LMFDB - Embedded newform 546.2.bu.a.71.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.14
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.a.323.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(1.59645 + 0.671817i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.68505 + 1.68505i) q^{5} +(1.71593 + 0.235733i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.09732 + 2.14505i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(1.59645 + 0.671817i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.68505 + 1.68505i) q^{5} +(1.71593 + 0.235733i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.09732 + 2.14505i) q^{9} +(2.06376 + 1.19151i) q^{10} +(-1.39701 - 5.21372i) q^{11} +(1.71848 - 0.216416i) q^{12} +(-3.48120 - 0.938747i) q^{13} +1.00000i q^{14} +(1.55806 + 3.82216i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.157166 + 0.272219i) q^{17} +(2.58104 + 1.52913i) q^{18} +(3.03381 + 0.812907i) q^{19} +(2.30183 + 0.616773i) q^{20} +(-1.06212 + 1.36818i) q^{21} +(-2.69882 - 4.67450i) q^{22} +(-3.97748 + 6.88919i) q^{23} +(1.60391 - 0.653816i) q^{24} +0.678813i q^{25} +(-3.60555 - 0.00575899i) q^{26} +(1.90720 + 4.83349i) q^{27} +(0.258819 + 0.965926i) q^{28} +(-8.99954 - 5.19588i) q^{29} +(2.49422 + 3.28866i) q^{30} +(-1.93478 + 1.93478i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.27240 - 9.26200i) q^{33} +(0.222266 + 0.222266i) q^{34} +(-2.06376 + 1.19151i) q^{35} +(2.88886 + 0.809005i) q^{36} +(5.26559 - 1.41091i) q^{37} +3.14083 q^{38} +(-4.92691 - 3.83739i) q^{39} +2.38303 q^{40} +(7.15363 - 1.91681i) q^{41} +(-0.671817 + 1.59645i) q^{42} +(3.91582 - 2.26080i) q^{43} +(-3.81671 - 3.81671i) q^{44} +(-0.0804188 + 7.14863i) q^{45} +(-2.05889 + 7.68390i) q^{46} +(-1.31948 + 1.31948i) q^{47} +(1.38004 - 1.04666i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.175690 + 0.655683i) q^{50} +(0.0680263 + 0.540171i) q^{51} +(-3.48418 + 0.927621i) q^{52} -13.4414i q^{53} +(3.09321 + 4.17517i) q^{54} +(6.43136 - 11.1394i) q^{55} +(0.500000 + 0.866025i) q^{56} +(4.29721 + 3.33593i) q^{57} +(-10.0377 - 2.68959i) q^{58} +(-10.6210 - 2.84589i) q^{59} +(3.26040 + 2.53105i) q^{60} +(-1.00026 - 1.73250i) q^{61} +(-1.36809 + 2.36961i) q^{62} +(-2.61479 + 1.47068i) q^{63} -1.00000i q^{64} +(-4.28417 - 7.44785i) q^{65} +(-1.16814 - 9.27573i) q^{66} +(0.360910 + 1.34693i) q^{67} +(0.272219 + 0.157166i) q^{68} +(-10.9781 + 8.32613i) q^{69} +(-1.68505 + 1.68505i) q^{70} +(-3.98667 + 14.8785i) q^{71} +(2.99981 + 0.0337465i) q^{72} +(10.3973 + 10.3973i) q^{73} +(4.72100 - 2.72567i) q^{74} +(-0.456038 + 1.08369i) q^{75} +(3.03381 - 0.812907i) q^{76} +5.39764 q^{77} +(-5.75222 - 2.43146i) q^{78} -0.912263 q^{79} +(2.30183 - 0.616773i) q^{80} +(-0.202466 + 8.99772i) q^{81} +(6.41377 - 3.70299i) q^{82} +(-7.71566 - 7.71566i) q^{83} +(-0.235733 + 1.71593i) q^{84} +(-0.193871 + 0.723536i) q^{85} +(3.19725 - 3.19725i) q^{86} +(-10.8767 - 14.3410i) q^{87} +(-4.67450 - 2.69882i) q^{88} +(0.444776 + 1.65993i) q^{89} +(1.77252 + 6.92586i) q^{90} +(1.80776 - 3.11962i) q^{91} +7.95495i q^{92} +(-4.38859 + 1.78896i) q^{93} +(-0.933016 + 1.61603i) q^{94} +(3.74234 + 6.48192i) q^{95} +(1.06212 - 1.36818i) q^{96} +(10.5820 + 2.83543i) q^{97} +(-0.965926 - 0.258819i) q^{98} +(8.25370 - 13.9315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	1.59645	+	0.671817i	0.921713	+	0.387874i
$3$	1.59645	+	0.671817i	0.921713	+	0.387874i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.68505	+	1.68505i	0.753579	+	0.753579i	0.975145	−	0.221566i	$-0.0711169\pi$
$5$	1.68505	+	1.68505i	0.753579	+	0.753579i	−0.221566	+	0.975145i	$0.571117\pi$
$6$	1.71593	+	0.235733i	0.700527	+	0.0962376i
$7$	−0.258819	+	0.965926i	−0.0978244	+	0.365086i
$7$	−0.258819	+	0.965926i	−0.0978244	+	0.365086i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.09732	+	2.14505i	0.699108	+	0.715016i
$10$	2.06376	+	1.19151i	0.652619	+	0.376789i
$11$	−1.39701	−	5.21372i	−0.421215	−	1.57200i	−0.772052	−	0.635560i	$-0.780769\pi$
$11$	−1.39701	−	5.21372i	−0.421215	−	1.57200i	0.350836	−	0.936437i	$-0.385897\pi$
$12$	1.71848	−	0.216416i	0.496082	−	0.0624739i
$13$	−3.48120	−	0.938747i	−0.965511	−	0.260362i
$13$	−3.48120	−	0.938747i	−0.965511	−	0.260362i
$14$			1.00000i			0.267261i
$15$	1.55806	+	3.82216i	0.402290	+	0.986877i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.157166	+	0.272219i	0.0381183	+	0.0660228i	0.884455	−	0.466625i	$-0.154530\pi$
$17$	0.157166	+	0.272219i	0.0381183	+	0.0660228i	−0.846337	+	0.532648i	$0.821197\pi$
$18$	2.58104	+	1.52913i	0.608357	+	0.360419i
$19$	3.03381	+	0.812907i	0.696004	+	0.186494i	0.589440	−	0.807812i	$-0.299348\pi$
$19$	3.03381	+	0.812907i	0.696004	+	0.186494i	0.106564	+	0.994306i	$0.466015\pi$
$20$	2.30183	+	0.616773i	0.514704	+	0.137915i
$21$	−1.06212	+	1.36818i	−0.231773	+	0.298560i
$22$	−2.69882	−	4.67450i	−0.575391	−	0.996606i
$23$	−3.97748	+	6.88919i	−0.829361	+	1.43650i	0.0691786	+	0.997604i	$0.477962\pi$
$23$	−3.97748	+	6.88919i	−0.829361	+	1.43650i	−0.898540	+	0.438892i	$0.855371\pi$
$24$	1.60391	−	0.653816i	0.327397	−	0.133460i
$25$			0.678813i			0.135763i
$26$	−3.60555	−	0.00575899i	−0.707106	−	0.00112943i
$27$	1.90720	+	4.83349i	0.367041	+	0.930205i
$28$	0.258819	+	0.965926i	0.0489122	+	0.182543i
$29$	−8.99954	−	5.19588i	−1.67117	−	0.964852i	−0.966984	−	0.254838i	$-0.917978\pi$
$29$	−8.99954	−	5.19588i	−1.67117	−	0.964852i	−0.704188	−	0.710013i	$-0.748689\pi$
$30$	2.49422	+	3.28866i	0.455380	+	0.600425i
$31$	−1.93478	+	1.93478i	−0.347496	+	0.347496i	−0.859176	−	0.511680i	$-0.829023\pi$
$31$	−1.93478	+	1.93478i	−0.347496	+	0.347496i	0.511680	+	0.859176i	$0.329023\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	1.27240	−	9.26200i	0.221497	−	1.61231i
$34$	0.222266	+	0.222266i	0.0381183	+	0.0381183i
$35$	−2.06376	+	1.19151i	−0.348839	+	0.201402i
$36$	2.88886	+	0.809005i	0.481477	+	0.134834i
$37$	5.26559	−	1.41091i	0.865658	−	0.231952i	0.201449	−	0.979499i	$-0.435435\pi$
$37$	5.26559	−	1.41091i	0.865658	−	0.231952i	0.664209	+	0.747547i	$0.268768\pi$
$38$	3.14083			0.509510
$39$	−4.92691	−	3.83739i	−0.788936	−	0.614475i
$40$	2.38303			0.376789
$41$	7.15363	−	1.91681i	1.11721	−	0.299355i	0.347455	−	0.937697i	$-0.387046\pi$
$41$	7.15363	−	1.91681i	1.11721	−	0.299355i	0.769753	+	0.638341i	$0.220379\pi$
$42$	−0.671817	+	1.59645i	−0.103664	+	0.246338i
$43$	3.91582	−	2.26080i	0.597157	−	0.344769i	−0.170765	−	0.985312i	$-0.554624\pi$
$43$	3.91582	−	2.26080i	0.597157	−	0.344769i	0.767922	+	0.640543i	$0.221291\pi$
$44$	−3.81671	−	3.81671i	−0.575391	−	0.575391i
$45$	−0.0804188	+	7.14863i	−0.0119881	+	1.06565i
$46$	−2.05889	+	7.68390i	−0.303567	+	1.13293i
$47$	−1.31948	+	1.31948i	−0.192466	+	0.192466i	−0.796761	−	0.604295i	$-0.793455\pi$
$47$	−1.31948	+	1.31948i	−0.192466	+	0.192466i	0.604295	+	0.796761i	$0.293455\pi$
$48$	1.38004	−	1.04666i	0.199191	−	0.151072i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	0.175690	+	0.655683i	0.0248463	+	0.0927276i
$51$	0.0680263	+	0.540171i	0.00952559	+	0.0756391i
$52$	−3.48418	+	0.927621i	−0.483169	+	0.128638i
$53$		−	13.4414i		−	1.84631i	−0.384423	−	0.923157i	$-0.625600\pi$
$53$		−	13.4414i		−	1.84631i	0.384423	−	0.923157i	$-0.374400\pi$
$54$	3.09321	+	4.17517i	0.420933	+	0.568169i
$55$	6.43136	−	11.1394i	0.867205	−	1.50204i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	4.29721	+	3.33593i	0.569179	+	0.441855i
$58$	−10.0377	−	2.68959i	−1.31801	−	0.353160i
$59$	−10.6210	−	2.84589i	−1.38274	−	0.370503i	−0.510622	−	0.859805i	$-0.670585\pi$
$59$	−10.6210	−	2.84589i	−1.38274	−	0.370503i	−0.872114	+	0.489302i	$0.837252\pi$
$60$	3.26040	+	2.53105i	0.420916	+	0.326758i
$61$	−1.00026	−	1.73250i	−0.128070	−	0.221824i	0.794859	−	0.606794i	$-0.207545\pi$
$61$	−1.00026	−	1.73250i	−0.128070	−	0.221824i	−0.922929	+	0.384971i	$0.874212\pi$
$62$	−1.36809	+	2.36961i	−0.173748	+	0.300940i
$63$	−2.61479	+	1.47068i	−0.329432	+	0.185288i
$64$		−	1.00000i		−	0.125000i
$65$	−4.28417	−	7.44785i	−0.531386	−	0.923792i
$66$	−1.16814	−	9.27573i	−0.143788	−	1.14176i
$67$	0.360910	+	1.34693i	0.0440921	+	0.164554i	0.984461	−	0.175601i	$-0.0561870\pi$
$67$	0.360910	+	1.34693i	0.0440921	+	0.164554i	−0.940369	+	0.340155i	$0.889520\pi$
$68$	0.272219	+	0.157166i	0.0330114	+	0.0190591i
$69$	−10.9781	+	8.32613i	−1.32161	+	1.00235i
$70$	−1.68505	+	1.68505i	−0.201402	+	0.201402i
$71$	−3.98667	+	14.8785i	−0.473131	+	1.76575i	0.155283	+	0.987870i	$0.450371\pi$
$71$	−3.98667	+	14.8785i	−0.473131	+	1.76575i	−0.628414	+	0.777879i	$0.716296\pi$
$72$	2.99981	+	0.0337465i	0.353531	+	0.00397706i
$73$	10.3973	+	10.3973i	1.21691	+	1.21691i	0.968707	+	0.248206i	$0.0798411\pi$
$73$	10.3973	+	10.3973i	1.21691	+	1.21691i	0.248206	+	0.968707i	$0.420159\pi$
$74$	4.72100	−	2.72567i	0.548805	−	0.316853i
$75$	−0.456038	+	1.08369i	−0.0526588	+	0.125134i
$76$	3.03381	−	0.812907i	0.348002	−	0.0932468i
$77$	5.39764			0.615119
$78$	−5.75222	−	2.43146i	−0.651310	−	0.275309i
$79$	−0.912263			−0.102638			−0.0513188	−	0.998682i	$-0.516342\pi$
$79$	−0.912263			−0.102638			−0.0513188	+	0.998682i	$0.516342\pi$
$80$	2.30183	−	0.616773i	0.257352	−	0.0689573i
$81$	−0.202466	+	8.99772i	−0.0224962	+	0.999747i
$82$	6.41377	−	3.70299i	0.708282	−	0.408927i
$83$	−7.71566	−	7.71566i	−0.846904	−	0.846904i	0.142841	−	0.989746i	$-0.454376\pi$
$83$	−7.71566	−	7.71566i	−0.846904	−	0.846904i	−0.989746	+	0.142841i	$0.954376\pi$
$84$	−0.235733	+	1.71593i	−0.0257206	+	0.187224i
$85$	−0.193871	+	0.723536i	−0.0210283	+	0.0784785i
$86$	3.19725	−	3.19725i	0.344769	−	0.344769i
$87$	−10.8767	−	14.3410i	−1.16610	−	1.53752i
$88$	−4.67450	−	2.69882i	−0.498303	−	0.287695i
$89$	0.444776	+	1.65993i	0.0471461	+	0.175952i	0.985484	−	0.169767i	$-0.0543017\pi$
$89$	0.444776	+	1.65993i	0.0471461	+	0.175952i	−0.938338	+	0.345719i	$0.887635\pi$
$90$	1.77252	+	6.92586i	0.186840	+	0.730049i
$91$	1.80776	−	3.11962i	0.189505	−	0.327025i
$92$			7.95495i			0.829361i
$93$	−4.38859	+	1.78896i	−0.455076	+	0.185507i
$94$	−0.933016	+	1.61603i	−0.0962332	+	0.166681i
$95$	3.74234	+	6.48192i	0.383956	+	0.665031i
$96$	1.06212	−	1.36818i	0.108402	−	0.139639i
$97$	10.5820	+	2.83543i	1.07444	+	0.287895i	0.752315	−	0.658803i	$-0.228937\pi$
$97$	10.5820	+	2.83543i	1.07444	+	0.287895i	0.322122	+	0.946698i	$0.395604\pi$
$98$	−0.965926	−	0.258819i	−0.0975732	−	0.0261447i
$99$	8.25370	−	13.9315i	0.829528	−	1.40017i
$100$	0.339407	+	0.587869i	0.0339407	+	0.0587869i
$101$	1.99214	−	3.45048i	0.198225	−	0.343336i	−0.749728	−	0.661746i	$-0.769816\pi$
$101$	1.99214	−	3.45048i	0.198225	−	0.343336i	0.947953	+	0.318410i	$0.103149\pi$
$102$	0.205515	+	0.504159i	0.0203490	+	0.0499192i
$103$		−	10.8341i		−	1.06752i	−0.845637	−	0.533758i	$-0.820779\pi$
$103$		−	10.8341i		−	1.06752i	0.845637	−	0.533758i	$-0.179221\pi$
$104$	−3.12537	+	1.79779i	−0.306468	+	0.176287i
$105$	−4.09518	+	0.515725i	−0.399648	+	0.0503296i
$106$	−3.47888	−	12.9834i	−0.337899	−	1.26106i
$107$	−0.796948	−	0.460118i	−0.0770439	−	0.0444813i	0.460983	−	0.887409i	$-0.347497\pi$
$107$	−0.796948	−	0.460118i	−0.0770439	−	0.0444813i	−0.538027	+	0.842928i	$0.680830\pi$
$108$	4.06843	+	3.23232i	0.391484	+	0.311030i
$109$	−10.7294	+	10.7294i	−1.02769	+	1.02769i	−0.0280885	+	0.999605i	$0.508942\pi$
$109$	−10.7294	+	10.7294i	−1.02769	+	1.02769i	−0.999605	+	0.0280885i	$0.991058\pi$
$110$	3.32912	−	12.4244i	0.317419	−	1.18462i
$111$	9.35414	+	1.28506i	0.887856	+	0.121973i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−3.00270	+	1.73361i	−0.282470	+	0.163084i	−0.634541	−	0.772889i	$-0.718811\pi$
$113$	−3.00270	+	1.73361i	−0.282470	+	0.163084i	0.352071	+	0.935973i	$0.385478\pi$
$114$	5.01419	+	2.11006i	0.469622	+	0.197626i
$115$	−18.3109	+	4.90640i	−1.70750	+	0.457524i
$116$	−10.3918			−0.964852
$117$	−5.28755	−	9.43620i	−0.488834	−	0.872377i
$118$	−10.9957			−1.01223
$119$	−0.303621	+	0.0813550i	−0.0278329	+	0.00745780i
$120$	3.80439	+	1.60096i	0.347292	+	0.146147i
$121$	−15.7050	+	9.06727i	−1.42773	+	0.824298i
$122$	−1.41458	−	1.41458i	−0.128070	−	0.128070i
$123$	12.7082	+	1.74583i	1.14586	+	0.157417i
$124$	−0.708177	+	2.64295i	−0.0635962	+	0.237344i
$125$	7.28143	−	7.28143i	0.651271	−	0.651271i
$126$	−2.14505	+	2.09732i	−0.191096	+	0.186844i
$127$	−6.18996	−	3.57378i	−0.549270	−	0.317121i	0.199557	−	0.979886i	$-0.436050\pi$
$127$	−6.18996	−	3.57378i	−0.549270	−	0.317121i	−0.748828	+	0.662765i	$0.769383\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	7.77027	−	0.978546i	0.684134	−	0.0861562i
$130$	−6.06584	−	6.08524i	−0.532009	−	0.533711i
$131$		−	9.26094i		−	0.809132i	−0.914509	−	0.404566i	$-0.867423\pi$
$131$		−	9.26094i		−	0.809132i	0.914509	−	0.404566i	$-0.132577\pi$
$132$	−3.52907	−	8.65733i	−0.307166	−	0.753524i
$133$	−1.57042	+	2.72004i	−0.136172	+	0.235857i
$134$	0.697224	+	1.20763i	0.0602310	+	0.104323i
$135$	−4.93095	+	11.3584i	−0.424389	+	0.977577i
$136$	0.303621	+	0.0813550i	0.0260353	+	0.00697613i
$137$	4.12926	+	1.10643i	0.352787	+	0.0945289i	0.430860	−	0.902419i	$-0.358210\pi$
$137$	4.12926	+	1.10643i	0.352787	+	0.0945289i	−0.0780734	+	0.996948i	$0.524877\pi$
$138$	−8.44910	+	10.8838i	−0.719235	+	0.926489i
$139$	3.34790	+	5.79873i	0.283965	+	0.491842i	0.972358	−	0.233496i	$-0.0750167\pi$
$139$	3.34790	+	5.79873i	0.283965	+	0.491842i	−0.688393	+	0.725338i	$0.741683\pi$
$140$	−1.19151	+	2.06376i	−0.100701	+	0.174420i
$141$	−2.99294	+	1.22004i	−0.252051	+	0.102746i
$142$			15.4033i			1.29262i
$143$	−0.0310850	+	19.4615i	−0.00259946	+	1.62745i
$144$	2.90633	−	0.743811i	0.242194	−	0.0619843i
$145$	−6.40936	−	23.9201i	−0.532268	−	1.98645i
$146$	12.7341	+	7.35201i	1.05388	+	0.608457i
$147$	−1.04666	−	1.38004i	−0.0863271	−	0.113824i
$148$	3.85468	−	3.85468i	0.316853	−	0.316853i
$149$	−1.76766	+	6.59700i	−0.144812	+	0.540447i	0.854951	+	0.518708i	$0.173587\pi$
$149$	−1.76766	+	6.59700i	−0.144812	+	0.540447i	−0.999764	+	0.0217390i	$0.993080\pi$
$150$	−0.160019	+	1.16480i	−0.0130655	+	0.0951054i
$151$	1.86863	+	1.86863i	0.152067	+	0.152067i	0.779040	−	0.626974i	$-0.215707\pi$
$151$	1.86863	+	1.86863i	0.152067	+	0.152067i	−0.626974	+	0.779040i	$0.715707\pi$
$152$	2.72004	−	1.57042i	0.220624	−	0.127378i
$153$	−0.254296	+	0.908060i	−0.0205586	+	0.0734123i
$154$	5.21372	−	1.39701i	0.420134	−	0.112574i
$155$	−6.52040			−0.523731
$156$	−6.18552	−	0.859828i	−0.495238	−	0.0688414i
$157$	11.2697			0.899423			0.449711	−	0.893174i	$-0.351527\pi$
$157$	11.2697			0.899423			0.449711	+	0.893174i	$0.351527\pi$
$158$	−0.881178	+	0.236111i	−0.0701028	+	0.0187840i
$159$	9.03014	−	21.4585i	0.716137	−	1.70177i
$160$	2.06376	−	1.19151i	0.163155	−	0.0941974i
$161$	−5.62500	−	5.62500i	−0.443312	−	0.443312i
$162$	2.13321	+	8.74353i	0.167601	+	0.686957i
$163$	−5.24444	+	19.5725i	−0.410776	+	1.53304i	0.382371	+	0.924009i	$0.375108\pi$
$163$	−5.24444	+	19.5725i	−0.410776	+	1.53304i	−0.793148	+	0.609029i	$0.791559\pi$
$164$	5.23682	−	5.23682i	0.408927	−	0.408927i
$165$	17.7510	−	13.4629i	1.38192	−	1.04809i
$166$	−9.44972	−	5.45580i	−0.733441	−	0.423452i
$167$	−4.34679	−	16.2224i	−0.336365	−	1.25533i	−0.902382	−	0.430937i	$-0.858183\pi$
$167$	−4.34679	−	16.2224i	−0.336365	−	1.25533i	0.566017	−	0.824393i	$-0.308483\pi$
$168$	0.216416	+	1.71848i	0.0166968	+	0.132583i
$169$	11.2375	+	6.53593i	0.864424	+	0.502764i
$170$			0.749060i			0.0574503i
$171$	4.61916	+	8.21260i	0.353236	+	0.628033i
$172$	2.26080	−	3.91582i	0.172384	−	0.298579i
$173$	5.22831	+	9.05569i	0.397501	+	0.688492i	0.993417	−	0.114555i	$-0.0365442\pi$
$173$	5.22831	+	9.05569i	0.397501	+	0.688492i	−0.595916	+	0.803047i	$0.703211\pi$
$174$	−14.2178	−	11.0373i	−1.07785	−	0.836734i
$175$	−0.655683	−	0.175690i	−0.0495650	−	0.0132809i
$176$	−5.21372	−	1.39701i	−0.392999	−	0.105304i
$177$	−15.0440	−	11.6787i	−1.13078	−	0.877824i
$178$	0.859240	+	1.48825i	0.0644028	+	0.111549i
$179$	−7.06557	+	12.2379i	−0.528106	+	0.914706i	0.471357	+	0.881942i	$0.343764\pi$
$179$	−7.06557	+	12.2379i	−0.528106	+	0.914706i	−0.999463	+	0.0327637i	$0.989569\pi$
$180$	3.50467	+	6.23110i	0.261223	+	0.464439i
$181$		−	5.93112i		−	0.440857i	−0.975403	−	0.220428i	$-0.929254\pi$
$181$		−	5.93112i		−	0.440857i	0.975403	−	0.220428i	$-0.0707455\pi$
$182$	0.938747	−	3.48120i	0.0695846	−	0.258044i
$183$	−0.432943	−	3.43784i	−0.0320041	−	0.254133i
$184$	2.05889	+	7.68390i	0.151784	+	0.566464i
$185$	11.2503	+	6.49535i	0.827136	+	0.477547i
$186$	−3.77604	+	2.86386i	−0.276872	+	0.209988i
$187$	1.19971	−	1.19971i	0.0877316	−	0.0877316i
$188$	−0.482964	+	1.80245i	−0.0352238	+	0.131457i
$189$	−5.16241	+	0.591214i	−0.375510	+	0.0430045i
$190$	5.29247	+	5.29247i	0.383956	+	0.383956i
$191$	−6.94728	+	4.01102i	−0.502688	+	0.290227i	−0.729823	−	0.683636i	$-0.760397\pi$
$191$	−6.94728	+	4.01102i	−0.502688	+	0.290227i	0.227135	+	0.973863i	$0.427064\pi$
$192$	0.671817	−	1.59645i	0.0484842	−	0.115214i
$193$	−11.0920	+	2.97208i	−0.798417	+	0.213935i	−0.634889	−	0.772604i	$-0.718954\pi$
$193$	−11.0920	+	2.97208i	−0.798417	+	0.213935i	−0.163528	+	0.986539i	$0.552287\pi$
$194$	10.9553			0.786543
$195$	−1.83588	−	14.7683i	−0.131470	−	1.05758i
$196$	−1.00000			−0.0714286
$197$	5.05278	−	1.35389i	0.359995	−	0.0964605i	−0.0742879	−	0.997237i	$-0.523668\pi$
$197$	5.05278	−	1.35389i	0.359995	−	0.0964605i	0.434283	+	0.900776i	$0.357002\pi$
$198$	4.36672	−	15.5930i	0.310329	−	1.10815i
$199$	−9.41221	+	5.43414i	−0.667214	+	0.385216i	−0.795020	−	0.606583i	$-0.792540\pi$
$199$	−9.41221	+	5.43414i	−0.667214	+	0.385216i	0.127806	+	0.991799i	$0.459206\pi$
$200$	0.479993	+	0.479993i	0.0339407	+	0.0339407i
$201$	−0.328717	+	2.39278i	−0.0231859	+	0.168774i
$202$	1.03121	−	3.84851i	0.0725554	−	0.270780i
$203$	7.34809	−	7.34809i	0.515735	−	0.515735i
$204$	0.328998	+	0.433789i	0.0230345	+	0.0303713i
$205$	15.2842	+	8.82432i	1.06749	+	0.616317i
$206$	−2.80407	−	10.4649i	−0.195369	−	0.729127i
$207$	−23.1197	+	5.91699i	−1.60693	+	0.411259i
$208$	−2.55358	+	2.54543i	−0.177059	+	0.176494i
$209$		−	16.9531i		−	1.17267i
$210$	−3.82216	+	1.55806i	−0.263754	+	0.107516i
$211$	7.68985	−	13.3192i	0.529391	−	0.916932i	−0.470022	−	0.882655i	$-0.655754\pi$
$211$	7.68985	−	13.3192i	0.529391	−	0.916932i	0.999412	−	0.0342769i	$-0.0109128\pi$
$212$	−6.72068	−	11.6406i	−0.461578	−	0.799477i
$213$	−16.3601	+	21.0745i	−1.12098	+	1.44400i
$214$	−0.888880	−	0.238175i	−0.0607626	−	0.0162813i
$215$	10.4079	+	2.78880i	0.709816	+	0.190195i
$216$	4.76638	+	2.06920i	0.324311	+	0.140791i
$217$	−1.36809	−	2.36961i	−0.0928722	−	0.160859i
$218$	−7.58686	+	13.1408i	−0.513847	+	0.890009i
$219$	9.61373	+	23.5839i	0.649636	+	1.59365i
$220$		−	12.8627i		−	0.867205i
$221$	−0.291581	−	1.09519i	−0.0196138	−	0.0736703i
$222$	9.36801	−	1.17976i	0.628740	−	0.0791801i
$223$	2.99845	+	11.1904i	0.200791	+	0.749363i	0.990691	+	0.136127i	$0.0434656\pi$
$223$	2.99845	+	11.1904i	0.200791	+	0.749363i	−0.789900	+	0.613235i	$0.789868\pi$
$224$	0.866025	+	0.500000i	0.0578638	+	0.0334077i
$225$	−1.45609	+	1.42369i	−0.0970725	+	0.0949127i
$226$	−2.45169	+	2.45169i	−0.163084	+	0.163084i
$227$	−0.908723	+	3.39140i	−0.0603141	+	0.225095i	−0.989504	−	0.144509i	$-0.953840\pi$
$227$	−0.908723	+	3.39140i	−0.0603141	+	0.225095i	0.929189	+	0.369604i	$0.120507\pi$
$228$	5.38946	+	0.740398i	0.356926	+	0.0490340i
$229$	16.3831	+	16.3831i	1.08263	+	1.08263i	0.996264	+	0.0863648i	$0.0275251\pi$
$229$	16.3831	+	16.3831i	1.08263	+	1.08263i	0.0863648	+	0.996264i	$0.472475\pi$
$230$	−16.4171	+	9.47843i	−1.08251	+	0.624989i
$231$	8.61708	+	3.62623i	0.566962	+	0.238588i
$232$	−10.0377	+	2.68959i	−0.659006	+	0.176580i
$233$	17.6100			1.15367			0.576835	−	0.816861i	$-0.304288\pi$
$233$	17.6100			1.15367			0.576835	+	0.816861i	$0.304288\pi$
$234$	−7.54965	−	7.74615i	−0.493536	−	0.506382i
$235$	−4.44680			−0.290077
$236$	−10.6210	+	2.84589i	−0.691368	+	0.185252i
$237$	−1.45638	−	0.612874i	−0.0946024	−	0.0398104i
$238$	−0.272219	+	0.157166i	−0.0176453	+	0.0101875i
$239$	−4.54828	−	4.54828i	−0.294203	−	0.294203i	0.544535	−	0.838738i	$-0.316706\pi$
$239$	−4.54828	−	4.54828i	−0.294203	−	0.294203i	−0.838738	+	0.544535i	$0.816706\pi$
$240$	4.08912	+	0.561758i	0.263951	+	0.0362613i
$241$	−2.02678	+	7.56405i	−0.130556	+	0.487243i	−0.999977	−	0.00683002i	$-0.997826\pi$
$241$	−2.02678	+	7.56405i	−0.130556	+	0.487243i	0.869420	+	0.494073i	$0.164493\pi$
$242$	−12.8231	+	12.8231i	−0.824298	+	0.824298i
$243$	−6.36805	+	14.2284i	−0.408511	+	0.912754i
$244$	−1.73250	−	1.00026i	−0.110912	−	0.0640350i
$245$	−0.616773	−	2.30183i	−0.0394042	−	0.147058i
$246$	12.7270	−	1.60277i	0.811444	−	0.102189i
$247$	−9.79819	−	5.67787i	−0.623444	−	0.361274i
$248$			2.73619i			0.173748i
$249$	−7.13418	−	17.5012i	−0.452110	−	1.10909i
$250$	5.14875	−	8.91790i	0.325636	−	0.564017i
$251$	1.15294	+	1.99695i	0.0727729	+	0.126046i	0.900116	−	0.435651i	$-0.143482\pi$
$251$	1.15294	+	1.99695i	0.0727729	+	0.126046i	−0.827343	+	0.561697i	$0.810148\pi$
$252$	−1.52913	+	2.58104i	−0.0963262	+	0.162590i
$253$	41.4749	+	11.1132i	2.60751	+	0.698679i
$254$	−6.90400	−	1.84992i	−0.433196	−	0.116074i
$255$	−0.795590	+	1.02485i	−0.0498218	+	0.0641783i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.50697	−	4.34221i	0.156381	−	0.270859i	−0.777180	−	0.629278i	$-0.783351\pi$
$257$	2.50697	−	4.34221i	0.156381	−	0.270859i	0.933561	+	0.358419i	$0.116684\pi$
$258$	7.25224	−	2.95630i	0.451504	−	0.184051i
$259$			5.45134i			0.338730i
$260$	−7.43413	−	4.30794i	−0.461045	−	0.267167i
$261$	−7.72952	−	30.2019i	−0.478445	−	1.86945i
$262$	−2.39691	−	8.94539i	−0.148082	−	0.552648i
$263$	8.92597	+	5.15341i	0.550399	+	0.317773i	0.749283	−	0.662250i	$-0.230398\pi$
$263$	8.92597	+	5.15341i	0.550399	+	0.317773i	−0.198884	+	0.980023i	$0.563732\pi$
$264$	−5.64950	−	7.44895i	−0.347703	−	0.458451i
$265$	22.6494	−	22.6494i	1.39134	−	1.39134i
$266$	−0.812907	+	3.03381i	−0.0498425	+	0.186015i
$267$	−0.405103	+	2.94880i	−0.0247919	+	0.180464i
$268$	0.986024	+	0.986024i	0.0602310	+	0.0602310i
$269$	−22.8265	+	13.1789i	−1.39176	+	0.803532i	−0.993510	−	0.113745i	$-0.963715\pi$
$269$	−22.8265	+	13.1789i	−1.39176	+	0.803532i	−0.398249	+	0.917277i	$0.630382\pi$
$270$	−1.82316	+	12.2476i	−0.110954	+	0.745366i
$271$	24.6221	−	6.59747i	1.49569	−	0.400768i	0.584033	−	0.811730i	$-0.301474\pi$
$271$	24.6221	−	6.59747i	1.49569	−	0.400768i	0.911653	+	0.410962i	$0.134807\pi$
$272$	0.314331			0.0190591
$273$	4.98182	−	3.76583i	0.301513	−	0.227919i
$274$	4.27493			0.258258
$275$	3.53914	−	0.948311i	0.213418	−	0.0571853i
$276$	−5.34427	+	12.6997i	−0.321687	+	0.764433i
$277$	11.5919	−	6.69261i	0.696493	−	0.402120i	−0.109547	−	0.993982i	$-0.534940\pi$
$277$	11.5919	−	6.69261i	0.696493	−	0.402120i	0.806040	+	0.591861i	$0.201607\pi$
$278$	4.73464	+	4.73464i	0.283965	+	0.283965i
$279$	−8.20804	−	0.0923367i	−0.491402	−	0.00552805i
$280$	−0.616773	+	2.30183i	−0.0368592	+	0.137560i
$281$	18.2454	−	18.2454i	1.08843	−	1.08843i	0.0927370	−	0.995691i	$-0.470438\pi$
$281$	18.2454	−	18.2454i	1.08843	−	1.08843i	0.995691	−	0.0927370i	$-0.0295616\pi$
$282$	−2.57519	+	1.95310i	−0.153350	+	0.116305i
$283$	12.5647	+	7.25421i	0.746891	+	0.431218i	0.824569	−	0.565761i	$-0.191417\pi$
$283$	12.5647	+	7.25421i	0.746891	+	0.431218i	−0.0776784	+	0.996978i	$0.524751\pi$
$284$	3.98667	+	14.8785i	0.236566	+	0.882875i
$285$	1.61980	+	12.8623i	0.0959489	+	0.761894i
$286$	5.00697	+	18.8064i	0.296068	+	1.11204i
$287$			7.40598i			0.437161i
$288$	2.61479	−	1.47068i	0.154078	−	0.0866606i
$289$	8.45060	−	14.6369i	0.497094	−	0.860992i
$290$	−12.3819	−	21.4461i	−0.727092	−	1.25936i
$291$	14.9887	+	11.6358i	0.878656	+	0.682102i
$292$	14.2030	+	3.80568i	0.831167	+	0.222711i
$293$	13.6841	+	3.66665i	0.799435	+	0.214208i	0.635336	−	0.772236i	$-0.280862\pi$
$293$	13.6841	+	3.66665i	0.799435	+	0.214208i	0.164099	+	0.986444i	$0.447528\pi$
$294$	−1.36818	−	1.06212i	−0.0797936	−	0.0619440i
$295$	−13.1015	−	22.6924i	−0.762798	−	1.32120i
$296$	2.72567	−	4.72100i	0.158426	−	0.274403i
$297$	22.5361	−	16.6960i	1.30768	−	0.968803i
$298$			6.82972i			0.395635i
$299$	20.3136	−	20.2488i	1.17477	−	1.17102i
$300$	0.146906	+	1.16652i	0.00848162	+	0.0673493i
$301$	1.17028	+	4.36753i	0.0674536	+	0.251740i
$302$	2.28859	+	1.32132i	0.131694	+	0.0760334i
$303$	5.49845	−	4.17018i	0.315877	−	0.239571i
$304$	2.22090	−	2.22090i	0.127378	−	0.127378i
$305$	1.23386	−	4.60484i	0.0706508	−	0.263672i
$306$	−0.0106076	+	0.942935i	−0.000606395	+	0.0539040i
$307$	−10.3618	−	10.3618i	−0.591379	−	0.591379i	0.346625	−	0.938004i	$-0.387328\pi$
$307$	−10.3618	−	10.3618i	−0.591379	−	0.591379i	−0.938004	+	0.346625i	$0.887328\pi$
$308$	4.67450	−	2.69882i	0.266354	−	0.153780i
$309$	7.27853	−	17.2961i	0.414061	−	0.983942i
$310$	−6.29822	+	1.68760i	−0.357715	+	0.0958495i
$311$	−6.34746			−0.359931			−0.179966	−	0.983673i	$-0.557599\pi$
$311$	−6.34746			−0.359931			−0.179966	+	0.983673i	$0.557599\pi$
$312$	−6.19730	+	0.770401i	−0.350853	+	0.0436154i
$313$	−19.2953			−1.09064			−0.545318	−	0.838229i	$-0.683591\pi$
$313$	−19.2953			−1.09064			−0.545318	+	0.838229i	$0.683591\pi$
$314$	10.8857	−	2.91682i	0.614317	−	0.164606i
$315$	−6.88423	−	1.92788i	−0.387882	−	0.108624i
$316$	−0.790043	+	0.456131i	−0.0444434	+	0.0256594i
$317$	19.2806	+	19.2806i	1.08290	+	1.08290i	0.996237	+	0.0866677i	$0.0276218\pi$
$317$	19.2806	+	19.2806i	1.08290	+	1.08290i	0.0866677	+	0.996237i	$0.472378\pi$
$318$	3.16857	−	23.0645i	0.177685	−	1.29339i
$319$	−14.5174	+	54.1798i	−0.812820	+	3.03349i
$320$	1.68505	−	1.68505i	0.0941974	−	0.0941974i
$321$	−0.963175	−	1.26996i	−0.0537592	−	0.0708823i
$322$	−6.88919	−	3.97748i	−0.383920	−	0.221656i
$323$	0.255522	+	0.953622i	0.0142176	+	0.0530609i
$324$	4.32352	+	7.89349i	0.240196	+	0.438527i
$325$	0.637234	−	2.36308i	0.0353474	−	0.131080i
$326$			20.2630i			1.12226i
$327$	−24.3373	+	9.92083i	−1.34585	+	0.548623i
$328$	3.70299	−	6.41377i	0.204463	−	0.354141i
$329$	−0.933016	−	1.61603i	−0.0514388	−	0.0890946i
$330$	13.6617	−	17.5985i	0.752053	−	0.968764i
$331$	18.2264	+	4.88375i	1.00181	+	0.268435i	0.722205	−	0.691679i	$-0.243129\pi$
$331$	18.2264	+	4.88375i	1.00181	+	0.268435i	0.279608	+	0.960114i	$0.409795\pi$
$332$	−10.5398	−	2.82413i	−0.578446	−	0.154994i
$333$	14.0701	+	8.33581i	0.771038	+	0.456800i
$334$	−8.39735	−	14.5446i	−0.459483	−	0.795847i
$335$	−1.66150	+	2.87781i	−0.0907776	+	0.157231i
$336$	0.653816	+	1.60391i	0.0356686	+	0.0875004i
$337$		−	7.09230i		−	0.386342i	−0.981165	−	0.193171i	$-0.938123\pi$
$337$		−	7.09230i		−	0.386342i	0.981165	−	0.193171i	$-0.0618772\pi$
$338$	12.5462	+	3.40474i	0.682425	+	0.185194i
$339$	−5.95834	+	0.750361i	−0.323612	+	0.0407540i
$340$	0.193871	+	0.723536i	0.0105141	+	0.0392393i
$341$	12.7903	+	7.38448i	0.692633	+	0.399892i
$342$	6.58734	+	6.73723i	0.356203	+	0.364308i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	1.17028	−	4.36753i	0.0630971	−	0.235481i
$345$	−32.5287	−	4.46876i	−1.75129	−	0.240590i
$346$	7.39394	+	7.39394i	0.397501	+	0.397501i
$347$	1.23698	−	0.714171i	0.0664046	−	0.0383387i	−0.466430	−	0.884558i	$-0.654460\pi$
$347$	1.23698	−	0.714171i	0.0664046	−	0.0383387i	0.532835	+	0.846219i	$0.321127\pi$
$348$	−16.5900	−	6.98137i	−0.889316	−	0.374241i
$349$	−1.85091	+	0.495949i	−0.0990768	+	0.0265475i	−0.308017	−	0.951381i	$-0.599665\pi$
$349$	−1.85091	+	0.495949i	−0.0990768	+	0.0265475i	0.208940	+	0.977928i	$0.432999\pi$
$350$	−0.678813			−0.0362841
$351$	−2.10192	−	18.6167i	−0.112192	−	0.993687i
$352$	−5.39764			−0.287695
$353$	10.8938	−	2.91899i	0.579820	−	0.155362i	0.0430234	−	0.999074i	$-0.486301\pi$
$353$	10.8938	−	2.91899i	0.579820	−	0.155362i	0.536796	+	0.843712i	$0.319634\pi$
$354$	−17.5541	−	7.38708i	−0.932988	−	0.392619i
$355$	−31.7888	+	18.3533i	−1.68717	+	0.974090i
$356$	1.21515	+	1.21515i	0.0644028	+	0.0644028i
$357$	−0.539372	−	0.0740983i	−0.0285466	−	0.00392170i
$358$	−3.65741	+	13.6496i	−0.193300	+	0.721406i
$359$	−7.42615	+	7.42615i	−0.391937	+	0.391937i	−0.875377	−	0.483440i	$-0.839387\pi$
$359$	−7.42615	+	7.42615i	−0.391937	+	0.391937i	0.483440	+	0.875377i	$0.339387\pi$
$360$	4.99798	+	5.11171i	0.263417	+	0.269411i
$361$	−7.91130	−	4.56759i	−0.416384	−	0.240399i
$362$	−1.53509	−	5.72902i	−0.0806824	−	0.301111i
$363$	−31.1638	+	3.92460i	−1.63568	+	0.205988i
$364$	0.00575899	−	3.60555i	0.000301853	−	0.188982i
$365$			35.0401i			1.83408i
$366$	−1.30797	−	3.20865i	−0.0683687	−	0.167719i
$367$	2.03209	−	3.51968i	0.106074	−	0.183726i	−0.808102	−	0.589042i	$-0.799505\pi$
$367$	2.03209	−	3.51968i	0.106074	−	0.183726i	0.914177	+	0.405316i	$0.132839\pi$
$368$	3.97748	+	6.88919i	0.207340	+	0.359124i
$369$	19.1151	+	11.3247i	0.995093	+	0.589541i
$370$	12.5480	+	3.36224i	0.652342	+	0.174794i
$371$	12.9834	+	3.47888i	0.674063	+	0.180615i
$372$	−2.90615	+	3.74358i	−0.150677	+	0.194096i
$373$	−8.51183	−	14.7429i	−0.440726	−	0.763360i	0.557017	−	0.830501i	$-0.311946\pi$
$373$	−8.51183	−	14.7429i	−0.440726	−	0.763360i	−0.997744	+	0.0671409i	$0.978612\pi$
$374$	0.848325	−	1.46934i	0.0438658	−	0.0759778i
$375$	16.5163	−	6.73267i	0.852896	−	0.347674i
$376$			1.86603i			0.0962332i
$377$	26.4516	+	26.5362i	1.36233	+	1.36668i
$378$	−4.83349	+	1.90720i	−0.248608	+	0.0980957i
$379$	−0.821206	−	3.06478i	−0.0421825	−	0.157427i	0.941622	−	0.336672i	$-0.109301\pi$
$379$	−0.821206	−	3.06478i	−0.0421825	−	0.157427i	−0.983805	+	0.179245i	$0.942635\pi$
$380$	6.48192	+	3.74234i	0.332516	+	0.191978i
$381$	−7.48106	−	9.86389i	−0.383266	−	0.505342i
$382$	−5.67243	+	5.67243i	−0.290227	+	0.290227i
$383$	−9.20354	+	34.3481i	−0.470279	+	1.75511i	0.168487	+	0.985704i	$0.446112\pi$
$383$	−9.20354	+	34.3481i	−0.470279	+	1.75511i	−0.638766	+	0.769401i	$0.720555\pi$
$384$	0.235733	−	1.71593i	0.0120297	−	0.0875659i
$385$	9.09532	+	9.09532i	0.463540	+	0.463540i
$386$	−9.94478	+	5.74162i	−0.506176	+	0.292241i
$387$	13.0623	+	3.65800i	0.663993	+	0.185946i
$388$	10.5820	−	2.83543i	0.537219	−	0.143947i
$389$	−19.8980			−1.00887			−0.504434	−	0.863450i	$-0.668299\pi$
$389$	−19.8980			−1.00887			−0.504434	+	0.863450i	$0.668299\pi$
$390$	−5.59565	−	13.7899i	−0.283347	−	0.698281i
$391$	−2.50049			−0.126455
$392$	−0.965926	+	0.258819i	−0.0487866	+	0.0130723i
$393$	6.22166	−	14.7847i	0.313841	−	0.745788i
$394$	4.53019	−	2.61551i	0.228228	−	0.131767i
$395$	−1.53721	−	1.53721i	−0.0773455	−	0.0773455i
$396$	0.182152	−	16.1919i	0.00915346	−	0.813674i
$397$	8.93785	−	33.3565i	0.448578	−	1.67411i	−0.257736	−	0.966215i	$-0.582976\pi$
$397$	8.93785	−	33.3565i	0.448578	−	1.67411i	0.706314	−	0.707899i	$-0.250357\pi$
$398$	−7.68504	+	7.68504i	−0.385216	+	0.385216i
$399$	−4.33446	+	3.28738i	−0.216995	+	0.164575i
$400$	0.587869	+	0.339407i	0.0293935	+	0.0169703i
$401$	−0.0962543	−	0.359226i	−0.00480671	−	0.0179389i	0.963481	−	0.267777i	$-0.0862892\pi$
$401$	−0.0962543	−	0.359226i	−0.00480671	−	0.0179389i	−0.968288	+	0.249838i	$0.919622\pi$
$402$	0.301781	+	2.39633i	0.0150515	+	0.119518i
$403$	8.55160	−	4.91908i	0.425986	−	0.245037i
$404$		−	3.98427i		−	0.198225i
$405$	−15.5028	+	14.8205i	−0.770341	+	0.736436i
$406$	5.19588	−	8.99954i	0.257867	−	0.446640i
$407$	−14.7122	−	25.4823i	−0.729257	−	1.26311i
$408$	0.430061	+	0.333857i	0.0212912	+	0.0165284i
$409$	7.07285	+	1.89516i	0.349730	+	0.0937098i	0.429407	−	0.903111i	$-0.358722\pi$
$409$	7.07285	+	1.89516i	0.349730	+	0.0937098i	−0.0796777	+	0.996821i	$0.525389\pi$
$410$	17.0473	+	4.56780i	0.841905	+	0.225588i
$411$	5.84885	+	4.54048i	0.288503	+	0.223965i
$412$	−5.41705	−	9.38260i	−0.266879	−	0.462248i
$413$	5.49783	−	9.52253i	0.270531	−	0.468573i
$414$	−20.8005	+	11.6992i	−1.02229	+	0.574984i
$415$		−	26.0026i		−	1.27642i
$416$	−1.80776	+	3.11962i	−0.0886328	+	0.152952i
$417$	1.44908	+	11.5066i	0.0709616	+	0.563479i
$418$	−4.38778	−	16.3754i	−0.214613	−	0.800948i
$419$	6.05575	+	3.49629i	0.295843	+	0.170805i	0.640574	−	0.767897i	$-0.278697\pi$
$419$	6.05575	+	3.49629i	0.295843	+	0.170805i	−0.344731	+	0.938702i	$0.612030\pi$
$420$	−3.28866	+	2.49422i	−0.160470	+	0.121705i
$421$	−17.6307	+	17.6307i	−0.859267	+	0.859267i	−0.991252	−	0.131985i	$-0.957865\pi$
$421$	−17.6307	+	17.6307i	−0.859267	+	0.859267i	0.131985	+	0.991252i	$0.457865\pi$
$422$	3.98056	−	14.8556i	0.193771	−	0.723161i
$423$	−5.59774	−	0.0629720i	−0.272171	−	0.00306180i
$424$	−9.50448	−	9.50448i	−0.461578	−	0.461578i
$425$	−0.184786	+	0.106686i	−0.00896343	+	0.00517504i
$426$	−10.3482	+	24.5907i	−0.501373	+	1.19142i
$427$	1.93235	−	0.517772i	0.0935130	−	0.0250567i
$428$	−0.920236			−0.0444813
$429$	−13.1242	+	31.0484i	−0.633641	+	1.49903i
$430$	10.7751			0.519621
$431$	−9.14787	+	2.45116i	−0.440637	+	0.118068i	−0.472315	−	0.881430i	$-0.656582\pi$
$431$	−9.14787	+	2.45116i	−0.440637	+	0.118068i	0.0316778	+	0.999498i	$0.489915\pi$
$432$	5.13952	+	0.765061i	0.247275	+	0.0368090i
$433$	−15.2953	+	8.83075i	−0.735046	+	0.424379i	−0.820265	−	0.571983i	$-0.806174\pi$
$433$	−15.2953	+	8.83075i	−0.735046	+	0.424379i	0.0852196	+	0.996362i	$0.472841\pi$
$434$	−1.93478	−	1.93478i	−0.0928722	−	0.0928722i
$435$	5.83766	−	42.4931i	0.279894	−	2.03739i
$436$	−3.92725	+	14.6567i	−0.188081	+	0.701928i
$437$	−17.6672	+	17.6672i	−0.845136	+	0.845136i
$438$	15.3901	+	20.2921i	0.735368	+	0.969594i
$439$	17.1442	+	9.89820i	0.818248	+	0.472415i	0.849812	−	0.527086i	$-0.176716\pi$
$439$	17.1442	+	9.89820i	0.818248	+	0.472415i	−0.0315642	+	0.999502i	$0.510049\pi$
$440$	−3.32912	−	12.4244i	−0.158709	−	0.592312i
$441$	−0.743811	−	2.90633i	−0.0354196	−	0.138397i
$442$	−0.565101	−	0.982404i	−0.0268791	−	0.0467282i
$443$		−	20.9178i		−	0.993835i	−0.867798	−	0.496918i	$-0.834465\pi$
$443$		−	20.9178i		−	0.993835i	0.867798	−	0.496918i	$-0.165535\pi$
$444$	8.74346	−	3.56418i	0.414946	−	0.169148i
$445$	−2.04759	+	3.54653i	−0.0970652	+	0.168122i
$446$	5.79256	+	10.0330i	0.274286	+	0.475077i
$447$	−7.25397	+	9.34426i	−0.343101	+	0.441968i
$448$	0.965926	+	0.258819i	0.0456357	+	0.0122281i
$449$	−6.41982	−	1.72019i	−0.302970	−	0.0811806i	0.104131	−	0.994564i	$-0.466794\pi$
$449$	−6.41982	−	1.72019i	−0.302970	−	0.0811806i	−0.407101	+	0.913383i	$0.633460\pi$
$450$	−1.03799	+	1.75204i	−0.0489315	+	0.0825921i
$451$	−19.9874	−	34.6192i	−0.941171	−	1.63016i
$452$	−1.73361	+	3.00270i	−0.0815421	+	0.141235i
$453$	1.72780	+	4.23855i	0.0811792	+	0.199145i
$454$			3.51104i			0.164781i
$455$	8.30289	−	2.21055i	0.389246	−	0.103632i
$456$	5.39745	−	0.679726i	0.252759	−	0.0318311i
$457$	−3.75260	−	14.0049i	−0.175539	−	0.655122i	−0.996459	−	0.0840783i	$-0.973205\pi$
$457$	−3.75260	−	14.0049i	−0.175539	−	0.655122i	0.820920	−	0.571044i	$-0.193461\pi$
$458$	20.0652	+	11.5846i	0.937584	+	0.541314i
$459$	−1.01602	+	1.27883i	−0.0474238	+	0.0596909i
$460$	−13.4045	+	13.4045i	−0.624989	+	0.624989i
$461$	2.64045	−	9.85429i	0.122978	−	0.458960i	−0.876782	−	0.480889i	$-0.840314\pi$
$461$	2.64045	−	9.85429i	0.122978	−	0.458960i	0.999760	+	0.0219289i	$0.00698073\pi$
$462$	9.26200	+	1.27240i	0.430907	+	0.0591975i
$463$	2.59471	+	2.59471i	0.120586	+	0.120586i	0.764825	−	0.644238i	$-0.222826\pi$
$463$	2.59471	+	2.59471i	0.120586	+	0.120586i	−0.644238	+	0.764825i	$0.722826\pi$
$464$	−8.99954	+	5.19588i	−0.417793	+	0.241213i
$465$	−10.4095	−	4.38052i	−0.482730	−	0.203142i
$466$	17.0100	−	4.55781i	0.787971	−	0.211136i
$467$	−2.35099			−0.108791			−0.0543954	−	0.998519i	$-0.517323\pi$
$467$	−2.35099			−0.108791			−0.0543954	+	0.998519i	$0.517323\pi$
$468$	−9.29725	−	5.52822i	−0.429765	−	0.255542i
$469$	−1.39445			−0.0643896
$470$	−4.29528	+	1.15092i	−0.198126	+	0.0530878i
$471$	17.9916	+	7.57120i	0.829009	+	0.348862i
$472$	−9.52253	+	5.49783i	−0.438310	+	0.253058i
$473$	−17.2576	−	17.2576i	−0.793507	−	0.793507i
$474$	−1.56538	−	0.215050i	−0.0719004	−	0.00987760i
$475$	−0.551812	+	2.05939i	−0.0253189	+	0.0944913i
$476$	−0.222266	+	0.222266i	−0.0101875	+	0.0101875i
$477$	28.8324	−	28.1909i	1.32014	−	1.29077i
$478$	−5.57048	−	3.21612i	−0.254788	−	0.147102i
$479$	6.34353	+	23.6744i	0.289843	+	1.08171i	0.945227	+	0.326414i	$0.105840\pi$
$479$	6.34353	+	23.6744i	0.289843	+	1.08171i	−0.655384	+	0.755296i	$0.727493\pi$
$480$	4.09518	−	0.515725i	0.186918	−	0.0235395i
$481$	−19.6551	−	0.0313942i	−0.896194	−	0.00143145i
$482$			7.83088i			0.356687i
$483$	−5.20108	−	12.7590i	−0.236657	−	0.580556i
$484$	−9.06727	+	15.7050i	−0.412149	+	0.713863i
$485$	13.0534	+	22.6091i	0.592722	+	1.02662i
$486$	−2.46848	+	15.3918i	−0.111972	+	0.698185i
$487$	−28.3651	−	7.60040i	−1.28534	−	0.344407i	−0.449454	−	0.893304i	$-0.648381\pi$
$487$	−28.3651	−	7.60040i	−1.28534	−	0.344407i	−0.835890	+	0.548897i	$0.815048\pi$
$488$	−1.93235	−	0.517772i	−0.0874734	−	0.0234384i
$489$	−21.5217	+	27.7233i	−0.973243	+	1.25369i
$490$	−1.19151	−	2.06376i	−0.0538271	−	0.0932312i
$491$	−2.03495	+	3.52464i	−0.0918360	+	0.159065i	−0.908284	−	0.418355i	$-0.862607\pi$
$491$	−2.03495	+	3.52464i	−0.0918360	+	0.159065i	0.816448	+	0.577419i	$0.195940\pi$
$492$	11.8785	−	4.84215i	0.535525	−	0.218301i
$493$		−	3.26646i		−	0.147114i
$494$	−10.9339	−	2.94845i	−0.491938	−	0.132657i
$495$	37.3833	−	9.56744i	1.68025	−	0.430024i
$496$	0.708177	+	2.64295i	0.0317981	+	0.118672i
$497$	−13.3397	−	7.70166i	−0.598366	−	0.345467i
$498$	−11.4207	−	15.0584i	−0.511775	−	0.674783i
$499$	3.98743	−	3.98743i	0.178502	−	0.178502i	−0.612201	−	0.790702i	$-0.709716\pi$
$499$	3.98743	−	3.98743i	0.178502	−	0.178502i	0.790702	+	0.612201i	$0.209716\pi$
$500$	2.66519	−	9.94662i	0.119191	−	0.444826i
$501$	3.95907	−	28.8186i	0.176878	−	1.28752i
$502$	1.63050	+	1.63050i	0.0727729	+	0.0727729i
$503$	−0.509042	+	0.293895i	−0.0226970	+	0.0131041i	−0.511306	−	0.859399i	$-0.670838\pi$
$503$	−0.509042	+	0.293895i	−0.0226970	+	0.0131041i	0.488609	+	0.872503i	$0.337505\pi$
$504$	−0.809005	+	2.88886i	−0.0360359	+	0.128680i
$505$	9.17111	−	2.45739i	0.408109	−	0.109352i
$506$	42.9380			1.90883
$507$	13.5492	+	17.9839i	0.601741	+	0.798691i
$508$	−7.14755			−0.317121
$509$	16.4316	−	4.40284i	0.728319	−	0.195153i	0.124439	−	0.992227i	$-0.460287\pi$
$509$	16.4316	−	4.40284i	0.728319	−	0.195153i	0.603881	+	0.797075i	$0.293620\pi$
$510$	−0.503231	+	1.19584i	−0.0222835	+	0.0529526i
$511$	−12.7341	+	7.35201i	−0.563322	+	0.325234i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.85690	+	16.2143i	0.0819843	+	0.715877i
$514$	1.29770	−	4.84310i	0.0572393	−	0.213620i
$515$	18.2560	−	18.2560i	0.804457	−	0.804457i
$516$	6.23998	−	4.73258i	0.274700	−	0.208340i
$517$	8.72275	+	5.03608i	0.383626	+	0.221487i
$518$	1.41091	+	5.26559i	0.0619919	+	0.231357i
$519$	2.26298	+	17.9695i	0.0993337	+	0.788772i
$520$	−8.29579	−	2.23706i	−0.363794	−	0.0981015i
$521$			6.59626i			0.288988i	0.989506	+	0.144494i	$0.0461554\pi$
$521$			6.59626i			0.288988i	−0.989506	+	0.144494i	$0.953845\pi$
$522$	−15.2830	−	27.1722i	−0.668917	−	1.18930i
$523$	−19.5875	+	33.9266i	−0.856503	+	1.48351i	0.0187410	+	0.999824i	$0.494034\pi$
$523$	−19.5875	+	33.9266i	−0.856503	+	1.48351i	−0.875244	+	0.483682i	$0.839299\pi$
$524$	−4.63047	−	8.02021i	−0.202283	−	0.350365i
$525$	−0.928736	−	0.720979i	−0.0405334	−	0.0314661i
$526$	9.95563	+	2.66760i	0.434086	+	0.116313i
$527$	−0.830763	−	0.222602i	−0.0361886	−	0.00969671i
$528$	−7.38493	−	5.73293i	−0.321388	−	0.249494i
$529$	−20.1407	−	34.8846i	−0.875680	−	1.51672i
$530$	16.0156	−	27.7398i	0.695672	−	1.20494i
$531$	−16.1711	−	28.7513i	−0.701766	−	1.24770i
$532$			3.14083i			0.136172i
$533$	−26.7026	−	0.0426510i	−1.15662	−	0.00184742i
$534$	0.371906	+	2.95317i	0.0160940	+	0.127796i
$535$	−0.567576	−	2.11822i	−0.0245385	−	0.0915788i
$536$	1.20763	+	0.697224i	0.0521616	+	0.0301155i
$537$	−19.5015	+	14.7905i	−0.841552	+	0.638258i
$538$	−18.6378	+	18.6378i	−0.803532	+	0.803532i
$539$	−1.39701	+	5.21372i	−0.0601736	+	0.224571i
$540$	1.40888	+	12.3022i	0.0606285	+	0.529400i
$541$	−9.44349	−	9.44349i	−0.406008	−	0.406008i	0.474336	−	0.880344i	$-0.342688\pi$
$541$	−9.44349	−	9.44349i	−0.406008	−	0.406008i	−0.880344	+	0.474336i	$0.842688\pi$
$542$	22.0756	−	12.7453i	0.948227	−	0.547459i
$543$	3.98463	−	9.46876i	0.170997	−	0.406343i
$544$	0.303621	−	0.0813550i	0.0130176	−	0.00348807i
$545$	−36.1594			−1.54890
$546$	3.83739	−	4.92691i	0.164225	−	0.210852i
$547$	−37.4451			−1.60104			−0.800519	−	0.599307i	$-0.795443\pi$
$547$	−37.4451			−1.60104			−0.800519	+	0.599307i	$0.795443\pi$
$548$	4.12926	−	1.10643i	0.176393	−	0.0472645i
$549$	1.61843	−	5.77921i	0.0690728	−	0.246651i
$550$	3.17311	−	1.83200i	0.135302	−	0.0781165i
$551$	−23.0791	−	23.0791i	−0.983203	−	0.983203i
$552$	−1.87525	+	13.6502i	−0.0798157	+	0.580990i
$553$	0.236111	−	0.881178i	0.0100405	−	0.0374715i
$554$	9.46478	−	9.46478i	0.402120	−	0.402120i
$555$	13.5968	+	17.9276i	0.577154	+	0.760986i
$556$	5.79873	+	3.34790i	0.245921	+	0.141982i
$557$	−6.25932	−	23.3601i	−0.265216	−	0.989799i	−0.962118	−	0.272633i	$-0.912106\pi$
$557$	−6.25932	−	23.3601i	−0.265216	−	0.989799i	0.696902	−	0.717166i	$-0.254561\pi$
$558$	−7.95225	+	2.03521i	−0.336646	+	0.0861571i
$559$	−15.7541	+	4.19433i	−0.666326	+	0.177401i
$560$			2.38303i			0.100701i
$561$	2.72127	−	1.10930i	0.114892	−	0.0468345i
$562$	12.9014	−	22.3459i	0.544214	−	0.942606i
$563$	7.44158	+	12.8892i	0.313625	+	0.543215i	0.979144	−	0.203166i	$-0.0651231\pi$
$563$	7.44158	+	12.8892i	0.313625	+	0.543215i	−0.665519	+	0.746381i	$0.731790\pi$
$564$	−1.98194	+	2.55306i	−0.0834549	+	0.107503i
$565$	−7.98094	−	2.13849i	−0.335761	−	0.0899668i
$566$	14.0140	+	3.75505i	0.589054	+	0.157837i
$567$	−8.63873	−	2.52435i	−0.362793	−	0.106013i
$568$	7.70166	+	13.3397i	0.323155	+	0.559720i
$569$	21.4049	−	37.0743i	0.897339	−	1.55424i	0.0664562	−	0.997789i	$-0.478831\pi$
$569$	21.4049	−	37.0743i	0.897339	−	1.55424i	0.830883	−	0.556447i	$-0.187836\pi$
$570$	4.89361	+	12.0047i	0.204971	+	0.502824i
$571$			4.14595i			0.173503i	0.996230	+	0.0867514i	$0.0276486\pi$
$571$			4.14595i			0.173503i	−0.996230	+	0.0867514i	$0.972351\pi$
$572$	9.70381	+	16.8697i	0.405737	+	0.705356i
$573$	−13.7857	+	1.73609i	−0.575905	+	0.0725264i
$574$	1.91681	+	7.15363i	0.0800060	+	0.298587i
$575$	−4.67647	−	2.69996i	−0.195022	−	0.112596i
$576$	2.14505	−	2.09732i	0.0893770	−	0.0873885i
$577$	8.72938	−	8.72938i	0.363409	−	0.363409i	−0.501657	−	0.865066i	$-0.667276\pi$
$577$	8.72938	−	8.72938i	0.363409	−	0.363409i	0.865066	+	0.501657i	$0.167276\pi$
$578$	4.37435	−	16.3253i	0.181949	−	0.679043i
$579$	−19.7045	−	2.70698i	−0.818891	−	0.112498i
$580$	−17.5107	−	17.5107i	−0.727092	−	0.727092i
$581$	9.44972	−	5.45580i	0.392040	−	0.226345i
$582$	17.4896	+	7.35994i	0.724966	+	0.305079i
$583$	−70.0796	+	18.7778i	−2.90240	+	0.777696i
$584$	14.7040			0.608457
$585$	6.99070	−	24.8103i	0.289030	−	1.02578i
$586$	14.1669			0.585227
$587$	20.4212	−	5.47185i	0.842874	−	0.225847i	0.188552	−	0.982063i	$-0.439621\pi$
$587$	20.4212	−	5.47185i	0.842874	−	0.225847i	0.654322	+	0.756216i	$0.272954\pi$
$588$	−1.59645	−	0.671817i	−0.0658366	−	0.0277053i
$589$	−7.44253	+	4.29695i	−0.306664	+	0.177053i
$590$	−18.5283	−	18.5283i	−0.762798	−	0.762798i
$591$	8.97608	+	1.23312i	0.369227	+	0.0507239i
$592$	1.41091	−	5.26559i	0.0579881	−	0.216415i
$593$	3.55722	−	3.55722i	0.146077	−	0.146077i	−0.630286	−	0.776363i	$-0.717062\pi$
$593$	3.55722	−	3.55722i	0.146077	−	0.146077i	0.776363	+	0.630286i	$0.217062\pi$
$594$	17.4469	−	21.9599i	0.715856	−	0.901026i
$595$	−0.648705	−	0.374530i	−0.0265943	−	0.0153542i
$596$	1.76766	+	6.59700i	0.0724062	+	0.270224i
$597$	−18.6769	+	2.35207i	−0.764395	+	0.0962638i
$598$	14.3807	−	24.8164i	0.588069	−	1.01482i
$599$			26.3024i			1.07469i	0.843363	+	0.537344i	$0.180572\pi$
$599$			26.3024i			1.07469i	−0.843363	+	0.537344i	$0.819428\pi$
$600$	0.443819	+	1.08875i	0.0181188	+	0.0444482i
$601$	4.78852	−	8.29396i	0.195328	−	0.338317i	−0.751680	−	0.659528i	$-0.770756\pi$
$601$	4.78852	−	8.29396i	0.195328	−	0.338317i	0.947008	+	0.321210i	$0.104090\pi$
$602$	2.26080	+	3.91582i	0.0921433	+	0.159597i
$603$	−2.13229	+	3.59912i	−0.0868337	+	0.146568i
$604$	2.55259	+	0.683966i	0.103864	+	0.0278302i
$605$	−41.7426	−	11.1849i	−1.69708	−	0.454731i
$606$	4.23177	−	5.45119i	0.171904	−	0.221439i
$607$	14.0402	+	24.3184i	0.569876	+	0.987054i	0.996578	+	0.0826613i	$0.0263420\pi$
$607$	14.0402	+	24.3184i	0.569876	+	0.987054i	−0.426702	+	0.904392i	$0.640325\pi$
$608$	1.57042	−	2.72004i	0.0636888	−	0.110312i
$609$	16.6675	−	6.79431i	0.675399	−	0.275319i
$610$		−	4.76728i		−	0.193022i
$611$	5.83205	−	3.35472i	0.235939	−	0.135718i
$612$	0.233803	+	0.913550i	0.00945094	+	0.0369281i
$613$	1.45241	+	5.42048i	0.0586624	+	0.218931i	0.989034	−	0.147686i	$-0.0471825\pi$
$613$	1.45241	+	5.42048i	0.0586624	+	0.218931i	−0.930372	+	0.366617i	$0.880516\pi$
$614$	−12.6905	−	7.32689i	−0.512149	−	0.295689i
$615$	18.4721	+	24.3558i	0.744868	+	0.982120i
$616$	3.81671	−	3.81671i	0.153780	−	0.153780i
$617$	−11.9962	+	44.7703i	−0.482948	+	1.80239i	0.106182	+	0.994347i	$0.466138\pi$
$617$	−11.9962	+	44.7703i	−0.482948	+	1.80239i	−0.589129	+	0.808039i	$0.700529\pi$
$618$	2.55395	−	18.5906i	0.102735	−	0.747824i
$619$	−7.09633	−	7.09633i	−0.285226	−	0.285226i	0.549963	−	0.835189i	$-0.314642\pi$
$619$	−7.09633	−	7.09633i	−0.285226	−	0.285226i	−0.835189	+	0.549963i	$0.814642\pi$
$620$	−5.64683	+	3.26020i	−0.226782	+	0.130933i
$621$	−40.8847	−	6.08603i	−1.64064	−	0.244224i
$622$	−6.13117	+	1.64284i	−0.245838	+	0.0658720i
$623$	−1.71848			−0.0688495
$624$	−5.78673	+	2.34813i	−0.231655	+	0.0940004i
$625$	27.9333			1.11733
$626$	−18.6379	+	4.99400i	−0.744918	+	0.199600i
$627$	11.3894	−	27.0648i	0.454848	−	1.08086i
$628$	9.75987	−	5.63487i	0.389461	−	0.224856i
$629$	1.21165	+	1.21165i	0.0483116	+	0.0483116i
$630$	−7.14863	−	0.0804188i	−0.284808	−	0.00320396i
$631$	6.92849	−	25.8575i	0.275819	−	1.02937i	−0.679472	−	0.733701i	$-0.737791\pi$
$631$	6.92849	−	25.8575i	0.275819	−	1.02937i	0.955291	−	0.295668i	$-0.0955422\pi$
$632$	−0.645067	+	0.645067i	−0.0256594	+	0.0256594i
$633$	21.2245	−	16.0973i	0.843600	−	0.639811i
$634$	23.6138	+	13.6334i	0.937823	+	0.541452i
$635$	−4.40841	−	16.4524i	−0.174943	−	0.652894i
$636$	−2.90893	−	23.0987i	−0.115346	−	0.915923i
$637$	2.54543	+	2.55358i	0.100854	+	0.101176i
$638$			56.0911i			2.22067i
$639$	−40.2764	+	22.6534i	−1.59331	+	0.896153i
$640$	1.19151	−	2.06376i	0.0470987	−	0.0815773i
$641$	−14.0090	−	24.2644i	−0.553324	−	0.958385i	−0.998032	−	0.0627092i	$-0.980026\pi$
$641$	−14.0090	−	24.2644i	−0.553324	−	0.958385i	0.444708	−	0.895676i	$-0.353307\pi$
$642$	−1.25905	−	0.977399i	−0.0496906	−	0.0385749i
$643$	19.7840	+	5.30111i	0.780206	+	0.209056i	0.626875	−	0.779119i	$-0.284333\pi$
$643$	19.7840	+	5.30111i	0.780206	+	0.209056i	0.153330	+	0.988175i	$0.451000\pi$
$644$	−7.68390	−	2.05889i	−0.302788	−	0.0811318i
$645$	14.7422	+	11.4444i	0.580474	+	0.450623i
$646$	0.493631	+	0.854994i	0.0194217	+	0.0336393i
$647$	8.36063	−	14.4810i	0.328690	−	0.569308i	−0.653562	−	0.756873i	$-0.726726\pi$
$647$	8.36063	−	14.4810i	0.328690	−	0.569308i	0.982252	+	0.187565i	$0.0600594\pi$
$648$	6.21919	+	6.50552i	0.244313	+	0.255561i
$649$			59.3507i			2.32972i
$650$	0.00390928	−	2.44749i	0.000153335	−	0.0959985i
$651$	−0.592154	−	4.70207i	−0.0232083	−	0.184289i
$652$	5.24444	+	19.5725i	0.205388	+	0.766519i
$653$	−40.3965	−	23.3229i	−1.58084	−	0.912696i	−0.994738	−	0.102456i	$-0.967330\pi$
$653$	−40.3965	−	23.3229i	−1.58084	−	0.912696i	−0.586098	−	0.810240i	$-0.699337\pi$
$654$	−20.9403	+	15.8817i	−0.818830	+	0.621025i
$655$	15.6052	−	15.6052i	0.609745	−	0.609745i
$656$	1.91681	−	7.15363i	0.0748388	−	0.279302i
$657$	−0.496209	+	44.1093i	−0.0193590	+	1.72087i
$658$	−1.31948	−	1.31948i	−0.0514388	−	0.0514388i
$659$	3.91850	−	2.26235i	0.152643	−	0.0881285i	−0.421733	−	0.906720i	$-0.638578\pi$
$659$	3.91850	−	2.26235i	0.152643	−	0.0881285i	0.574376	+	0.818592i	$0.305245\pi$
$660$	8.64140	−	20.5347i	0.336366	−	0.799313i
$661$	−5.63401	+	1.50963i	−0.219138	+	0.0587178i	−0.366717	−	0.930332i	$-0.619518\pi$
$661$	−5.63401	+	1.50963i	−0.219138	+	0.0587178i	0.147580	+	0.989050i	$0.452852\pi$
$662$	18.8694			0.733378
$663$	0.270271	−	1.94430i	0.0104965	−	0.0755105i
$664$	−10.9116			−0.423452
$665$	−7.22965	+	1.93718i	−0.280354	+	0.0751205i
$666$	15.7482	+	4.41016i	0.610229	+	0.170890i
$667$	71.5909	−	41.3330i	2.77201	−	1.60042i
$668$	−11.8756	−	11.8756i	−0.459483	−	0.459483i
$669$	−2.73100	+	19.8793i	−0.105586	+	0.768579i
$670$	−0.860057	+	3.20978i	−0.0332269	+	0.124005i
$671$	−7.63539	+	7.63539i	−0.294761	+	0.294761i
$672$	1.04666	+	1.38004i	0.0403758	+	0.0532361i
$673$	−17.4292	−	10.0628i	−0.671847	−	0.387891i	0.124929	−	0.992166i	$-0.460130\pi$
$673$	−17.4292	−	10.0628i	−0.671847	−	0.387891i	−0.796776	+	0.604275i	$0.793463\pi$
$674$	−1.83562	−	6.85063i	−0.0707055	−	0.263877i
$675$	−3.28103	+	1.29463i	−0.126287	+	0.0498304i
$676$	12.9999	+	0.0415286i	0.499997	+	0.00159725i
$677$			15.6707i			0.602275i	0.953581	+	0.301138i	$0.0973663\pi$
$677$			15.6707i			0.602275i	−0.953581	+	0.301138i	$0.902634\pi$
$678$	−5.56110	+	2.26692i	−0.213573	+	0.0870607i
$679$	−5.47764	+	9.48755i	−0.210212	+	0.364099i
$680$	0.374530	+	0.648705i	0.0143626	+	0.0248767i
$681$	−3.72914	+	4.80372i	−0.142901	+	0.184079i
$682$	14.2657	+	3.82249i	0.546262	+	0.146371i
$683$	−10.0052	−	2.68088i	−0.382838	−	0.102581i	0.0622669	−	0.998060i	$-0.480167\pi$
$683$	−10.0052	−	2.68088i	−0.382838	−	0.102581i	−0.445105	+	0.895478i	$0.646834\pi$
$684$	8.10661	+	4.80274i	0.309964	+	0.183637i
$685$	5.09363	+	8.82243i	0.194618	+	0.337088i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	15.1484	+	37.1614i	0.577949	+	1.41780i
$688$		−	4.52160i		−	0.172384i
$689$	−12.6180	+	46.7921i	−0.480709	+	1.78264i
$690$	−32.5769	+	4.10257i	−1.24018	+	0.156182i
$691$	−6.97535	−	26.0324i	−0.265355	−	0.990318i	−0.962033	−	0.272934i	$-0.912006\pi$
$691$	−6.97535	−	26.0324i	−0.265355	−	0.990318i	0.696678	−	0.717384i	$-0.254661\pi$
$692$	9.05569	+	5.22831i	0.344246	+	0.198750i
$693$	11.3206	+	11.5782i	0.430034	+	0.439820i
$694$	1.00999	−	1.00999i	0.0383387	−	0.0383387i
$695$	−4.12978	+	15.4126i	−0.156652	+	0.584632i
$696$	−17.8316	−	2.44968i	−0.675905	−	0.0928550i
$697$	1.64610	+	1.64610i	0.0623504	+	0.0623504i
$698$	−1.65948	+	0.958100i	−0.0628121	+	0.0362646i
$699$	28.1135	+	11.8307i	1.06335	+	0.447478i
$700$	−0.655683	+	0.175690i	−0.0247825	+	0.00664045i
$701$	−23.7687			−0.897732			−0.448866	−	0.893599i	$-0.648172\pi$
$701$	−23.7687			−0.897732			−0.448866	+	0.893599i	$0.648172\pi$
$702$	−6.84866	−	17.4383i	−0.258486	−	0.658168i
$703$	17.1217			0.645759
$704$	−5.21372	+	1.39701i	−0.196500	+	0.0526519i
$705$	−7.09911	−	2.98744i	−0.267368	−	0.112513i
$706$	9.76714	−	5.63906i	0.367591	−	0.212229i
$707$	2.81731	+	2.81731i	0.105956	+	0.105956i
$708$	−18.8678	−	2.59204i	−0.709097	−	0.0974149i
$709$	4.49421	−	16.7726i	0.168783	−	0.629908i	−0.828744	−	0.559628i	$-0.810944\pi$
$709$	4.49421	−	16.7726i	0.168783	−	0.629908i	0.997527	−	0.0702802i	$-0.0223893\pi$
$710$	−25.9554	+	25.9554i	−0.974090	+	0.974090i
$711$	−1.91331	−	1.95685i	−0.0717548	−	0.0733875i
$712$	1.48825	+	0.859240i	0.0557745	+	0.0322014i
$713$	−5.63351	−	21.0246i	−0.210977	−	0.787376i
$714$	−0.540171	+	0.0680263i	−0.0202154	+	0.00254582i
$715$	−32.8460	+	32.7412i	−1.22837	+	1.22445i
$716$			14.1311i			0.528106i
$717$	−4.20550	−	10.3167i	−0.157057	−	0.385285i
$718$	−5.25108	+	9.09513i	−0.195968	+	0.339427i
$719$	−12.1046	−	20.9657i	−0.451424	−	0.781889i	0.547051	−	0.837099i	$-0.315750\pi$
$719$	−12.1046	−	20.9657i	−0.451424	−	0.781889i	−0.998475	+	0.0552105i	$0.982417\pi$
$720$	6.15068	+	3.64396i	0.229222	+	0.135802i
$721$	10.4649	+	2.80407i	0.389735	+	0.104429i
$722$	−8.82391	−	2.36436i	−0.328392	−	0.0879923i
$723$	−8.31732	+	10.7140i	−0.309324	+	0.398459i
$724$	−2.96556	−	5.13650i	−0.110214	−	0.190897i
$725$	3.52703	−	6.10900i	0.130991	−	0.226883i
$726$	−29.0862	+	11.8567i	−1.07949	+	0.440042i
$727$		−	16.2953i		−	0.604359i	−0.953251	−	0.302180i	$-0.902286\pi$
$727$		−	16.2953i		−	0.604359i	0.953251	−	0.302180i	$-0.0977143\pi$
$728$	−0.927621	−	3.48418i	−0.0343799	−	0.129132i
$729$	−19.7252	+	18.4368i	−0.730563	+	0.682846i
$730$	9.06904	+	33.8461i	0.335660	+	1.25270i
$731$	1.23087	+	0.710641i	0.0455252	+	0.0262840i
$732$	−2.09386	−	2.76079i	−0.0773913	−	0.102042i
$733$	−13.4669	+	13.4669i	−0.497412	+	0.497412i	−0.910631	−	0.413220i	$-0.864404\pi$
$733$	−13.4669	+	13.4669i	−0.497412	+	0.497412i	0.413220	+	0.910631i	$0.364404\pi$
$734$	1.05189	−	3.92570i	0.0388259	−	0.144900i
$735$	0.561758	−	4.08912i	0.0207208	−	0.150829i
$736$	5.62500	+	5.62500i	0.207340	+	0.207340i
$737$	6.51834	−	3.76337i	0.240106	−	0.138625i
$738$	21.3948	+	5.99147i	0.787555	+	0.220549i
$739$	17.4861	−	4.68539i	0.643237	−	0.172355i	0.0775678	−	0.996987i	$-0.475285\pi$
$739$	17.4861	−	4.68539i	0.643237	−	0.172355i	0.565669	+	0.824632i	$0.308618\pi$
$740$	12.9907			0.477547
$741$	−11.8279	−	15.6470i	−0.434507	−	0.574808i
$742$	13.4414			0.493448
$743$	−18.3442	+	4.91530i	−0.672982	+	0.180325i	−0.579098	−	0.815258i	$-0.696595\pi$
$743$	−18.3442	+	4.91530i	−0.672982	+	0.180325i	−0.0938844	+	0.995583i	$0.529928\pi$
$744$	−1.83822	+	4.36819i	−0.0673923	+	0.160146i
$745$	−14.0949	+	8.13770i	−0.516397	+	0.298142i
$746$	−12.0376	−	12.0376i	−0.440726	−	0.440726i
$747$	0.368228	−	32.7327i	0.0134728	−	1.19763i
$748$	0.439125	−	1.63884i	0.0160560	−	0.0599218i
$749$	0.650705	−	0.650705i	0.0237763	−	0.0237763i
$750$	14.2109	−	10.7780i	0.518910	−	0.393556i
$751$	44.4408	+	25.6579i	1.62167	+	0.936270i	0.986474	+	0.163915i	$0.0524123\pi$
$751$	44.4408	+	25.6579i	1.62167	+	0.936270i	0.635192	+	0.772354i	$0.280921\pi$
$752$	0.482964	+	1.80245i	0.0176119	+	0.0657285i
$753$	0.499029	+	3.96260i	0.0181856	+	0.144405i
$754$	32.4183	+	18.7858i	1.18061	+	0.684140i
$755$			6.29748i			0.229189i
$756$	−4.17517	+	3.09321i	−0.151849	+	0.112499i
$757$	2.39348	−	4.14563i	0.0869925	−	0.150675i	−0.819246	−	0.573442i	$-0.805608\pi$
$757$	2.39348	−	4.14563i	0.0869925	−	0.150675i	0.906239	+	0.422767i	$0.138941\pi$
$758$	−1.58645	−	2.74781i	−0.0576224	−	0.0998049i
$759$	58.7467	+	45.6052i	2.13237	+	1.65536i
$760$	7.22965	+	1.93718i	0.262247	+	0.0702688i
$761$	−34.2877	−	9.18737i	−1.24293	−	0.333042i	−0.423328	−	0.905976i	$-0.639138\pi$
$761$	−34.2877	−	9.18737i	−1.24293	−	0.333042i	−0.819601	+	0.572935i	$0.805805\pi$
$762$	−9.77911	−	7.59154i	−0.354260	−	0.275013i
$763$	−7.58686	−	13.1408i	−0.274663	−	0.475730i
$764$	−4.01102	+	6.94728i	−0.145113	+	0.251344i
$765$	−1.95863	+	1.10163i	−0.0708145	+	0.0398294i
$766$			35.5598i			1.28483i
$767$	34.3023	+	19.8775i	1.23858	+	0.717736i
$768$	−0.216416	−	1.71848i	−0.00780923	−	0.0620102i
$769$	−0.535980	−	2.00030i	−0.0193279	−	0.0721328i	0.955588	−	0.294705i	$-0.0952214\pi$
$769$	−0.535980	−	2.00030i	−0.0193279	−	0.0721328i	−0.974916	+	0.222572i	$0.928555\pi$
$770$	11.1394	+	6.43136i	0.401438	+	0.231770i
$771$	6.91943	−	5.24790i	0.249197	−	0.188998i
$772$	−8.11988	+	8.11988i	−0.292241	+	0.292241i
$773$	8.53659	−	31.8590i	0.307040	−	1.14589i	−0.624135	−	0.781316i	$-0.714549\pi$
$773$	8.53659	−	31.8590i	0.307040	−	1.14589i	0.931175	−	0.364572i	$-0.118785\pi$
$774$	13.5639	+	0.152588i	0.487546	+	0.00548467i
$775$	−1.31335	−	1.31335i	−0.0471770	−	0.0471770i
$776$	9.48755	−	5.47764i	0.340583	−	0.196636i
$777$	−3.66230	+	8.70281i	−0.131384	+	0.312212i
$778$	−19.2200	+	5.14997i	−0.689069	+	0.184636i
$779$	23.2609			0.833409
$780$	−8.97408	−	11.8718i	−0.321324	−	0.425079i
$781$	83.1416			2.97504
$782$	−2.41529	+	0.647175i	−0.0863706	+	0.0231429i
$783$	7.95034	−	53.4087i	0.284122	−	1.90867i
$784$	−0.866025	+	0.500000i	−0.0309295	+	0.0178571i
$785$	18.9901	+	18.9901i	0.677786	+	0.677786i
$786$	2.18311	−	15.8912i	0.0778690	−	0.566819i
$787$	8.91489	−	33.2708i	0.317782	−	1.18598i	−0.603590	−	0.797295i	$-0.706264\pi$
$787$	8.91489	−	33.2708i	0.317782	−	1.18598i	0.921372	−	0.388682i	$-0.127070\pi$
$788$	3.69889	−	3.69889i	0.131767	−	0.131767i
$789$	10.7877	+	14.2238i	0.384054	+	0.506381i
$790$	−1.88269	−	1.08697i	−0.0669832	−	0.0386728i
$791$	−0.897382	−	3.34908i	−0.0319072	−	0.119079i
$792$	−4.01483	−	15.6873i	−0.142661	−	0.557425i
$793$	1.85572	+	6.97016i	0.0658986	+	0.247518i
$794$		−	34.5332i		−	1.22554i
$795$	51.3750	−	20.9425i	1.82208	−	0.742753i
$796$	−5.43414	+	9.41221i	−0.192608	+	0.333607i
$797$	4.46685	+	7.73681i	0.158224	+	0.274052i	0.934228	−	0.356676i	$-0.116090\pi$
$797$	4.46685	+	7.73681i	0.158224	+	0.274052i	−0.776004	+	0.630728i	$0.782757\pi$
$798$	−3.33593	+	4.29721i	−0.118091	+	0.152120i
$799$	−0.566566	−	0.151811i	−0.0200437	−	0.00537068i
$800$	0.655683	+	0.175690i	0.0231819	+	0.00621157i
$801$	−2.62778	+	4.43547i	−0.0928481	+	0.156719i
$802$	−0.185949	−	0.322073i	−0.00656609	−	0.0113728i
$803$	39.6835	−	68.7339i	1.40040	−	2.42557i
$804$	0.911713	+	2.23657i	0.0321536	+	0.0788777i
$805$		−	18.9569i		−	0.668142i
$806$	6.98706	−	6.96478i	0.246109	−	0.245324i
$807$	−45.2953	+	5.70425i	−1.59447	+	0.200799i
$808$	−1.03121	−	3.84851i	−0.0362777	−	0.135390i
$809$	−13.0875	−	7.55610i	−0.460134	−	0.265658i	0.251967	−	0.967736i	$-0.418923\pi$
$809$	−13.0875	−	7.55610i	−0.460134	−	0.265658i	−0.712100	+	0.702078i	$0.752256\pi$
$810$	−11.1387	+	18.3279i	−0.391376	+	0.643977i
$811$	−21.0190	+	21.0190i	−0.738076	+	0.738076i	−0.972205	−	0.234129i	$-0.924776\pi$
$811$	−21.0190	+	21.0190i	−0.738076	+	0.738076i	0.234129	+	0.972205i	$0.424776\pi$
$812$	2.68959	−	10.0377i	0.0943860	−	0.352253i
$813$	43.7403	+	6.00899i	1.53404	+	0.210745i
$814$	−20.8062	−	20.8062i	−0.729257	−	0.729257i
$815$	−41.8179	+	24.1436i	−1.46482	+	0.845713i
$816$	0.501815	+	0.211173i	0.0175671	+	0.00739254i
$817$	13.7177	−	3.67564i	0.479921	−	0.128594i
$818$	7.32235			0.256020
$819$	10.4832	−	2.66511i	0.366312	−	0.0931265i
$820$	17.6486			0.616317
$821$	18.3654	−	4.92099i	0.640956	−	0.171744i	0.0763195	−	0.997083i	$-0.475683\pi$
$821$	18.3654	−	4.92099i	0.640956	−	0.171744i	0.564636	+	0.825340i	$0.309016\pi$
$822$	6.82472	+	2.87197i	0.238040	+	0.100171i
$823$	23.3797	−	13.4983i	0.814966	−	0.470521i	−0.0337117	−	0.999432i	$-0.510733\pi$
$823$	23.3797	−	13.4983i	0.814966	−	0.470521i	0.848677	+	0.528911i	$0.177399\pi$
$824$	−7.66086	−	7.66086i	−0.266879	−	0.266879i
$825$	6.28717	+	0.863724i	0.218891	+	0.0300710i
$826$	2.84589	−	10.6210i	0.0990211	−	0.369552i
$827$	23.7729	−	23.7729i	0.826664	−	0.826664i	−0.160390	−	0.987054i	$-0.551275\pi$
$827$	23.7729	−	23.7729i	0.826664	−	0.826664i	0.987054	+	0.160390i	$0.0512751\pi$
$828$	−17.0638	+	16.6841i	−0.593007	+	0.579813i
$829$	−32.2116	−	18.5974i	−1.11876	−	0.645914i	−0.177673	−	0.984090i	$-0.556857\pi$
$829$	−32.2116	−	18.5974i	−1.11876	−	0.645914i	−0.941083	+	0.338176i	$0.890190\pi$
$830$	−6.72997	−	25.1166i	−0.233601	−	0.871810i
$831$	23.0022	−	2.89677i	0.797938	−	0.100488i
$832$	−0.938747	+	3.48120i	−0.0325452	+	0.120689i
$833$		−	0.314331i		−	0.0108909i
$834$	4.37782	+	10.7394i	0.151592	+	0.371877i
$835$	20.0111	−	34.6603i	0.692513	−	1.19947i
$836$	−8.47654	−	14.6818i	−0.293167	−	0.507781i
$837$	−13.0417	−	5.66171i	−0.450787	−	0.195697i
$838$	6.75431	+	1.80981i	0.233324	+	0.0625189i
$839$	33.8229	+	9.06283i	1.16770	+	0.312884i	0.790036	−	0.613060i	$-0.210062\pi$
$839$	33.8229	+	9.06283i	1.16770	+	0.312884i	0.377661	+	0.925944i	$0.376728\pi$
$840$	−2.53105	+	3.26040i	−0.0873297	+	0.112494i
$841$	39.4944	+	68.4064i	1.36188	+	2.35884i
$842$	−12.4668	+	21.5931i	−0.429634	+	0.744147i
$843$	41.3854	−	16.8703i	1.42539	−	0.581045i
$844$		−	15.3797i		−	0.529391i
$845$	7.92241	+	29.9492i	0.272539	+	1.03028i
$846$	−5.42330	+	1.38798i	−0.186457	+	0.0477196i
$847$	−4.69357	−	17.5166i	−0.161273	−	0.601879i
$848$	−11.6406	−	6.72068i	−0.399739	−	0.230789i
$849$	15.1854	+	20.0221i	0.521161	+	0.687158i
$850$	−0.150877	+	0.150877i	−0.00517504	+	0.00517504i
$851$	−11.2237	+	41.8876i	−0.384745	+	1.43589i
$852$	−3.63107	+	26.4311i	−0.124398	+	0.905514i
$853$	33.0168	+	33.0168i	1.13047	+	1.13047i	0.990098	+	0.140376i	$0.0448312\pi$
$853$	33.0168	+	33.0168i	1.13047	+	1.13047i	0.140376	+	0.990098i	$0.455169\pi$
$854$	1.73250	−	1.00026i	0.0592849	−	0.0342281i
$855$	−6.05514	+	21.6222i	−0.207081	+	0.739464i
$856$	−0.888880	+	0.238175i	−0.0303813	+	0.00814064i
$857$	−6.18194			−0.211171			−0.105586	−	0.994410i	$-0.533672\pi$
$857$	−6.18194			−0.211171			−0.105586	+	0.994410i	$0.533672\pi$
$858$	−4.64105	+	33.3872i	−0.158443	+	1.13982i
$859$	−37.6870			−1.28587			−0.642933	−	0.765923i	$-0.722282\pi$
$859$	−37.6870			−1.28587			−0.642933	+	0.765923i	$0.722282\pi$
$860$	10.4079	−	2.78880i	0.354908	−	0.0950973i
$861$	−4.97546	+	11.8233i	−0.169563	+	0.402937i
$862$	−8.20176	+	4.73529i	−0.279353	+	0.161285i
$863$	−10.1579	−	10.1579i	−0.345778	−	0.345778i	0.512756	−	0.858534i	$-0.328624\pi$
$863$	−10.1579	−	10.1579i	−0.345778	−	0.345778i	−0.858534	+	0.512756i	$0.828624\pi$
$864$	5.16241	−	0.591214i	0.175629	−	0.0201135i
$865$	−6.44935	+	24.0693i	−0.219285	+	0.818381i
$866$	−12.4886	+	12.4886i	−0.424379	+	0.424379i
$867$	23.3243	−	17.6898i	0.792134	−	0.600777i
$868$	−2.36961	−	1.36809i	−0.0804297	−	0.0464361i
$869$	1.27444	+	4.75629i	0.0432325	+	0.161346i
$870$	−5.35929	−	42.5561i	−0.181697	−	1.44279i
$871$	0.00803062	−	5.02775i	0.000272107	−	0.170359i
$872$			15.1737i			0.513847i
$873$	16.1117	+	28.6457i	0.545298	+	0.969510i
$874$	−12.4926	+	21.6378i	−0.422568	+	0.731909i
$875$	5.14875	+	8.91790i	0.174060	+	0.301480i
$876$	20.1177	+	15.6174i	0.679714	+	0.527663i
$877$	−8.10852	−	2.17267i	−0.273805	−	0.0733659i	0.119304	−	0.992858i	$-0.461934\pi$
$877$	−8.10852	−	2.17267i	−0.273805	−	0.0733659i	−0.393109	+	0.919492i	$0.628600\pi$
$878$	19.1219	+	5.12369i	0.645332	+	0.172916i
$879$	19.3827	+	15.0469i	0.653764	+	0.507518i
$880$	−6.43136	−	11.1394i	−0.216801	−	0.375511i
$881$	−24.6336	+	42.6666i	−0.829925	+	1.43747i	0.0681706	+	0.997674i	$0.478284\pi$
$881$	−24.6336	+	42.6666i	−0.829925	+	1.43747i	−0.898096	+	0.439799i	$0.855050\pi$
$882$	−1.47068	−	2.61479i	−0.0495204	−	0.0880444i
$883$		−	19.2589i		−	0.648115i	−0.946037	−	0.324058i	$-0.894953\pi$
$883$		−	19.2589i		−	0.648115i	0.946037	−	0.324058i	$-0.105047\pi$
$884$	−0.800110	−	0.802670i	−0.0269106	−	0.0269967i
$885$	−5.67074	−	45.0292i	−0.190620	−	1.51364i
$886$	−5.41393	−	20.2051i	−0.181885	−	0.678802i
$887$	−21.1568	−	12.2149i	−0.710377	−	0.410136i	0.100824	−	0.994904i	$-0.467852\pi$
$887$	−21.1568	−	12.2149i	−0.710377	−	0.410136i	−0.811200	+	0.584768i	$0.801185\pi$
$888$	7.52305	−	5.70570i	0.252457	−	0.191471i
$889$	5.05408	−	5.05408i	0.169508	−	0.169508i
$890$	−1.05991	+	3.95564i	−0.0355283	+	0.132594i
$891$	47.1945	−	11.5143i	1.58107	−	0.385745i
$892$	8.19192	+	8.19192i	0.274286	+	0.274286i
$893$	−5.07568	+	2.93044i	−0.169851	+	0.0980636i
$894$	−4.58832	+	10.9033i	−0.153456	+	0.364662i
$895$	−32.5274	+	8.71570i	−1.08727	+	0.291334i
$896$	1.00000			0.0334077
$897$	46.0332	−	18.6793i	1.53700	−	0.623682i
$898$	−6.64629			−0.221790
$899$	27.4649	−	7.35921i	0.916007	−	0.245443i
$900$	−0.549163	+	1.96100i	−0.0183054	+	0.0653665i
$901$	3.65900	−	2.11252i	0.121899	−	0.0703783i
$902$	−28.2665	−	28.2665i	−0.941171	−	0.941171i
$903$	−1.06589	+	7.75877i	−0.0354706	+	0.258196i
$904$	−0.897382	+	3.34908i	−0.0298465	+	0.111389i
$905$	9.99426	−	9.99426i	0.332220	−	0.332220i
$906$	2.76595	+	3.64694i	0.0918924	+	0.121161i
$907$	−25.9337	−	14.9728i	−0.861115	−	0.497165i	0.00327049	−	0.999995i	$-0.498959\pi$
$907$	−25.9337	−	14.9728i	−0.861115	−	0.497165i	−0.864386	+	0.502830i	$0.832292\pi$
$908$	0.908723	+	3.39140i	0.0301570	+	0.112548i
$909$	11.5796	−	2.96355i	0.384071	−	0.0982947i
$910$	7.44785	−	4.28417i	0.246894	−	0.142019i
$911$		−	16.2065i		−	0.536944i	−0.963288	−	0.268472i	$-0.913481\pi$
$911$		−	16.2065i		−	0.536944i	0.963288	−	0.268472i	$-0.0865186\pi$
$912$	5.03761	−	2.05353i	0.166812	−	0.0679991i
$913$	−29.4485	+	51.0062i	−0.974602	+	1.68806i
$914$	−7.24947	−	12.5565i	−0.239791	−	0.415331i
$915$	5.06342	−	6.52248i	0.167391	−	0.215627i
$916$	22.3798	+	5.99665i	0.739449	+	0.198135i
$917$	8.94539	+	2.39691i	0.295403	+	0.0791529i
$918$	−0.650414	+	1.49822i	−0.0214669	+	0.0494488i
$919$	15.2431	+	26.4019i	0.502825	+	0.870918i	0.999995	+	0.00326484i	$0.00103923\pi$
$919$	15.2431	+	26.4019i	0.502825	+	0.870918i	−0.497170	+	0.867653i	$0.665627\pi$
$920$	−9.47843	+	16.4171i	−0.312495	+	0.541257i
$921$	−9.58088	−	23.5033i	−0.315701	−	0.774461i
$922$		−	10.2019i		−	0.335982i
$923$	27.8455	−	48.0524i	0.916547	−	1.58167i
$924$	9.27573	−	1.16814i	0.305149	−	0.0384288i
$925$	0.957745	+	3.57435i	0.0314905	+	0.117524i
$926$	3.17785	+	1.83473i	0.104431	+	0.0602931i
$927$	23.2397	−	22.7226i	0.763291	−	0.746308i
$928$	−7.34809	+	7.34809i	−0.241213	+	0.241213i
$929$	−10.7916	+	40.2748i	−0.354061	+	1.32137i	0.527601	+	0.849492i	$0.323091\pi$
$929$	−10.7916	+	40.2748i	−0.354061	+	1.32137i	−0.881662	+	0.471881i	$0.843575\pi$
$930$	−11.1886	−	1.53707i	−0.366888	−	0.0504026i
$931$	−2.22090	−	2.22090i	−0.0727872	−	0.0727872i
$932$	15.2507	−	8.80500i	0.499554	−	0.288417i
$933$	−10.1334	−	4.26433i	−0.331753	−	0.139608i
$934$	−2.27088	+	0.608481i	−0.0743055	+	0.0199101i
$935$	4.04316			0.132225
$936$	−10.4113	−	2.93354i	−0.340303	−	0.0958858i
$937$	19.7513			0.645247			0.322624	−	0.946527i	$-0.395435\pi$
$937$	19.7513			0.645247			0.322624	+	0.946527i	$0.395435\pi$
$938$	−1.34693	+	0.360910i	−0.0439789	+	0.0117841i
$939$	−30.8041	−	12.9629i	−1.00525	−	0.423029i
$940$	−3.85104	+	2.22340i	−0.125607	+	0.0725193i
$941$	36.2352	+	36.2352i	1.18123	+	1.18123i	0.979425	+	0.201809i	$0.0646822\pi$
$941$	36.2352	+	36.2352i	1.18123	+	1.18123i	0.201809	+	0.979425i	$0.435318\pi$
$942$	19.3381	+	2.65665i	0.630070	+	0.0865583i
$943$	−15.2481	+	56.9068i	−0.496547	+	1.85314i
$944$	−7.77511	+	7.77511i	−0.253058	+	0.253058i
$945$	−9.69516	−	7.70271i	−0.315384	−	0.250569i
$946$	−21.1362	−	12.2030i	−0.687197	−	0.396754i
$947$	−4.36413	−	16.2871i	−0.141815	−	0.529261i	−0.999877	−	0.0157140i	$-0.994998\pi$
$947$	−4.36413	−	16.2871i	−0.141815	−	0.529261i	0.858061	−	0.513547i	$-0.171669\pi$
$948$	−1.56770	+	0.197428i	−0.0509166	+	0.00641217i
$949$	−26.4347	−	45.9556i	−0.858106	−	1.49178i
$950$			2.13204i			0.0691724i
$951$	17.8275	+	43.7335i	0.578097	+	1.41816i
$952$	−0.157166	+	0.272219i	−0.00509377	+	0.00882267i
$953$	−9.36666	−	16.2235i	−0.303416	−	0.525531i	0.673492	−	0.739195i	$-0.264794\pi$
$953$	−9.36666	−	16.2235i	−0.303416	−	0.525531i	−0.976907	+	0.213663i	$0.931460\pi$
$954$	20.5536	−	34.6927i	0.665448	−	1.12322i
$955$	−18.4653	−	4.94777i	−0.597524	−	0.160106i
$956$	−6.21306	−	1.66478i	−0.200945	−	0.0538430i
$957$	−59.5753	+	76.7424i	−1.92580	+	2.48073i
$958$	12.2548	+	21.2259i	0.395933	+	0.685776i
$959$	−2.13746	+	3.70220i	−0.0690223	+	0.119550i
$960$	3.82216	−	1.55806i	0.123360	−	0.0502862i
$961$			23.5133i			0.758493i
$962$	−18.9935	+	5.05678i	−0.612374	+	0.163037i
$963$	−0.684482	−	2.67451i	−0.0220571	−	0.0861848i
$964$	2.02678	+	7.56405i	0.0652782	+	0.243622i
$965$	−23.6987	−	13.6824i	−0.762887	−	0.440453i
$966$	−8.32613	−	10.9781i	−0.267889	−	0.353216i
$967$	20.0618	−	20.0618i	0.645145	−	0.645145i	−0.306670	−	0.951816i	$-0.599215\pi$
$967$	20.0618	−	20.0618i	0.645145	−	0.645145i	0.951816	+	0.306670i	$0.0992149\pi$
$968$	−4.69357	+	17.5166i	−0.150857	+	0.563006i
$969$	−0.232730	+	1.69408i	−0.00747637	+	0.0544216i
$970$	18.4602	+	18.4602i	0.592722	+	0.592722i
$971$	−36.7628	+	21.2250i	−1.17977	+	0.681143i	−0.955962	−	0.293489i	$-0.905184\pi$
$971$	−36.7628	+	21.2250i	−1.17977	+	0.681143i	−0.223812	+	0.974632i	$0.571850\pi$
$972$	1.59932	+	15.5062i	0.0512981	+	0.497362i
$973$	−6.46764	+	1.73300i	−0.207343	+	0.0555574i
$974$	−29.3657			−0.940937
$975$	2.60487	−	3.34445i	0.0834227	−	0.107108i
$976$	−2.00052			−0.0640350
$977$	44.3962	−	11.8959i	1.42036	−	0.380584i	0.534748	−	0.845011i	$-0.320406\pi$
$977$	44.3962	−	11.8959i	1.42036	−	0.380584i	0.885611	+	0.464427i	$0.153740\pi$
$978$	−13.6130	+	32.3489i	−0.435296	+	1.03440i
$979$	8.03303	−	4.63787i	0.256737	−	0.148227i
$980$	−1.68505	−	1.68505i	−0.0538271	−	0.0538271i
$981$	−45.5183	−	0.512060i	−1.45329	−	0.0163488i
$982$	−1.05337	+	3.93122i	−0.0336143	+	0.125450i
$983$	19.4241	−	19.4241i	0.619534	−	0.619534i	−0.325878	−	0.945412i	$-0.605660\pi$
$983$	19.4241	−	19.4241i	0.619534	−	0.619534i	0.945412	+	0.325878i	$0.105660\pi$
$984$	10.2205	−	7.75154i	0.325818	−	0.247110i
$985$	10.7956	+	6.23283i	0.343976	+	0.198594i
$986$	−0.845422	−	3.15516i	−0.0269237	−	0.100481i
$987$	−0.403839	−	3.20673i	−0.0128543	−	0.102071i
$988$	−11.3244	−	0.0180880i	−0.360278	−	0.000575457i
$989$			35.9691i			1.14375i
$990$	33.6333	−	18.9169i	1.06894	−	0.601220i
$991$	2.01935	−	3.49762i	0.0641468	−	0.111105i	−0.832168	−	0.554523i	$-0.812901\pi$
$991$	2.01935	−	3.49762i	0.0641468	−	0.111105i	0.896315	+	0.443417i	$0.146234\pi$
$992$	1.36809	+	2.36961i	0.0434370	+	0.0752351i
$993$	25.8166	+	20.0415i	0.819265	+	0.635997i
$994$	−14.8785	−	3.98667i	−0.471916	−	0.126450i
$995$	−25.0169	−	6.70326i	−0.793089	−	0.212508i
$996$	−14.9290	−	11.5894i	−0.473043	−	0.367224i
$997$	−1.06748	−	1.84893i	−0.0338074	−	0.0585561i	0.848627	−	0.528992i	$-0.177430\pi$
$997$	−1.06748	−	1.84893i	−0.0338074	−	0.0585561i	−0.882434	+	0.470436i	$0.844097\pi$
$998$	2.81954	−	4.88358i	0.0892509	−	0.154587i
$999$	16.8622	+	22.7603i	0.533495	+	0.720104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.71.14	✓	56
3.2	odd	2		546.2.bu.b.71.2	yes	56
13.11	odd	12		546.2.bu.b.323.2	yes	56
39.11	even	12	inner	546.2.bu.a.323.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.14	✓	56	1.1	even	1	trivial
546.2.bu.a.323.14	yes	56	39.11	even	12	inner
546.2.bu.b.71.2	yes	56	3.2	odd	2
546.2.bu.b.323.2	yes	56	13.11	odd	12

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.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.59645 + 0.671817i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.68505 + 1.68505i) q^{5} +(1.71593 + 0.235733i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.09732 + 2.14505i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.59645 + 0.671817i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.68505 + 1.68505i) q^{5} +(1.71593 + 0.235733i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.09732 + 2.14505i) q^{9} +(2.06376 + 1.19151i) q^{10} +(-1.39701 - 5.21372i) q^{11} +(1.71848 - 0.216416i) q^{12} +(-3.48120 - 0.938747i) q^{13} +1.00000i q^{14} +(1.55806 + 3.82216i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.157166 + 0.272219i) q^{17} +(2.58104 + 1.52913i) q^{18} +(3.03381 + 0.812907i) q^{19} +(2.30183 + 0.616773i) q^{20} +(-1.06212 + 1.36818i) q^{21} +(-2.69882 - 4.67450i) q^{22} +(-3.97748 + 6.88919i) q^{23} +(1.60391 - 0.653816i) q^{24} +0.678813i q^{25} +(-3.60555 - 0.00575899i) q^{26} +(1.90720 + 4.83349i) q^{27} +(0.258819 + 0.965926i) q^{28} +(-8.99954 - 5.19588i) q^{29} +(2.49422 + 3.28866i) q^{30} +(-1.93478 + 1.93478i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.27240 - 9.26200i) q^{33} +(0.222266 + 0.222266i) q^{34} +(-2.06376 + 1.19151i) q^{35} +(2.88886 + 0.809005i) q^{36} +(5.26559 - 1.41091i) q^{37} +3.14083 q^{38} +(-4.92691 - 3.83739i) q^{39} +2.38303 q^{40} +(7.15363 - 1.91681i) q^{41} +(-0.671817 + 1.59645i) q^{42} +(3.91582 - 2.26080i) q^{43} +(-3.81671 - 3.81671i) q^{44} +(-0.0804188 + 7.14863i) q^{45} +(-2.05889 + 7.68390i) q^{46} +(-1.31948 + 1.31948i) q^{47} +(1.38004 - 1.04666i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.175690 + 0.655683i) q^{50} +(0.0680263 + 0.540171i) q^{51} +(-3.48418 + 0.927621i) q^{52} -13.4414i q^{53} +(3.09321 + 4.17517i) q^{54} +(6.43136 - 11.1394i) q^{55} +(0.500000 + 0.866025i) q^{56} +(4.29721 + 3.33593i) q^{57} +(-10.0377 - 2.68959i) q^{58} +(-10.6210 - 2.84589i) q^{59} +(3.26040 + 2.53105i) q^{60} +(-1.00026 - 1.73250i) q^{61} +(-1.36809 + 2.36961i) q^{62} +(-2.61479 + 1.47068i) q^{63} -1.00000i q^{64} +(-4.28417 - 7.44785i) q^{65} +(-1.16814 - 9.27573i) q^{66} +(0.360910 + 1.34693i) q^{67} +(0.272219 + 0.157166i) q^{68} +(-10.9781 + 8.32613i) q^{69} +(-1.68505 + 1.68505i) q^{70} +(-3.98667 + 14.8785i) q^{71} +(2.99981 + 0.0337465i) q^{72} +(10.3973 + 10.3973i) q^{73} +(4.72100 - 2.72567i) q^{74} +(-0.456038 + 1.08369i) q^{75} +(3.03381 - 0.812907i) q^{76} +5.39764 q^{77} +(-5.75222 - 2.43146i) q^{78} -0.912263 q^{79} +(2.30183 - 0.616773i) q^{80} +(-0.202466 + 8.99772i) q^{81} +(6.41377 - 3.70299i) q^{82} +(-7.71566 - 7.71566i) q^{83} +(-0.235733 + 1.71593i) q^{84} +(-0.193871 + 0.723536i) q^{85} +(3.19725 - 3.19725i) q^{86} +(-10.8767 - 14.3410i) q^{87} +(-4.67450 - 2.69882i) q^{88} +(0.444776 + 1.65993i) q^{89} +(1.77252 + 6.92586i) q^{90} +(1.80776 - 3.11962i) q^{91} +7.95495i q^{92} +(-4.38859 + 1.78896i) q^{93} +(-0.933016 + 1.61603i) q^{94} +(3.74234 + 6.48192i) q^{95} +(1.06212 - 1.36818i) q^{96} +(10.5820 + 2.83543i) q^{97} +(-0.965926 - 0.258819i) q^{98} +(8.25370 - 13.9315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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