	1.65440i	0.561904	−	0.827202i	$-0.310069\pi$
$264$	1.57380	+	4.44114i	0.0968609	+	0.273334i
$265$	1.73512	+	1.73512i	0.106588	+	0.106588i
$266$	−8.13650	+	1.38407i	−0.498881	+	0.0848630i
$267$	−14.5826	+	10.0271i	−0.892439	+	0.613648i
$268$	−0.116226	−	0.0311427i	−0.00709964	−	0.00190234i
$269$	12.4157	−	7.16823i	0.757001	−	0.437055i	−0.0712170	−	0.997461i	$-0.522688\pi$
$269$	12.4157	−	7.16823i	0.757001	−	0.437055i	0.828218	+	0.560406i	$0.189355\pi$
$270$	4.43145	+	2.71153i	0.269689	+	0.165018i
$271$	4.03836	+	15.0714i	0.245313	+	0.915521i	0.973226	+	0.229851i	$0.0738239\pi$
$271$	4.03836	+	15.0714i	0.245313	+	0.915521i	−0.727913	+	0.685670i	$0.759509\pi$
$272$	2.39192			0.145031
$273$	13.5964	+	9.38811i	0.822894	+	0.568194i
$274$	8.85446			0.534917
$275$	−2.81655	−	10.5115i	−0.169845	−	0.633868i
$276$	3.48308	+	9.82896i	0.209657	+	0.591634i
$277$	5.88612	−	3.39835i	0.353663	−	0.204187i	−0.312635	−	0.949873i	$-0.601212\pi$
$277$	5.88612	−	3.39835i	0.353663	−	0.204187i	0.666297	+	0.745686i	$0.267878\pi$
$278$	21.7443	+	5.82637i	1.30414	+	0.349442i
$279$	2.41337	−	3.32483i	0.144485	−	0.199052i
$280$	0.919729	−	2.48023i	0.0549643	−	0.148222i
$281$	−13.1459	−	13.1459i	−0.784217	−	0.784217i	0.196322	−	0.980539i	$-0.437100\pi$
$281$	−13.1459	−	13.1459i	−0.784217	−	0.784217i	−0.980539	+	0.196322i	$0.937100\pi$
$282$	−1.21238	+	0.429630i	−0.0721962	+	0.0255841i
$283$			32.0628i			1.90594i	0.303070	+	0.952968i	$0.401988\pi$
$283$			32.0628i			1.90594i	−0.303070	+	0.952968i	$0.598012\pi$
$284$	−10.0639	−	10.0639i	−0.597182	−	0.597182i
$285$	4.10858	+	3.50748i	0.243371	+	0.207765i
$286$	5.45505	−	8.15138i	0.322564	−	0.482001i
$287$	0.463995	+	1.01093i	0.0273888	+	0.0596736i
$288$	−2.74009	+	1.22143i	−0.161462	+	0.0719734i
$289$	5.63936	−	9.76766i	0.331727	−	0.574568i
$290$	−1.43778	−	2.49031i	−0.0844294	−	0.146236i
$291$	−7.00175	+	4.81446i	−0.410450	+	0.282229i
$292$	3.06752	+	3.06752i	0.179513	+	0.179513i
$293$	29.4602	−	7.89384i	1.72108	−	0.461163i	0.742985	−	0.669308i	$-0.233409\pi$
$293$	29.4602	−	7.89384i	1.72108	−	0.461163i	0.978098	+	0.208145i	$0.0667427\pi$
$294$	11.0915	−	4.89674i	0.646871	−	0.285584i
$295$	5.44236	−	9.42644i	0.316866	−	0.548829i
$296$	−0.544604	+	0.943282i	−0.0316545	+	0.0548272i
$297$	13.7425	−	3.30899i	0.797420	−	0.192007i
$298$	19.4345	+	11.2205i	1.12581	+	0.649986i
$299$	12.0729	−	18.0403i	0.698194	−	1.04330i
$300$	6.53089	−	2.31435i	0.377061	−	0.133619i
$301$	−1.56442	−	9.19670i	−0.0901717	−	0.530089i
$302$	−10.7335	+	6.19697i	−0.617641	+	0.356595i
$303$	7.24221	−	2.56642i	0.416054	−	0.147437i
$304$	−3.01319	+	0.807382i	−0.172818	+	0.0463065i
$305$	−1.74515	−	0.467611i	−0.0999270	−	0.0267754i
$306$	0.746894	−	7.13678i	0.0426971	−	0.407983i
$307$	−19.5251	+	19.5251i	−1.11436	+	1.11436i	−0.121801	+	0.992554i	$0.538867\pi$
$307$	−19.5251	+	19.5251i	−1.11436	+	1.11436i	−0.992554	+	0.121801i	$0.961133\pi$
$308$	−3.00227	−	6.54124i	−0.171070	−	0.372722i
$309$	−8.18170	+	9.58386i	−0.465441	+	0.545207i
$310$	0.354378	+	1.32256i	0.0201273	+	0.0751162i
$311$	0.849686	−	1.47170i	0.0481813	−	0.0834525i	−0.840929	−	0.541146i	$-0.817991\pi$
$311$	0.849686	−	1.47170i	0.0481813	−	0.0834525i	0.889110	+	0.457693i	$0.151324\pi$
$312$	5.44722	+	3.05414i	0.308388	+	0.172907i
$313$	13.0269	+	22.5633i	0.736325	+	1.27535i	0.954140	+	0.299362i	$0.0967737\pi$
$313$	13.0269	+	22.5633i	0.736325	+	1.27535i	−0.217815	+	0.975990i	$0.569893\pi$
$314$	5.52795	+	1.48121i	0.311960	+	0.0835895i
$315$	−7.11308	−	3.51867i	−0.400777	−	0.198255i
$316$	9.90318	+	5.71760i	0.557097	+	0.321640i
$317$	7.45184	+	1.99671i	0.418537	+	0.112147i	0.461940	−	0.886911i	$-0.347153\pi$
$317$	7.45184	+	1.99671i	0.418537	+	0.112147i	−0.0434034	+	0.999058i	$0.513820\pi$
$318$	0.334469	+	4.23777i	0.0187561	+	0.237642i
$319$	−7.55732	−	2.02498i	−0.423129	−	0.113377i
$320$	0.258772	−	0.965749i	0.0144658	−	0.0539870i
$321$	−33.7707	−	6.25126i	−1.88490	−	0.348911i
$322$	−6.64451	−	14.4768i	−0.370284	−	0.806761i
$323$	1.93119	−	7.20731i	0.107454	−	0.401025i
$324$	2.78877	+	8.55703i	0.154932	+	0.475391i
$325$	−11.9870	−	8.02189i	−0.664917	−	0.444975i
$326$	20.1946	+	11.6593i	1.11847	+	0.645751i
$327$	21.1685	−	14.5556i	1.17062	−	0.804928i
$328$	0.210211	+	0.364096i	0.0116070	+	0.0201038i
$329$	1.78568	−	0.819585i	0.0984478	−	0.0451852i
$330$	−2.02714	+	4.25243i	−0.111591	+	0.234089i
$331$	−24.1387	−	24.1387i	−1.32678	−	1.32678i	−0.908160	−	0.418623i	$-0.862513\pi$
$331$	−24.1387	−	24.1387i	−1.32678	−	1.32678i	−0.418623	−	0.908160i	$-0.637487\pi$
$332$	−2.74661	+	10.2505i	−0.150740	+	0.562569i
$333$	2.64442	+	1.91949i	0.144913	+	0.105187i
$334$	7.41185			0.405558
$335$	−0.0601520	−	0.104186i	−0.00328646	−	0.00569231i
$336$	4.00153	−	2.23333i	0.218301	−	0.121838i
$337$			10.9669i			0.597406i	0.954346	+	0.298703i	$0.0965539\pi$
$337$			10.9669i			0.597406i	−0.954346	+	0.298703i	$0.903446\pi$
$338$	−1.67832	−	12.8912i	−0.0912886	−	0.701189i
$339$	7.10797	+	1.31575i	0.386052	+	0.0714616i
$340$	1.69103	+	1.69103i	0.0917091	+	0.0917091i
$341$	3.22628	+	1.86270i	0.174713	+	0.100871i
$342$	1.46810	+	9.24258i	0.0793857	+	0.499782i
$343$	−16.2041	+	8.96805i	−0.874941	+	0.484229i
$344$	−0.912585	−	3.40581i	−0.0492033	−	0.183629i
$345$	−4.48639	+	9.41131i	−0.241539	+	0.506688i
$346$	−4.57401	−	17.0704i	−0.245900	−	0.917713i
$347$	−22.4989	+	12.9898i	−1.20781	+	0.697327i	−0.962279	−	0.272063i	$-0.912294\pi$
$347$	−22.4989	+	12.9898i	−1.20781	+	0.697327i	−0.245526	+	0.969390i	$0.578961\pi$
$348$	0.906722	−	4.89832i	0.0486054	−	0.262577i
$349$	−22.9606	−	6.15227i	−1.22905	−	0.329324i	−0.414842	−	0.909893i	$-0.636163\pi$
$349$	−22.9606	−	6.15227i	−1.22905	−	0.329324i	−0.814210	+	0.580570i	$0.802830\pi$
$350$	−9.61918	+	4.41497i	−0.514167	+	0.235990i
$351$	10.8136	−	15.2992i	0.577187	−	0.816612i
$352$	−1.36017	−	2.35588i	−0.0724971	−	0.125569i
$353$	13.7872	−	13.7872i	0.733819	−	0.733819i	−0.237555	−	0.971374i	$-0.576346\pi$
$353$	13.7872	−	13.7872i	0.733819	−	0.733819i	0.971374	+	0.237555i	$0.0763460\pi$
$354$	17.7734	−	6.29833i	0.944644	−	0.334752i
$355$		−	14.2299i		−	0.755244i
$356$	7.22489	−	7.22489i	0.382918	−	0.382918i
$357$	−0.159403	+	10.9600i	−0.00843649	+	0.580064i
$358$	2.50274	+	9.34034i	0.132274	+	0.493652i
$359$	−3.89480	+	14.5356i	−0.205560	+	0.767160i	0.783718	+	0.621116i	$0.213321\pi$
$359$	−3.89480	+	14.5356i	−0.205560	+	0.767160i	−0.989278	+	0.146043i	$0.953346\pi$
$360$	−2.80071	−	1.07366i	−0.147610	−	0.0565869i
$361$		−	9.26882i		−	0.487832i
$362$	−4.85710	+	1.30146i	−0.255283	+	0.0684030i
$363$	−2.08260	−	5.87693i	−0.109308	−	0.308459i
$364$	−8.70535	−	3.90087i	−0.456285	−	0.204461i
$365$			4.33733i			0.227026i
$366$	−1.77336	−	2.57903i	−0.0926952	−	0.134808i
$367$	−23.8923			−1.24717			−0.623585	−	0.781756i	$-0.714324\pi$
$367$	−23.8923			−1.24717			−0.623585	+	0.781756i	$0.714324\pi$
$368$	−3.01026	−	5.21393i	−0.156921	−	0.271795i
$369$	1.15199	−	0.513516i	0.0599704	−	0.0267326i
$370$	−1.05190	+	0.281856i	−0.0546858	+	0.0146530i
$371$	−1.08893	−	6.40147i	−0.0565347	−	0.332348i
$372$	−1.02069	+	2.14114i	−0.0529201	+	0.111013i
$373$	18.6649			0.966433			0.483217	−	0.875501i	$-0.339468\pi$
$373$	18.6649			0.966433			0.483217	+	0.875501i	$0.339468\pi$
$374$	6.50682			0.336459
$375$	14.0694	+	6.70692i	0.726541	+	0.346344i
$376$	0.643127	−	0.371309i	0.0331667	−	0.0191488i
$377$	−9.30376	+	4.57980i	−0.479168	+	0.235872i
$378$	−5.41410	−	12.6368i	−0.278471	−	0.649965i
$379$	−6.24281	+	23.2985i	−0.320672	+	1.19676i	0.597921	+	0.801555i	$0.295994\pi$
$379$	−6.24281	+	23.2985i	−0.320672	+	1.19676i	−0.918592	+	0.395207i	$0.870673\pi$
$380$	−2.70106	−	1.55946i	−0.138561	−	0.0799984i
$381$	3.07136	−	3.59773i	0.157351	−	0.184317i
$382$	−22.2866	+	5.97168i	−1.14028	+	0.305538i
$383$	−24.4270	+	24.4270i	−1.24816	+	1.24816i	−0.291630	+	0.956531i	$0.594198\pi$
$383$	−24.4270	+	24.4270i	−1.24816	+	1.24816i	−0.956531	+	0.291630i	$0.905802\pi$
$384$	1.42721	−	0.981362i	0.0728320	−	0.0500799i
$385$	2.50197	−	6.74705i	0.127512	−	0.343861i
$386$	0.631891	+	0.364823i	0.0321624	+	0.0185690i
$387$	−10.4469	+	1.65939i	−0.531046	+	0.0843517i
$388$	3.46900	−	3.46900i	0.176112	−	0.176112i
$389$	−2.31745	+	4.01394i	−0.117499	+	0.203515i	−0.918776	−	0.394779i	$-0.870821\pi$
$389$	−2.31745	+	4.01394i	−0.117499	+	0.203515i	0.801277	+	0.598294i	$0.204154\pi$
$390$	1.69185	+	6.01027i	0.0856704	+	0.304342i
$391$	14.4006			0.728271
$392$	−5.78214	+	3.94549i	−0.292042	+	0.199277i
$393$	−16.3929	+	19.2023i	−0.826912	+	0.968626i
$394$			13.2964i			0.669864i
$395$	2.95911	+	11.0435i	0.148889	+	0.555661i
$396$	−7.45396	+	3.32269i	−0.374576	+	0.166972i
$397$	18.3441	−	18.3441i	0.920664	−	0.920664i	−0.0764126	−	0.997076i	$-0.524347\pi$
$397$	18.3441	−	18.3441i	0.920664	−	0.920664i	0.997076	+	0.0764126i	$0.0243466\pi$
$398$	6.18318	+	6.18318i	0.309935	+	0.309935i
$399$	−3.49869	−	13.8605i	−0.175154	−	0.693894i
$400$	−3.46442	+	2.00018i	−0.173221	+	0.100009i
$401$	5.37680	−	1.44071i	0.268505	−	0.0719456i	−0.122055	−	0.992523i	$-0.538948\pi$
$401$	5.37680	−	1.44071i	0.268505	−	0.0719456i	0.390559	+	0.920578i	$0.372282\pi$
$402$	0.0379343	−	0.204930i	0.00189199	−	0.0102210i
$403$	4.84348	−	0.959812i	0.241271	−	0.0478116i
$404$	−3.84175	+	2.21803i	−0.191134	+	0.110351i
$405$	−4.07803	+	8.02122i	−0.202639	+	0.398578i
$406$	−0.708970	+	7.57632i	−0.0351856	+	0.376006i
$407$	−1.48150	+	2.56604i	−0.0734354	+	0.127194i
$408$	0.325969	+	4.13008i	0.0161379	+	0.204470i
$409$	10.2588	−	38.2863i	0.507264	−	1.89314i	0.0612229	−	0.998124i	$-0.480500\pi$
$409$	10.2588	−	38.2863i	0.507264	−	1.89314i	0.446041	−	0.895012i	$-0.352833\pi$
$410$	−0.108793	+	0.406022i	−0.00537291	+	0.0200520i
$411$	1.20668	+	15.2888i	0.0595212	+	0.754142i
$412$	3.63766	−	6.30061i	0.179215	−	0.310409i
$413$	−26.1779	+	12.0150i	−1.28813	+	0.591221i
$414$	−16.4968	+	7.35365i	−0.810774	+	0.361412i
$415$	−9.18866	+	5.30508i	−0.451054	+	0.260416i
$416$	−3.41337	−	1.16142i	−0.167354	−	0.0569432i
$417$	−7.09698	+	38.3395i	−0.347541	+	1.87749i
$418$	−8.19688	+	2.19635i	−0.400922	+	0.107427i
$419$	0.209157	−	0.120757i	0.0102180	−	0.00589935i	−0.494882	−	0.868960i	$-0.664789\pi$
$419$	0.209157	−	0.120757i	0.0102180	−	0.00589935i	0.505100	+	0.863061i	$0.331456\pi$
$420$	4.40790	+	1.25007i	0.215084	+	0.0609974i
$421$	6.40219	+	6.40219i	0.312024	+	0.312024i	0.845693	−	0.533669i	$-0.179187\pi$
$421$	6.40219	+	6.40219i	0.312024	+	0.312024i	−0.533669	+	0.845693i	$0.679187\pi$
$422$	−12.5568	+	12.5568i	−0.611256	+	0.611256i
$423$	−0.907057	−	2.03485i	−0.0441026	−	0.0989376i
$424$	−0.635216	−	2.37066i	−0.0308488	−	0.115129i
$425$		−	9.56855i		−	0.464143i
$426$	16.0056	−	18.7486i	0.775476	−	0.908375i
$427$	3.05099	+	3.68094i	0.147648	+	0.178133i
$428$	19.8288			0.958459
$429$	14.8183	+	8.30827i	0.715432	+	0.401127i
$430$	1.76266	−	3.05301i	0.0850028	−	0.147229i
$431$	−2.17225	+	2.17225i	−0.104633	+	0.104633i	−0.757485	−	0.652852i	$-0.773572\pi$
$431$	−2.17225	+	2.17225i	−0.104633	+	0.104633i	0.652852	+	0.757485i	$0.273572\pi$
$432$	−2.48244	−	4.56481i	−0.119436	−	0.219625i
$433$	17.7654	+	10.2569i	0.853750	+	0.492913i	0.861914	−	0.507054i	$-0.169265\pi$
$433$	17.7654	+	10.2569i	0.853750	+	0.492913i	−0.00816416	+	0.999967i	$0.502599\pi$
$434$	1.25976	−	3.39720i	0.0604706	−	0.163071i
$435$	4.10403	−	2.82197i	0.196773	−	0.135303i
$436$	−10.4879	+	10.4879i	−0.502277	+	0.502277i
$437$	−18.1410	+	4.86087i	−0.867802	+	0.232527i
$438$	−4.87859	+	5.71467i	−0.233108	+	0.273057i
$439$	17.5660	+	10.1417i	0.838378	+	0.484038i	0.856712	−	0.515794i	$-0.172503\pi$
$439$	17.5660	+	10.1417i	0.838378	+	0.484038i	−0.0183347	+	0.999832i	$0.505836\pi$
$440$	0.703945	−	2.62716i	0.0335593	−	0.125245i
$441$	9.96666	+	18.4842i	0.474603	+	0.880200i
$442$	6.48809	−	5.68166i	0.308607	−	0.270249i
$443$	26.0451	−	15.0372i	1.23744	−	0.714437i	0.268870	−	0.963176i	$-0.413350\pi$
$443$	26.0451	−	15.0372i	1.23744	−	0.714437i	0.968570	+	0.248740i	$0.0800164\pi$
$444$	−1.70297	−	0.811808i	−0.0808192	−	0.0385267i
$445$	10.2157			0.484269
$446$	−3.43472			−0.162639
$447$	−16.7257	+	35.0863i	−0.791099	+	1.65952i
$448$	−2.03700	+	1.68839i	−0.0962390	+	0.0797687i
$449$	25.8278	−	6.92055i	1.21889	−	0.326601i	0.408646	−	0.912693i	$-0.366001\pi$
$449$	25.8278	−	6.92055i	1.21889	−	0.326601i	0.810244	+	0.586092i	$0.199334\pi$
$450$	4.88617	+	10.9614i	0.230336	+	0.516724i
$451$	0.571843	+	0.990462i	0.0269270	+	0.0466390i
$452$	−4.17350			−0.196305
$453$	−12.1629	−	17.6887i	−0.571465	−	0.831090i
$454$		−	17.4906i		−	0.820873i
$455$	−3.39666	−	8.91232i	−0.159238	−	0.417816i
$456$	−1.80473	−	5.09279i	−0.0845141	−	0.238492i
$457$	2.58511	−	0.692679i	0.120926	−	0.0324021i	−0.197848	−	0.980233i	$-0.563395\pi$
$457$	2.58511	−	0.692679i	0.120926	−	0.0324021i	0.318775	+	0.947831i	$0.396729\pi$
$458$		−	5.07085i		−	0.236945i
$459$	12.4247	+	0.317052i	0.579937	+	0.0147987i
$460$	1.55794	−	5.81432i	0.0726394	−	0.271094i
$461$	−0.317785	−	1.18599i	−0.0148007	−	0.0552371i	0.958131	−	0.286332i	$-0.0924360\pi$
$461$	−0.317785	−	1.18599i	−0.0148007	−	0.0552371i	−0.972931	+	0.231095i	$0.925769\pi$
$462$	10.8855	−	6.07540i	0.506439	−	0.282653i
$463$	0.583009	−	0.583009i	0.0270947	−	0.0270947i	−0.693430	−	0.720524i	$-0.743901\pi$
$463$	0.583009	−	0.583009i	0.0270947	−	0.0270947i	0.720524	+	0.693430i	$0.243901\pi$
$464$			2.87609i			0.133519i
$465$	−2.23534	+	0.792135i	−0.103661	+	0.0367344i
$466$	−17.0593	+	17.0593i	−0.790258	+	0.790258i
$467$	12.3655	+	21.4176i	0.572206	+	0.991089i	0.996339	+	0.0854895i	$0.0272454\pi$
$467$	12.3655	+	21.4176i	0.572206	+	0.991089i	−0.424133	+	0.905600i	$0.639421\pi$
$468$	−4.53118	+	9.82183i	−0.209454	+	0.454014i
$469$	−0.0296610	+	0.316968i	−0.00136962	+	0.0146362i
$470$	0.717183	+	0.192169i	0.0330812	+	0.00886408i
$471$	−1.80423	+	9.74687i	−0.0831346	+	0.449112i
$472$	−9.42817	+	5.44335i	−0.433967	+	0.250551i
$473$	−2.48253	−	9.26494i	−0.114147	−	0.426003i
$474$	−8.52288	+	17.8788i	−0.391469	+	0.821202i
$475$	3.22982	+	12.0539i	0.148194	+	0.553069i
$476$	−1.06126	−	6.23880i	−0.0486429	−	0.285955i
$477$	−7.27170	+	1.15504i	−0.332948	+	0.0528857i
$478$	−16.8735	−	9.74191i	−0.771776	−	0.445585i
$479$	−24.5744	−	24.5744i	−1.12283	−	1.12283i	−0.991314	−	0.131517i	$-0.958015\pi$
$479$	−24.5744	−	24.5744i	−1.12283	−	1.12283i	−0.131517	−	0.991314i	$-0.541985\pi$
$480$	1.70281	+	0.315204i	0.0777221	+	0.0143870i
$481$	0.763391	+	3.85229i	0.0348076	+	0.175649i
$482$			9.45234i			0.430542i
$483$	24.0913	−	13.4458i	1.09619	−	0.611807i
$484$	1.79990	+	3.11751i	0.0818135	+	0.141705i
$485$	4.90500			0.222725
$486$	−14.3952	+	5.98147i	−0.652980	+	0.271325i
$487$	5.30619	−	19.8030i	0.240447	−	0.897359i	−0.735171	−	0.677882i	$-0.762898\pi$
$487$	5.30619	−	19.8030i	0.240447	−	0.897359i	0.975618	−	0.219477i	$-0.0704352\pi$
$488$	1.27777	+	1.27777i	0.0578420	+	0.0578420i
$489$	−17.3799	+	36.4585i	−0.785944	+	1.64871i
$490$	−6.87721	−	1.29847i	−0.310681	−	0.0586589i
$491$	9.58871	+	16.6081i	0.432732	+	0.749514i	0.997107	−	0.0760042i	$-0.0242162\pi$
$491$	9.58871	+	16.6081i	0.432732	+	0.749514i	−0.564375	+	0.825518i	$0.690883\pi$
$492$	−0.600030	+	0.412586i	−0.0270514	+	0.0186008i
$493$	−5.95771	−	3.43969i	−0.268322	−	0.154916i
$494$	−6.25547	+	9.34743i	−0.281447	+	0.420561i
$495$	−7.61885	−	2.92071i	−0.342442	−	0.131276i
$496$	0.354443	−	1.32280i	0.0159150	−	0.0593954i
$497$	−21.7843	+	30.7147i	−0.977158	+	1.37774i
$498$	−18.0736	−	3.34559i	−0.809900	−	0.149920i
$499$	5.18555	−	19.3527i	0.232137	−	0.866348i	−0.747281	−	0.664508i	$-0.768641\pi$
$499$	5.18555	−	19.3527i	0.232137	−	0.866348i	0.979418	−	0.201840i	$-0.0646921\pi$
$500$	−8.69209	−	2.32904i	−0.388722	−	0.104158i
$501$	1.01008	+	12.7979i	0.0451272	+	0.571768i
$502$	−22.6913	−	6.08011i	−1.01276	−	0.271369i
$503$	28.1802	+	16.2699i	1.25649	+	0.725437i	0.972391	−	0.233357i	$-0.0749710\pi$
$503$	28.1802	+	16.2699i	1.25649	+	0.725437i	0.284103	+	0.958794i	$0.408304\pi$
$504$	4.40158	+	6.60501i	0.196062	+	0.294210i
$505$	−4.28413	−	1.14793i	−0.190641	−	0.0510821i
$506$	−8.18892	−	14.1836i	−0.364042	−	0.630539i
$507$	22.0303	−	4.65473i	0.978399	−	0.206724i
$508$	−1.36556	+	2.36521i	−0.0605867	+	0.104939i
$509$	−2.60341	−	9.71608i	−0.115394	−	0.430657i	0.883922	−	0.467635i	$-0.154894\pi$
$509$	−2.60341	−	9.71608i	−0.115394	−	0.430657i	−0.999316	+	0.0369773i	$0.988227\pi$
$510$	−2.68942	+	3.15033i	−0.119090	+	0.139499i
$511$	6.63994	−	9.36198i	0.293734	−	0.414150i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−15.7589	+	3.79451i	−0.695773	+	0.167532i
$514$	2.62301	+	0.702832i	0.115696	+	0.0310006i
$515$	7.02613	−	1.88265i	0.309608	−	0.0829593i
$516$	5.75639	−	2.03989i	0.253411	−	0.0898010i
$517$	1.74952	−	1.01009i	0.0769437	−	0.0444235i
$518$	2.70198	+	1.00196i	0.118718	+	0.0440236i
$519$	28.8519	−	10.2242i	1.26646	−	0.448793i
$520$	−1.59208	−	3.23427i	−0.0698173	−	0.141832i
$521$	9.70219	+	5.60156i	0.425060	+	0.245409i	0.697240	−	0.716838i	$-0.254411\pi$
$521$	9.70219	+	5.60156i	0.425060	+	0.245409i	−0.272180	+	0.962246i	$0.587744\pi$
$522$	8.58140	+	0.898080i	0.375598	+	0.0393079i
$523$	−12.8961	+	22.3367i	−0.563906	+	0.976714i	0.433245	+	0.901276i	$0.357369\pi$
$523$	−12.8961	+	22.3367i	−0.563906	+	0.976714i	−0.997151	+	0.0754375i	$0.975965\pi$
$524$	7.28842	−	12.6239i	0.318396	−	0.551479i
$525$	−8.93414	−	16.0076i	−0.389918	−	0.698628i
$526$	−25.9157	+	6.94410i	−1.12998	+	0.302777i
$527$	2.31623	+	2.31623i	0.100897	+	0.100897i
$528$	3.88249	−	2.66963i	0.168963	−	0.116181i
$529$	−6.62338	−	11.4720i	−0.287973	−	0.498784i
$530$	1.22692	−	2.12509i	0.0532939	−	0.0923078i
$531$	13.2974	+	29.8306i	0.577056	+	1.29454i
$532$	3.44279	+	7.50103i	0.149264	+	0.325211i
$533$	1.43506	+	0.488286i	0.0621592	+	0.0211500i
$534$	13.4597	+	11.4905i	0.582457	+	0.497241i
$535$	14.0185	+	14.0185i	0.606072	+	0.606072i
$536$			0.120326i			0.00519730i
$537$	−15.7867	+	5.59433i	−0.681247	+	0.241413i
$538$	−10.1374	−	10.1374i	−0.437055	−	0.437055i
$539$	−15.7293	+	10.7330i	−0.677510	+	0.462305i
$540$	1.47219	−	4.98225i	0.0633530	−	0.214402i
$541$	30.3041	+	8.11996i	1.30288	+	0.349104i	0.842537	−	0.538639i	$-0.181061\pi$
$541$	30.3041	+	8.11996i	1.30288	+	0.349104i	0.460339	+	0.887743i	$0.347728\pi$
$542$	13.5126	−	7.80152i	0.580417	−	0.335104i
$543$	−2.90912	−	8.20930i	−0.124842	−	0.352295i
$544$	−0.619074	−	2.31042i	−0.0265426	−	0.0990583i
$545$	−14.8294			−0.635220
$546$	5.54920	−	15.5630i	0.237484	−	0.666034i
$547$	−34.3963			−1.47068			−0.735340	−	0.677699i	$-0.762977\pi$
$547$	−34.3963			−1.47068			−0.735340	+	0.677699i	$0.762977\pi$
$548$	−2.29170	−	8.55275i	−0.0978967	−	0.365355i
$549$	4.21149	−	3.41350i	0.179742	−	0.145685i
$550$	−9.42437	+	5.44116i	−0.401856	+	0.232012i
$551$	8.66620	+	2.32210i	0.369193	+	0.0989249i
$552$	8.59256	−	5.90832i	0.365724	−	0.251475i
$553$	10.5192	−	28.3671i	0.447323	−	1.20629i
$554$	−4.80600	−	4.80600i	−0.204187	−	0.204187i
$555$	−0.630028	−	1.77789i	−0.0267432	−	0.0754671i
$556$		−	22.5114i		−	0.954695i
$557$	−3.99312	−	3.99312i	−0.169194	−	0.169194i	0.617431	−	0.786625i	$-0.288173\pi$
$557$	−3.99312	−	3.99312i	−0.169194	−	0.169194i	−0.786625	+	0.617431i	$0.788173\pi$
$558$	−3.83616	−	1.47061i	−0.162398	−	0.0622557i
$559$	−10.5654	−	7.07057i	−0.446869	−	0.299053i
$560$	−2.63376	−	0.246460i	−0.111297	−	0.0104148i
$561$	0.886745	+	11.2352i	0.0374384	+	0.474350i
$562$	−9.29554	+	16.1003i	−0.392109	+	0.679152i
$563$	−16.8095	−	29.1150i	−0.708438	−	1.22705i	−0.965436	−	0.260639i	$-0.916067\pi$
$563$	−16.8095	−	29.1150i	−0.708438	−	1.22705i	0.256998	−	0.966412i	$-0.417267\pi$
$564$	0.728778	+	1.05987i	0.0306871	+	0.0446287i
$565$	−2.95057	−	2.95057i	−0.124131	−	0.124131i
$566$	30.9703	−	8.29847i	1.30178	−	0.348811i
$567$	21.0818	−	11.0705i	0.885353	−	0.464919i
$568$	−7.11625	+	12.3257i	−0.298591	+	0.517175i
$569$	8.75998	−	15.1727i	0.367237	−	0.636074i	−0.621895	−	0.783100i	$-0.713637\pi$
$569$	8.75998	−	15.1727i	0.367237	−	0.636074i	0.989133	+	0.147027i	$0.0469704\pi$
$570$	2.32459	−	4.87639i	0.0973662	−	0.204249i
$571$	26.9908	+	15.5831i	1.12953	+	0.652134i	0.943816	−	0.330470i	$-0.107207\pi$
$571$	26.9908	+	15.5831i	1.12953	+	0.652134i	0.185712	+	0.982604i	$0.440541\pi$
$572$	−9.28550	−	3.15944i	−0.388246	−	0.132103i
$573$	−13.3484	−	37.6681i	−0.557638	−	1.57361i
$574$	0.856397	−	0.709834i	0.0357453	−	0.0296279i
$575$	−20.8576	+	12.0422i	−0.869823	+	0.502193i
$576$	1.88900	+	2.33060i	0.0787083	+	0.0971082i
$577$	27.1097	−	7.26401i	1.12859	−	0.302405i	0.354235	−	0.935156i	$-0.384741\pi$
$577$	27.1097	−	7.26401i	1.12859	−	0.302405i	0.774355	+	0.632752i	$0.218075\pi$
$578$	−10.8944	−	2.91915i	−0.453148	−	0.121421i
$579$	−0.543819	+	1.14079i	−0.0226003	+	0.0474097i
$580$	−2.03333	+	2.03333i	−0.0844294	+	0.0844294i
$581$	27.9548	+	2.61593i	1.15976	+	0.108527i
$582$	6.46260	+	5.51710i	0.267883	+	0.228691i
$583$	−1.72800	−	6.44898i	−0.0715664	−	0.267089i
$584$	2.16906	−	3.75693i	0.0897565	−	0.155463i
$585$	−10.1473	+	3.74037i	−0.419537	+	0.154645i
$586$	−15.2497	−	26.4133i	−0.629960	−	1.09112i
$587$	−31.1188	−	8.33825i	−1.28441	−	0.344156i	−0.448875	−	0.893595i	$-0.648175\pi$
$587$	−31.1188	−	8.33825i	−1.28441	−	0.344156i	−0.835534	+	0.549438i	$0.814842\pi$
$588$	−7.60059	−	9.44622i	−0.313443	−	0.389556i
$589$	−3.69967	−	2.13601i	−0.152442	−	0.0880127i
$590$	−10.5138	−	2.81717i	−0.432847	−	0.115981i
$591$	−22.9587	+	1.81203i	−0.944394	+	0.0745369i
$592$	1.05209	+	0.281908i	0.0432408	+	0.0115863i
$593$	−9.44763	+	35.2590i	−0.387967	+	1.44791i	0.445468	+	0.895298i	$0.353037\pi$
$593$	−9.44763	+	35.2590i	−0.387967	+	1.44791i	−0.833436	+	0.552617i	$0.813629\pi$
$594$	−6.75306	−	12.4178i	−0.277081	−	0.509509i
$595$	3.66040	−	5.16098i	0.150062	−	0.211580i
$596$	5.80816	−	21.6763i	0.237911	−	0.887898i
$597$	−9.83375	+	11.5190i	−0.402468	+	0.471442i
$598$	−20.5503	−	6.99235i	−0.840364	−	0.285939i
$599$	33.3012	+	19.2265i	1.36065	+	0.785572i	0.989711	−	0.143084i	$-0.0457019\pi$
$599$	33.3012	+	19.2265i	1.36065	+	0.785572i	0.370941	+	0.928656i	$0.379035\pi$
$600$	−3.92581	−	5.70936i	−0.160270	−	0.233084i
$601$	3.79158	+	6.56721i	0.154662	+	0.267882i	0.932936	−	0.360043i	$-0.117238\pi$
$601$	3.79158	+	6.56721i	0.154662	+	0.267882i	−0.778274	+	0.627925i	$0.783905\pi$
$602$	−8.47842	+	3.89139i	−0.345555	+	0.158601i
$603$	0.359018	+	0.0375727i	0.0146203	+	0.00153008i
$604$	8.76384	+	8.76384i	0.356595	+	0.356595i
$605$	−0.931525	+	3.47650i	−0.0378719	+	0.141340i
$606$	−4.35339	−	6.33120i	−0.176844	−	0.257187i
$607$	25.7165			1.04380			0.521900	−	0.853006i	$-0.325223\pi$
$607$	25.7165			1.04380			0.521900	+	0.853006i	$0.325223\pi$
$608$	1.55974	+	2.70155i	0.0632559	+	0.109562i
$609$	−13.1785	−	0.191669i	−0.534020	−	0.00776681i
$610$			1.80671i			0.0731516i
$611$	0.862492	−	2.53483i	0.0348927	−	0.102548i
$612$	−7.08691	+	1.12569i	−0.286471	+	0.0455033i
$613$	−12.3024	−	12.3024i	−0.496889	−	0.496889i	0.413579	−	0.910468i	$-0.364278\pi$
$613$	−12.3024	−	12.3024i	−0.496889	−	0.496889i	−0.910468	+	0.413579i	$0.864278\pi$
$614$	23.9133	+	13.8063i	0.965061	+	0.557178i
$615$	−0.715897	−	0.132519i	−0.0288677	−	0.00534367i
$616$	−5.54131	+	4.59297i	−0.223266	+	0.185056i
$617$	6.86571	+	25.6232i	0.276403	+	1.03155i	0.954895	+	0.296942i	$0.0959670\pi$
$617$	6.86571	+	25.6232i	0.276403	+	1.03155i	−0.678492	+	0.734607i	$0.737366\pi$
$618$	11.3749	+	5.42243i	0.457565	+	0.218122i
$619$	9.25074	+	34.5242i	0.371819	+	1.38765i	0.857938	+	0.513753i	$0.171745\pi$
$619$	9.25074	+	34.5242i	0.371819	+	1.38765i	−0.486119	+	0.873892i	$0.661588\pi$
$620$	1.18577	−	0.684606i	0.0476217	−	0.0274944i
$621$	−14.9456	−	27.4826i	−0.599746	−	1.10284i
$622$	−1.64147	−	0.439830i	−0.0658169	−	0.0176356i
$623$	−22.0501	−	15.6390i	−0.883420	−	0.626562i
$624$	1.54023	−	6.05208i	0.0616585	−	0.242277i
$625$	5.50238	+	9.53040i	0.220095	+	0.381216i
$626$	18.4228	−	18.4228i	0.736325	−	0.736325i
$627$	−4.90946	−	13.8541i	−0.196065	−	0.553279i
$628$		−	5.72295i		−	0.228371i
$629$	−1.84222	+	1.84222i	−0.0734543	+	0.0734543i
$630$	−1.55777	+	7.78141i	−0.0620632	+	0.310019i
$631$	−1.50154	−	5.60383i	−0.0597754	−	0.223085i	0.929576	−	0.368630i	$-0.120173\pi$
$631$	−1.50154	−	5.60383i	−0.0597754	−	0.223085i	−0.989352	+	0.145545i	$0.953506\pi$
$632$	2.95965	−	11.0456i	0.117729	−	0.439369i
$633$	−23.3929	−	19.9704i	−0.929783	−	0.793751i
$634$		−	7.71471i		−	0.306390i
$635$	−2.63757	+	0.706734i	−0.104669	+	0.0280459i
$636$	4.00680	−	1.41989i	0.158880	−	0.0563022i
$637$	−6.31213	+	24.4368i	−0.250096	+	0.968221i
$638$			7.82392i			0.309752i
$639$	34.5542	+	25.0816i	1.36694	+	0.992212i
$640$	−0.999817			−0.0395212
$641$	1.57968	+	2.73609i	0.0623937	+	0.108069i	0.895535	−	0.444991i	$-0.146793\pi$
$641$	1.57968	+	2.73609i	0.0623937	+	0.108069i	−0.833141	+	0.553060i	$0.813460\pi$
$642$	2.70225	+	34.2379i	0.106649	+	1.35126i
$643$	−6.54863	+	1.75470i	−0.258253	+	0.0691986i	−0.385622	−	0.922657i	$-0.626013\pi$
$643$	−6.54863	+	1.75470i	−0.258253	+	0.0691986i	0.127370	+	0.991855i	$0.459347\pi$
$644$	−12.2638	+	10.1650i	−0.483261	+	0.400556i
$645$	5.51179	+	2.62748i	0.217026	+	0.103457i
$646$	−7.46156			−0.293571
$647$	−24.5209			−0.964015			−0.482008	−	0.876167i	$-0.660092\pi$
$647$	−24.5209			−0.964015			−0.482008	+	0.876167i	$0.660092\pi$
$648$	7.54367	−	4.90847i	0.296343	−	0.192823i
$649$	−25.6477	+	14.8077i	−1.00676	+	0.581254i
$650$	−4.64610	+	13.6547i	−0.182235	+	0.535583i
$651$	6.03756	+	1.71224i	0.236631	+	0.0671081i
$652$	6.03532	−	22.5241i	0.236361	−	0.882112i
$653$	13.8663	+	8.00568i	0.542628	+	0.313287i	0.746144	−	0.665785i	$-0.231903\pi$
$653$	13.8663	+	8.00568i	0.542628	+	0.313287i	−0.203515	+	0.979072i	$0.565237\pi$
$654$	−19.5385	−	16.6799i	−0.764015	−	0.652236i
$655$	14.0776	−	3.77207i	0.550056	−	0.147387i
$656$	0.297283	−	0.297283i	0.0116070	−	0.0116070i
$657$	−10.5323	−	7.64498i	−0.410903	−	0.298259i
$658$	−1.25383	−	1.51271i	−0.0488793	−	0.0589717i
$659$	20.1690	+	11.6446i	0.785671	+	0.453608i	0.838436	−	0.544999i	$-0.183470\pi$
$659$	20.1690	+	11.6446i	0.785671	+	0.453608i	−0.0527651	+	0.998607i	$0.516803\pi$
$660$	4.63220	+	0.857461i	0.180308	+	0.0333766i
$661$	7.78413	−	7.78413i	0.302768	−	0.302768i	−0.539328	−	0.842096i	$-0.681322\pi$
$661$	7.78413	−	7.78413i	0.302768	−	0.302768i	0.842096	+	0.539328i	$0.181322\pi$
$662$	−17.0686	+	29.5638i	−0.663392	+	1.14903i
$663$	10.6946	+	10.4286i	0.415344	+	0.405012i
$664$	10.6121			0.411829
$665$	−2.86908	+	7.73704i	−0.111258	+	0.300029i
$666$	1.16965	−	3.05111i	0.0453232	−	0.118228i
$667$			17.3156i			0.670462i
$668$	−1.91833	−	7.15930i	−0.0742223	−	0.277002i
$669$	−0.468081	−	5.93066i	−0.0180971	−	0.229293i
$670$	−0.0850678	+	0.0850678i	−0.00328646	+	0.00328646i
$671$	3.47596	+	3.47596i	0.134188	+	0.134188i
$672$	−3.19290	−	3.28715i	−0.123169	−	0.126805i
$673$	18.9312	−	10.9299i	0.729745	−	0.421318i	−0.0885839	−	0.996069i	$-0.528234\pi$
$673$	18.9312	−	10.9299i	0.729745	−	0.421318i	0.818329	+	0.574750i	$0.194901\pi$
$674$	10.5932	−	2.83845i	0.408036	−	0.109333i
$675$	−18.2609	+	9.93066i	−0.702863	+	0.382231i
$676$	−12.0176	+	4.95762i	−0.462214	+	0.190678i
$677$	−23.4518	+	13.5399i	−0.901327	+	0.520381i	−0.877630	−	0.479338i	$-0.840877\pi$
$677$	−23.4518	+	13.5399i	−0.901327	+	0.520381i	−0.0236963	+	0.999719i	$0.507543\pi$
$678$	−0.568763	−	7.20631i	−0.0218432	−	0.276757i
$679$	−10.5873	−	7.50898i	−0.406302	−	0.288168i
$680$	1.19574	−	2.07108i	0.0458546	−	0.0794224i
$681$	30.2006	−	2.38360i	1.15729	−	0.0913399i
$682$	0.964202	−	3.59845i	0.0369212	−	0.137792i
$683$	−5.15907	+	19.2539i	−0.197406	+	0.736731i	0.794224	+	0.607625i	$0.207877\pi$
$683$	−5.15907	+	19.2539i	−0.197406	+	0.736731i	−0.991631	+	0.129106i	$0.958789\pi$
$684$	8.54768	−	3.81023i	0.326829	−	0.145688i
$685$	4.42642	−	7.66678i	0.169125	−	0.292933i
$686$	12.8564	+	13.3309i	0.490860	+	0.508976i
$687$	8.75573	−	0.691052i	0.334052	−	0.0263653i
$688$	−3.05357	+	1.76298i	−0.116416	+	0.0672129i
$689$	−7.35419	−	4.92156i	−0.280172	−	0.187496i
$690$	10.2518	+	1.89770i	0.390279	+	0.0722441i
$691$	27.7515	−	7.43599i	1.05572	−	0.282879i	0.311105	−	0.950376i	$-0.399301\pi$
$691$	27.7515	−	7.43599i	1.05572	−	0.282879i	0.744612	+	0.667497i	$0.232634\pi$
$692$	−15.3049	+	8.83631i	−0.581807	+	0.335906i
$693$	11.9738	+	17.9678i	0.454845	+	0.682541i
$694$	18.3703	+	18.3703i	0.697327	+	0.697327i
$695$	15.9150	−	15.9150i	0.603691	−	0.603691i
$696$	−4.96609	+	0.391952i	−0.188239	+	0.0148569i
$697$	0.260272	+	0.971349i	0.00985852	+	0.0367925i
$698$			23.7706i			0.899729i
$699$	−31.7808	−	27.1312i	−1.20206	−	1.02620i
$700$	6.75416	+	8.14873i	0.255283	+	0.307993i
$701$	−7.84194			−0.296186			−0.148093	−	0.988973i	$-0.547313\pi$
$701$	−7.84194			−0.296186			−0.148093	+	0.988973i	$0.547313\pi$
$702$	−17.5767	−	6.48539i	−0.663389	−	0.244775i
$703$	1.69888	−	2.94255i	0.0640746	−	0.110981i
$704$	−1.92357	+	1.92357i	−0.0724971	+	0.0724971i
$705$	−0.234077	+	1.26454i	−0.00881584	+	0.0476252i
$706$	−16.8858	−	9.74903i	−0.635506	−	0.366909i
$707$	7.48979	+	9.03625i	0.281683	+	0.339843i
$708$	−10.6838	−	15.5376i	−0.401522	−	0.583940i
$709$	−23.5819	+	23.5819i	−0.885637	+	0.885637i	−0.994100	−	0.108464i	$-0.965407\pi$
$709$	−23.5819	+	23.5819i	−0.885637	+	0.885637i	0.108464	+	0.994100i	$0.465407\pi$
$710$	−13.7450	+	3.68297i	−0.515841	+	0.138219i
$711$	−32.0325	−	12.2798i	−1.20131	−	0.460528i
$712$	−8.84864	−	5.10877i	−0.331617	−	0.191459i
$713$	2.13393	−	7.96395i	0.0799164	−	0.298252i
$714$	10.6278	−	2.68268i	0.397735	−	0.100397i
$715$	−4.33098	−	8.79830i	−0.161970	−	0.329038i
$716$	8.37432	−	4.83492i	0.312963	−	0.180689i
$717$	14.5217	−	30.4628i	0.542322	−	1.13765i
$718$	15.0484			0.561600
$719$	38.2189			1.42532			0.712662	−	0.701507i	$-0.247489\pi$
$719$	38.2189			1.42532			0.712662	+	0.701507i	$0.247489\pi$
$720$	−0.312200	+	2.98316i	−0.0116350	+	0.111176i
$721$	−18.0478	−	6.69255i	−0.672133	−	0.249243i
$722$	−8.95299	+	2.39895i	−0.333196	+	0.0892795i
$723$	−16.3212	+	1.28816i	−0.606991	+	0.0479072i
$724$	2.51422	+	4.35475i	0.0934402	+	0.161843i
$725$	11.5054			0.427300
$726$	−5.13766	+	3.53270i	−0.190677	+	0.131111i
$727$		−	39.4219i		−	1.46208i	−0.682337	−	0.731038i	$-0.739036\pi$
$727$		−	39.4219i		−	1.46208i	0.682337	−	0.731038i	$-0.260964\pi$
$728$	−1.51484	+	9.41835i	−0.0561438	+	0.349067i
$729$	−12.2899	−	24.0408i	−0.455180	−	0.890400i
$730$	4.18954	−	1.12258i	0.155062	−	0.0415487i
$731$		−	8.43381i		−	0.311936i
$732$	−2.03217	+	2.38044i	−0.0751112	+	0.0879836i
$733$	−11.2625	+	42.0320i	−0.415988	+	1.55249i	0.366860	+	0.930276i	$0.380433\pi$
$733$	−11.2625	+	42.0320i	−0.415988	+	1.55249i	−0.782848	+	0.622213i	$0.786234\pi$
$734$	6.18379	+	23.0782i	0.228248	+	0.851833i
$735$	1.30482	−	12.0517i	0.0481290	−	0.444534i
$736$	−4.25716	+	4.25716i	−0.156921	+	0.156921i
$737$			0.327327i			0.0120572i
$738$	−0.794176	−	0.979834i	−0.0292340	−	0.0360682i
$739$	−2.59644	+	2.59644i	−0.0955117	+	0.0955117i	−0.753248	−	0.657736i	$-0.771514\pi$
$739$	−2.59644	+	2.59644i	−0.0955117	+	0.0955117i	0.657736	+	0.753248i	$0.271514\pi$
$740$	0.544504	+	0.943109i	0.0200164	+	0.0346694i
$741$	−16.9925	−	9.52734i	−0.624236	−	0.349996i
$742$	−5.90151	+	2.70865i	−0.216651	+	0.0994378i
$743$	−17.5705	−	4.70799i	−0.644598	−	0.172720i	−0.0783128	−	0.996929i	$-0.524953\pi$
$743$	−17.5705	−	4.70799i	−0.644598	−	0.172720i	−0.566285	+	0.824209i	$0.691620\pi$
$744$	2.33235	+	0.431740i	0.0855083	+	0.0158283i
$745$	19.4309	−	11.2184i	0.711894	−	0.411012i
$746$	−4.83084	−	18.0289i	−0.176870	−	0.660086i
$747$	3.31370	−	31.6634i	0.121242	−	1.15850i
$748$	−1.68409	−	6.28510i	−0.0615763	−	0.229806i
$749$	−8.79776	−	51.7190i	−0.321463	−	1.88977i
$750$	2.83696	−	15.3259i	0.103591	−	0.559622i
$751$	19.0177	+	10.9799i	0.693965	+	0.400661i	0.805096	−	0.593145i	$-0.202114\pi$
$751$	19.0177	+	10.9799i	0.693965	+	0.400661i	−0.111130	+	0.993806i	$0.535447\pi$
$752$	−0.525111	−	0.525111i	−0.0191488	−	0.0191488i
$753$	7.40606	−	40.0092i	0.269892	−	1.45802i
$754$	6.83174	+	7.80140i	0.248797	+	0.284110i
$755$			12.3917i			0.450979i
$756$	−10.8049	+	8.50025i	−0.392970	+	0.309151i
$757$	7.52013	+	13.0252i	0.273324	+	0.473411i	0.969711	−	0.244256i	$-0.0785436\pi$
$757$	7.52013	+	13.0252i	0.273324	+	0.473411i	−0.696387	+	0.717666i	$0.745210\pi$
$758$	24.1204			0.876091
$759$	23.3746	−	16.0726i	0.848445	−	0.583398i
$760$	−0.807234	+	3.01264i	−0.0292815	+	0.109280i
$761$	−16.1182	−	16.1182i	−0.584285	−	0.584285i	0.351793	−	0.936078i	$-0.385572\pi$
$761$	−16.1182	−	16.1182i	−0.584285	−	0.584285i	−0.936078	+	0.351793i	$0.885572\pi$
$762$	−4.27006	−	2.03555i	−0.154688	−	0.0737402i
$763$	32.0086	+	22.7020i	1.15879	+	0.821867i
$764$	11.5364	+	19.9816i	0.417373	+	0.722911i
$765$	−5.80612	−	4.21445i	−0.209921	−	0.152374i
$766$	29.9168	+	17.2725i	1.08094	+	0.624081i
$767$	−12.6440	+	37.1604i	−0.456549	+	1.34178i
$768$	−1.31731	−	1.12458i	−0.0475344	−	0.0405799i
$769$	−2.22659	+	8.30976i	−0.0802930	+	0.299658i	−0.994381	−	0.105858i	$-0.966241\pi$
$769$	−2.22659	+	8.30976i	−0.0802930	+	0.299658i	0.914088	+	0.405515i	$0.132908\pi$
$770$	−7.16470	−	0.670452i	−0.258198	−	0.0241614i
$771$	−0.856106	+	4.62488i	−0.0308319	+	0.166561i
$772$	0.188846	−	0.704783i	0.00679672	−	0.0253657i
$773$	25.4321	+	6.81450i	0.914728	+	0.245101i	0.685330	−	0.728232i	$-0.259658\pi$
$773$	25.4321	+	6.81450i	0.914728	+	0.245101i	0.229397	+	0.973333i	$0.426324\pi$
$774$	4.30671	+	9.66145i	0.154801	+	0.347274i
$775$	−5.29168	−	1.41790i	−0.190083	−	0.0509325i
$776$	−4.24863	−	2.45295i	−0.152517	−	0.0880558i
$777$	−1.36184	+	4.80201i	−0.0488558	+	0.172271i
$778$	4.47697	+	1.19960i	0.160507	+	0.0430077i
$779$	−0.655750	−	1.13579i	−0.0234947	−	0.0406940i
$780$	5.36759	−	3.18978i	0.192191	−	0.114212i
$781$	−19.3586	+	33.5300i	−0.692704	+	1.19980i
$782$	−3.72715	−	13.9099i	−0.133283	−	0.497418i
$783$	−0.381229	+	14.9397i	−0.0136240	+	0.533903i
$784$	5.30758	+	4.56395i	0.189556	+	0.162998i
$785$	4.04600	−	4.04600i	0.144408	−	0.144408i
$786$	22.7907	+	10.8644i	0.812919	+	0.387520i
$787$	8.36343	+	2.24097i	0.298124	+	0.0798821i	0.404781	−	0.914414i	$-0.367348\pi$
$787$	8.36343	+	2.24097i	0.298124	+	0.0798821i	−0.106657	+	0.994296i	$0.534015\pi$
$788$	12.8434	−	3.44137i	0.457526	−	0.122594i
$789$	−15.5220	−	43.8019i	−0.552599	−	1.55939i
$790$	9.90137	−	5.71656i	0.352275	−	0.203386i
$791$	1.85173	+	10.8857i	0.0658399	+	0.387050i
$792$	5.13870	+	6.34000i	0.182596	+	0.225282i
$793$	6.50113	+	0.430797i	0.230862	+	0.0152980i
$794$	−22.4668	−	12.9712i	−0.797318	−	0.460332i
$795$	3.83655	+	1.82889i	0.136068	+	0.0648641i
$796$	4.37217	−	7.57282i	0.154967	−	0.268412i
$797$	−10.9178	+	18.9102i	−0.386729	+	0.669834i	−0.992007	−	0.126180i	$-0.959728\pi$
$797$	−10.9178	+	18.9102i	−0.386729	+	0.669834i	0.605279	+	0.796014i	$0.293062\pi$
$798$	−12.4827	+	6.96684i	−0.441883	+	0.246624i
$799$	1.71576	−	0.459736i	0.0606992	−	0.0162643i
$800$	2.82869	+	2.82869i	0.100009	+	0.100009i
$801$	−18.0061	+	24.8065i	−0.636214	+	0.876494i
$802$	−2.78324	−	4.82071i	−0.0982795	−	0.170225i
$803$	5.90057	−	10.2201i	0.208227	−	0.360659i
$804$	−0.207765	+	0.0163980i	−0.00732730	+	0.000578312i
$805$	−15.8566	−	1.48382i	−0.558873	−	0.0522977i
$806$	−2.18069	−	4.43003i	−0.0768116	−	0.156041i
$807$	16.1226	−	18.8856i	0.567541	−	0.664804i
$808$	3.13677	+	3.13677i	0.110351	+	0.110351i
$809$		−	29.6857i		−	1.04369i	−0.853039	−	0.521847i	$-0.825243\pi$
$809$		−	29.6857i		−	1.04369i	0.853039	−	0.521847i	$-0.174757\pi$
$810$	8.80338	+	1.86303i	0.309319	+	0.0654601i
$811$	6.15669	+	6.15669i	0.216190	+	0.216190i	0.806891	−	0.590700i	$-0.201148\pi$
$811$	6.15669	+	6.15669i	0.216190	+	0.216190i	−0.590700	+	0.806891i	$0.701148\pi$
$812$	7.50166	−	1.27608i	0.263256	−	0.0447817i
$813$	15.3122	+	22.2688i	0.537023	+	0.781001i
$814$	2.86205	+	0.766883i	0.100315	+	0.0268792i
$815$	20.1909	−	11.6572i	0.707255	−	0.408334i
$816$	3.90499	−	1.38381i	0.136702	−	0.0484429i
$817$	2.84679	+	10.6244i	0.0995967	+	0.371700i
$818$	−39.6369			−1.38587
$819$	27.6285	+	7.46079i	0.965420	+	0.260701i
$820$	0.420345			0.0146791
$821$	−5.28601	−	19.7277i	−0.184483	−	0.688500i	−0.994741	−	0.102426i	$-0.967339\pi$
$821$	−5.28601	−	19.7277i	−0.184483	−	0.688500i	0.810258	−	0.586074i	$-0.199327\pi$
$822$	14.4556	−	5.12260i	0.504196	−	0.178671i
$823$	48.5127	−	28.0088i	1.69105	−	0.976326i	0.737371	−	0.675488i	$-0.236067\pi$
$823$	48.5127	−	28.0088i	1.69105	−	0.976326i	0.953675	−	0.300839i	$-0.0972665\pi$
$824$	−7.02742	−	1.88299i	−0.244812	−	0.0655971i
$825$	−10.6795	−	15.5314i	−0.371812	−	0.540733i
$826$	18.3810	+	22.1762i	0.639556	+	0.771608i
$827$	−22.2898	−	22.2898i	−0.775093	−	0.775093i	0.203899	−	0.978992i	$-0.434639\pi$
$827$	−22.2898	−	22.2898i	−0.775093	−	0.775093i	−0.978992	+	0.203899i	$0.934639\pi$
$828$	11.3728	+	14.0314i	0.395231	+	0.487626i
$829$		−	4.43854i		−	0.154157i	−0.997025	−	0.0770785i	$-0.975441\pi$
$829$		−	4.43854i		−	0.154157i	0.997025	−	0.0770785i	$-0.0245592\pi$
$830$	7.50251	+	7.50251i	0.260416	+	0.260416i
$831$	7.64346	−	8.95338i	0.265149	−	0.310589i
$832$	−0.238399	+	3.59766i	−0.00826499	+	0.124726i
$833$	−15.8017	+	5.53615i	−0.547496	+	0.191816i
$834$	38.8700	−	3.06784i	1.34596	−	0.106230i
$835$	3.70525	−	6.41768i	0.128225	−	0.222093i
$836$	4.24302	+	7.34912i	0.146748	+	0.254175i
$837$	2.01648	−	6.82425i	0.0696997	−	0.235880i
$838$	−0.170776	−	0.170776i	−0.00589935	−	0.00589935i
$839$	3.32216	−	0.890169i	0.114694	−	0.0307320i	−0.201016	−	0.979588i	$-0.564424\pi$
$839$	3.32216	−	0.890169i	0.114694	−	0.0307320i	0.315709	+	0.948856i	$0.397758\pi$
$840$	0.0666300	−	4.58125i	0.00229895	−	0.158068i
$841$	−10.3641	+	17.9511i	−0.357381	+	0.619002i
$842$	4.52704	−	7.84105i	0.156012	−	0.270221i
$843$	−29.0670	−	13.8563i	−1.00112	−	0.477236i
$844$	15.3789	+	8.87901i	0.529363	+	0.305628i
$845$	−12.0011	−	4.99122i	−0.412850	−	0.171703i
$846$	−1.73075	+	1.40281i	−0.0595043	+	0.0482295i
$847$	7.33277	−	6.07784i	0.251957	−	0.208837i
$848$	−2.12547	+	1.22714i	−0.0729891	+	0.0421403i
$849$	18.5494	+	52.3449i	0.636615	+	1.79647i
$850$	−9.24251	+	2.47652i	−0.317016	+	0.0849441i
$851$	6.33416	+	1.69723i	0.217132	+	0.0581804i
$852$	−22.2524	−	10.6078i	−0.762353	−	0.363416i
$853$	−13.9504	+	13.9504i	−0.477651	+	0.477651i	−0.904380	−	0.426728i	$-0.859666\pi$
$853$	−13.9504	+	13.9504i	−0.477651	+	0.477651i	0.426728	+	0.904380i	$0.359666\pi$
$854$	2.76586	−	3.89972i	0.0946458	−	0.133446i
$855$	8.73676	+	3.34927i	0.298791	+	0.114543i
$856$	−5.13206	−	19.1531i	−0.175410	−	0.654640i
$857$	11.0508	−	19.1405i	0.377487	−	0.653827i	−0.613209	−	0.789921i	$-0.710122\pi$
$857$	11.0508	−	19.1405i	0.377487	−	0.653827i	0.990696	+	0.136094i	$0.0434549\pi$
$858$	4.18993	−	16.4637i	0.143042	−	0.562061i
$859$	−17.9237	−	31.0447i	−0.611548	−	1.05923i	−0.990980	−	0.134013i	$-0.957214\pi$
$859$	−17.9237	−	31.0447i	−0.611548	−	1.05923i	0.379431	−	0.925220i	$-0.376120\pi$
$860$	−3.40519	−	0.912418i	−0.116116	−	0.0311132i
$861$	1.34237	+	1.38199i	0.0457477	+	0.0470981i
$862$	2.66045	+	1.53601i	0.0906152	+	0.0523167i
$863$	6.32672	+	1.69524i	0.215364	+	0.0577067i	0.364888	−	0.931051i	$-0.381107\pi$
$863$	6.32672	+	1.69524i	0.215364	+	0.0577067i	−0.149524	+	0.988758i	$0.547774\pi$
$864$	−3.76677	+	3.57931i	−0.128148	+	0.121771i
$865$	−17.0673	−	4.57317i	−0.580306	−	0.155493i
$866$	5.30934	−	19.8147i	0.180419	−	0.673332i
$867$	3.55575	−	19.2090i	0.120760	−	0.652371i
$868$	−3.60750	−	0.337579i	−0.122446	−	0.0114582i
$869$	8.05123	−	30.0476i	0.273119	−	1.01929i
$870$	−3.78801	−	3.23381i	−0.128426	−	0.109636i
$871$	0.285818	+	0.326385i	0.00968456	+	0.0110591i
$872$	12.8450	+	7.41604i	0.434985	+	0.251139i
$873$	−8.64555	+	11.9107i	−0.292607	+	0.403117i
$874$	9.39047	+	16.2648i	0.317637	+	0.550164i
$875$	−2.21823	+	23.7048i	−0.0749898	+	0.801369i
$876$	6.78262	+	3.23329i	0.229163	+	0.109243i
$877$	34.2929	+	34.2929i	1.15799	+	1.15799i	0.984908	+	0.173080i	$0.0553719\pi$
$877$	34.2929	+	34.2929i	1.15799	+	1.15799i	0.173080	+	0.984908i	$0.444628\pi$
$878$	5.24974	−	19.5923i	0.177170	−	0.661208i
$879$	43.5291	−	29.9310i	1.46820	−	1.00955i
$880$	−2.71983			−0.0916856
$881$	9.72164	+	16.8384i	0.327530	+	0.567299i	0.982021	−	0.188771i	$-0.0604503\pi$
$881$	9.72164	+	16.8384i	0.327530	+	0.567299i	−0.654491	+	0.756070i	$0.727117\pi$
$882$	15.2748	−	14.4111i	0.514329	−	0.485248i
$883$		−	39.2848i		−	1.32204i	−0.750369	−	0.661020i	$-0.770124\pi$
$883$		−	39.2848i		−	1.32204i	0.750369	−	0.661020i	$-0.229876\pi$
$884$	−7.16731	−	4.79649i	−0.241063	−	0.161323i
$885$	3.43154	−	18.5380i	0.115350	−	0.623146i
$886$	−21.2657	−	21.2657i	−0.714437	−	0.714437i
$887$	15.4677	+	8.93029i	0.519355	+	0.299850i	0.736671	−	0.676252i	$-0.236397\pi$
$887$	15.4677	+	8.93029i	0.519355	+	0.299850i	−0.217316	+	0.976101i	$0.569730\pi$
$888$	−0.343386	+	1.85505i	−0.0115233	+	0.0622514i
$889$	6.77502	+	2.51234i	0.227227	+	0.0842613i
$890$	−2.64401	−	9.86757i	−0.0886273	−	0.330762i
$891$	20.5213	−	13.3527i	0.687489	−	0.447331i
$892$	0.888970	+	3.31768i	0.0297649	+	0.111084i
$893$	−2.00622	+	1.15829i	−0.0671357	+	0.0387608i
$894$	38.2197	+	7.07480i	1.27826	+	0.236617i
$895$	9.33863	+	2.50228i	0.312156	+	0.0836419i
$896$	2.15807	+	1.53060i	0.0720960	+	0.0511338i
$897$	9.27298	−	36.4367i	0.309616	−	1.21659i
$898$	−13.3695	−	23.1566i	−0.446145	−	0.772746i
$899$	−2.78508	+	2.78508i	−0.0928875	+	0.0928875i
$900$	9.32324	−	7.55669i	0.310775	−	0.251890i
$901$		−	5.87046i		−	0.195573i
$902$	0.808709	−	0.808709i	0.0269270	−	0.0269270i
$903$	−7.87463	−	14.1092i	−0.262051	−	0.469525i
$904$	1.08018	+	4.03129i	0.0359263	+	0.134079i
$905$	−1.30122	+	4.85621i	−0.0432539	+	0.161426i
$906$	−13.9380	+	16.3267i	−0.463060	+	0.542418i
$907$			26.6657i			0.885421i	0.896665	+	0.442710i	$0.145983\pi$
$907$			26.6657i			0.885421i	−0.896665	+	0.442710i	$0.854017\pi$
$908$	−16.8946	+	4.52689i	−0.560667	+	0.150230i
$909$	10.3387	−	8.37973i	0.342913	−	0.277938i
$910$	−7.72952	+	5.58760i	−0.256231	+	0.185227i
$911$			24.7584i			0.820283i	0.912022	+	0.410142i	$0.134521\pi$
$911$			24.7584i			0.820283i	−0.912022	+	0.410142i	$0.865479\pi$
$912$	−4.45216	+	3.06134i	−0.147426	+	0.101371i
$913$	28.8684			0.955405
$914$	−1.33815	−	2.31775i	−0.0442621	−	0.0766643i
$915$	−3.11962	+	0.246218i	−0.103131	+	0.00813970i
$916$	−4.89806	+	1.31243i	−0.161836	+	0.0433640i
$917$	−36.1605	−	13.4092i	−1.19413	−	0.442811i
$918$	−2.90951	−	12.0834i	−0.0960281	−	0.398813i
$919$	38.4736			1.26913			0.634563	−	0.772871i	$-0.281180\pi$
$919$	38.4736			1.26913			0.634563	+	0.772871i	$0.281180\pi$
$920$	−6.01943			−0.198455
$921$	−20.5802	+	43.1721i	−0.678142	+	1.42257i
$922$	−1.06333	+	0.613914i	−0.0350189	+	0.0202182i
$923$	9.97510	+	50.3372i	0.328334	+	1.65687i
$924$	−8.68576	−	8.94214i	−0.285741	−	0.294175i
$925$	1.12773	−	4.20876i	0.0370797	−	0.138383i
$926$	−0.714038	−	0.412250i	−0.0234647	−	0.0135474i
$927$	−7.81265	+	20.3798i	−0.256601	+	0.669359i
$928$	2.77809	−	0.744387i	0.0911952	−	0.0244357i
$929$	42.8316	−	42.8316i	1.40526	−	1.40526i	0.623178	−	0.782080i	$-0.285841\pi$
$929$	42.8316	−	42.8316i	1.40526	−	1.40526i	0.782080	−	0.623178i	$-0.214159\pi$
$930$	1.34369	+	1.95415i	0.0440614	+	0.0640792i
$931$	18.0373	−	12.3079i	0.591148	−	0.403375i
$932$	20.8933	+	12.0628i	0.684383	+	0.395129i
$933$	0.535748	−	2.89423i	0.0175396	−	0.0947529i
$934$	17.4874	−	17.4874i	0.572206	−	0.572206i
$935$	3.25281	−	5.63404i	0.106378	−	0.184253i
$936$	10.6599	+	1.83471i	0.348430	+	0.0599693i
$937$	22.4479			0.733342			0.366671	−	0.930351i	$-0.380497\pi$
$937$	22.4479			0.733342			0.366671	+	0.930351i	$0.380497\pi$
$938$	0.313845	−	0.0533871i	0.0102474	−	0.00174315i
$939$	34.3210	+	29.2997i	1.12002	+	0.956160i
$940$		−	0.742483i		−	0.0242171i
$941$	−8.93620	−	33.3503i	−0.291312	−	1.08719i	−0.944103	−	0.329652i	$-0.893069\pi$
$941$	−8.93620	−	33.3503i	−0.291312	−	1.08719i	0.652791	−	0.757538i	$-0.273598\pi$
$942$	9.88172	−	0.779921i	0.321964	−	0.0254112i
$943$	1.78980	−	1.78980i	0.0582839	−	0.0582839i
$944$	7.69807	+	7.69807i	0.250551	+	0.250551i
$945$	−13.6483	−	1.62933i	−0.443979	−	0.0530022i
$946$	−8.30672	+	4.79589i	−0.270075	+	0.155928i
$947$	17.1702	−	4.60075i	0.557958	−	0.149504i	0.0311900	−	0.999513i	$-0.490070\pi$
$947$	17.1702	−	4.60075i	0.557958	−	0.149504i	0.526768	+	0.850009i	$0.323404\pi$
$948$	19.4755	+	3.60509i	0.632535	+	0.117088i
$949$	−3.04045	−	15.3430i	−0.0986973	−	0.498055i
$950$	10.8072	−	6.23954i	0.350632	−	0.202437i
$951$	13.3208	−	1.05136i	0.431958	−	0.0340926i
$952$	−5.75155	+	2.63982i	−0.186409	+	0.0855571i
$953$	−12.0178	+	20.8154i	−0.389294	+	0.674277i	−0.992355	−	0.123418i	$-0.960614\pi$
$953$	−12.0178	+	20.8154i	−0.389294	+	0.674277i	0.603061	+	0.797695i	$0.293948\pi$
$954$	2.99774	+	6.72497i	0.0970554	+	0.217729i
$955$	−5.97059	+	22.2825i	−0.193204	+	0.721046i
$956$	−5.04279	+	18.8199i	−0.163095	+	0.608680i
$957$	−13.5094	+	1.06624i	−0.436697	+	0.0344666i
$958$	−17.3767	+	30.0973i	−0.561415	+	0.972400i
$959$	−21.2912	+	9.77215i	−0.687529	+	0.315559i
$960$	−0.136254	−	1.72636i	−0.00439759	−	0.0557182i
$961$	−25.2226	+	14.5623i	−0.813633	+	0.469751i
$962$	3.52344	−	1.73442i	0.113600	−	0.0559201i
$963$	−58.7498	+	9.33185i	−1.89318	+	0.300715i
$964$	9.13026	−	2.44645i	0.294066	−	0.0787947i
$965$	0.631776	−	0.364756i	0.0203376	−	0.0117419i
$966$	−19.2230	−	19.7904i	−0.618489	−	0.636745i
$967$	−17.5794	−	17.5794i	−0.565315	−	0.565315i	0.365497	−	0.930813i	$-0.380899\pi$
$967$	−17.5794	−	17.5794i	−0.565315	−	0.565315i	−0.930813	+	0.365497i	$0.880899\pi$
$968$	2.54544	−	2.54544i	0.0818135	−	0.0818135i
$969$	−1.01686	−	12.8837i	−0.0326661	−	0.413885i
$970$	−1.26951	−	4.73787i	−0.0407614	−	0.152124i
$971$		−	0.974630i		−	0.0312774i	−0.999878	−	0.0156387i	$-0.995022\pi$
$971$		−	0.974630i		−	0.0312774i	0.999878	−	0.0156387i	$-0.00497815\pi$
$972$	9.50341	+	12.3566i	0.304822	+	0.396338i
$973$	−58.7160	+	9.98800i	−1.88235	+	0.320200i
$974$	−20.5016			−0.656912
$975$	−24.2105	−	6.16148i	−0.775358	−	0.197325i
$976$	0.903521	−	1.56494i	0.0289210	−	0.0500927i
$977$	−33.0189	+	33.0189i	−1.05637	+	1.05637i	−0.0580560	+	0.998313i	$0.518490\pi$
$977$	−33.0189	+	33.0189i	−1.05637	+	1.05637i	−0.998313	+	0.0580560i	$0.981510\pi$
$978$	39.7144	+	7.35150i	1.26993	+	0.235075i
$979$	−24.0712	−	13.8975i	−0.769320	−	0.444167i
$980$	0.525728	+	6.97894i	0.0167938	+	0.222934i
$981$	26.1382	−	36.0098i	0.834528	−	1.14971i
$982$	13.5605	−	13.5605i	0.432732	−	0.432732i
$983$	−14.3662	+	3.84942i	−0.458212	+	0.122777i	−0.480539	−	0.876973i	$-0.659559\pi$
$983$	−14.3662	+	3.84942i	−0.458212	+	0.122777i	0.0223274	+	0.999751i	$0.492892\pi$
$984$	0.553827	+	0.472799i	0.0176553	+	0.0150723i
$985$	11.5129	+	6.64699i	0.366832	+	0.211791i
$986$	−1.78051	+	6.64496i	−0.0567031	+	0.211619i
$987$	2.44110	−	2.37111i	0.0777011	−	0.0754733i
$988$	10.6480	+	3.62303i	0.338757	+	0.115264i
$989$	−18.3841	+	10.6141i	−0.584580	+	0.337508i
$990$	−0.849288	+	8.11518i	−0.0269921	+	0.257917i
$991$	−15.8515			−0.503538			−0.251769	−	0.967787i	$-0.581012\pi$
$991$	−15.8515			−0.503538			−0.251769	+	0.967787i	$0.581012\pi$
$992$	−1.36946			−0.0434805
$993$	−53.3733	−	25.4432i	−1.69375	−	0.807415i
$994$	35.3063	+	13.0924i	1.11985	+	0.415267i
$995$	8.44484	−	2.26279i	0.267719	−	0.0717352i
$996$	1.44621	+	18.3237i	0.0458249	+	0.580609i
$997$	−24.7142	−	42.8063i	−0.782707	−	1.35569i	−0.930359	−	0.366649i	$-0.880505\pi$
$997$	−24.7142	−	42.8063i	−0.782707	−	1.35569i	0.147652	−	0.989039i	$-0.452828\pi$
$998$	−20.0354			−0.634211
$999$	5.42770	+	1.60382i	0.171725	+	0.0507425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.11.17	✓	152
3.2	odd	2	inner	546.2.bw.a.11.36	yes	152
7.2	even	3		546.2.ch.a.401.9	yes	152
13.6	odd	12		546.2.ch.a.305.24	yes	152
21.2	odd	6		546.2.ch.a.401.24	yes	152
39.32	even	12		546.2.ch.a.305.9	yes	152
91.58	odd	12	inner	546.2.bw.a.149.36	yes	152
273.149	even	12	inner	546.2.bw.a.149.17	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.17	✓	152	1.1	even	1	trivial
546.2.bw.a.11.36	yes	152	3.2	odd	2	inner
546.2.bw.a.149.17	yes	152	273.149	even	12	inner
546.2.bw.a.149.36	yes	152	91.58	odd	12	inner
546.2.ch.a.305.9	yes	152	39.32	even	12
546.2.ch.a.305.24	yes	152	13.6	odd	12
546.2.ch.a.401.9	yes	152	7.2	even	3
546.2.ch.a.401.24	yes	152	21.2	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.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.63257 - 0.578534i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.965749 - 0.258772i) q^{5} +(-0.981362 - 1.42721i) q^{6} +(1.68839 + 2.03700i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.33060 - 1.88900i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.63257 - 0.578534i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.965749 - 0.258772i) q^{5} +(-0.981362 - 1.42721i) q^{6} +(1.68839 + 2.03700i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.33060 - 1.88900i) q^{9} +0.999817i q^{10} +(1.92357 + 1.92357i) q^{11} +(-1.12458 + 1.31731i) q^{12} +(3.59766 + 0.238399i) q^{13} +(1.53060 - 2.15807i) q^{14} +(-1.72636 + 0.136254i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.19596 + 2.07146i) q^{17} +(-2.42784 - 1.76228i) q^{18} +(-2.20581 - 2.20581i) q^{19} +(0.965749 - 0.258772i) q^{20} +(3.93489 + 2.34876i) q^{21} +(1.36017 - 2.35588i) q^{22} +(3.01026 - 5.21393i) q^{23} +(1.56349 + 0.745319i) q^{24} +(-3.46442 - 2.00018i) q^{25} +(-0.700868 - 3.53678i) q^{26} +(2.71202 - 4.43226i) q^{27} +(-2.48068 - 0.919898i) q^{28} +(-2.49077 + 1.43804i) q^{29} +(0.578428 + 1.63228i) q^{30} +(1.32280 - 0.354443i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(4.25321 + 2.02752i) q^{33} +(1.69134 - 1.69134i) q^{34} +(-1.10344 - 2.40413i) q^{35} +(-1.07386 + 2.80122i) q^{36} +(0.281908 + 1.05209i) q^{37} +(-1.55974 + 2.70155i) q^{38} +(6.01137 - 1.69216i) q^{39} +(-0.499908 - 0.865867i) q^{40} +(0.406096 + 0.108813i) q^{41} +(1.25030 - 4.40871i) q^{42} +(-3.05357 - 1.76298i) q^{43} +(-2.62764 - 0.704074i) q^{44} +(-2.73959 + 1.22121i) q^{45} +(-5.81538 - 1.55823i) q^{46} +(0.192204 - 0.717315i) q^{47} +(0.315262 - 1.70312i) q^{48} +(-1.29871 + 6.87847i) q^{49} +(-1.03537 + 3.86406i) q^{50} +(3.15090 + 2.68991i) q^{51} +(-3.23487 + 1.59237i) q^{52} +(-2.12547 - 1.22714i) q^{53} +(-4.98316 - 1.47246i) q^{54} +(-1.35992 - 2.35545i) q^{55} +(-0.246505 + 2.63424i) q^{56} +(-4.87728 - 2.32501i) q^{57} +(2.03370 + 2.03370i) q^{58} +(-2.81769 + 10.5158i) q^{59} +(1.42695 - 0.981182i) q^{60} +1.80704 q^{61} +(-0.684731 - 1.18599i) q^{62} +(7.78283 + 1.55806i) q^{63} +1.00000i q^{64} +(-3.41275 - 1.16121i) q^{65} +(0.857618 - 4.63305i) q^{66} +(0.0850834 + 0.0850834i) q^{67} +(-2.07146 - 1.19596i) q^{68} +(1.89804 - 10.2537i) q^{69} +(-2.03662 + 1.68808i) q^{70} +(3.68364 + 13.7475i) q^{71} +(2.98370 + 0.312257i) q^{72} +(-1.12279 - 4.19031i) q^{73} +(0.943282 - 0.544604i) q^{74} +(-6.81309 - 1.26116i) q^{75} +(3.01319 + 0.807382i) q^{76} +(-0.670575 + 7.16601i) q^{77} +(-3.19036 - 5.36857i) q^{78} +(-5.71760 - 9.90318i) q^{79} +(-0.706977 + 0.706977i) q^{80} +(1.86337 - 8.80499i) q^{81} -0.420422i q^{82} +(7.50388 - 7.50388i) q^{83} +(-4.58209 - 0.0666422i) q^{84} +(-0.618961 - 2.30999i) q^{85} +(-0.912585 + 3.40581i) q^{86} +(-3.23440 + 3.78871i) q^{87} +2.72033i q^{88} +(-9.86938 + 2.64449i) q^{89} +(1.88865 + 2.33017i) q^{90} +(5.58862 + 7.73093i) q^{91} +6.02053i q^{92} +(1.95451 - 1.34394i) q^{93} -0.742619 q^{94} +(1.55946 + 2.70106i) q^{95} +(-1.72668 + 0.136279i) q^{96} +(-4.73874 + 1.26974i) q^{97} +(6.98022 - 0.525824i) q^{98} +(8.11667 + 0.849444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more