LMFDB - Embedded newform 546.2.bn.e.173.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.12
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.e.101.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.925467 - 1.46407i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.64914 - 1.52948i) q^{5} +(-1.73066 - 0.0694407i) q^{6} +(2.61668 + 0.391106i) q^{7} +1.00000 q^{8} +(-1.28702 - 2.70990i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.925467 - 1.46407i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.64914 - 1.52948i) q^{5} +(-1.73066 - 0.0694407i) q^{6} +(2.61668 + 0.391106i) q^{7} +1.00000 q^{8} +(-1.28702 - 2.70990i) q^{9} +3.05896i q^{10} -2.26580 q^{11} +(0.805192 + 1.53351i) q^{12} +(-3.11743 - 1.81152i) q^{13} +(-0.969634 - 2.46167i) q^{14} +(-4.69096 + 2.46305i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.79771 - 3.11373i) q^{17} +(-1.70333 + 2.46955i) q^{18} -0.827642 q^{19} +(2.64914 - 1.52948i) q^{20} +(2.99426 - 3.46906i) q^{21} +(1.13290 + 1.96224i) q^{22} +(-4.00182 + 2.31045i) q^{23} +(0.925467 - 1.46407i) q^{24} +(2.17863 + 3.77350i) q^{25} +(-0.0101040 + 3.60554i) q^{26} +(-5.15859 - 0.623627i) q^{27} +(-1.64705 + 2.07056i) q^{28} +(-7.61619 - 4.39721i) q^{29} +(4.47855 + 2.83097i) q^{30} +(4.78177 + 8.28226i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.09693 + 3.31730i) q^{33} -3.59543 q^{34} +(-6.33377 - 5.03827i) q^{35} +(2.99036 + 0.240356i) q^{36} +(1.16568 - 0.673004i) q^{37} +(0.413821 + 0.716759i) q^{38} +(-5.53728 + 2.88765i) q^{39} +(-2.64914 - 1.52948i) q^{40} +(7.03626 + 4.06239i) q^{41} +(-4.50143 - 0.858576i) q^{42} +(-4.70036 - 8.14127i) q^{43} +(1.13290 - 1.96224i) q^{44} +(-0.735241 + 9.14739i) q^{45} +(4.00182 + 2.31045i) q^{46} +(-2.73905 - 1.58139i) q^{47} +(-1.73066 - 0.0694407i) q^{48} +(6.69407 + 2.04680i) q^{49} +(2.17863 - 3.77350i) q^{50} +(-2.89501 - 5.51364i) q^{51} +(3.12754 - 1.79402i) q^{52} +(1.44524 - 0.834408i) q^{53} +(2.03922 + 4.77929i) q^{54} +(6.00243 + 3.46551i) q^{55} +(2.61668 + 0.391106i) q^{56} +(-0.765955 + 1.21173i) q^{57} +8.79442i q^{58} +(9.34806 + 5.39710i) q^{59} +(0.212417 - 5.29402i) q^{60} -10.5604i q^{61} +(4.78177 - 8.28226i) q^{62} +(-2.30787 - 7.59432i) q^{63} +1.00000 q^{64} +(5.48784 + 9.56703i) q^{65} +(3.92133 + 0.157339i) q^{66} +4.06211i q^{67} +(1.79771 + 3.11373i) q^{68} +(-0.320879 + 7.99721i) q^{69} +(-1.19638 + 8.00434i) q^{70} +(-3.81286 - 6.60406i) q^{71} +(-1.28702 - 2.70990i) q^{72} +(-5.74190 - 9.94525i) q^{73} +(-1.16568 - 0.673004i) q^{74} +(7.54092 + 0.302571i) q^{75} +(0.413821 - 0.716759i) q^{76} +(-5.92889 - 0.886170i) q^{77} +(5.26942 + 3.35160i) q^{78} +(2.91514 - 5.04917i) q^{79} +3.05896i q^{80} +(-5.68714 + 6.97541i) q^{81} -8.12477i q^{82} -3.79233i q^{83} +(1.50717 + 4.32764i) q^{84} +(-9.52479 + 5.49914i) q^{85} +(-4.70036 + 8.14127i) q^{86} +(-13.4864 + 7.08120i) q^{87} -2.26580 q^{88} +(7.22886 - 4.17358i) q^{89} +(8.28949 - 3.93696i) q^{90} +(-7.44885 - 5.95942i) q^{91} -4.62091i q^{92} +(16.5512 + 0.664099i) q^{93} +3.16278i q^{94} +(2.19254 + 1.26586i) q^{95} +(0.805192 + 1.53351i) q^{96} +(-7.99888 - 13.8545i) q^{97} +(-1.57445 - 6.82064i) q^{98} +(2.91614 + 6.14011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.925467	−	1.46407i	0.534318	−	0.845283i
$3$	0.925467	−	1.46407i	0.534318	−	0.845283i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.64914	−	1.52948i	−1.18473	−	0.684005i	−0.227627	−	0.973748i	$-0.573097\pi$
$5$	−2.64914	−	1.52948i	−1.18473	−	0.684005i	−0.957104	+	0.289743i	$0.906430\pi$
$6$	−1.73066	−	0.0694407i	−0.706538	−	0.0283491i
$7$	2.61668	+	0.391106i	0.989014	+	0.147824i
$7$	2.61668	+	0.391106i	0.989014	+	0.147824i
$8$	1.00000			0.353553
$9$	−1.28702	−	2.70990i	−0.429008	−	0.903301i
$10$			3.05896i			0.967329i
$11$	−2.26580			−0.683166			−0.341583	−	0.939852i	$-0.610963\pi$
$11$	−2.26580			−0.683166			−0.341583	+	0.939852i	$0.610963\pi$
$12$	0.805192	+	1.53351i	0.232439	+	0.442687i
$13$	−3.11743	−	1.81152i	−0.864621	−	0.502425i
$13$	−3.11743	−	1.81152i	−0.864621	−	0.502425i
$14$	−0.969634	−	2.46167i	−0.259146	−	0.657908i
$15$	−4.69096	+	2.46305i	−1.21120	+	0.635957i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.79771	−	3.11373i	0.436010	−	0.755191i	−0.561368	−	0.827566i	$-0.689725\pi$
$17$	1.79771	−	3.11373i	0.436010	−	0.755191i	0.997377	+	0.0723757i	$0.0230581\pi$
$18$	−1.70333	+	2.46955i	−0.401479	+	0.582078i
$19$	−0.827642			−0.189874			−0.0949370	−	0.995483i	$-0.530265\pi$
$19$	−0.827642			−0.189874			−0.0949370	+	0.995483i	$0.530265\pi$
$20$	2.64914	−	1.52948i	0.592366	−	0.342003i
$21$	2.99426	−	3.46906i	0.653402	−	0.757012i
$22$	1.13290	+	1.96224i	0.241536	+	0.418352i
$23$	−4.00182	+	2.31045i	−0.834438	+	0.481763i	−0.855370	−	0.518018i	$-0.826670\pi$
$23$	−4.00182	+	2.31045i	−0.834438	+	0.481763i	0.0209317	+	0.999781i	$0.493337\pi$
$24$	0.925467	−	1.46407i	0.188910	−	0.298853i
$25$	2.17863	+	3.77350i	0.435726	+	0.754699i
$26$	−0.0101040	+	3.60554i	−0.00198156	+	0.707104i
$27$	−5.15859	−	0.623627i	−0.992772	−	0.120017i
$28$	−1.64705	+	2.07056i	−0.311263	+	0.391299i
$29$	−7.61619	−	4.39721i	−1.41429	−	0.816542i	−0.418503	−	0.908216i	$-0.637445\pi$
$29$	−7.61619	−	4.39721i	−1.41429	−	0.816542i	−0.995789	+	0.0916739i	$0.970778\pi$
$30$	4.47855	+	2.83097i	0.817667	+	0.516862i
$31$	4.78177	+	8.28226i	0.858831	+	1.48754i	0.873045	+	0.487639i	$0.162142\pi$
$31$	4.78177	+	8.28226i	0.858831	+	1.48754i	−0.0142145	+	0.999899i	$0.504525\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.09693	+	3.31730i	−0.365028	+	0.577469i
$34$	−3.59543			−0.616611
$35$	−6.33377	−	5.03827i	−1.07060	−	0.851622i
$36$	2.99036	+	0.240356i	0.498393	+	0.0400594i
$37$	1.16568	−	0.673004i	0.191636	−	0.110641i	−0.401112	−	0.916029i	$-0.631376\pi$
$37$	1.16568	−	0.673004i	0.191636	−	0.110641i	0.592748	+	0.805388i	$0.298043\pi$
$38$	0.413821	+	0.716759i	0.0671306	+	0.116274i
$39$	−5.53728	+	2.88765i	−0.886674	+	0.462395i
$40$	−2.64914	−	1.52948i	−0.418866	−	0.241832i
$41$	7.03626	+	4.06239i	1.09888	+	0.634438i	0.935926	−	0.352196i	$-0.114565\pi$
$41$	7.03626	+	4.06239i	1.09888	+	0.634438i	0.162953	+	0.986634i	$0.447898\pi$
$42$	−4.50143	−	0.858576i	−0.694585	−	0.132481i
$43$	−4.70036	−	8.14127i	−0.716799	−	1.24153i	−0.962262	−	0.272126i	$-0.912273\pi$
$43$	−4.70036	−	8.14127i	−0.716799	−	1.24153i	0.245463	−	0.969406i	$-0.421060\pi$
$44$	1.13290	−	1.96224i	0.170791	−	0.295819i
$45$	−0.735241	+	9.14739i	−0.109603	+	1.36361i
$46$	4.00182	+	2.31045i	0.590037	+	0.340658i
$47$	−2.73905	−	1.58139i	−0.399531	−	0.230669i	0.286751	−	0.958005i	$-0.407425\pi$
$47$	−2.73905	−	1.58139i	−0.399531	−	0.230669i	−0.686282	+	0.727336i	$0.740758\pi$
$48$	−1.73066	−	0.0694407i	−0.249799	−	0.0100229i
$49$	6.69407	+	2.04680i	0.956296	+	0.292400i
$50$	2.17863	−	3.77350i	0.308105	−	0.533653i
$51$	−2.89501	−	5.51364i	−0.405382	−	0.772064i
$52$	3.12754	−	1.79402i	0.433712	−	0.248786i
$53$	1.44524	−	0.834408i	0.198519	−	0.114615i	−0.397446	−	0.917626i	$-0.630103\pi$
$53$	1.44524	−	0.834408i	0.198519	−	0.114615i	0.595964	+	0.803011i	$0.296770\pi$
$54$	2.03922	+	4.77929i	0.277503	+	0.650379i
$55$	6.00243	+	3.46551i	0.809368	+	0.467289i
$56$	2.61668	+	0.391106i	0.349669	+	0.0522638i
$57$	−0.765955	+	1.21173i	−0.101453	+	0.160497i
$58$			8.79442i			1.15476i
$59$	9.34806	+	5.39710i	1.21701	+	0.702643i	0.964278	−	0.264892i	$-0.0853364\pi$
$59$	9.34806	+	5.39710i	1.21701	+	0.702643i	0.252735	+	0.967535i	$0.418670\pi$
$60$	0.212417	−	5.29402i	0.0274229	−	0.683455i
$61$		−	10.5604i		−	1.35212i	−0.736845	−	0.676062i	$-0.763685\pi$
$61$		−	10.5604i		−	1.35212i	0.736845	−	0.676062i	$-0.236315\pi$
$62$	4.78177	−	8.28226i	0.607285	−	1.05185i
$63$	−2.30787	−	7.59432i	−0.290765	−	0.956795i
$64$	1.00000			0.125000
$65$	5.48784	+	9.56703i	0.680682	+	1.18664i
$66$	3.92133	+	0.157339i	0.482683	+	0.0193671i
$67$			4.06211i			0.496266i	0.968726	+	0.248133i	$0.0798170\pi$
$67$			4.06211i			0.496266i	−0.968726	+	0.248133i	$0.920183\pi$
$68$	1.79771	+	3.11373i	0.218005	+	0.377595i
$69$	−0.320879	+	7.99721i	−0.0386293	+	0.962752i
$70$	−1.19638	+	8.00434i	−0.142995	+	0.956702i
$71$	−3.81286	−	6.60406i	−0.452503	−	0.783758i	0.546038	−	0.837760i	$-0.316135\pi$
$71$	−3.81286	−	6.60406i	−0.452503	−	0.783758i	−0.998541	+	0.0540027i	$0.982802\pi$
$72$	−1.28702	−	2.70990i	−0.151677	−	0.319365i
$73$	−5.74190	−	9.94525i	−0.672038	−	1.16400i	−0.977325	−	0.211744i	$-0.932086\pi$
$73$	−5.74190	−	9.94525i	−0.672038	−	1.16400i	0.305287	−	0.952260i	$-0.401248\pi$
$74$	−1.16568	−	0.673004i	−0.135507	−	0.0782351i
$75$	7.54092	+	0.302571i	0.870751	+	0.0349379i
$76$	0.413821	−	0.716759i	0.0474685	−	0.0822179i
$77$	−5.92889	−	0.886170i	−0.675660	−	0.100988i
$78$	5.26942	+	3.35160i	0.596644	+	0.379494i
$79$	2.91514	−	5.04917i	0.327979	−	0.568077i	−0.654132	−	0.756381i	$-0.726966\pi$
$79$	2.91514	−	5.04917i	0.327979	−	0.568077i	0.982111	+	0.188304i	$0.0602991\pi$
$80$			3.05896i			0.342003i
$81$	−5.68714	+	6.97541i	−0.631905	+	0.775046i
$82$		−	8.12477i		−	0.897231i
$83$		−	3.79233i		−	0.416262i	−0.978101	−	0.208131i	$-0.933262\pi$
$83$		−	3.79233i		−	0.416262i	0.978101	−	0.208131i	$-0.0667381\pi$
$84$	1.50717	+	4.32764i	0.164445	+	0.472184i
$85$	−9.52479	+	5.49914i	−1.03311	+	0.596465i
$86$	−4.70036	+	8.14127i	−0.506853	+	0.877896i
$87$	−13.4864	+	7.08120i	−1.44589	+	0.759184i
$88$	−2.26580			−0.241536
$89$	7.22886	−	4.17358i	0.766257	−	0.442399i	−0.0652806	−	0.997867i	$-0.520794\pi$
$89$	7.22886	−	4.17358i	0.766257	−	0.442399i	0.831538	+	0.555468i	$0.187461\pi$
$90$	8.28949	−	3.93696i	0.873789	−	0.414992i
$91$	−7.44885	−	5.95942i	−0.780851	−	0.624717i
$92$		−	4.62091i		−	0.481763i
$93$	16.5512	+	0.664099i	1.71628	+	0.0688638i
$94$			3.16278i			0.326216i
$95$	2.19254	+	1.26586i	0.224950	+	0.129875i
$96$	0.805192	+	1.53351i	0.0821795	+	0.156514i
$97$	−7.99888	−	13.8545i	−0.812164	−	1.40671i	−0.911347	−	0.411639i	$-0.864956\pi$
$97$	−7.99888	−	13.8545i	−0.812164	−	1.40671i	0.0991832	−	0.995069i	$-0.468377\pi$
$98$	−1.57445	−	6.82064i	−0.159044	−	0.688988i
$99$	2.91614	+	6.14011i	0.293083	+	0.617104i
$100$	−4.35726			−0.435726
$101$	7.13992			0.710448			0.355224	−	0.934781i	$-0.384405\pi$
$101$	7.13992			0.710448			0.355224	+	0.934781i	$0.384405\pi$
$102$	−3.32745	+	5.26397i	−0.329466	+	0.521211i
$103$	1.53644	+	0.887062i	0.151390	+	0.0874048i	0.573781	−	0.819009i	$-0.305476\pi$
$103$	1.53644	+	0.887062i	0.151390	+	0.0874048i	−0.422392	+	0.906413i	$0.638809\pi$
$104$	−3.11743	−	1.81152i	−0.305690	−	0.177634i
$105$	−13.2381	+	4.61036i	−1.29191	+	0.449925i
$106$	−1.44524	−	0.834408i	−0.140374	−	0.0810449i
$107$	5.44777	−	3.14527i	0.526656	−	0.304065i	−0.212998	−	0.977053i	$-0.568323\pi$
$107$	5.44777	−	3.14527i	0.526656	−	0.304065i	0.739654	+	0.672988i	$0.234989\pi$
$108$	3.11937	−	4.15566i	0.300162	−	0.399879i
$109$	−9.02357	+	5.20976i	−0.864302	+	0.499005i	−0.865450	−	0.500995i	$-0.832968\pi$
$109$	−9.02357	+	5.20976i	−0.864302	+	0.499005i	0.00114874	+	0.999999i	$0.499634\pi$
$110$		−	6.93101i		−	0.660846i
$111$	0.0934678	−	2.32948i	0.00887157	−	0.221104i
$112$	−0.969634	−	2.46167i	−0.0916218	−	0.232606i
$113$	7.25521	−	4.18880i	0.682513	−	0.394049i	−0.118288	−	0.992979i	$-0.537741\pi$
$113$	7.25521	−	4.18880i	0.682513	−	0.394049i	0.800801	+	0.598930i	$0.204407\pi$
$114$	1.43236	+	0.0574720i	0.134153	+	0.00538275i
$115$	14.1352			1.31811
$116$	7.61619	−	4.39721i	0.707146	−	0.408271i
$117$	−0.896828	+	10.7794i	−0.0829118	+	0.996557i
$118$		−	10.7942i		−	0.993687i
$119$	5.92185	−	7.44455i	0.542855	−	0.682441i
$120$	−4.69096	+	2.46305i	−0.428225	+	0.224845i
$121$	−5.86613			−0.533285
$122$	−9.14560	+	5.28021i	−0.828004	+	0.478048i
$123$	12.4595	−	6.54200i	1.12343	−	0.589872i
$124$	−9.56353			−0.858831
$125$			1.96613i			0.175856i
$126$	−5.42294	+	5.79584i	−0.483114	+	0.516334i
$127$	−0.0429290	+	0.0743552i	−0.00380933	+	0.00659795i	−0.867924	−	0.496697i	$-0.834546\pi$
$127$	−0.0429290	+	0.0743552i	−0.00380933	+	0.00659795i	0.864114	+	0.503295i	$0.167879\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−16.2694	−	0.652793i	−1.43244	−	0.0574753i
$130$	5.54137	−	9.53612i	0.486010	−	0.836373i
$131$	−1.03041	+	1.78473i	−0.0900276	+	0.155932i	−0.907523	−	0.420003i	$-0.862029\pi$
$131$	−1.03041	+	1.78473i	−0.0900276	+	0.155932i	0.817495	+	0.575936i	$0.195362\pi$
$132$	−1.82441	−	3.47464i	−0.158794	−	0.302429i
$133$	−2.16568	−	0.323696i	−0.187788	−	0.0280680i
$134$	3.51789	−	2.03106i	0.303900	−	0.175456i
$135$	12.7120	+	9.54205i	1.09408	+	0.821249i
$136$	1.79771	−	3.11373i	0.154153	−	0.267000i
$137$	4.48732	−	7.77227i	0.383378	−	0.664030i	−0.608165	−	0.793811i	$-0.708094\pi$
$137$	4.48732	−	7.77227i	0.383378	−	0.664030i	0.991543	+	0.129781i	$0.0414274\pi$
$138$	7.08623	−	3.72072i	0.603220	−	0.316729i
$139$	18.0789	−	10.4379i	1.53343	−	0.885328i	0.534233	−	0.845338i	$-0.320601\pi$
$139$	18.0789	−	10.4379i	1.53343	−	0.885328i	0.999200	−	0.0399902i	$-0.0127327\pi$
$140$	7.53015	−	2.96608i	0.636414	−	0.250679i
$141$	−4.85016	+	2.54664i	−0.408457	+	0.214466i
$142$	−3.81286	+	6.60406i	−0.319968	+	0.554200i
$143$	7.06350	+	4.10455i	0.590679	+	0.343239i
$144$	−1.70333	+	2.46955i	−0.141944	+	0.205796i
$145$	13.4509	+	23.2977i	1.11704	+	1.93477i
$146$	−5.74190	+	9.94525i	−0.475203	+	0.823075i
$147$	9.19181	−	7.90637i	0.758128	−	0.652106i
$148$			1.34601i			0.110641i
$149$	−1.70300			−0.139515			−0.0697576	−	0.997564i	$-0.522223\pi$
$149$	−1.70300			−0.139515			−0.0697576	+	0.997564i	$0.522223\pi$
$150$	−3.50843	−	6.68192i	−0.286462	−	0.545576i
$151$	19.2492	−	11.1135i	1.56648	−	0.904406i	0.569902	−	0.821712i	$-0.306981\pi$
$151$	19.2492	−	11.1135i	1.56648	−	0.904406i	0.996575	−	0.0826936i	$-0.0263523\pi$
$152$	−0.827642			−0.0671306
$153$	−10.7516	−	0.864184i	−0.869216	−	0.0698651i
$154$	2.19700	+	5.57766i	0.177039	+	0.449460i
$155$		−	29.2545i		−	2.34978i
$156$	0.267858	−	6.23925i	0.0214458	−	0.499540i
$157$	10.2785	−	5.93431i	0.820316	−	0.473610i	−0.0302095	−	0.999544i	$-0.509617\pi$
$157$	10.2785	−	5.93431i	0.820316	−	0.473610i	0.850525	+	0.525934i	$0.176284\pi$
$158$	−5.83028			−0.463833
$159$	0.115884	−	2.88815i	0.00919018	−	0.229045i
$160$	2.64914	−	1.52948i	0.209433	−	0.120916i
$161$	−11.3751	+	4.48059i	−0.896487	+	0.353120i
$162$	8.88446	+	1.43750i	0.698029	+	0.112941i
$163$		−	9.61240i		−	0.752901i	−0.926437	−	0.376451i	$-0.877144\pi$
$163$		−	9.61240i		−	0.752901i	0.926437	−	0.376451i	$-0.122856\pi$
$164$	−7.03626	+	4.06239i	−0.549440	+	0.317219i
$165$	10.6288	−	5.58079i	0.827451	−	0.434464i
$166$	−3.28425	+	1.89616i	−0.254908	+	0.147171i
$167$	21.5888	+	12.4643i	1.67059	+	0.964517i	0.967307	+	0.253608i	$0.0816174\pi$
$167$	21.5888	+	12.4643i	1.67059	+	0.964517i	0.703285	+	0.710908i	$0.251716\pi$
$168$	2.99426	−	3.46906i	0.231012	−	0.267644i
$169$	6.43680	+	11.2946i	0.495138	+	0.868814i
$170$	9.52479	+	5.49914i	0.730518	+	0.421765i
$171$	1.06519	+	2.24283i	0.0814574	+	0.171513i
$172$	9.40073			0.716799
$173$	−4.02553			−0.306055			−0.153028	−	0.988222i	$-0.548902\pi$
$173$	−4.02553			−0.306055			−0.153028	+	0.988222i	$0.548902\pi$
$174$	12.8757	+	8.13894i	0.976103	+	0.617012i
$175$	4.22495	+	10.7261i	0.319376	+	0.810819i
$176$	1.13290	+	1.96224i	0.0853957	+	0.147910i
$177$	16.5531	−	8.69141i	1.24421	−	0.653286i
$178$	−7.22886	−	4.17358i	−0.541826	−	0.312823i
$179$			12.6376i			0.944577i	0.881444	+	0.472289i	$0.156572\pi$
$179$			12.6376i			0.944577i	−0.881444	+	0.472289i	$0.843428\pi$
$180$	−7.55425	−	5.21043i	−0.563061	−	0.388363i
$181$		−	1.79097i		−	0.133122i	−0.997782	−	0.0665610i	$-0.978797\pi$
$181$		−	1.79097i		−	0.133122i	0.997782	−	0.0665610i	$-0.0212027\pi$
$182$	−1.43659	+	9.43060i	−0.106487	+	0.699043i
$183$	−15.4612	−	9.77332i	−1.14293	−	0.722465i
$184$	−4.00182	+	2.31045i	−0.295018	+	0.170329i
$185$	−4.11739			−0.302717
$186$	−7.70048	−	14.6658i	−0.564626	−	1.07535i
$187$	−4.07327	+	7.05510i	−0.297867	+	0.515920i
$188$	2.73905	−	1.58139i	0.199765	−	0.115335i
$189$	−13.2545	−	3.64939i	−0.964123	−	0.265454i
$190$		−	2.53173i		−	0.183671i
$191$		−	9.76173i		−	0.706334i	−0.935560	−	0.353167i	$-0.885105\pi$
$191$		−	9.76173i		−	0.706334i	0.935560	−	0.353167i	$-0.114895\pi$
$192$	0.925467	−	1.46407i	0.0667898	−	0.105660i
$193$		−	10.4318i		−	0.750899i	−0.926843	−	0.375450i	$-0.877488\pi$
$193$		−	10.4318i		−	0.750899i	0.926843	−	0.375450i	$-0.122512\pi$
$194$	−7.99888	+	13.8545i	−0.574286	+	0.994693i
$195$	19.0856	+	0.819367i	1.36675	+	0.0586761i
$196$	−5.11962	+	4.77383i	−0.365687	+	0.340988i
$197$	−3.77403	+	6.53681i	−0.268888	+	0.465728i	−0.968575	−	0.248721i	$-0.919990\pi$
$197$	−3.77403	+	6.53681i	−0.268888	+	0.465728i	0.699687	+	0.714450i	$0.253323\pi$
$198$	3.85942	−	5.59551i	0.274277	−	0.397655i
$199$	−10.5985	−	6.11903i	−0.751306	−	0.433767i	0.0748595	−	0.997194i	$-0.476149\pi$
$199$	−10.5985	−	6.11903i	−0.751306	−	0.433767i	−0.826166	+	0.563427i	$0.809483\pi$
$200$	2.17863	+	3.77350i	0.154052	+	0.266826i
$201$	5.94723	+	3.75935i	0.419485	+	0.265164i
$202$	−3.56996	−	6.18335i	−0.251181	−	0.435059i
$203$	−18.2094	−	14.4849i	−1.27805	−	1.01664i
$204$	6.22246	+	0.249669i	0.435659	+	0.0174803i
$205$	−12.4267	−	21.5237i	−0.867918	−	1.50328i
$206$		−	1.77412i		−	0.123609i
$207$	11.4115	+	7.87095i	0.793157	+	0.547069i
$208$	−0.0101040	+	3.60554i	−0.000700588	+	0.249999i
$209$	1.87527			0.129715
$210$	10.6117	+	9.15934i	0.732279	+	0.632054i
$211$	−3.36247	+	5.82397i	−0.231482	+	0.400939i	−0.958244	−	0.285950i	$-0.907691\pi$
$211$	−3.36247	+	5.82397i	−0.231482	+	0.400939i	0.726762	+	0.686889i	$0.241024\pi$
$212$			1.66882i			0.114615i
$213$	−13.1975	−	0.529535i	−0.904278	−	0.0362831i
$214$	−5.44777	−	3.14527i	−0.372402	−	0.215006i
$215$			28.7565i			1.96118i
$216$	−5.15859	−	0.623627i	−0.350998	−	0.0424325i
$217$	9.27313	+	23.5422i	0.629501	+	1.59815i
$218$	9.02357	+	5.20976i	0.611154	+	0.352850i
$219$	−19.8745	−	0.797443i	−1.34300	−	0.0538862i
$220$	−6.00243	+	3.46551i	−0.404684	+	0.233644i
$221$	−11.2448	+	6.45026i	−0.756410	+	0.433892i
$222$	−2.06412	+	1.08379i	−0.138535	+	0.0727395i
$223$	−6.23733	+	10.8034i	−0.417683	+	0.723448i	−0.995706	−	0.0925727i	$-0.970491\pi$
$223$	−6.23733	+	10.8034i	−0.417683	+	0.723448i	0.578023	+	0.816020i	$0.303824\pi$
$224$	−1.64705	+	2.07056i	−0.110048	+	0.138345i
$225$	7.42186	−	10.7604i	0.494791	−	0.717363i
$226$	−7.25521	−	4.18880i	−0.482609	−	0.278635i
$227$	18.5738	+	10.7236i	1.23278	+	0.711748i	0.967609	−	0.252452i	$-0.0812369\pi$
$227$	18.5738	+	10.7236i	1.23278	+	0.711748i	0.265175	+	0.964200i	$0.414570\pi$
$228$	−0.666410	−	1.26920i	−0.0441341	−	0.0840548i
$229$	−11.7463	+	20.3453i	−0.776220	+	1.34445i	0.157886	+	0.987457i	$0.449532\pi$
$229$	−11.7463	+	20.3453i	−0.776220	+	1.34445i	−0.934106	+	0.356995i	$0.883801\pi$
$230$	−7.06760	−	12.2414i	−0.466024	−	0.807176i
$231$	−6.78441	+	7.86022i	−0.446381	+	0.517164i
$232$	−7.61619	−	4.39721i	−0.500028	−	0.288691i
$233$	−11.1727	−	6.45055i	−0.731947	−	0.422590i	0.0871872	−	0.996192i	$-0.472212\pi$
$233$	−11.1727	−	6.45055i	−0.731947	−	0.422590i	−0.819134	+	0.573602i	$0.805545\pi$
$234$	9.78366	−	4.61303i	0.639578	−	0.301563i
$235$	4.83741	+	8.37864i	0.315558	+	0.546562i
$236$	−9.34806	+	5.39710i	−0.608507	+	0.351322i
$237$	−4.69450	−	8.94083i	−0.304940	−	0.580769i
$238$	−9.40810	−	1.40619i	−0.609836	−	0.0911500i
$239$	−23.0402			−1.49035			−0.745175	−	0.666869i	$-0.767634\pi$
$239$	−23.0402			−1.49035			−0.745175	+	0.666869i	$0.767634\pi$
$240$	4.47855	+	2.83097i	0.289089	+	0.182738i
$241$	−13.8893	+	24.0570i	−0.894688	+	1.54964i	−0.0604968	+	0.998168i	$0.519269\pi$
$241$	−13.8893	+	24.0570i	−0.894688	+	1.54964i	−0.834191	+	0.551476i	$0.814065\pi$
$242$	2.93307	+	5.08022i	0.188545	+	0.326569i
$243$	4.94926	+	14.7819i	0.317495	+	0.948260i
$244$	9.14560	+	5.28021i	0.585487	+	0.338031i
$245$	−14.6030	−	15.6607i	−0.932951	−	1.00053i
$246$	−11.8953	−	7.51920i	−0.758414	−	0.479407i
$247$	2.58012	+	1.49929i	0.164169	+	0.0953974i
$248$	4.78177	+	8.28226i	0.303642	+	0.525924i
$249$	−5.55225	−	3.50967i	−0.351860	−	0.222417i
$250$	1.70271	−	0.983063i	0.107689	−	0.0621743i
$251$	−6.68358	−	11.5763i	−0.421864	−	0.730690i	0.574258	−	0.818674i	$-0.305291\pi$
$251$	−6.68358	−	11.5763i	−0.421864	−	0.730690i	−0.996122	+	0.0879848i	$0.971957\pi$
$252$	7.73081	+	1.79848i	0.486995	+	0.113294i
$253$	9.06735	−	5.23504i	0.570059	−	0.329124i
$254$	0.0858580			0.00538721
$255$	−0.763729	+	19.0343i	−0.0478265	+	1.19197i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.35563	−	2.34802i	−0.0845618	−	0.146465i	0.820643	−	0.571442i	$-0.193616\pi$
$257$	−1.35563	−	2.34802i	−0.0845618	−	0.146465i	−0.905204	+	0.424976i	$0.860282\pi$
$258$	7.56939	+	14.4161i	0.471249	+	0.897510i
$259$	3.31343	−	1.30514i	0.205886	−	0.0810972i
$260$	−11.0292	−	0.0309078i	−0.684002	−	0.00191682i
$261$	−2.11380	+	26.2985i	−0.130841	+	1.62783i
$262$	2.06083			0.127318
$263$			14.7063i			0.906832i	0.891299	+	0.453416i	$0.149795\pi$
$263$			14.7063i			0.906832i	−0.891299	+	0.453416i	$0.850205\pi$
$264$	−2.09693	+	3.31730i	−0.129057	+	0.204166i
$265$	−5.10485			−0.313588
$266$	0.802510	+	2.03738i	0.0492050	+	0.124920i
$267$	0.579633	−	14.4461i	0.0354730	−	0.884086i
$268$	−3.51789	−	2.03106i	−0.214889	−	0.124066i
$269$	3.75936	−	6.51140i	0.229212	−	0.397007i	−0.728363	−	0.685192i	$-0.759718\pi$
$269$	3.75936	−	6.51140i	0.229212	−	0.397007i	0.957575	+	0.288185i	$0.0930517\pi$
$270$	1.90765	−	15.7799i	0.116096	−	0.960337i
$271$	−0.0123926	−	0.0214646i	−0.000752797	−	0.00130388i	0.865649	−	0.500652i	$-0.166906\pi$
$271$	−0.0123926	−	0.0214646i	−0.000752797	−	0.00130388i	−0.866402	+	0.499348i	$0.833573\pi$
$272$	−3.59543			−0.218005
$273$	−15.6187	+	5.39041i	−0.945286	+	0.326243i
$274$	−8.97465			−0.542178
$275$	−4.93635	−	8.55000i	−0.297673	−	0.515585i
$276$	−6.76535	−	4.27650i	−0.407226	−	0.257415i
$277$	−3.09062	+	5.35311i	−0.185697	+	0.321637i	−0.943811	−	0.330485i	$-0.892788\pi$
$277$	−3.09062	+	5.35311i	−0.185697	+	0.321637i	0.758114	+	0.652122i	$0.226121\pi$
$278$	−18.0789	−	10.4379i	−1.08430	−	0.626021i
$279$	16.2899	−	23.6176i	0.975250	−	1.41395i
$280$	−6.33377	−	5.03827i	−0.378515	−	0.301094i
$281$	29.5748			1.76428			0.882142	−	0.470984i	$-0.156101\pi$
$281$	29.5748			1.76428			0.882142	+	0.470984i	$0.156101\pi$
$282$	4.63054	+	2.92704i	0.275745	+	0.174303i
$283$		−	21.2029i		−	1.26038i	−0.776439	−	0.630192i	$-0.782976\pi$
$283$		−	21.2029i		−	1.26038i	0.776439	−	0.630192i	$-0.217024\pi$
$284$	7.62571			0.452503
$285$	3.88244	−	2.03852i	0.229976	−	0.120752i
$286$	0.0228937	−	8.16944i	0.00135374	−	0.483069i
$287$	16.8228	+	13.3819i	0.993021	+	0.789909i
$288$	2.99036	+	0.240356i	0.176208	+	0.0141631i
$289$	2.03645	+	3.52724i	0.119791	+	0.207485i
$290$	13.4509	−	23.2977i	0.789865	−	1.36809i
$291$	−27.6867	−	1.11090i	−1.62302	−	0.0651219i
$292$	11.4838			0.672038
$293$	−10.1781	+	5.87631i	−0.594609	+	0.343298i	−0.766918	−	0.641745i	$-0.778211\pi$
$293$	−10.1781	+	5.87631i	−0.594609	+	0.343298i	0.172309	+	0.985043i	$0.444877\pi$
$294$	−11.4430	−	4.00716i	−0.667370	−	0.233702i
$295$	−16.5095	−	28.5954i	−0.961223	−	1.66489i
$296$	1.16568	−	0.673004i	0.0677536	−	0.0391176i
$297$	11.6884	+	1.41302i	0.678228	+	0.0819916i
$298$	0.851501	+	1.47484i	0.0493261	+	0.0854353i
$299$	16.6609	+	0.0466898i	0.963522	+	0.00270014i
$300$	−4.03250	+	6.37935i	−0.232816	+	0.368312i
$301$	−9.11527	−	23.1415i	−0.525395	−	1.33385i
$302$	−19.2492	−	11.1135i	−1.10767	−	0.639512i
$303$	6.60775	−	10.4534i	0.379605	−	0.600530i
$304$	0.413821	+	0.716759i	0.0237342	+	0.0411089i
$305$	−16.1520	+	27.9761i	−0.924860	+	1.60190i
$306$	4.62740	+	9.74326i	0.264531	+	0.556985i
$307$	12.2431			0.698749			0.349375	−	0.936983i	$-0.386394\pi$
$307$	12.2431			0.698749			0.349375	+	0.936983i	$0.386394\pi$
$308$	3.73189	−	4.69149i	0.212644	−	0.267322i
$309$	2.72064	−	1.42851i	0.154772	−	0.0812651i
$310$	−25.3351	+	14.6272i	−1.43894	+	0.830772i
$311$	4.81504	+	8.33990i	0.273036	+	0.472912i	0.969638	−	0.244546i	$-0.0786388\pi$
$311$	4.81504	+	8.33990i	0.273036	+	0.472912i	−0.696602	+	0.717458i	$0.745306\pi$
$312$	−5.53728	+	2.88765i	−0.313487	+	0.163481i
$313$	12.0523	+	6.95841i	0.681237	+	0.393312i	0.800321	−	0.599572i	$-0.204662\pi$
$313$	12.0523	+	6.95841i	0.681237	+	0.393312i	−0.119084	+	0.992884i	$0.537996\pi$
$314$	−10.2785	−	5.93431i	−0.580051	−	0.334893i
$315$	−5.50150	+	23.6483i	−0.309974	+	1.33243i
$316$	2.91514	+	5.04917i	0.163990	+	0.284038i
$317$	−11.8204	+	20.4735i	−0.663900	+	1.14991i	0.315682	+	0.948865i	$0.397767\pi$
$317$	−11.8204	+	20.4735i	−0.663900	+	1.14991i	−0.979582	+	0.201044i	$0.935567\pi$
$318$	−2.55915	+	1.34372i	−0.143510	+	0.0753519i
$319$	17.2568	+	9.96322i	0.966195	+	0.557833i
$320$	−2.64914	−	1.52948i	−0.148091	−	0.0855006i
$321$	0.436820	−	10.8868i	0.0243809	−	0.607641i
$322$	9.56788	+	7.61087i	0.533197	+	0.424137i
$323$	−1.48786	+	2.57705i	−0.0827869	+	0.143391i
$324$	−3.19732	−	8.41292i	−0.177629	−	0.467384i
$325$	0.0440258	−	15.7103i	0.00244211	−	0.871448i
$326$	−8.32458	+	4.80620i	−0.461056	+	0.266191i
$327$	−0.723540	+	18.0326i	−0.0400118	+	0.997207i
$328$	7.03626	+	4.06239i	0.388512	+	0.224308i
$329$	−6.54873	−	5.20925i	−0.361043	−	0.287195i
$330$	−10.1475	−	6.41442i	−0.558602	−	0.353102i
$331$		−	15.0644i		−	0.828014i	−0.910274	−	0.414007i	$-0.864129\pi$
$331$		−	15.0644i		−	0.828014i	0.910274	−	0.414007i	$-0.135871\pi$
$332$	3.28425	+	1.89616i	0.180247	+	0.104066i
$333$	−3.32403	−	2.29270i	−0.182156	−	0.125639i
$334$		−	24.9286i		−	1.36403i
$335$	6.21292	−	10.7611i	0.339448	−	0.587942i
$336$	−4.50143	−	0.858576i	−0.245573	−	0.0468391i
$337$	−9.93070			−0.540960			−0.270480	−	0.962726i	$-0.587182\pi$
$337$	−9.93070			−0.540960			−0.270480	+	0.962726i	$0.587182\pi$
$338$	6.56300	−	11.2217i	0.356980	−	0.610381i
$339$	0.581746	−	14.4988i	0.0315961	−	0.787464i
$340$		−	10.9983i		−	0.596465i
$341$	−10.8345	−	18.7660i	−0.586724	−	1.01624i
$342$	1.40975	−	2.04390i	0.0762305	−	0.110521i
$343$	16.7158	+	7.97393i	0.902566	+	0.430552i
$344$	−4.70036	−	8.14127i	−0.253427	−	0.438948i
$345$	13.0816	−	20.6950i	0.704292	−	1.11418i
$346$	2.01276	+	3.48621i	0.108207	+	0.187420i
$347$	2.91766	+	1.68451i	0.156628	+	0.0904293i	0.576265	−	0.817263i	$-0.304509\pi$
$347$	2.91766	+	1.68451i	0.156628	+	0.0904293i	−0.419637	+	0.907692i	$0.637843\pi$
$348$	0.610691	−	15.2201i	0.0327365	−	0.815885i
$349$	−15.4110	+	26.6927i	−0.824935	+	1.42883i	0.0770347	+	0.997028i	$0.475455\pi$
$349$	−15.4110	+	26.6927i	−0.824935	+	1.42883i	−0.901969	+	0.431800i	$0.857879\pi$
$350$	7.17662	−	9.02197i	0.383607	−	0.482245i
$351$	14.9519	+	11.2890i	0.798072	+	0.602563i
$352$	1.13290	−	1.96224i	0.0603839	−	0.104588i
$353$		−	19.6388i		−	1.04527i	−0.852557	−	0.522634i	$-0.824950\pi$
$353$		−	19.6388i		−	1.04527i	0.852557	−	0.522634i	$-0.175050\pi$
$354$	−15.8035	−	9.98968i	−0.839947	−	0.530945i
$355$			23.3268i			1.23806i
$356$			8.34716i			0.442399i
$357$	−5.41890	−	15.5597i	−0.286799	−	0.823507i
$358$	10.9445	−	6.31879i	0.578433	−	0.333958i
$359$	−5.20022	+	9.00705i	−0.274457	+	0.475374i	−0.969998	−	0.243113i	$-0.921831\pi$
$359$	−5.20022	+	9.00705i	−0.274457	+	0.475374i	0.695541	+	0.718487i	$0.255165\pi$
$360$	−0.735241	+	9.14739i	−0.0387506	+	0.482110i
$361$	−18.3150			−0.963948
$362$	−1.55103	+	0.895486i	−0.0815202	+	0.0470657i
$363$	−5.42891	+	8.58845i	−0.284944	+	0.450777i
$364$	8.88543	−	3.47118i	0.465723	−	0.181939i
$365$			35.1285i			1.83871i
$366$	−0.733324	+	18.2765i	−0.0383315	+	0.955328i
$367$			22.6438i			1.18200i	0.806673	+	0.590998i	$0.201266\pi$
$367$			22.6438i			1.18200i	−0.806673	+	0.590998i	$0.798734\pi$
$368$	4.00182	+	2.31045i	0.208610	+	0.120441i
$369$	1.95284	−	24.2960i	0.101661	−	1.26480i
$370$	2.05870	+	3.56576i	0.107026	+	0.185375i
$371$	4.10807	−	1.61814i	0.213280	−	0.0840097i
$372$	−8.85073	+	14.0017i	−0.458889	+	0.725955i
$373$	16.7805			0.868861			0.434431	−	0.900705i	$-0.356950\pi$
$373$	16.7805			0.868861			0.434431	+	0.900705i	$0.356950\pi$
$374$	8.14653			0.421247
$375$	2.87855	+	1.81958i	0.148648	+	0.0939629i
$376$	−2.73905	−	1.58139i	−0.141255	−	0.0815539i
$377$	15.7774	+	27.5049i	0.812575	+	1.41657i
$378$	3.46679	+	13.3034i	0.178312	+	0.684255i
$379$	−3.91399	−	2.25974i	−0.201048	−	0.116075i	0.396096	−	0.918209i	$-0.370365\pi$
$379$	−3.91399	−	2.25974i	−0.201048	−	0.116075i	−0.597144	+	0.802134i	$0.703698\pi$
$380$	−2.19254	+	1.26586i	−0.112475	+	0.0649374i
$381$	0.0691321	+	0.131664i	0.00354175	+	0.00674537i
$382$	−8.45391	+	4.88087i	−0.432540	+	0.249727i
$383$			3.45864i			0.176728i	0.996088	+	0.0883641i	$0.0281639\pi$
$383$			3.45864i			0.176728i	−0.996088	+	0.0883641i	$0.971836\pi$
$384$	−1.73066	−	0.0694407i	−0.0883173	−	0.00354363i
$385$	14.3511	+	11.4157i	0.731399	+	0.581799i
$386$	−9.03423	+	5.21591i	−0.459830	+	0.265483i
$387$	−16.0126	+	23.2155i	−0.813964	+	1.18011i
$388$	15.9978			0.812164
$389$	−3.12443	+	1.80389i	−0.158415	+	0.0914609i	−0.577112	−	0.816665i	$-0.695820\pi$
$389$	−3.12443	+	1.80389i	−0.158415	+	0.0914609i	0.418697	+	0.908126i	$0.362487\pi$
$390$	−8.83323	−	16.9383i	−0.447288	−	0.857706i
$391$			16.6141i			0.840213i
$392$	6.69407	+	2.04680i	0.338102	+	0.103379i
$393$	1.65936	+	3.16031i	0.0837036	+	0.159416i
$394$	7.54806			0.380266
$395$	−15.4452	+	8.91731i	−0.777134	+	0.448679i
$396$	−6.77556	−	0.544600i	−0.340485	−	0.0273672i
$397$	30.3439			1.52292			0.761458	−	0.648214i	$-0.224484\pi$
$397$	30.3439			1.52292			0.761458	+	0.648214i	$0.224484\pi$
$398$			12.2381i			0.613439i
$399$	−2.47818	+	2.87114i	−0.124064	+	0.143737i
$400$	2.17863	−	3.77350i	0.108931	−	0.188675i
$401$	−16.6091	−	28.7678i	−0.829419	−	1.43660i	−0.898495	−	0.438984i	$-0.855338\pi$
$401$	−16.6091	−	28.7678i	−0.829419	−	1.43660i	0.0690758	−	0.997611i	$-0.477995\pi$
$402$	0.282076	−	7.03013i	0.0140687	−	0.350631i
$403$	0.0966302	−	34.4817i	0.00481349	−	1.71765i
$404$	−3.56996	+	6.18335i	−0.177612	+	0.307633i
$405$	25.7348	−	9.78047i	1.27877	−	0.485996i
$406$	−3.43955	+	23.0122i	−0.170702	+	1.14208i
$407$	−2.64120	+	1.52490i	−0.130919	+	0.0755863i
$408$	−2.89501	−	5.51364i	−0.143324	−	0.272966i
$409$	7.72952	−	13.3879i	0.382200	−	0.661990i	−0.609176	−	0.793035i	$-0.708500\pi$
$409$	7.72952	−	13.3879i	0.382200	−	0.661990i	0.991376	+	0.131045i	$0.0418331\pi$
$410$	−12.4267	+	21.5237i	−0.613710	+	1.06298i
$411$	−7.22631	−	13.7628i	−0.356448	−	0.678866i
$412$	−1.53644	+	0.887062i	−0.0756948	+	0.0437024i
$413$	22.3501	+	17.7786i	1.09978	+	0.874828i
$414$	1.11066	−	13.8182i	0.0545862	−	0.679126i
$415$	−5.80030	+	10.0464i	−0.284725	+	0.493159i
$416$	3.12754	−	1.79402i	0.153340	−	0.0879590i
$417$	1.44963	−	36.1287i	0.0709885	−	1.76923i
$418$	−0.937637	−	1.62403i	−0.0458613	−	0.0794341i
$419$	−6.78747	+	11.7562i	−0.331590	+	0.574330i	−0.982824	−	0.184547i	$-0.940918\pi$
$419$	−6.78747	+	11.7562i	−0.331590	+	0.574330i	0.651234	+	0.758877i	$0.274252\pi$
$420$	2.62635	−	13.7697i	0.128153	−	0.671893i
$421$			22.2151i			1.08270i	0.840797	+	0.541350i	$0.182087\pi$
$421$			22.2151i			1.08270i	−0.840797	+	0.541350i	$0.817913\pi$
$422$	6.72494			0.327365
$423$	−0.760194	+	9.45783i	−0.0369619	+	0.459855i
$424$	1.44524	−	0.834408i	0.0701869	−	0.0405224i
$425$	15.6662			0.759922
$426$	6.14016	+	11.6941i	0.297492	+	0.566583i
$427$	4.13025	−	27.6333i	0.199877	−	1.33727i
$428$			6.29055i			0.304065i
$429$	12.5464	−	6.54286i	0.605745	−	0.315892i
$430$	24.9038	−	14.3782i	1.20097	−	0.693380i
$431$	−8.80577			−0.424159			−0.212079	−	0.977252i	$-0.568024\pi$
$431$	−8.80577			−0.424159			−0.212079	+	0.977252i	$0.568024\pi$
$432$	2.03922	+	4.77929i	0.0981120	+	0.229944i
$433$	3.16975	−	1.83006i	0.152328	−	0.0879468i	−0.421898	−	0.906643i	$-0.638636\pi$
$433$	3.16975	−	1.83006i	0.152328	−	0.0879468i	0.574227	+	0.818696i	$0.305303\pi$
$434$	15.7516	−	19.8019i	0.756102	−	0.950521i
$435$	46.5579	+	1.86808i	2.23228	+	0.0895677i
$436$		−	10.4195i		−	0.499005i
$437$	3.31208	−	1.91223i	0.158438	−	0.0914743i
$438$	9.24665	+	17.6106i	0.441822	+	0.841465i
$439$	−15.4018	+	8.89222i	−0.735087	+	0.424402i	−0.820280	−	0.571962i	$-0.806182\pi$
$439$	−15.4018	+	8.89222i	−0.735087	+	0.424402i	0.0851935	+	0.996364i	$0.472849\pi$
$440$	6.00243	+	3.46551i	0.286155	+	0.165212i
$441$	−3.06879	−	20.7746i	−0.146133	−	0.989265i
$442$	11.2085	+	6.51318i	0.533134	+	0.309801i
$443$	−20.0861	−	11.5967i	−0.954319	−	0.550976i	−0.0598990	−	0.998204i	$-0.519078\pi$
$443$	−20.0861	−	11.5967i	−0.954319	−	0.550976i	−0.894420	+	0.447228i	$0.852411\pi$
$444$	1.97066	+	1.24569i	0.0935232	+	0.0591176i
$445$	−25.5337			−1.21041
$446$	12.4747			0.590692
$447$	−1.57607	+	2.49332i	−0.0745456	+	0.117930i
$448$	2.61668	+	0.391106i	0.123627	+	0.0184780i
$449$	−4.03168	−	6.98308i	−0.190267	−	0.329552i	0.755072	−	0.655642i	$-0.227602\pi$
$449$	−4.03168	−	6.98308i	−0.190267	−	0.329552i	−0.945339	+	0.326090i	$0.894269\pi$
$450$	−13.0298	−	1.04729i	−0.614228	−	0.0493699i
$451$	−15.9428	−	9.20457i	−0.750716	−	0.433426i
$452$			8.37759i			0.394049i
$453$	1.54346	−	38.4674i	0.0725182	−	1.80736i
$454$		−	21.4471i		−	1.00656i
$455$	10.6182	+	27.1802i	0.497789	+	1.27423i
$456$	−0.765955	+	1.21173i	−0.0358691	+	0.0567444i
$457$	13.3000	−	7.67875i	0.622147	−	0.359197i	−0.155557	−	0.987827i	$-0.549717\pi$
$457$	13.3000	−	7.67875i	0.622147	−	0.359197i	0.777704	+	0.628630i	$0.216384\pi$
$458$	23.4927			1.09774
$459$	−11.2155	+	14.9414i	−0.523494	+	0.697403i
$460$	−7.06760	+	12.2414i	−0.329528	+	0.570760i
$461$	−1.90360	+	1.09904i	−0.0886596	+	0.0511876i	−0.543674	−	0.839296i	$-0.682967\pi$
$461$	−1.90360	+	1.09904i	−0.0886596	+	0.0511876i	0.455015	+	0.890484i	$0.349634\pi$
$462$	10.1994	+	1.94536i	0.474517	+	0.0905065i
$463$		−	9.47072i		−	0.440142i	−0.975484	−	0.220071i	$-0.929371\pi$
$463$		−	9.47072i		−	0.440142i	0.975484	−	0.220071i	$-0.0706289\pi$
$464$			8.79442i			0.408271i
$465$	−42.8307	−	27.0741i	−1.98623	−	1.25553i
$466$			12.9011i			0.597632i
$467$	7.74149	−	13.4087i	0.358234	−	0.620479i	−0.629432	−	0.777055i	$-0.716712\pi$
$467$	7.74149	−	13.4087i	0.358234	−	0.620479i	0.987666	+	0.156577i	$0.0500458\pi$
$468$	−8.88683	−	6.16638i	−0.410794	−	0.285041i
$469$	−1.58872	+	10.6293i	−0.0733601	+	0.490814i
$470$	4.83741	−	8.37864i	0.223133	−	0.386478i
$471$	0.824166	−	20.5405i	0.0379756	−	0.946458i
$472$	9.34806	+	5.39710i	0.430279	+	0.248422i
$473$	10.6501	+	18.4465i	0.489692	+	0.848172i
$474$	−5.39573	+	8.53597i	−0.247834	+	0.392070i
$475$	−1.80312	−	3.12310i	−0.0827330	−	0.143298i
$476$	3.48625	+	8.85075i	0.159792	+	0.405673i
$477$	−4.12122	−	2.84255i	−0.188698	−	0.130151i
$478$	11.5201	+	19.9534i	0.526918	+	0.912649i
$479$		−	41.3112i		−	1.88756i	−0.330577	−	0.943779i	$-0.607243\pi$
$479$		−	41.3112i		−	1.88756i	0.330577	−	0.943779i	$-0.392757\pi$
$480$	0.212417	−	5.29402i	0.00969545	−	0.241638i
$481$	−4.85308	−	0.0136001i	−0.221282	−	0.000620111i
$482$	27.7786			1.26528
$483$	−3.96740	+	20.8007i	−0.180523	+	0.946464i
$484$	2.93307	−	5.08022i	0.133321	−	0.230919i
$485$			48.9366i			2.22210i
$486$	10.3269	−	11.6771i	0.468437	−	0.529686i
$487$	−2.19492	−	1.26724i	−0.0994614	−	0.0574240i	0.449444	−	0.893308i	$-0.351622\pi$
$487$	−2.19492	−	1.26724i	−0.0994614	−	0.0574240i	−0.548906	+	0.835884i	$0.684955\pi$
$488$		−	10.5604i		−	0.478048i
$489$	−14.0733	−	8.89595i	−0.636415	−	0.402289i
$490$	−6.26110	+	20.4769i	−0.282847	+	0.925053i
$491$	−22.3657	−	12.9129i	−1.00935	−	0.582749i	−0.0983491	−	0.995152i	$-0.531356\pi$
$491$	−22.3657	−	12.9129i	−1.00935	−	0.582749i	−0.911001	+	0.412403i	$0.864690\pi$
$492$	−0.564190	+	14.0612i	−0.0254357	+	0.633928i
$493$	−27.3835	+	15.8099i	−1.23329	+	0.712040i
$494$	0.00836251	−	2.98409i	0.000376247	−	0.134261i
$495$	1.66591	−	20.7262i	0.0748772	−	0.931573i
$496$	4.78177	−	8.28226i	0.214708	−	0.371885i
$497$	−7.39415	−	18.7720i	−0.331673	−	0.842038i
$498$	−0.263342	+	6.56323i	−0.0118006	+	0.294105i
$499$	24.8498	+	14.3470i	1.11243	+	0.642261i	0.939458	−	0.342665i	$-0.111330\pi$
$499$	24.8498	+	14.3470i	1.11243	+	0.642261i	0.172972	+	0.984927i	$0.444663\pi$
$500$	−1.70271	−	0.983063i	−0.0761477	−	0.0439639i
$501$	38.2284	−	20.0723i	1.70792	−	0.896764i
$502$	−6.68358	+	11.5763i	−0.298303	+	0.516676i
$503$	−14.9785	−	25.9435i	−0.667858	−	1.15676i	−0.978502	−	0.206238i	$-0.933878\pi$
$503$	−14.9785	−	25.9435i	−0.667858	−	1.15676i	0.310644	−	0.950526i	$-0.399455\pi$
$504$	−2.30787	−	7.59432i	−0.102801	−	0.338278i
$505$	−18.9146	−	10.9204i	−0.841690	−	0.485950i
$506$	−9.06735	−	5.23504i	−0.403093	−	0.232726i
$507$	22.4931	+	1.02881i	0.998956	+	0.0456912i
$508$	−0.0429290	−	0.0743552i	−0.00190467	−	0.00329898i
$509$	−11.2118	+	6.47312i	−0.496953	+	0.286916i	−0.727454	−	0.686156i	$-0.759297\pi$
$509$	−11.2118	+	6.47312i	−0.496953	+	0.286916i	0.230501	+	0.973072i	$0.425963\pi$
$510$	16.8660	−	8.85572i	0.746840	−	0.392138i
$511$	−11.1351	−	28.2693i	−0.492587	−	1.25056i
$512$	1.00000			0.0441942
$513$	4.26947	+	0.516140i	0.188502	+	0.0227881i
$514$	−1.35563	+	2.34802i	−0.0597942	+	0.103567i
$515$	−2.71349	−	4.69990i	−0.119571	−	0.207102i
$516$	8.70006	−	13.7634i	0.382999	−	0.605898i
$517$	6.20614	+	3.58312i	0.272946	+	0.157585i
$518$	−2.78699	−	2.21694i	−0.122453	−	0.0974069i
$519$	−3.72549	+	5.89367i	−0.163531	+	0.258703i
$520$	5.48784	+	9.56703i	0.240658	+	0.419542i
$521$	19.0122	+	32.9301i	0.832940	+	1.44269i	0.895696	+	0.444666i	$0.146678\pi$
$521$	19.0122	+	32.9301i	0.832940	+	1.44269i	−0.0627562	+	0.998029i	$0.519989\pi$
$522$	23.8320	−	11.3186i	1.04310	−	0.495403i
$523$	29.0753	−	16.7866i	1.27137	−	0.734028i	0.296127	−	0.955148i	$-0.404305\pi$
$523$	29.0753	−	16.7866i	1.27137	−	0.734028i	0.975247	+	0.221120i	$0.0709714\pi$
$524$	−1.03041	−	1.78473i	−0.0450138	−	0.0779662i
$525$	19.6139	+	3.74104i	0.856020	+	0.163272i
$526$	12.7361	−	7.35317i	0.555319	−	0.320614i
$527$	34.3850			1.49783
$528$	3.92133	+	0.157339i	0.170654	+	0.00684731i
$529$	−0.823599	+	1.42651i	−0.0358086	+	0.0620224i
$530$	2.55242	+	4.42093i	0.110870	+	0.192033i
$531$	2.59446	−	32.2785i	0.112590	−	1.40077i
$532$	1.36317	−	1.71368i	0.0591008	−	0.0742976i
$533$	−14.5760	−	25.4105i	−0.631356	−	1.10065i
$534$	−12.8005	+	6.72107i	−0.553932	+	0.290849i
$535$	−19.2426			−0.831928
$536$			4.06211i			0.175456i
$537$	18.5023	+	11.6957i	0.798435	+	0.504705i
$538$	−7.51872			−0.324155
$539$	−15.1675	−	4.63765i	−0.653309	−	0.199758i
$540$	−14.6197	+	6.23790i	−0.629130	+	0.268436i
$541$	−1.91892	−	1.10789i	−0.0825009	−	0.0476319i	0.458182	−	0.888858i	$-0.348501\pi$
$541$	−1.91892	−	1.10789i	−0.0825009	−	0.0476319i	−0.540683	+	0.841226i	$0.681834\pi$
$542$	−0.0123926	+	0.0214646i	−0.000532308	+	0.000921984i
$543$	−2.62212	−	1.65749i	−0.112526	−	0.0711295i
$544$	1.79771	+	3.11373i	0.0770763	+	0.133500i
$545$	31.8730			1.36529
$546$	12.4776	+	10.8310i	0.533991	+	0.463523i
$547$	35.2174			1.50579			0.752895	−	0.658141i	$-0.228657\pi$
$547$	35.2174			1.50579			0.752895	+	0.658141i	$0.228657\pi$
$548$	4.48732	+	7.77227i	0.191689	+	0.332015i
$549$	−28.6177	+	13.5915i	−1.22138	+	0.580072i
$550$	−4.93635	+	8.55000i	−0.210487	+	0.364573i
$551$	6.30348	+	3.63931i	0.268537	+	0.155040i
$552$	−0.320879	+	7.99721i	−0.0136575	+	0.340384i
$553$	9.60277	−	12.0720i	0.408351	−	0.513352i
$554$	6.18124			0.262616
$555$	−3.81051	+	6.02816i	−0.161747	+	0.255881i
$556$			20.8757i			0.885328i
$557$	−8.14764			−0.345227			−0.172613	−	0.984990i	$-0.555221\pi$
$557$	−8.14764			−0.345227			−0.172613	+	0.984990i	$0.555221\pi$
$558$	−28.5984	−	2.29866i	−1.21067	−	0.0973099i
$559$	−0.0949852	+	33.8947i	−0.00401745	+	1.43359i
$560$	−1.19638	+	8.00434i	−0.0505563	+	0.338245i
$561$	6.55952	+	12.4928i	0.276943	+	0.527447i
$562$	−14.7874	−	25.6125i	−0.623769	−	1.08040i
$563$	−10.9475	+	18.9616i	−0.461380	+	0.799134i	−0.999030	−	0.0440340i	$-0.985979\pi$
$563$	−10.9475	+	18.9616i	−0.461380	+	0.799134i	0.537650	+	0.843168i	$0.319312\pi$
$564$	0.219626	−	5.47369i	0.00924790	−	0.230484i
$565$	−25.6268			−1.07813
$566$	−18.3623	+	10.6015i	−0.771824	+	0.445613i
$567$	−17.6096	+	16.0282i	−0.739533	+	0.673120i
$568$	−3.81286	−	6.60406i	−0.159984	−	0.277100i
$569$	34.1087	−	19.6927i	1.42991	−	0.825560i	0.432799	−	0.901490i	$-0.357526\pi$
$569$	34.1087	−	19.6927i	1.42991	−	0.825560i	0.997113	+	0.0759301i	$0.0241926\pi$
$570$	−3.70663	−	2.34303i	−0.155254	−	0.0981386i
$571$	−10.0406	−	17.3909i	−0.420187	−	0.727786i	0.575770	−	0.817612i	$-0.304702\pi$
$571$	−10.0406	−	17.3909i	−0.420187	−	0.727786i	−0.995958	+	0.0898257i	$0.971369\pi$
$572$	−7.08639	+	4.06489i	−0.296297	+	0.169962i
$573$	−14.2919	−	9.03416i	−0.597053	−	0.377407i
$574$	3.17765	−	21.2600i	0.132632	−	0.887374i
$575$	−17.4370	−	10.0672i	−0.727172	−	0.419833i
$576$	−1.28702	−	2.70990i	−0.0536260	−	0.112913i
$577$	−10.1331	−	17.5510i	−0.421847	−	0.730660i	0.574274	−	0.818663i	$-0.305285\pi$
$577$	−10.1331	−	17.5510i	−0.421847	−	0.730660i	−0.996120	+	0.0880038i	$0.971951\pi$
$578$	2.03645	−	3.52724i	0.0847053	−	0.146714i
$579$	−15.2730	−	9.65431i	−0.634723	−	0.401219i
$580$	−26.9018			−1.11704
$581$	1.48320	−	9.92333i	0.0615337	−	0.411689i
$582$	12.8813	+	24.5328i	0.533946	+	1.01692i
$583$	−3.27462	+	1.89060i	−0.135621	+	0.0783009i
$584$	−5.74190	−	9.94525i	−0.237601	−	0.411538i
$585$	18.8627	−	27.1845i	0.779878	−	1.12394i
$586$	10.1781	+	5.87631i	0.420452	+	0.242748i
$587$	5.90203	+	3.40754i	0.243603	+	0.140644i	0.616831	−	0.787095i	$-0.288416\pi$
$587$	5.90203	+	3.40754i	0.243603	+	0.140644i	−0.373229	+	0.927739i	$0.621749\pi$
$588$	2.25121	+	11.9135i	0.0928383	+	0.491305i
$589$	−3.95759	−	6.85474i	−0.163070	−	0.282445i
$590$	−16.5095	+	28.5954i	−0.679687	+	1.17725i
$591$	6.07763	+	11.5751i	0.250000	+	0.476134i
$592$	−1.16568	−	0.673004i	−0.0479090	−	0.0276603i
$593$	−30.3893	−	17.5453i	−1.24794	−	0.720498i	−0.277242	−	0.960800i	$-0.589420\pi$
$593$	−30.3893	−	17.5453i	−1.24794	−	0.720498i	−0.970698	+	0.240302i	$0.922754\pi$
$594$	−4.62047	−	10.8289i	−0.189580	−	0.444316i
$595$	−27.0741	+	10.6643i	−1.10993	+	0.437194i
$596$	0.851501	−	1.47484i	0.0348788	−	0.0604119i
$597$	−18.7673	+	9.85399i	−0.768093	+	0.403297i
$598$	−8.29000	−	14.4521i	−0.339003	−	0.590989i
$599$	3.02800	−	1.74821i	0.123721	−	0.0714301i	−0.436863	−	0.899528i	$-0.643910\pi$
$599$	3.02800	−	1.74821i	0.123721	−	0.0714301i	0.560583	+	0.828098i	$0.310577\pi$
$600$	7.54092	+	0.302571i	0.307857	+	0.0123524i
$601$	30.2974	+	17.4922i	1.23586	+	0.713521i	0.968244	−	0.250006i	$-0.0804325\pi$
$601$	30.2974	+	17.4922i	1.23586	+	0.713521i	0.267611	+	0.963527i	$0.413766\pi$
$602$	−15.4835	+	19.4648i	−0.631059	+	0.793325i
$603$	11.0079	−	5.22803i	0.448277	−	0.212902i
$604$			22.2271i			0.904406i
$605$	15.5402	+	8.97214i	0.631799	+	0.364769i
$606$	−12.3568	−	0.495801i	−0.501959	−	0.0201405i
$607$		−	17.5126i		−	0.710815i	−0.934711	−	0.355408i	$-0.884342\pi$
$607$		−	17.5126i		−	0.710815i	0.934711	−	0.355408i	$-0.115658\pi$
$608$	0.413821	−	0.716759i	0.0167826	−	0.0290684i
$609$	−38.0591	+	13.2546i	−1.54223	+	0.537105i
$610$	32.3040			1.30795
$611$	5.67408	+	9.89171i	0.229549	+	0.400176i
$612$	6.12421	−	8.87907i	0.247556	−	0.358915i
$613$			13.3294i			0.538370i	0.963089	+	0.269185i	$0.0867543\pi$
$613$			13.3294i			0.538370i	−0.963089	+	0.269185i	$0.913246\pi$
$614$	−6.12154	−	10.6028i	−0.247045	−	0.427895i
$615$	−43.0127	−	1.72584i	−1.73444	−	0.0695925i
$616$	−5.92889	−	0.886170i	−0.238882	−	0.0357048i
$617$	16.4579	+	28.5059i	0.662569	+	1.14760i	0.979938	+	0.199301i	$0.0638673\pi$
$617$	16.4579	+	28.5059i	0.662569	+	1.14760i	−0.317369	+	0.948302i	$0.602799\pi$
$618$	−2.59745	−	1.64189i	−0.104485	−	0.0660466i
$619$	−3.67239	−	6.36076i	−0.147606	−	0.255661i	0.782736	−	0.622353i	$-0.213823\pi$
$619$	−3.67239	−	6.36076i	−0.147606	−	0.255661i	−0.930342	+	0.366693i	$0.880490\pi$
$620$	25.3351	+	14.6272i	1.01748	+	0.587444i
$621$	22.0847	−	9.42305i	0.886227	−	0.378134i
$622$	4.81504	−	8.33990i	0.193066	−	0.334399i
$623$	20.5479	−	8.09369i	0.823236	−	0.324267i
$624$	5.26942	+	3.35160i	0.210946	+	0.134171i
$625$	13.9003	−	24.0760i	0.556012	−	0.963041i
$626$		−	13.9168i		−	0.556228i
$627$	1.73550	−	2.74554i	0.0693093	−	0.109646i
$628$			11.8686i			0.473610i
$629$		−	4.83947i		−	0.192962i
$630$	23.2308	−	7.05970i	0.925535	−	0.281265i
$631$	−23.3905	+	13.5045i	−0.931159	+	0.537605i	−0.887178	−	0.461427i	$-0.847338\pi$
$631$	−23.3905	+	13.5045i	−0.931159	+	0.537605i	−0.0439813	+	0.999032i	$0.514004\pi$
$632$	2.91514	−	5.04917i	0.115958	−	0.200845i
$633$	5.41487	+	10.3128i	0.215222	+	0.409897i
$634$	23.6408			0.938897
$635$	0.227450	−	0.131318i	0.00902607	−	0.00521120i
$636$	2.44327	+	1.54443i	0.0968819	+	0.0612408i
$637$	−17.1605	−	18.5072i	−0.679924	−	0.733282i
$638$		−	19.9264i		−	0.788895i
$639$	−12.9891	+	18.8320i	−0.513842	+	0.744984i
$640$			3.05896i			0.120916i
$641$	17.9909	+	10.3870i	0.710597	+	0.410263i	0.811282	−	0.584655i	$-0.198770\pi$
$641$	17.9909	+	10.3870i	0.710597	+	0.410263i	−0.100685	+	0.994918i	$0.532103\pi$
$642$	−9.64664	+	5.06510i	−0.380723	+	0.199903i
$643$	−0.127258	−	0.220417i	−0.00501857	−	0.00869242i	0.863505	−	0.504340i	$-0.168264\pi$
$643$	−0.127258	−	0.220417i	−0.00501857	−	0.00869242i	−0.868524	+	0.495647i	$0.834931\pi$
$644$	1.80727	−	12.0915i	0.0712163	−	0.476470i
$645$	42.1016	+	26.6132i	1.65775	+	1.04789i
$646$	2.97572			0.117078
$647$	24.4315			0.960502			0.480251	−	0.877131i	$-0.340546\pi$
$647$	24.4315			0.960502			0.480251	+	0.877131i	$0.340546\pi$
$648$	−5.68714	+	6.97541i	−0.223412	+	0.274020i
$649$	−21.1809	−	12.2288i	−0.831422	−	0.480022i
$650$	−13.6275	+	7.81700i	−0.534514	+	0.306608i
$651$	43.0495	+	8.21102i	1.68724	+	0.321815i
$652$	8.32458	+	4.80620i	0.326016	+	0.188225i
$653$	0.677915	−	0.391394i	0.0265289	−	0.0153164i	−0.486677	−	0.873582i	$-0.661791\pi$
$653$	0.677915	−	0.391394i	0.0265289	−	0.0153164i	0.513206	+	0.858266i	$0.328458\pi$
$654$	15.9785	−	8.38972i	0.624809	−	0.328064i
$655$	5.45942	−	3.15200i	0.213317	−	0.123159i
$656$		−	8.12477i		−	0.317219i
$657$	−19.5607	+	28.3597i	−0.763136	+	1.10642i
$658$	−1.23698	+	8.27599i	−0.0482226	+	0.322632i
$659$	37.5123	−	21.6577i	1.46127	−	0.843666i	0.462202	−	0.886775i	$-0.347060\pi$
$659$	37.5123	−	21.6577i	1.46127	−	0.843666i	0.999070	+	0.0431091i	$0.0137263\pi$
$660$	−0.481295	+	11.9952i	−0.0187344	+	0.466913i
$661$	13.0259			0.506648			0.253324	−	0.967382i	$-0.418476\pi$
$661$	13.0259			0.506648			0.253324	+	0.967382i	$0.418476\pi$
$662$	−13.0461	+	7.53219i	−0.507053	+	0.292747i
$663$	−0.963063	+	22.4328i	−0.0374023	+	0.871217i
$664$		−	3.79233i		−	0.147171i
$665$	5.24209	+	4.16988i	0.203280	+	0.161701i
$666$	−0.323522	+	4.02504i	−0.0125362	+	0.155967i
$667$	40.6382			1.57352
$668$	−21.5888	+	12.4643i	−0.835296	+	0.482258i
$669$	10.0445	+	19.1301i	0.388343	+	0.739612i
$670$	−12.4258			−0.480052
$671$			23.9279i			0.923725i
$672$	1.50717	+	4.32764i	0.0581402	+	0.166942i
$673$	−16.1195	+	27.9199i	−0.621363	+	1.07623i	0.367869	+	0.929877i	$0.380087\pi$
$673$	−16.1195	+	27.9199i	−0.621363	+	1.07623i	−0.989232	+	0.146355i	$0.953246\pi$
$674$	4.96535	+	8.60024i	0.191258	+	0.331269i
$675$	−8.88541	−	20.8246i	−0.341999	−	0.801539i
$676$	−12.9998	−	0.0728609i	−0.499992	−	0.00280234i
$677$	12.3401	−	21.3737i	0.474268	−	0.821457i	−0.525298	−	0.850919i	$-0.676046\pi$
$677$	12.3401	−	21.3737i	0.474268	−	0.821457i	0.999566	+	0.0294618i	$0.00937935\pi$
$678$	−12.8472	+	6.74557i	−0.493392	+	0.259062i
$679$	−15.5120	−	39.3812i	−0.595295	−	1.51131i
$680$	−9.52479	+	5.49914i	−0.365259	+	0.210882i
$681$	32.8895	−	17.2691i	1.26033	−	0.661752i
$682$	−10.8345	+	18.7660i	−0.414876	+	0.718587i
$683$	8.12183	−	14.0674i	0.310773	−	0.538275i	−0.667757	−	0.744379i	$-0.732745\pi$
$683$	8.12183	−	14.0674i	0.310773	−	0.538275i	0.978530	+	0.206105i	$0.0660787\pi$
$684$	−2.47494	−	0.198929i	−0.0946318	−	0.00760624i
$685$	−23.7751	+	13.7266i	−0.908400	+	0.524465i
$686$	−1.45225	−	18.4632i	−0.0554472	−	0.704930i
$687$	18.9161	+	36.0264i	0.721694	+	1.37449i
$688$	−4.70036	+	8.14127i	−0.179200	+	0.310383i
$689$	−6.01698	−	0.0168618i	−0.229229	−	0.000642382i
$690$	−24.4632	−	0.981558i	−0.931298	−	0.0373673i
$691$	−8.07718	−	13.9901i	−0.307271	−	0.532208i	0.670494	−	0.741915i	$-0.266082\pi$
$691$	−8.07718	−	13.9901i	−0.307271	−	0.532208i	−0.977764	+	0.209707i	$0.932749\pi$
$692$	2.01276	−	3.48621i	0.0765138	−	0.132526i
$693$	5.22919	+	17.2072i	0.198640	+	0.653649i
$694$		−	3.36902i		−	0.127886i
$695$	−63.8581			−2.42227
$696$	−13.4864	+	7.08120i	−0.511200	+	0.268412i
$697$	25.2984	−	14.6060i	0.958243	−	0.553242i
$698$	30.8221			1.16663
$699$	−19.7840	+	10.3879i	−0.748301	+	0.392905i
$700$	−11.4016	−	1.70415i	−0.430939	−	0.0644108i
$701$			36.9386i			1.39515i	0.716510	+	0.697577i	$0.245738\pi$
$701$			36.9386i			1.39515i	−0.716510	+	0.697577i	$0.754262\pi$
$702$	2.30063	−	18.5932i	0.0868318	−	0.701755i
$703$	−0.964763	+	0.557006i	−0.0363867	+	0.0210079i
$704$	−2.26580			−0.0853957
$705$	16.7438	+	0.671827i	0.630608	+	0.0253025i
$706$	−17.0077	+	9.81940i	−0.640093	+	0.369558i
$707$	18.6829	+	2.79247i	0.702643	+	0.105021i
$708$	−0.749558	+	18.6811i	−0.0281701	+	0.702078i
$709$			2.69201i			0.101100i	0.998722	+	0.0505502i	$0.0160975\pi$
$709$			2.69201i			0.101100i	−0.998722	+	0.0505502i	$0.983902\pi$
$710$	20.2016	−	11.6634i	0.758152	−	0.437719i
$711$	−17.4346	−	1.40135i	−0.653850	−	0.0525546i
$712$	7.22886	−	4.17358i	0.270913	−	0.156412i
$713$	−38.2716	−	22.0961i	−1.43328	−	0.827506i
$714$	−10.7656	+	12.4728i	−0.402894	+	0.466781i
$715$	−12.4344	−	21.6770i	−0.465019	−	0.810674i
$716$	−10.9445	−	6.31879i	−0.409014	−	0.236144i
$717$	−21.3230	+	33.7326i	−0.796321	+	1.25977i
$718$	10.4004			0.388141
$719$	19.2501			0.717908			0.358954	−	0.933355i	$-0.383133\pi$
$719$	19.2501			0.717908			0.358954	+	0.933355i	$0.383133\pi$
$720$	8.28949	−	3.93696i	0.308931	−	0.146722i
$721$	3.67343	+	2.92207i	0.136806	+	0.108824i
$722$	9.15750	+	15.8613i	0.340807	+	0.590295i
$723$	22.3671	+	42.5988i	0.831841	+	1.58427i
$724$	1.55103	+	0.895486i	0.0576435	+	0.0332805i
$725$		−	38.3196i		−	1.42315i
$726$	10.1523	+	0.407349i	0.376786	+	0.0151181i
$727$		−	29.4029i		−	1.09049i	−0.838276	−	0.545246i	$-0.816436\pi$
$727$		−	29.4029i		−	1.09049i	0.838276	−	0.545246i	$-0.183564\pi$
$728$	−7.44885	−	5.95942i	−0.276073	−	0.220871i
$729$	26.2222	+	6.43408i	0.971192	+	0.238299i
$730$	30.4222	−	17.5642i	1.12597	−	0.650082i
$731$	−33.7996			−1.25012
$732$	16.1946	−	8.50317i	0.598569	−	0.314286i
$733$	13.5812	−	23.5234i	0.501635	−	0.868857i	−0.498363	−	0.866968i	$-0.666065\pi$
$733$	13.5812	−	23.5234i	0.501635	−	0.868857i	0.999998	−	0.00188874i	$-0.000601204\pi$
$734$	19.6101	−	11.3219i	0.723821	−	0.417898i
$735$	−36.4430	+	6.88637i	−1.34422	+	0.254007i
$736$		−	4.62091i		−	0.170329i
$737$		−	9.20395i		−	0.339032i
$738$	−22.0173	+	10.4568i	−0.810469	+	0.384919i
$739$			18.3986i			0.676803i	0.941002	+	0.338402i	$0.109886\pi$
$739$			18.3986i			0.676803i	−0.941002	+	0.338402i	$0.890114\pi$
$740$	2.05870	−	3.56576i	0.0756791	−	0.131080i
$741$	4.58288	−	2.38994i	0.168356	−	0.0877967i
$742$	−3.45539	−	2.74862i	−0.126851	−	0.100905i
$743$	−16.4058	+	28.4156i	−0.601869	+	1.04247i	0.390669	+	0.920531i	$0.372244\pi$
$743$	−16.4058	+	28.4156i	−0.601869	+	1.04247i	−0.992538	+	0.121937i	$0.961089\pi$
$744$	16.5512	+	0.664099i	0.606797	+	0.0243470i
$745$	4.51149	+	2.60471i	0.165288	+	0.0954292i
$746$	−8.39025	−	14.5323i	−0.307189	−	0.532067i
$747$	−10.2768	+	4.88082i	−0.376010	+	0.178580i
$748$	−4.07327	−	7.05510i	−0.148933	−	0.257960i
$749$	15.4852	−	6.09953i	0.565818	−	0.222872i
$750$	0.136529	−	3.40269i	0.00498534	−	0.124249i
$751$	−5.74008	−	9.94211i	−0.209459	−	0.362793i	0.742086	−	0.670305i	$-0.233837\pi$
$751$	−5.74008	−	9.94211i	−0.209459	−	0.362793i	−0.951544	+	0.307512i	$0.900503\pi$
$752$			3.16278i			0.115335i
$753$	−23.1340	−	0.928225i	−0.843049	−	0.0338264i
$754$	15.9313	−	27.4160i	0.580182	−	0.998433i
$755$	−67.9918			−2.47447
$756$	9.78772	−	9.65404i	0.355976	−	0.351114i
$757$	−6.81712	+	11.8076i	−0.247772	+	0.429154i	−0.962907	−	0.269832i	$-0.913032\pi$
$757$	−6.81712	+	11.8076i	−0.247772	+	0.429154i	0.715135	+	0.698986i	$0.246365\pi$
$758$			4.51949i			0.164155i
$759$	0.727050	−	18.1201i	0.0263902	−	0.657719i
$760$	2.19254	+	1.26586i	0.0795317	+	0.0459177i
$761$		−	33.9871i		−	1.23203i	−0.787733	−	0.616016i	$-0.788746\pi$
$761$		−	33.9871i		−	1.23203i	0.787733	−	0.616016i	$-0.211254\pi$
$762$	0.0794587	−	0.125702i	0.00287848	−	0.00455372i
$763$	−25.6494	+	10.1031i	−0.928571	+	0.365758i
$764$	8.45391	+	4.88087i	0.305852	+	0.176584i
$765$	27.1608	+	18.7337i	0.981999	+	0.677319i
$766$	2.99527	−	1.72932i	0.108223	−	0.0624828i
$767$	−19.3650	−	33.7593i	−0.699230	−	1.21898i
$768$	0.805192	+	1.53351i	0.0290549	+	0.0553359i
$769$	−19.7746	+	34.2506i	−0.713090	+	1.23511i	0.250602	+	0.968090i	$0.419372\pi$
$769$	−19.7746	+	34.2506i	−0.713090	+	1.23511i	−0.963692	+	0.267018i	$0.913962\pi$
$770$	2.71076	−	18.1363i	0.0976891	−	0.653586i
$771$	−4.69226	−	0.188272i	−0.168988	−	0.00678044i
$772$	9.03423	+	5.21591i	0.325149	+	0.187725i
$773$	7.00876	+	4.04651i	0.252088	+	0.145543i	0.620720	−	0.784032i	$-0.286840\pi$
$773$	7.00876	+	4.04651i	0.252088	+	0.145543i	−0.368632	+	0.929575i	$0.620174\pi$
$774$	28.1115	+	2.25952i	1.01045	+	0.0812169i
$775$	−20.8354	+	36.0880i	−0.748429	+	1.29632i
$776$	−7.99888	−	13.8545i	−0.287143	−	0.497347i
$777$	1.15565	−	6.05896i	0.0414587	−	0.217364i
$778$	3.12443	+	1.80389i	0.112016	+	0.0646726i
$779$	−5.82350	−	3.36220i	−0.208649	−	0.120463i
$780$	−10.2524	+	16.1190i	−0.367095	+	0.577152i
$781$	8.63918	+	14.9635i	0.309134	+	0.535436i
$782$	14.3883	−	8.30707i	0.514523	−	0.297060i
$783$	36.5466	+	27.4331i	1.30607	+	0.980379i
$784$	−1.57445	−	6.82064i	−0.0562305	−	0.243594i
$785$	−36.3057			−1.29581
$786$	1.90723	−	3.01720i	0.0680285	−	0.107620i
$787$	−3.99395	+	6.91773i	−0.142369	+	0.246590i	−0.928388	−	0.371612i	$-0.878805\pi$
$787$	−3.99395	+	6.91773i	−0.142369	+	0.246590i	0.786019	+	0.618202i	$0.212139\pi$
$788$	−3.77403	−	6.53681i	−0.134444	−	0.232864i
$789$	21.5312	+	13.6102i	0.766530	+	0.484537i
$790$	15.4452	+	8.91731i	0.549517	+	0.317264i
$791$	20.6229	−	8.12320i	0.733264	−	0.288828i
$792$	2.91614	+	6.14011i	0.103621	+	0.218179i
$793$	−19.1304	+	32.9214i	−0.679341	+	1.16907i
$794$	−15.1719	−	26.2786i	−0.538432	−	0.932592i
$795$	−4.72437	+	7.47387i	−0.167556	+	0.265071i
$796$	10.5985	−	6.11903i	0.375653	−	0.216883i
$797$	−12.1440	−	21.0340i	−0.430162	−	0.745063i	0.566725	−	0.823907i	$-0.308210\pi$
$797$	−12.1440	−	21.0340i	−0.430162	−	0.745063i	−0.996887	+	0.0788442i	$0.974877\pi$
$798$	3.72557	+	0.710593i	0.131884	+	0.0251547i
$799$	−9.84804	+	5.68577i	−0.348398	+	0.201148i
$800$	−4.35726			−0.154052
$801$	−20.6137	−	14.2180i	−0.728349	−	0.502368i
$802$	−16.6091	+	28.7678i	−0.586488	+	1.01583i
$803$	13.0100	+	22.5340i	0.459113	+	0.795207i
$804$	−6.22931	+	3.27078i	−0.219691	+	0.115351i
$805$	36.9873	+	5.52836i	1.30363	+	0.194849i
$806$	−29.9103	+	17.1572i	−1.05355	+	0.604335i
$807$	−6.05401	−	11.5301i	−0.213111	−	0.405877i
$808$	7.13992			0.251181
$809$			19.8524i			0.697974i	0.937128	+	0.348987i	$0.113474\pi$
$809$			19.8524i			0.697974i	−0.937128	+	0.348987i	$0.886526\pi$
$810$	−21.3375	−	17.3968i	−0.749725	−	0.611260i
$811$	44.1058			1.54876			0.774382	−	0.632719i	$-0.218061\pi$
$811$	44.1058			1.54876			0.774382	+	0.632719i	$0.218061\pi$
$812$	21.6489	−	8.52737i	0.759729	−	0.299252i
$813$	−0.0428947	−	0.00172110i	−0.00150438	−	6.03617e-5i
$814$	2.64120	+	1.52490i	0.0925739	+	0.0534476i
$815$	−14.7020	+	25.4646i	−0.514988	+	0.891986i
$816$	−3.32745	+	5.26397i	−0.116484	+	0.184276i
$817$	3.89022	+	6.73805i	0.136101	+	0.235735i
$818$	−15.4590			−0.540513
$819$	−6.56261	+	27.8556i	−0.229316	+	0.973352i
$820$	24.8534			0.867918
$821$	−24.3372	−	42.1533i	−0.849375	−	1.47116i	−0.881767	−	0.471685i	$-0.843646\pi$
$821$	−24.3372	−	42.1533i	−0.849375	−	1.47116i	0.0323923	−	0.999475i	$-0.489687\pi$
$822$	−8.30574	+	13.1395i	−0.289696	+	0.458294i
$823$	−0.629038	+	1.08953i	−0.0219269	+	0.0379785i	−0.876781	−	0.480891i	$-0.840313\pi$
$823$	−0.629038	+	1.08953i	−0.0219269	+	0.0379785i	0.854854	+	0.518869i	$0.173647\pi$
$824$	1.53644	+	0.887062i	0.0535243	+	0.0309023i
$825$	−17.0863	−	0.685567i	−0.594867	−	0.0238684i
$826$	4.22168	−	28.2450i	0.146891	−	0.982770i
$827$	−45.8818			−1.59547			−0.797734	−	0.603010i	$-0.793968\pi$
$827$	−45.8818			−1.59547			−0.797734	+	0.603010i	$0.793968\pi$
$828$	−12.5222	+	5.94722i	−0.435177	+	0.206680i
$829$		−	10.4905i		−	0.364350i	−0.983266	−	0.182175i	$-0.941686\pi$
$829$		−	10.4905i		−	0.364350i	0.983266	−	0.182175i	$-0.0583137\pi$
$830$	11.6006			0.402663
$831$	4.97708	+	9.47902i	0.172653	+	0.328824i
$832$	−3.11743	−	1.81152i	−0.108078	−	0.0628031i
$833$	18.4072	−	17.1640i	0.637772	−	0.594696i
$834$	−32.0132	+	16.8090i	−1.10853	+	0.582047i
$835$	−38.1278	−	66.0394i	−1.31947	−	2.28539i
$836$	−0.937637	+	1.62403i	−0.0324288	+	0.0561684i
$837$	−19.5021	−	45.7069i	−0.674093	−	1.57986i
$838$	13.5749			0.468938
$839$	25.7265	−	14.8532i	0.888179	−	0.512790i	0.0148325	−	0.999890i	$-0.495278\pi$
$839$	25.7265	−	14.8532i	0.888179	−	0.512790i	0.873346	+	0.487100i	$0.161945\pi$
$840$	−13.2381	+	4.61036i	−0.456757	+	0.159073i
$841$	24.1709	+	41.8653i	0.833481	+	1.44363i
$842$	19.2389	−	11.1076i	0.663015	−	0.382792i
$843$	27.3705	−	43.2997i	0.942689	−	1.49132i
$844$	−3.36247	−	5.82397i	−0.115741	−	0.200469i
$845$	0.222879	−	39.7659i	0.00766726	−	1.36799i
$846$	8.57082	−	4.07057i	0.294671	−	0.139949i
$847$	−15.3498	−	2.29428i	−0.527426	−	0.0788324i
$848$	−1.44524	−	0.834408i	−0.0496296	−	0.0286537i
$849$	−31.0427	−	19.6226i	−1.06538	−	0.673446i
$850$	−7.83310	−	13.5673i	−0.268673	−	0.465356i
$851$	−3.10989	+	5.38649i	−0.106606	+	0.184646i
$852$	7.05734	−	11.1646i	0.241781	−	0.382493i
$853$	−32.2400			−1.10388			−0.551939	−	0.833885i	$-0.686112\pi$
$853$	−32.2400			−1.10388			−0.551939	+	0.833885i	$0.686112\pi$
$854$	−25.9963	+	10.2398i	−0.889574	+	0.350397i
$855$	0.608516	−	7.57076i	0.0208108	−	0.258915i
$856$	5.44777	−	3.14527i	0.186201	−	0.107503i
$857$	12.4374	+	21.5422i	0.424853	+	0.735867i	0.996407	−	0.0846975i	$-0.0269924\pi$
$857$	12.4374	+	21.5422i	0.424853	+	0.735867i	−0.571554	+	0.820565i	$0.693659\pi$
$858$	−11.9395	−	7.59406i	−0.407607	−	0.259257i
$859$	−36.6844	−	21.1798i	−1.25166	−	0.722644i	−0.280218	−	0.959937i	$-0.590407\pi$
$859$	−36.6844	−	21.1798i	−1.25166	−	0.722644i	−0.971438	+	0.237293i	$0.923740\pi$
$860$	−24.9038	−	14.3782i	−0.849214	−	0.490294i
$861$	35.1611	−	12.2454i	1.19829	−	0.417321i
$862$	4.40288	+	7.62602i	0.149963	+	0.259743i
$863$	21.7601	−	37.6895i	0.740721	−	1.28297i	−0.211446	−	0.977390i	$-0.567817\pi$
$863$	21.7601	−	37.6895i	0.740721	−	1.28297i	0.952167	−	0.305577i	$-0.0988493\pi$
$864$	3.11937	−	4.15566i	0.106123	−	0.141378i
$865$	10.6642	+	6.15697i	0.362593	+	0.209343i
$866$	−3.16975	−	1.83006i	−0.107712	−	0.0621878i
$867$	7.04881	+	0.282826i	0.239390	+	0.00960526i
$868$	−25.0247	−	3.74036i	−0.849395	−	0.126956i
$869$	−6.60514	+	11.4404i	−0.224064	+	0.388090i
$870$	−21.6611	−	41.2543i	−0.734381	−	1.39865i
$871$	7.35859	−	12.6634i	0.249336	−	0.429082i
$872$	−9.02357	+	5.20976i	−0.305577	+	0.176425i
$873$	−27.2495	+	39.5072i	−0.922257	+	1.33712i
$874$	−3.31208	−	1.91223i	−0.112033	−	0.0646821i
$875$	−0.768964	+	5.14473i	−0.0259957	+	0.173924i
$876$	10.6279	−	16.8131i	0.359082	−	0.568062i
$877$		−	2.04217i		−	0.0689590i	−0.999405	−	0.0344795i	$-0.989023\pi$
$877$		−	2.04217i		−	0.0689590i	0.999405	−	0.0344795i	$-0.0109773\pi$
$878$	15.4018	+	8.89222i	0.519785	+	0.300098i
$879$	−0.816111	+	20.3398i	−0.0275267	+	0.686044i
$880$		−	6.93101i		−	0.233644i
$881$	−9.47062	+	16.4036i	−0.319073	+	0.552651i	−0.980295	−	0.197539i	$-0.936705\pi$
$881$	−9.47062	+	16.4036i	−0.319073	+	0.552651i	0.661222	+	0.750191i	$0.270038\pi$
$882$	−16.4569	+	13.0449i	−0.554133	+	0.439246i
$883$	10.7657			0.362296			0.181148	−	0.983456i	$-0.442019\pi$
$883$	10.7657			0.362296			0.181148	+	0.983456i	$0.442019\pi$
$884$	0.0363283	−	12.9634i	0.00122185	−	0.436008i
$885$	−57.1448	−	2.29287i	−1.92090	−	0.0770740i
$886$			23.1934i			0.779198i
$887$	9.34061	+	16.1784i	0.313627	+	0.543218i	0.979145	−	0.203164i	$-0.0651225\pi$
$887$	9.34061	+	16.1784i	0.313627	+	0.543218i	−0.665518	+	0.746382i	$0.731789\pi$
$888$	0.0934678	−	2.32948i	0.00313657	−	0.0781722i
$889$	−0.141412	+	0.177774i	−0.00474282	+	0.00596236i
$890$	12.7668	+	22.1128i	0.427945	+	0.741223i
$891$	12.8860	−	15.8049i	0.431696	−	0.529485i
$892$	−6.23733	−	10.8034i	−0.208841	−	0.361724i
$893$	2.26695	+	1.30882i	0.0758605	+	0.0437981i
$894$	2.94731	+	0.118258i	0.0985729	+	0.00395513i
$895$	19.3289	−	33.4787i	0.646096	−	1.11907i
$896$	−0.969634	−	2.46167i	−0.0323932	−	0.0822386i
$897$	15.4874	−	24.3495i	0.517110	−	0.813007i
$898$	−4.03168	+	6.98308i	−0.134539	+	0.233028i
$899$		−	84.1058i		−	2.80508i
$900$	5.60789	+	11.8077i	0.186930	+	0.393591i
$901$		−	6.00011i		−	0.199892i
$902$			18.4091i			0.612957i
$903$	−42.3167	−	8.07124i	−1.40821	−	0.268594i
$904$	7.25521	−	4.18880i	0.241305	−	0.139317i
$905$	−2.73926	+	4.74454i	−0.0910561	+	0.157714i
$906$	−34.0855	+	17.8970i	−1.13242	+	0.594589i
$907$	−31.0425			−1.03075			−0.515375	−	0.856965i	$-0.672347\pi$
$907$	−31.0425			−1.03075			−0.515375	+	0.856965i	$0.672347\pi$
$908$	−18.5738	+	10.7236i	−0.616392	+	0.355874i
$909$	−9.18924	−	19.3485i	−0.304788	−	0.641748i
$910$	18.2297	−	22.7857i	0.604307	−	0.755340i
$911$		−	11.8527i		−	0.392697i	−0.980534	−	0.196349i	$-0.937092\pi$
$911$		−	11.8527i		−	0.392697i	0.980534	−	0.196349i	$-0.0629084\pi$
$912$	1.43236	+	0.0574720i	0.0474303	+	0.00190309i
$913$			8.59268i			0.284376i
$914$	−13.3000	−	7.67875i	−0.439924	−	0.253990i
$915$	26.0109	+	49.5386i	0.859893	+	1.63770i
$916$	−11.7463	−	20.3453i	−0.388110	−	0.672226i
$917$	−3.39428	+	4.26707i	−0.112089	+	0.140911i
$918$	18.5473	+	2.24221i	0.612154	+	0.0740038i
$919$	−9.09168			−0.299907			−0.149953	−	0.988693i	$-0.547912\pi$
$919$	−9.09168			−0.299907			−0.149953	+	0.988693i	$0.547912\pi$
$920$	14.1352			0.466024
$921$	11.3306	−	17.9248i	0.373355	−	0.590641i
$922$	1.90360	+	1.09904i	0.0626918	+	0.0361951i
$923$	−0.0770504	+	27.4948i	−0.00253614	+	0.905002i
$924$	−3.41494	−	9.80558i	−0.112343	−	0.322580i
$925$	5.07916	+	2.93245i	0.167002	+	0.0964184i
$926$	−8.20189	+	4.73536i	−0.269531	+	0.155614i
$927$	0.426422	−	5.30526i	0.0140055	−	0.174248i
$928$	7.61619	−	4.39721i	0.250014	−	0.144346i
$929$			3.19356i			0.104777i	0.998627	+	0.0523887i	$0.0166835\pi$
$929$			3.19356i			0.104777i	−0.998627	+	0.0523887i	$0.983317\pi$
$930$	−2.03145	+	50.6295i	−0.0666140	+	1.66021i
$931$	−5.54029	−	1.69402i	−0.181576	−	0.0555192i
$932$	11.1727	−	6.45055i	0.365973	−	0.211295i
$933$	16.6664	+	0.668720i	0.545633	+	0.0218929i
$934$	−15.4830			−0.506619
$935$	21.5813	−	12.4600i	0.705784	−	0.407485i
$936$	−0.896828	+	10.7794i	−0.0293138	+	0.352336i
$937$			50.2345i			1.64109i	0.571581	+	0.820545i	$0.306330\pi$
$937$			50.2345i			1.64109i	−0.571581	+	0.820545i	$0.693670\pi$
$938$	9.99957	−	3.93876i	0.326497	−	0.128605i
$939$	21.3416	−	11.2057i	0.696458	−	0.365684i
$940$	−9.67482			−0.315558
$941$	23.4013	−	13.5107i	0.762861	−	0.440438i	−0.0674613	−	0.997722i	$-0.521490\pi$
$941$	23.4013	−	13.5107i	0.762861	−	0.440438i	0.830322	+	0.557284i	$0.188157\pi$
$942$	−18.2007	+	9.55652i	−0.593011	+	0.311368i
$943$	−37.5438			−1.22260
$944$		−	10.7942i		−	0.351322i
$945$	29.5314	+	29.9403i	0.960655	+	0.973957i
$946$	10.6501	−	18.4465i	0.346265	−	0.599748i
$947$	14.1760	+	24.5536i	0.460658	+	0.797884i	0.998994	−	0.0448470i	$-0.0142800\pi$
$947$	14.1760	+	24.5536i	0.460658	+	0.797884i	−0.538336	+	0.842731i	$0.680947\pi$
$948$	10.0902	+	0.404859i	0.327715	+	0.0131492i
$949$	−0.116033	+	41.4052i	−0.00376657	+	1.34407i
$950$	−1.80312	+	3.12310i	−0.0585011	+	0.101327i
$951$	19.0354	+	36.2535i	0.617265	+	1.17560i
$952$	5.92185	−	7.44455i	0.191928	−	0.241279i
$953$	16.5831	−	9.57426i	0.537180	−	0.310141i	−0.206755	−	0.978393i	$-0.566290\pi$
$953$	16.5831	−	9.57426i	0.537180	−	0.310141i	0.743935	+	0.668252i	$0.232957\pi$
$954$	−0.401111	+	4.99035i	−0.0129864	+	0.161569i
$955$	−14.9304	+	25.8602i	−0.483136	+	0.836817i
$956$	11.5201	−	19.9534i	0.372587	−	0.645340i
$957$	30.5575	−	16.0446i	0.987783	−	0.518648i
$958$	−35.7766	+	20.6556i	−1.15589	+	0.667353i
$959$	14.7817	−	18.5826i	0.477326	−	0.600062i
$960$	−4.69096	+	2.46305i	−0.151400	+	0.0794947i
$961$	−30.2306	+	52.3609i	−0.975180	+	1.68906i
$962$	2.41476	+	4.20969i	0.0778551	+	0.135726i
$963$	−15.5348	−	10.7149i	−0.500602	−	0.345283i
$964$	−13.8893	−	24.0570i	−0.447344	−	0.774822i
$965$	−15.9553	+	27.6354i	−0.513619	+	0.889614i
$966$	19.9976	−	6.96447i	0.643413	−	0.224078i
$967$			40.5538i			1.30412i	0.758167	+	0.652061i	$0.226095\pi$
$967$			40.5538i			1.30412i	−0.758167	+	0.652061i	$0.773905\pi$
$968$	−5.86613			−0.188545
$969$	2.39603	+	4.56332i	0.0769715	+	0.146595i
$970$	42.3803	−	24.4683i	1.36075	−	0.785630i
$971$	−24.2314			−0.777624			−0.388812	−	0.921317i	$-0.627114\pi$
$971$	−24.2314			−0.777624			−0.388812	+	0.921317i	$0.627114\pi$
$972$	−15.2761	−	3.10477i	−0.489982	−	0.0995855i
$973$	51.3891	−	20.2418i	1.64746	−	0.648923i
$974$			2.53448i			0.0812099i
$975$	−22.9602	−	14.6038i	−0.735316	−	0.467695i
$976$	−9.14560	+	5.28021i	−0.292744	+	0.169016i
$977$	13.8222			0.442211			0.221105	−	0.975250i	$-0.429034\pi$
$977$	13.8222			0.442211			0.221105	+	0.975250i	$0.429034\pi$
$978$	−0.667492	+	16.6358i	−0.0213440	+	0.531953i
$979$	−16.3792	+	9.45652i	−0.523481	+	0.302232i
$980$	20.8641	−	4.81619i	0.666479	−	0.153848i
$981$	25.7315	+	17.7479i	0.821544	+	0.566648i
$982$			25.8257i			0.824131i
$983$	6.38037	−	3.68371i	0.203502	−	0.117492i	−0.394786	−	0.918773i	$-0.629181\pi$
$983$	6.38037	−	3.68371i	0.203502	−	0.117492i	0.598288	+	0.801281i	$0.295848\pi$
$984$	12.4595	−	6.54200i	0.397193	−	0.208551i
$985$	19.9959	−	11.5446i	0.637121	−	0.367842i
$986$	27.3835	+	15.8099i	0.872067	+	0.503488i
$987$	−13.6874	+	4.76683i	−0.435673	+	0.151730i
$988$	−2.58848	+	1.48480i	−0.0823506	+	0.0472379i
$989$	37.6201	+	21.7200i	1.19625	+	0.690654i
$990$	−18.7824	+	8.92037i	−0.596943	+	0.283508i
$991$	−60.8260			−1.93220			−0.966100	−	0.258167i	$-0.916881\pi$
$991$	−60.8260			−1.93220			−0.966100	+	0.258167i	$0.916881\pi$
$992$	−9.56353			−0.303642
$993$	−22.0554	−	13.9416i	−0.699906	−	0.442423i
$994$	−12.5599	+	15.7895i	−0.398377	+	0.500813i
$995$	18.7179	+	32.4204i	0.593397	+	1.02779i
$996$	5.81559	−	3.05355i	0.184274	−	0.0967555i
$997$	35.6118	+	20.5605i	1.12784	+	0.651157i	0.943390	−	0.331685i	$-0.107617\pi$
$997$	35.6118	+	20.5605i	1.12784	+	0.651157i	0.184447	+	0.982842i	$0.440951\pi$
$998$		−	28.6941i		−	0.908295i
$999$	−6.43296	+	2.74481i	−0.203530	+	0.0868418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.173.12	yes	34
3.2	odd	2		546.2.bn.f.173.6	yes	34
7.3	odd	6		546.2.bi.f.17.17	yes	34
13.10	even	6		546.2.bi.e.257.11	yes	34
21.17	even	6		546.2.bi.e.17.11	✓	34
39.23	odd	6		546.2.bi.f.257.17	yes	34
91.10	odd	6		546.2.bn.f.101.6	yes	34
273.101	even	6	inner	546.2.bn.e.101.12	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.11	✓	34	21.17	even	6
546.2.bi.e.257.11	yes	34	13.10	even	6
546.2.bi.f.17.17	yes	34	7.3	odd	6
546.2.bi.f.257.17	yes	34	39.23	odd	6
546.2.bn.e.101.12	yes	34	273.101	even	6	inner
546.2.bn.e.173.12	yes	34	1.1	even	1	trivial
546.2.bn.f.101.6	yes	34	91.10	odd	6
546.2.bn.f.173.6	yes	34	3.2	odd	2

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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.925467 - 1.46407i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.64914 - 1.52948i) q^{5} +(-1.73066 - 0.0694407i) q^{6} +(2.61668 + 0.391106i) q^{7} +1.00000 q^{8} +(-1.28702 - 2.70990i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.925467 - 1.46407i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.64914 - 1.52948i) q^{5} +(-1.73066 - 0.0694407i) q^{6} +(2.61668 + 0.391106i) q^{7} +1.00000 q^{8} +(-1.28702 - 2.70990i) q^{9} +3.05896i q^{10} -2.26580 q^{11} +(0.805192 + 1.53351i) q^{12} +(-3.11743 - 1.81152i) q^{13} +(-0.969634 - 2.46167i) q^{14} +(-4.69096 + 2.46305i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.79771 - 3.11373i) q^{17} +(-1.70333 + 2.46955i) q^{18} -0.827642 q^{19} +(2.64914 - 1.52948i) q^{20} +(2.99426 - 3.46906i) q^{21} +(1.13290 + 1.96224i) q^{22} +(-4.00182 + 2.31045i) q^{23} +(0.925467 - 1.46407i) q^{24} +(2.17863 + 3.77350i) q^{25} +(-0.0101040 + 3.60554i) q^{26} +(-5.15859 - 0.623627i) q^{27} +(-1.64705 + 2.07056i) q^{28} +(-7.61619 - 4.39721i) q^{29} +(4.47855 + 2.83097i) q^{30} +(4.78177 + 8.28226i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.09693 + 3.31730i) q^{33} -3.59543 q^{34} +(-6.33377 - 5.03827i) q^{35} +(2.99036 + 0.240356i) q^{36} +(1.16568 - 0.673004i) q^{37} +(0.413821 + 0.716759i) q^{38} +(-5.53728 + 2.88765i) q^{39} +(-2.64914 - 1.52948i) q^{40} +(7.03626 + 4.06239i) q^{41} +(-4.50143 - 0.858576i) q^{42} +(-4.70036 - 8.14127i) q^{43} +(1.13290 - 1.96224i) q^{44} +(-0.735241 + 9.14739i) q^{45} +(4.00182 + 2.31045i) q^{46} +(-2.73905 - 1.58139i) q^{47} +(-1.73066 - 0.0694407i) q^{48} +(6.69407 + 2.04680i) q^{49} +(2.17863 - 3.77350i) q^{50} +(-2.89501 - 5.51364i) q^{51} +(3.12754 - 1.79402i) q^{52} +(1.44524 - 0.834408i) q^{53} +(2.03922 + 4.77929i) q^{54} +(6.00243 + 3.46551i) q^{55} +(2.61668 + 0.391106i) q^{56} +(-0.765955 + 1.21173i) q^{57} +8.79442i q^{58} +(9.34806 + 5.39710i) q^{59} +(0.212417 - 5.29402i) q^{60} -10.5604i q^{61} +(4.78177 - 8.28226i) q^{62} +(-2.30787 - 7.59432i) q^{63} +1.00000 q^{64} +(5.48784 + 9.56703i) q^{65} +(3.92133 + 0.157339i) q^{66} +4.06211i q^{67} +(1.79771 + 3.11373i) q^{68} +(-0.320879 + 7.99721i) q^{69} +(-1.19638 + 8.00434i) q^{70} +(-3.81286 - 6.60406i) q^{71} +(-1.28702 - 2.70990i) q^{72} +(-5.74190 - 9.94525i) q^{73} +(-1.16568 - 0.673004i) q^{74} +(7.54092 + 0.302571i) q^{75} +(0.413821 - 0.716759i) q^{76} +(-5.92889 - 0.886170i) q^{77} +(5.26942 + 3.35160i) q^{78} +(2.91514 - 5.04917i) q^{79} +3.05896i q^{80} +(-5.68714 + 6.97541i) q^{81} -8.12477i q^{82} -3.79233i q^{83} +(1.50717 + 4.32764i) q^{84} +(-9.52479 + 5.49914i) q^{85} +(-4.70036 + 8.14127i) q^{86} +(-13.4864 + 7.08120i) q^{87} -2.26580 q^{88} +(7.22886 - 4.17358i) q^{89} +(8.28949 - 3.93696i) q^{90} +(-7.44885 - 5.95942i) q^{91} -4.62091i q^{92} +(16.5512 + 0.664099i) q^{93} +3.16278i q^{94} +(2.19254 + 1.26586i) q^{95} +(0.805192 + 1.53351i) q^{96} +(-7.99888 - 13.8545i) q^{97} +(-1.57445 - 6.82064i) q^{98} +(2.91614 + 6.14011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Introduction

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