LMFDB - Embedded newform 546.2.bi.f.17.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			17.17
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.73066 + 0.0694407i) q^{3} +1.00000 q^{4} +(-2.64914 + 1.52948i) q^{5} +(1.73066 + 0.0694407i) q^{6} +(0.969634 - 2.46167i) q^{7} +1.00000 q^{8} +(2.99036 + 0.240356i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.73066 + 0.0694407i) q^{3} +1.00000 q^{4} +(-2.64914 + 1.52948i) q^{5} +(1.73066 + 0.0694407i) q^{6} +(0.969634 - 2.46167i) q^{7} +1.00000 q^{8} +(2.99036 + 0.240356i) q^{9} +(-2.64914 + 1.52948i) q^{10} +(1.13290 + 1.96224i) q^{11} +(1.73066 + 0.0694407i) q^{12} +(3.11743 + 1.81152i) q^{13} +(0.969634 - 2.46167i) q^{14} +(-4.69096 + 2.46305i) q^{15} +1.00000 q^{16} +3.59543 q^{17} +(2.99036 + 0.240356i) q^{18} +(-0.413821 + 0.716759i) q^{19} +(-2.64914 + 1.52948i) q^{20} +(1.84905 - 4.19297i) q^{21} +(1.13290 + 1.96224i) q^{22} -4.62091i q^{23} +(1.73066 + 0.0694407i) q^{24} +(2.17863 - 3.77350i) q^{25} +(3.11743 + 1.81152i) q^{26} +(5.15859 + 0.623627i) q^{27} +(0.969634 - 2.46167i) q^{28} +(-7.61619 - 4.39721i) q^{29} +(-4.69096 + 2.46305i) q^{30} +(-4.78177 + 8.28226i) q^{31} +1.00000 q^{32} +(1.82441 + 3.47464i) q^{33} +3.59543 q^{34} +(1.19638 + 8.00434i) q^{35} +(2.99036 + 0.240356i) q^{36} +1.34601i q^{37} +(-0.413821 + 0.716759i) q^{38} +(5.26942 + 3.35160i) q^{39} +(-2.64914 + 1.52948i) q^{40} +(-7.03626 - 4.06239i) q^{41} +(1.84905 - 4.19297i) q^{42} +(-4.70036 - 8.14127i) q^{43} +(1.13290 + 1.96224i) q^{44} +(-8.28949 + 3.93696i) q^{45} -4.62091i q^{46} +(-2.73905 + 1.58139i) q^{47} +(1.73066 + 0.0694407i) q^{48} +(-5.11962 - 4.77383i) q^{49} +(2.17863 - 3.77350i) q^{50} +(6.22246 + 0.249669i) q^{51} +(3.11743 + 1.81152i) q^{52} +(-1.44524 - 0.834408i) q^{53} +(5.15859 + 0.623627i) q^{54} +(-6.00243 - 3.46551i) q^{55} +(0.969634 - 2.46167i) q^{56} +(-0.765955 + 1.21173i) q^{57} +(-7.61619 - 4.39721i) q^{58} +10.7942i q^{59} +(-4.69096 + 2.46305i) q^{60} +(-9.14560 - 5.28021i) q^{61} +(-4.78177 + 8.28226i) q^{62} +(3.49123 - 7.12821i) q^{63} +1.00000 q^{64} +(-11.0292 - 0.0309078i) q^{65} +(1.82441 + 3.47464i) q^{66} +(3.51789 - 2.03106i) q^{67} +3.59543 q^{68} +(0.320879 - 7.99721i) q^{69} +(1.19638 + 8.00434i) q^{70} +(-3.81286 - 6.60406i) q^{71} +(2.99036 + 0.240356i) q^{72} +(5.74190 - 9.94525i) q^{73} +1.34601i q^{74} +(4.03250 - 6.37935i) 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} +(-2.64914 + 1.52948i) q^{80} +(8.88446 + 1.43750i) q^{81} +(-7.03626 - 4.06239i) q^{82} +3.79233i q^{83} +(1.84905 - 4.19297i) q^{84} +(-9.52479 + 5.49914i) q^{85} +(-4.70036 - 8.14127i) q^{86} +(-12.8757 - 8.13894i) q^{87} +(1.13290 + 1.96224i) q^{88} -8.34716i q^{89} +(-8.28949 + 3.93696i) q^{90} +(7.48213 - 5.91758i) q^{91} -4.62091i q^{92} +(-8.85073 + 14.0017i) q^{93} +(-2.73905 + 1.58139i) q^{94} -2.53173i q^{95} +(1.73066 + 0.0694407i) q^{96} +(7.99888 + 13.8545i) q^{97} +(-5.11962 - 4.77383i) q^{98} +(2.91614 + 6.14011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.73066	+	0.0694407i	0.999196	+	0.0400916i
$3$	1.73066	+	0.0694407i	0.999196	+	0.0400916i
$4$	1.00000			0.500000
$5$	−2.64914	+	1.52948i	−1.18473	+	0.684005i	−0.957104	−	0.289743i	$-0.906430\pi$
$5$	−2.64914	+	1.52948i	−1.18473	+	0.684005i	−0.227627	+	0.973748i	$0.573097\pi$
$6$	1.73066	+	0.0694407i	0.706538	+	0.0283491i
$7$	0.969634	−	2.46167i	0.366487	−	0.930423i
$7$	0.969634	−	2.46167i	0.366487	−	0.930423i
$8$	1.00000			0.353553
$9$	2.99036	+	0.240356i	0.996785	+	0.0801188i
$10$	−2.64914	+	1.52948i	−0.837732	+	0.483665i
$11$	1.13290	+	1.96224i	0.341583	+	0.591639i	0.984727	−	0.174106i	$-0.0557037\pi$
$11$	1.13290	+	1.96224i	0.341583	+	0.591639i	−0.643144	+	0.765745i	$0.722370\pi$
$12$	1.73066	+	0.0694407i	0.499598	+	0.0200458i
$13$	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
$16$	1.00000			0.250000
$17$	3.59543			0.872019			0.436010	−	0.899942i	$-0.356391\pi$
$17$	3.59543			0.872019			0.436010	+	0.899942i	$0.356391\pi$
$18$	2.99036	+	0.240356i	0.704834	+	0.0566525i
$19$	−0.413821	+	0.716759i	−0.0949370	+	0.164436i	−0.909582	−	0.415524i	$-0.863598\pi$
$19$	−0.413821	+	0.716759i	−0.0949370	+	0.164436i	0.814645	+	0.579959i	$0.196932\pi$
$20$	−2.64914	+	1.52948i	−0.592366	+	0.342003i
$21$	1.84905	−	4.19297i	0.403495	−	0.914982i
$22$	1.13290	+	1.96224i	0.241536	+	0.418352i
$23$		−	4.62091i		−	0.963526i	−0.876302	−	0.481763i	$-0.839997\pi$
$23$		−	4.62091i		−	0.963526i	0.876302	−	0.481763i	$-0.160003\pi$
$24$	1.73066	+	0.0694407i	0.353269	+	0.0141745i
$25$	2.17863	−	3.77350i	0.435726	−	0.754699i
$26$	3.11743	+	1.81152i	0.611379	+	0.355268i
$27$	5.15859	+	0.623627i	0.992772	+	0.120017i
$28$	0.969634	−	2.46167i	0.183244	−	0.465212i
$29$	−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	$0.970778\pi$
$30$	−4.69096	+	2.46305i	−0.856449	+	0.449690i
$31$	−4.78177	+	8.28226i	−0.858831	+	1.48754i	0.0142145	+	0.999899i	$0.495475\pi$
$31$	−4.78177	+	8.28226i	−0.858831	+	1.48754i	−0.873045	+	0.487639i	$0.837858\pi$
$32$	1.00000			0.176777
$33$	1.82441	+	3.47464i	0.317588	+	0.604858i
$34$	3.59543			0.616611
$35$	1.19638	+	8.00434i	0.202225	+	1.35298i
$36$	2.99036	+	0.240356i	0.498393	+	0.0400594i
$37$			1.34601i			0.221282i	0.993860	+	0.110641i	$0.0352904\pi$
$37$			1.34601i			0.221282i	−0.993860	+	0.110641i	$0.964710\pi$
$38$	−0.413821	+	0.716759i	−0.0671306	+	0.116274i
$39$	5.26942	+	3.35160i	0.843783	+	0.536685i
$40$	−2.64914	+	1.52948i	−0.418866	+	0.241832i
$41$	−7.03626	−	4.06239i	−1.09888	−	0.634438i	−0.162953	−	0.986634i	$-0.552102\pi$
$41$	−7.03626	−	4.06239i	−1.09888	−	0.634438i	−0.935926	+	0.352196i	$0.885435\pi$
$42$	1.84905	−	4.19297i	0.285314	−	0.646990i
$43$	−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
$45$	−8.28949	+	3.93696i	−1.23572	+	0.586887i
$46$		−	4.62091i		−	0.681316i
$47$	−2.73905	+	1.58139i	−0.399531	+	0.230669i	−0.686282	−	0.727336i	$-0.740758\pi$
$47$	−2.73905	+	1.58139i	−0.399531	+	0.230669i	0.286751	+	0.958005i	$0.407425\pi$
$48$	1.73066	+	0.0694407i	0.249799	+	0.0100229i
$49$	−5.11962	−	4.77383i	−0.731374	−	0.681976i
$50$	2.17863	−	3.77350i	0.308105	−	0.533653i
$51$	6.22246	+	0.249669i	0.871318	+	0.0349607i
$52$	3.11743	+	1.81152i	0.432310	+	0.251212i
$53$	−1.44524	−	0.834408i	−0.198519	−	0.114615i	0.397446	−	0.917626i	$-0.369897\pi$
$53$	−1.44524	−	0.834408i	−0.198519	−	0.114615i	−0.595964	+	0.803011i	$0.703230\pi$
$54$	5.15859	+	0.623627i	0.701996	+	0.0848649i
$55$	−6.00243	−	3.46551i	−0.809368	−	0.467289i
$56$	0.969634	−	2.46167i	0.129573	−	0.328954i
$57$	−0.765955	+	1.21173i	−0.101453	+	0.160497i
$58$	−7.61619	−	4.39721i	−1.00006	−	0.577382i
$59$			10.7942i			1.40529i	0.711543	+	0.702643i	$0.247997\pi$
$59$			10.7942i			1.40529i	−0.711543	+	0.702643i	$0.752003\pi$
$60$	−4.69096	+	2.46305i	−0.605601	+	0.317979i
$61$	−9.14560	−	5.28021i	−1.17097	−	0.676062i	−0.217065	−	0.976157i	$-0.569648\pi$
$61$	−9.14560	−	5.28021i	−1.17097	−	0.676062i	−0.953909	+	0.300095i	$0.902982\pi$
$62$	−4.78177	+	8.28226i	−0.607285	+	1.05185i
$63$	3.49123	−	7.12821i	0.439853	−	0.898070i
$64$	1.00000			0.125000
$65$	−11.0292	−	0.0309078i	−1.36800	−	0.00383365i
$66$	1.82441	+	3.47464i	0.224569	+	0.427699i
$67$	3.51789	−	2.03106i	0.429779	−	0.248133i	−0.269474	−	0.963008i	$-0.586850\pi$
$67$	3.51789	−	2.03106i	0.429779	−	0.248133i	0.699252	+	0.714875i	$0.253516\pi$
$68$	3.59543			0.436010
$69$	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	$0.982802\pi$
$72$	2.99036	+	0.240356i	0.352417	+	0.0283263i
$73$	5.74190	−	9.94525i	0.672038	−	1.16400i	−0.305287	−	0.952260i	$-0.598752\pi$
$73$	5.74190	−	9.94525i	0.672038	−	1.16400i	0.977325	−	0.211744i	$-0.0679142\pi$
$74$			1.34601i			0.156470i
$75$	4.03250	−	6.37935i	0.465633	−	0.736623i
$76$	−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	0.982111	−	0.188304i	$-0.0602991\pi$
$79$	2.91514	+	5.04917i	0.327979	+	0.568077i	−0.654132	+	0.756381i	$0.726966\pi$
$80$	−2.64914	+	1.52948i	−0.296183	+	0.171001i
$81$	8.88446	+	1.43750i	0.987162	+	0.159722i
$82$	−7.03626	−	4.06239i	−0.777025	−	0.448615i
$83$			3.79233i			0.416262i	0.978101	+	0.208131i	$0.0667381\pi$
$83$			3.79233i			0.416262i	−0.978101	+	0.208131i	$0.933262\pi$
$84$	1.84905	−	4.19297i	0.201747	−	0.457491i
$85$	−9.52479	+	5.49914i	−1.03311	+	0.596465i
$86$	−4.70036	−	8.14127i	−0.506853	−	0.877896i
$87$	−12.8757	−	8.13894i	−1.38042	−	0.872586i
$88$	1.13290	+	1.96224i	0.120768	+	0.209176i
$89$		−	8.34716i		−	0.884798i	−0.896818	−	0.442399i	$-0.854128\pi$
$89$		−	8.34716i		−	0.884798i	0.896818	−	0.442399i	$-0.145872\pi$
$90$	−8.28949	+	3.93696i	−0.873789	+	0.414992i
$91$	7.48213	−	5.91758i	0.784340	−	0.620331i
$92$		−	4.62091i		−	0.481763i
$93$	−8.85073	+	14.0017i	−0.917778	+	1.45191i
$94$	−2.73905	+	1.58139i	−0.282511	+	0.163108i
$95$		−	2.53173i		−	0.259750i
$96$	1.73066	+	0.0694407i	0.176635	+	0.00708727i
$97$	7.99888	+	13.8545i	0.812164	+	1.40671i	0.911347	+	0.411639i	$0.135044\pi$
$97$	7.99888	+	13.8545i	0.812164	+	1.40671i	−0.0991832	+	0.995069i	$0.531623\pi$
$98$	−5.11962	−	4.77383i	−0.517160	−	0.482230i
$99$	2.91614	+	6.14011i	0.293083	+	0.617104i
$100$	2.17863	−	3.77350i	0.217863	−	0.377350i
$101$	3.56996	+	6.18335i	0.355224	+	0.615266i	0.987156	−	0.159758i	$-0.0510712\pi$
$101$	3.56996	+	6.18335i	0.355224	+	0.615266i	−0.631932	+	0.775024i	$0.717738\pi$
$102$	6.22246	+	0.249669i	0.616115	+	0.0247209i
$103$	1.53644	−	0.887062i	0.151390	−	0.0874048i	−0.422392	−	0.906413i	$-0.638809\pi$
$103$	1.53644	−	0.887062i	0.151390	−	0.0874048i	0.573781	+	0.819009i	$0.305476\pi$
$104$	3.11743	+	1.81152i	0.305690	+	0.177634i
$105$	1.51470	+	13.9359i	0.147819	+	1.36000i
$106$	−1.44524	−	0.834408i	−0.140374	−	0.0810449i
$107$			6.29055i			0.608130i	0.952651	+	0.304065i	$0.0983440\pi$
$107$			6.29055i			0.608130i	−0.952651	+	0.304065i	$0.901656\pi$
$108$	5.15859	+	0.623627i	0.496386	+	0.0600086i
$109$	9.02357	+	5.20976i	0.864302	+	0.499005i	0.865450	−	0.500995i	$-0.167032\pi$
$109$	9.02357	+	5.20976i	0.864302	+	0.499005i	−0.00114874	+	0.999999i	$0.500366\pi$
$110$	−6.00243	−	3.46551i	−0.572309	−	0.330423i
$111$	−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	$0.204407\pi$
$114$	−0.765955	+	1.21173i	−0.0717382	+	0.113489i
$115$	7.06760	+	12.2414i	0.659057	+	1.14152i
$116$	−7.61619	−	4.39721i	−0.707146	−	0.408271i
$117$	8.88683	+	6.16638i	0.821588	+	0.570082i
$118$			10.7942i			0.993687i
$119$	3.48625	−	8.85075i	0.319584	−	0.811347i
$120$	−4.69096	+	2.46305i	−0.428225	+	0.224845i
$121$	2.93307	−	5.08022i	0.266642	−	0.461838i
$122$	−9.14560	−	5.28021i	−0.828004	−	0.478048i
$123$	−11.8953	−	7.51920i	−1.07256	−	0.677984i
$124$	−4.78177	+	8.28226i	−0.429415	+	0.743769i
$125$		−	1.96613i		−	0.175856i
$126$	3.49123	−	7.12821i	0.311023	−	0.635031i
$127$	−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	$0.167879\pi$
$128$	1.00000			0.0883883
$129$	−7.56939	−	14.4161i	−0.666447	−	1.26927i
$130$	−11.0292	−	0.0309078i	−0.967325	−	0.00271080i
$131$	1.03041	+	1.78473i	0.0900276	+	0.155932i	0.907523	−	0.420003i	$-0.137971\pi$
$131$	1.03041	+	1.78473i	0.0900276	+	0.155932i	−0.817495	+	0.575936i	$0.804638\pi$
$132$	1.82441	+	3.47464i	0.158794	+	0.302429i
$133$	1.36317	+	1.71368i	0.118202	+	0.148595i
$134$	3.51789	−	2.03106i	0.303900	−	0.175456i
$135$	−14.6197	+	6.23790i	−1.25826	+	0.536873i
$136$	3.59543			0.308305
$137$	−8.97465			−0.766756			−0.383378	−	0.923592i	$-0.625239\pi$
$137$	−8.97465			−0.766756			−0.383378	+	0.923592i	$0.625239\pi$
$138$	0.320879	−	7.99721i	0.0273151	−	0.680768i
$139$	−18.0789	+	10.4379i	−1.53343	+	0.885328i	−0.534233	+	0.845338i	$0.679399\pi$
$139$	−18.0789	+	10.4379i	−1.53343	+	0.885328i	−0.999200	+	0.0399902i	$0.987267\pi$
$140$	1.19638	+	8.00434i	0.101113	+	0.676490i
$141$	−4.85016	+	2.54664i	−0.408457	+	0.214466i
$142$	−3.81286	−	6.60406i	−0.319968	−	0.554200i
$143$	−0.0228937	+	8.16944i	−0.00191447	+	0.683163i
$144$	2.99036	+	0.240356i	0.249196	+	0.0200297i
$145$	26.9018			2.23407
$146$	5.74190	−	9.94525i	0.475203	−	0.823075i
$147$	−8.52881	−	8.61739i	−0.703445	−	0.710750i
$148$			1.34601i			0.110641i
$149$	0.851501	−	1.47484i	0.0697576	−	0.120824i	−0.829037	−	0.559194i	$-0.811111\pi$
$149$	0.851501	−	1.47484i	0.0697576	−	0.120824i	0.898795	+	0.438370i	$0.144444\pi$
$150$	4.03250	−	6.37935i	0.329252	−	0.520871i
$151$	−19.2492	−	11.1135i	−1.56648	−	0.904406i	−0.996575	−	0.0826936i	$-0.973648\pi$
$151$	−19.2492	−	11.1135i	−1.56648	−	0.904406i	−0.569902	−	0.821712i	$-0.693019\pi$
$152$	−0.413821	+	0.716759i	−0.0335653	+	0.0581368i
$153$	10.7516	+	0.864184i	0.869216	+	0.0698651i
$154$	5.92889	−	0.886170i	0.477764	−	0.0714096i
$155$		−	29.2545i		−	2.34978i
$156$	5.26942	+	3.35160i	0.421891	+	0.268343i
$157$	10.2785	+	5.93431i	0.820316	+	0.473610i	0.850525	−	0.525934i	$-0.176284\pi$
$157$	10.2785	+	5.93431i	0.820316	+	0.473610i	−0.0302095	+	0.999544i	$0.509617\pi$
$158$	2.91514	+	5.04917i	0.231916	+	0.401691i
$159$	−2.44327	−	1.54443i	−0.193764	−	0.122482i
$160$	−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
$163$	8.32458	+	4.80620i	0.652031	+	0.376451i	0.789234	−	0.614092i	$-0.210478\pi$
$163$	8.32458	+	4.80620i	0.652031	+	0.376451i	−0.137203	+	0.990543i	$0.543811\pi$
$164$	−7.03626	−	4.06239i	−0.549440	−	0.317219i
$165$	−10.1475	−	6.41442i	−0.789983	−	0.499362i
$166$			3.79233i			0.294342i
$167$	−21.5888	−	12.4643i	−1.67059	−	0.964517i	−0.967307	−	0.253608i	$-0.918383\pi$
$167$	−21.5888	−	12.4643i	−1.67059	−	0.964517i	−0.703285	−	0.710908i	$-0.748284\pi$
$168$	1.84905	−	4.19297i	0.142657	−	0.323495i
$169$	6.43680	+	11.2946i	0.495138	+	0.868814i
$170$	−9.52479	+	5.49914i	−0.730518	+	0.421765i
$171$	−1.40975	+	2.04390i	−0.107806	+	0.156301i
$172$	−4.70036	−	8.14127i	−0.358399	−	0.620766i
$173$	−2.01276	+	3.48621i	−0.153028	+	0.265051i	−0.932339	−	0.361585i	$-0.882236\pi$
$173$	−2.01276	+	3.48621i	−0.153028	+	0.265051i	0.779312	+	0.626637i	$0.215569\pi$
$174$	−12.8757	−	8.13894i	−0.976103	−	0.617012i
$175$	−7.17662	−	9.02197i	−0.542502	−	0.681997i
$176$	1.13290	+	1.96224i	0.0853957	+	0.147910i
$177$	−0.749558	+	18.6811i	−0.0563402	+	1.40416i
$178$		−	8.34716i		−	0.625646i
$179$	10.9445	−	6.31879i	0.818028	−	0.472289i	−0.0317081	−	0.999497i	$-0.510095\pi$
$179$	10.9445	−	6.31879i	0.818028	−	0.472289i	0.849736	+	0.527209i	$0.176761\pi$
$180$	−8.28949	+	3.93696i	−0.617862	+	0.293443i
$181$			1.79097i			0.133122i	0.997782	+	0.0665610i	$0.0212027\pi$
$181$			1.79097i			0.133122i	−0.997782	+	0.0665610i	$0.978797\pi$
$182$	7.48213	−	5.91758i	0.554612	−	0.438640i
$183$	−15.4612	−	9.77332i	−1.14293	−	0.722465i
$184$		−	4.62091i		−	0.340658i
$185$	−2.05870	−	3.56576i	−0.151358	−	0.262160i
$186$	−8.85073	+	14.0017i	−0.648967	+	1.02666i
$187$	4.07327	+	7.05510i	0.297867	+	0.515920i
$188$	−2.73905	+	1.58139i	−0.199765	+	0.115335i
$189$	6.53711	−	12.0941i	0.475505	−	0.879713i
$190$		−	2.53173i		−	0.183671i
$191$	8.45391	+	4.88087i	0.611703	+	0.353167i	0.773632	−	0.633635i	$-0.218438\pi$
$191$	8.45391	+	4.88087i	0.611703	+	0.353167i	−0.161928	+	0.986803i	$0.551771\pi$
$192$	1.73066	+	0.0694407i	0.124900	+	0.00501145i
$193$	−9.03423	+	5.21591i	−0.650298	+	0.375450i	−0.788570	−	0.614945i	$-0.789178\pi$
$193$	−9.03423	+	5.21591i	−0.650298	+	0.375450i	0.138272	+	0.990394i	$0.455845\pi$
$194$	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	$0.253323\pi$
$198$	2.91614	+	6.14011i	0.207241	+	0.436358i
$199$		−	12.2381i		−	0.867534i	−0.901025	−	0.433767i	$-0.857184\pi$
$199$		−	12.2381i		−	0.867534i	0.901025	−	0.433767i	$-0.142816\pi$
$200$	2.17863	−	3.77350i	0.154052	−	0.266826i
$201$	6.22931	−	3.27078i	0.439381	−	0.230703i
$202$	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
$205$	24.8534			1.73584
$206$	1.53644	−	0.887062i	0.107049	−	0.0618045i
$207$	1.11066	−	13.8182i	0.0771966	−	0.960429i
$208$	3.11743	+	1.81152i	0.216155	+	0.125606i
$209$	−1.87527			−0.129715
$210$	1.51470	+	13.9359i	0.104524	+	0.961665i
$211$	−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	$0.241024\pi$
$212$	−1.44524	−	0.834408i	−0.0992593	−	0.0573074i
$213$	−6.14016	−	11.6941i	−0.420717	−	0.801269i
$214$			6.29055i			0.430013i
$215$	24.9038	+	14.3782i	1.69843	+	0.980588i
$216$	5.15859	+	0.623627i	0.350998	+	0.0424325i
$217$	15.7516	+	19.8019i	1.06929	+	1.34424i
$218$	9.02357	+	5.20976i	0.611154	+	0.352850i
$219$	10.6279	−	16.8131i	0.718164	−	1.13612i
$220$	−6.00243	−	3.46551i	−0.404684	−	0.233644i
$221$	11.2085	+	6.51318i	0.753966	+	0.438124i
$222$	−0.0934678	+	2.32948i	−0.00627315	+	0.156344i
$223$	6.23733	−	10.8034i	0.417683	−	0.723448i	−0.578023	−	0.816020i	$-0.696176\pi$
$223$	6.23733	−	10.8034i	0.417683	−	0.723448i	0.995706	+	0.0925727i	$0.0295091\pi$
$224$	0.969634	−	2.46167i	0.0647864	−	0.164477i
$225$	7.42186	−	10.7604i	0.494791	−	0.717363i
$226$	7.25521	−	4.18880i	0.482609	−	0.278635i
$227$			21.4471i			1.42350i	0.702434	+	0.711748i	$0.252096\pi$
$227$			21.4471i			1.42350i	−0.702434	+	0.711748i	$0.747904\pi$
$228$	−0.765955	+	1.21173i	−0.0507266	+	0.0802487i
$229$	11.7463	+	20.3453i	0.776220	+	1.34445i	0.934106	+	0.356995i	$0.116199\pi$
$229$	11.7463	+	20.3453i	0.776220	+	1.34445i	−0.157886	+	0.987457i	$0.550468\pi$
$230$	7.06760	+	12.2414i	0.466024	+	0.807176i
$231$	10.3224	−	1.12195i	0.679166	−	0.0738189i
$232$	−7.61619	−	4.39721i	−0.500028	−	0.288691i
$233$	11.1727	−	6.45055i	0.731947	−	0.422590i	−0.0871872	−	0.996192i	$-0.527788\pi$
$233$	11.1727	−	6.45055i	0.731947	−	0.422590i	0.819134	+	0.573602i	$0.194455\pi$
$234$	8.88683	+	6.16638i	0.580950	+	0.403109i
$235$	4.83741	−	8.37864i	0.315558	−	0.546562i
$236$			10.7942i			0.702643i
$237$	4.69450	+	8.94083i	0.304940	+	0.580769i
$238$	3.48625	−	8.85075i	0.225980	−	0.573709i
$239$	−23.0402			−1.49035			−0.745175	−	0.666869i	$-0.767634\pi$
$239$	−23.0402			−1.49035			−0.745175	+	0.666869i	$0.767634\pi$
$240$	−4.69096	+	2.46305i	−0.302800	+	0.158989i
$241$	−27.7786			−1.78938			−0.894688	−	0.446692i	$-0.852602\pi$
$241$	−27.7786			−1.78938			−0.894688	+	0.446692i	$0.852602\pi$
$242$	2.93307	−	5.08022i	0.188545	−	0.326569i
$243$	15.2761	+	3.10477i	0.979965	+	0.199171i
$244$	−9.14560	−	5.28021i	−0.585487	−	0.338031i
$245$	20.8641	+	4.81619i	1.33296	+	0.307695i
$246$	−11.8953	−	7.51920i	−0.758414	−	0.479407i
$247$	−2.58848	+	1.48480i	−0.164701	+	0.0944758i
$248$	−4.78177	+	8.28226i	−0.303642	+	0.525924i
$249$	−0.263342	+	6.56323i	−0.0166886	+	0.415928i
$250$		−	1.96613i		−	0.124349i
$251$	6.68358	+	11.5763i	0.421864	+	0.730690i	0.996122	−	0.0879848i	$-0.0280427\pi$
$251$	6.68358	+	11.5763i	0.421864	+	0.730690i	−0.574258	+	0.818674i	$0.694709\pi$
$252$	3.49123	−	7.12821i	0.219927	−	0.449035i
$253$	9.06735	−	5.23504i	0.570059	−	0.329124i
$254$	−0.0429290	+	0.0743552i	−0.00269360	+	0.00466546i
$255$	−16.8660	+	8.85572i	−1.05619	+	0.554567i
$256$	1.00000			0.0625000
$257$	−2.71126			−0.169124			−0.0845618	−	0.996418i	$-0.526949\pi$
$257$	−2.71126			−0.169124			−0.0845618	+	0.996418i	$0.526949\pi$
$258$	−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
$261$	−21.7182	−	14.9798i	−1.34432	−	0.927228i
$262$	1.03041	+	1.78473i	0.0636591	+	0.110261i
$263$	12.7361	−	7.35317i	0.785340	−	0.453416i	−0.0529797	−	0.998596i	$-0.516872\pi$
$263$	12.7361	−	7.35317i	0.785340	−	0.453416i	0.838319	+	0.545180i	$0.183539\pi$
$264$	1.82441	+	3.47464i	0.112284	+	0.213850i
$265$	5.10485			0.313588
$266$	1.36317	+	1.71368i	0.0835811	+	0.105073i
$267$	0.579633	−	14.4461i	0.0354730	−	0.884086i
$268$	3.51789	−	2.03106i	0.214889	−	0.124066i
$269$	7.51872			0.458424			0.229212	−	0.973376i	$-0.426385\pi$
$269$	7.51872			0.458424			0.229212	+	0.973376i	$0.426385\pi$
$270$	−14.6197	+	6.23790i	−0.889724	+	0.379626i
$271$	−0.0247852			−0.00150559			−0.000752797	−	1.00000i	$-0.500240\pi$
$271$	−0.0247852			−0.00150559			−0.000752797		1.00000i	$0.500240\pi$
$272$	3.59543			0.218005
$273$	13.3599	−	9.72174i	0.808580	−	0.588387i
$274$	−8.97465			−0.542178
$275$	9.87269			0.595346
$276$	0.320879	−	7.99721i	0.0193147	−	0.481376i
$277$	6.18124			0.371395			0.185697	−	0.982607i	$-0.440546\pi$
$277$	6.18124			0.371395			0.185697	+	0.982607i	$0.440546\pi$
$278$	−18.0789	+	10.4379i	−1.08430	+	0.626021i
$279$	−16.2899	+	23.6176i	−0.975250	+	1.41395i
$280$	1.19638	+	8.00434i	0.0714974	+	0.478351i
$281$	29.5748			1.76428			0.882142	−	0.470984i	$-0.156101\pi$
$281$	29.5748			1.76428			0.882142	+	0.470984i	$0.156101\pi$
$282$	−4.85016	+	2.54664i	−0.288823	+	0.151650i
$283$	18.3623	−	10.6015i	1.09152	−	0.630192i	0.157543	−	0.987512i	$-0.449643\pi$
$283$	18.3623	−	10.6015i	1.09152	−	0.630192i	0.933982	+	0.357320i	$0.116310\pi$
$284$	−3.81286	−	6.60406i	−0.226251	−	0.391879i
$285$	0.175805	−	4.38155i	0.0104138	−	0.259541i
$286$	−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
$289$	−4.07291			−0.239583
$290$	26.9018			1.57973
$291$	12.8813	+	24.5328i	0.755113	+	1.43814i
$292$	5.74190	−	9.94525i	0.336019	−	0.582002i
$293$	10.1781	−	5.87631i	0.594609	−	0.343298i	−0.172309	−	0.985043i	$-0.555123\pi$
$293$	10.1781	−	5.87631i	0.594609	−	0.343298i	0.766918	+	0.641745i	$0.221789\pi$
$294$	−8.52881	−	8.61739i	−0.497410	−	0.502576i
$295$	−16.5095	−	28.5954i	−0.961223	−	1.66489i
$296$			1.34601i			0.0782351i
$297$	4.62047	+	10.8289i	0.268107	+	0.628358i
$298$	0.851501	−	1.47484i	0.0493261	−	0.0854353i
$299$	8.37086	−	14.4054i	0.484100	−	0.833085i
$300$	4.03250	−	6.37935i	0.232816	−	0.368312i
$301$	−24.5987	+	3.67668i	−1.41785	+	0.211920i
$302$	−19.2492	−	11.1135i	−1.10767	−	0.639512i
$303$	5.74900	+	10.9492i	0.330271	+	0.629013i
$304$	−0.413821	+	0.716759i	−0.0237342	+	0.0411089i
$305$	32.3040			1.84972
$306$	10.7516	+	0.864184i	0.614628	+	0.0494021i
$307$	−12.2431			−0.698749			−0.349375	−	0.936983i	$-0.613606\pi$
$307$	−12.2431			−0.698749			−0.349375	+	0.936983i	$0.613606\pi$
$308$	5.92889	−	0.886170i	0.337830	−	0.0504942i
$309$	2.72064	−	1.42851i	0.154772	−	0.0812651i
$310$		−	29.2545i		−	1.66154i
$311$	−4.81504	+	8.33990i	−0.273036	+	0.472912i	−0.969638	−	0.244546i	$-0.921361\pi$
$311$	−4.81504	+	8.33990i	−0.273036	+	0.472912i	0.696602	+	0.717458i	$0.254694\pi$
$312$	5.26942	+	3.35160i	0.298322	+	0.189747i
$313$	12.0523	−	6.95841i	0.681237	−	0.393312i	−0.119084	−	0.992884i	$-0.537996\pi$
$313$	12.0523	−	6.95841i	0.681237	−	0.393312i	0.800321	+	0.599572i	$0.204662\pi$
$314$	10.2785	+	5.93431i	0.580051	+	0.334893i
$315$	1.65371	+	24.2234i	0.0931758	+	1.36483i
$316$	2.91514	+	5.04917i	0.163990	+	0.284038i
$317$	−11.8204	−	20.4735i	−0.663900	−	1.14991i	−0.979582	−	0.201044i	$-0.935567\pi$
$317$	−11.8204	−	20.4735i	−0.663900	−	1.14991i	0.315682	−	0.948865i	$-0.397767\pi$
$318$	−2.44327	−	1.54443i	−0.137012	−	0.0866075i
$319$		−	19.9264i		−	1.11567i
$320$	−2.64914	+	1.52948i	−0.148091	+	0.0855006i
$321$	−0.436820	+	10.8868i	−0.0243809	+	0.607641i
$322$	−11.3751	−	4.48059i	−0.633912	−	0.249694i
$323$	−1.48786	+	2.57705i	−0.0827869	+	0.143391i
$324$	8.88446	+	1.43750i	0.493581	+	0.0798612i
$325$	13.6275	−	7.81700i	0.755917	−	0.433609i
$326$	8.32458	+	4.80620i	0.461056	+	0.266191i
$327$	15.2550	+	9.64292i	0.843601	+	0.533255i
$328$	−7.03626	−	4.06239i	−0.388512	−	0.224308i
$329$	1.23698	+	8.27599i	0.0681970	+	0.456270i
$330$	−10.1475	−	6.41442i	−0.558602	−	0.353102i
$331$	13.0461	+	7.53219i	0.717081	+	0.414007i	0.813677	−	0.581317i	$-0.197462\pi$
$331$	13.0461	+	7.53219i	0.717081	+	0.414007i	−0.0965965	+	0.995324i	$0.530796\pi$
$332$			3.79233i			0.208131i
$333$	−0.323522	+	4.02504i	−0.0177289	+	0.220571i
$334$	−21.5888	−	12.4643i	−1.18129	−	0.682016i
$335$	−6.21292	+	10.7611i	−0.339448	+	0.587942i
$336$	1.84905	−	4.19297i	0.100874	−	0.228745i
$337$	−9.93070			−0.540960			−0.270480	−	0.962726i	$-0.587182\pi$
$337$	−9.93070			−0.540960			−0.270480	+	0.962726i	$0.587182\pi$
$338$	6.43680	+	11.2946i	0.350116	+	0.614344i
$339$	12.8472	−	6.74557i	0.697762	−	0.366369i
$340$	−9.52479	+	5.49914i	−0.516554	+	0.298233i
$341$	−21.6691			−1.17345
$342$	−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
$345$	11.3815	+	21.6765i	0.612762	+	1.16702i
$346$	−2.01276	+	3.48621i	−0.108207	+	0.187420i
$347$		−	3.36902i		−	0.180859i	−0.995903	−	0.0904293i	$-0.971176\pi$
$347$		−	3.36902i		−	0.180859i	0.995903	−	0.0904293i	$-0.0288239\pi$
$348$	−12.8757	−	8.13894i	−0.690209	−	0.436293i
$349$	15.4110	−	26.6927i	0.824935	−	1.42883i	−0.0770347	−	0.997028i	$-0.524545\pi$
$349$	15.4110	−	26.6927i	0.824935	−	1.42883i	0.901969	−	0.431800i	$-0.142121\pi$
$350$	−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
$353$	17.0077	−	9.81940i	0.905228	−	0.522634i	0.0263354	−	0.999653i	$-0.491616\pi$
$353$	17.0077	−	9.81940i	0.905228	−	0.522634i	0.878893	+	0.477019i	$0.158283\pi$
$354$	−0.749558	+	18.6811i	−0.0398385	+	0.992888i
$355$	20.2016	+	11.6634i	1.07219	+	0.619028i
$356$		−	8.34716i		−	0.442399i
$357$	6.64811	−	15.0755i	0.351855	−	0.797882i
$358$	10.9445	−	6.31879i	0.578433	−	0.333958i
$359$	−5.20022	−	9.00705i	−0.274457	−	0.475374i	0.695541	−	0.718487i	$-0.255165\pi$
$359$	−5.20022	−	9.00705i	−0.274457	−	0.475374i	−0.969998	+	0.243113i	$0.921831\pi$
$360$	−8.28949	+	3.93696i	−0.436895	+	0.207496i
$361$	9.15750	+	15.8613i	0.481974	+	0.834803i
$362$			1.79097i			0.0941315i
$363$	5.42891	−	8.58845i	0.284944	−	0.450777i
$364$	7.48213	−	5.91758i	0.392170	−	0.310165i
$365$			35.1285i			1.83871i
$366$	−15.4612	−	9.77332i	−0.808172	−	0.510860i
$367$	−19.6101	+	11.3219i	−1.02364	+	0.590998i	−0.915156	−	0.403101i	$-0.867932\pi$
$367$	−19.6101	+	11.3219i	−1.02364	+	0.590998i	−0.108482	+	0.994098i	$0.534599\pi$
$368$		−	4.62091i		−	0.240882i
$369$	−20.0645	−	13.8392i	−1.04452	−	0.720439i
$370$	−2.05870	−	3.56576i	−0.107026	−	0.185375i
$371$	−3.45539	+	2.74862i	−0.179395	+	0.142701i
$372$	−8.85073	+	14.0017i	−0.458889	+	0.725955i
$373$	−8.39025	+	14.5323i	−0.434431	+	0.752456i	−0.997249	−	0.0741246i	$-0.976384\pi$
$373$	−8.39025	+	14.5323i	−0.434431	+	0.752456i	0.562818	+	0.826581i	$0.309717\pi$
$374$	4.07327	+	7.05510i	0.210624	+	0.364811i
$375$	0.136529	−	3.40269i	0.00705034	−	0.175714i
$376$	−2.73905	+	1.58139i	−0.141255	+	0.0815539i
$377$	−15.7774	−	27.5049i	−0.812575	−	1.41657i
$378$	6.53711	−	12.0941i	0.336233	−	0.622051i
$379$	−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	$0.703698\pi$
$380$		−	2.53173i		−	0.129875i
$381$	−0.0794587	+	0.125702i	−0.00407079	+	0.00643993i
$382$	8.45391	+	4.88087i	0.432540	+	0.249727i
$383$	2.99527	+	1.72932i	0.153051	+	0.0883641i	0.574570	−	0.818456i	$-0.305169\pi$
$383$	2.99527	+	1.72932i	0.153051	+	0.0883641i	−0.421519	+	0.906820i	$0.638503\pi$
$384$	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
$387$	−12.0990	−	25.4751i	−0.615024	−	1.29497i
$388$	7.99888	+	13.8545i	0.406082	+	0.703354i
$389$	3.12443	+	1.80389i	0.158415	+	0.0914609i	0.577112	−	0.816665i	$-0.304180\pi$
$389$	3.12443	+	1.80389i	0.158415	+	0.0914609i	−0.418697	+	0.908126i	$0.637513\pi$
$390$	−19.0856	−	0.819367i	−0.966439	−	0.0414903i
$391$		−	16.6141i		−	0.840213i
$392$	−5.11962	−	4.77383i	−0.258580	−	0.241115i
$393$	1.65936	+	3.16031i	0.0837036	+	0.159416i
$394$	−3.77403	+	6.53681i	−0.190133	+	0.329320i
$395$	−15.4452	−	8.91731i	−0.777134	−	0.448679i
$396$	2.91614	+	6.14011i	0.146542	+	0.308552i
$397$	15.1719	−	26.2786i	0.761458	−	1.31888i	−0.180641	−	0.983549i	$-0.557817\pi$
$397$	15.1719	−	26.2786i	0.761458	−	1.31888i	0.942099	−	0.335335i	$-0.108850\pi$
$398$		−	12.2381i		−	0.613439i
$399$	2.24018	+	3.06046i	0.112149	+	0.153215i
$400$	2.17863	−	3.77350i	0.108931	−	0.188675i
$401$	33.2182			1.65884			0.829419	−	0.558627i	$-0.188672\pi$
$401$	33.2182			1.65884			0.829419	+	0.558627i	$0.188672\pi$
$402$	6.22931	−	3.27078i	0.310690	−	0.163132i
$403$	−29.9103	+	17.1572i	−1.48994	+	0.854659i
$404$	3.56996	+	6.18335i	0.177612	+	0.307633i
$405$	−25.7348	+	9.78047i	−1.27877	+	0.485996i
$406$	−18.2094	+	14.4849i	−0.903717	+	0.718871i
$407$	−2.64120	+	1.52490i	−0.130919	+	0.0755863i
$408$	6.22246	+	0.249669i	0.308057	+	0.0123605i
$409$	15.4590			0.764400			0.382200	−	0.924080i	$-0.375166\pi$
$409$	15.4590			0.764400			0.382200	+	0.924080i	$0.375166\pi$
$410$	24.8534			1.22742
$411$	−15.5320	−	0.623206i	−0.766139	−	0.0307405i
$412$	1.53644	−	0.887062i	0.0756948	−	0.0437024i
$413$	26.5718	+	10.4664i	1.30751	+	0.515019i
$414$	1.11066	−	13.8182i	0.0545862	−	0.679126i
$415$	−5.80030	−	10.0464i	−0.284725	−	0.493159i
$416$	3.11743	+	1.81152i	0.152845	+	0.0888170i
$417$	−32.0132	+	16.8090i	−1.56769	+	0.823138i
$418$	−1.87527			−0.0917226
$419$	6.78747	−	11.7562i	0.331590	−	0.574330i	−0.651234	−	0.758877i	$-0.725748\pi$
$419$	6.78747	−	11.7562i	0.331590	−	0.574330i	0.982824	+	0.184547i	$0.0590818\pi$
$420$	1.51470	+	13.9359i	0.0739096	+	0.680000i
$421$			22.2151i			1.08270i	0.840797	+	0.541350i	$0.182087\pi$
$421$			22.2151i			1.08270i	−0.840797	+	0.541350i	$0.817913\pi$
$422$	−3.36247	+	5.82397i	−0.163683	+	0.283507i
$423$	−8.57082	+	4.07057i	−0.416727	+	0.197918i
$424$	−1.44524	−	0.834408i	−0.0701869	−	0.0405224i
$425$	7.83310	−	13.5673i	0.379961	−	0.658112i
$426$	−6.14016	−	11.6941i	−0.297492	−	0.566583i
$427$	−21.8660	+	17.3936i	−1.05817	+	0.841733i
$428$			6.29055i			0.304065i
$429$	−0.606913	+	14.1369i	−0.0293020	+	0.682537i
$430$	24.9038	+	14.3782i	1.20097	+	0.693380i
$431$	4.40288	+	7.62602i	0.212079	+	0.367332i	0.952365	−	0.304960i	$-0.0986431\pi$
$431$	4.40288	+	7.62602i	0.212079	+	0.367332i	−0.740286	+	0.672292i	$0.765310\pi$
$432$	5.15859	+	0.623627i	0.248193	+	0.0300043i
$433$	−3.16975	+	1.83006i	−0.152328	+	0.0879468i	−0.574227	−	0.818696i	$-0.694697\pi$
$433$	−3.16975	+	1.83006i	−0.152328	+	0.0879468i	0.421898	+	0.906643i	$0.361364\pi$
$434$	15.7516	+	19.8019i	0.756102	+	0.950521i
$435$	46.5579	+	1.86808i	2.23228	+	0.0895677i
$436$	9.02357	+	5.20976i	0.432151	+	0.249502i
$437$	3.31208	+	1.91223i	0.158438	+	0.0914743i
$438$	10.6279	−	16.8131i	0.507819	−	0.803362i
$439$			17.7844i			0.848805i	0.905474	+	0.424402i	$0.139516\pi$
$439$			17.7844i			0.848805i	−0.905474	+	0.424402i	$0.860484\pi$
$440$	−6.00243	−	3.46551i	−0.286155	−	0.165212i
$441$	−14.1621	−	15.5060i	−0.674384	−	0.738381i
$442$	11.2085	+	6.51318i	0.533134	+	0.309801i
$443$	20.0861	−	11.5967i	0.954319	−	0.550976i	0.0598990	−	0.998204i	$-0.480922\pi$
$443$	20.0861	−	11.5967i	0.954319	−	0.550976i	0.894420	+	0.447228i	$0.147589\pi$
$444$	−0.0934678	+	2.32948i	−0.00443579	+	0.110552i
$445$	12.7668	+	22.1128i	0.605206	+	1.04825i
$446$	6.23733	−	10.8034i	0.295346	−	0.511555i
$447$	1.57607	−	2.49332i	0.0745456	−	0.117930i
$448$	0.969634	−	2.46167i	0.0458109	−	0.116303i
$449$	−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	$0.894269\pi$
$450$	7.42186	−	10.7604i	0.349870	−	0.507252i
$451$		−	18.4091i		−	0.866853i
$452$	7.25521	−	4.18880i	0.341256	−	0.197024i
$453$	−32.5420	−	20.5704i	−1.52896	−	0.966482i
$454$			21.4471i			1.00656i
$455$	−10.7704	+	27.1203i	−0.504923	+	1.27142i
$456$	−0.765955	+	1.21173i	−0.0358691	+	0.0567444i
$457$			15.3575i			0.718393i	0.933262	+	0.359197i	$0.116949\pi$
$457$			15.3575i			0.718393i	−0.933262	+	0.359197i	$0.883051\pi$
$458$	11.7463	+	20.3453i	0.548870	+	0.950671i
$459$	18.5473	+	2.24221i	0.865716	+	0.104657i
$460$	7.06760	+	12.2414i	0.329528	+	0.570760i
$461$	1.90360	−	1.09904i	0.0886596	−	0.0511876i	−0.455015	−	0.890484i	$-0.650366\pi$
$461$	1.90360	−	1.09904i	0.0886596	−	0.0511876i	0.543674	+	0.839296i	$0.317033\pi$
$462$	10.3224	−	1.12195i	0.480243	−	0.0521979i
$463$		−	9.47072i		−	0.440142i	−0.975484	−	0.220071i	$-0.929371\pi$
$463$		−	9.47072i		−	0.440142i	0.975484	−	0.220071i	$-0.0706289\pi$
$464$	−7.61619	−	4.39721i	−0.353573	−	0.204135i
$465$	2.03145	−	50.6295i	0.0942064	−	2.34789i
$466$	11.1727	−	6.45055i	0.517564	−	0.298816i
$467$	−7.74149	−	13.4087i	−0.358234	−	0.620479i	0.629432	−	0.777055i	$-0.283288\pi$
$467$	−7.74149	−	13.4087i	−0.358234	−	0.620479i	−0.987666	+	0.156577i	$0.949954\pi$
$468$	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
$471$	17.3765	+	10.9840i	0.800669	+	0.506117i
$472$			10.7942i			0.496844i
$473$	10.6501	−	18.4465i	0.489692	−	0.848172i
$474$	4.69450	+	8.94083i	0.215625	+	0.410666i
$475$	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
$478$	−23.0402			−1.05384
$479$	35.7766	−	20.6556i	1.63467	−	0.943779i	0.652048	−	0.758178i	$-0.273910\pi$
$479$	35.7766	−	20.6556i	1.63467	−	0.943779i	0.982625	−	0.185601i	$-0.0594233\pi$
$480$	−4.69096	+	2.46305i	−0.214112	+	0.112422i
$481$	−2.43832	+	4.19609i	−0.111178	+	0.191325i
$482$	−27.7786			−1.26528
$483$	−19.3754	−	8.54427i	−0.881609	−	0.388778i
$484$	2.93307	−	5.08022i	0.133321	−	0.230919i
$485$	−42.3803	−	24.4683i	−1.92439	−	1.11105i
$486$	15.2761	+	3.10477i	0.692940	+	0.140835i
$487$			2.53448i			0.114848i	0.998350	+	0.0574240i	$0.0182887\pi$
$487$			2.53448i			0.114848i	−0.998350	+	0.0574240i	$0.981711\pi$
$488$	−9.14560	−	5.28021i	−0.414002	−	0.239024i
$489$	14.0733	+	8.89595i	0.636415	+	0.402289i
$490$	20.8641	+	4.81619i	0.942543	+	0.217573i
$491$	−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	$0.864690\pi$
$492$	−11.8953	−	7.51920i	−0.536280	−	0.338992i
$493$	−27.3835	−	15.8099i	−1.23329	−	0.712040i
$494$	−2.58848	+	1.48480i	−0.116461	+	0.0668045i
$495$	−17.1165	−	11.8058i	−0.769327	−	0.530632i
$496$	−4.78177	+	8.28226i	−0.214708	+	0.371885i
$497$	−19.9541	+	2.98246i	−0.895063	+	0.133782i
$498$	−0.263342	+	6.56323i	−0.0118006	+	0.294105i
$499$	−24.8498	+	14.3470i	−1.11243	+	0.642261i	−0.939458	−	0.342665i	$-0.888670\pi$
$499$	−24.8498	+	14.3470i	−1.11243	+	0.642261i	−0.172972	+	0.984927i	$0.555337\pi$
$500$		−	1.96613i		−	0.0879278i
$501$	−36.4973	−	23.0706i	−1.63058	−	1.03072i
$502$	6.68358	+	11.5763i	0.298303	+	0.516676i
$503$	14.9785	+	25.9435i	0.667858	+	1.15676i	0.978502	+	0.206238i	$0.0661221\pi$
$503$	14.9785	+	25.9435i	0.667858	+	1.15676i	−0.310644	+	0.950526i	$0.600545\pi$
$504$	3.49123	−	7.12821i	0.155512	−	0.317516i
$505$	−18.9146	−	10.9204i	−0.841690	−	0.485950i
$506$	9.06735	−	5.23504i	0.403093	−	0.232726i
$507$	10.3556	+	19.9940i	0.459908	+	0.887967i
$508$	−0.0429290	+	0.0743552i	−0.00190467	+	0.00329898i
$509$			12.9462i			0.573832i	0.957956	+	0.286916i	$0.0926301\pi$
$509$			12.9462i			0.573832i	−0.957956	+	0.286916i	$0.907370\pi$
$510$	−16.8660	+	8.85572i	−0.746840	+	0.392138i
$511$	−18.9144	−	23.7779i	−0.836723	−	1.05187i
$512$	1.00000			0.0441942
$513$	−2.58172	+	3.43940i	−0.113986	+	0.151853i
$514$	−2.71126			−0.119588
$515$	−2.71349	+	4.69990i	−0.119571	+	0.207102i
$516$	−7.56939	−	14.4161i	−0.333224	−	0.634636i
$517$	−6.20614	−	3.58312i	−0.272946	−	0.157585i
$518$	3.31343	+	1.30514i	0.145584	+	0.0573444i
$519$	−3.72549	+	5.89367i	−0.163531	+	0.258703i
$520$	−11.0292	−	0.0309078i	−0.483663	−	0.00135540i
$521$	−19.0122	+	32.9301i	−0.832940	+	1.44269i	0.0627562	+	0.998029i	$0.480011\pi$
$521$	−19.0122	+	32.9301i	−0.832940	+	1.44269i	−0.895696	+	0.444666i	$0.853322\pi$
$522$	−21.7182	−	14.9798i	−0.950581	−	0.655649i
$523$		−	33.5733i		−	1.46806i	−0.679119	−	0.734028i	$-0.737638\pi$
$523$		−	33.5733i		−	1.46806i	0.679119	−	0.734028i	$-0.262362\pi$
$524$	1.03041	+	1.78473i	0.0450138	+	0.0779662i
$525$	−11.7938	−	16.1123i	−0.514723	−	0.703198i
$526$	12.7361	−	7.35317i	0.555319	−	0.320614i
$527$	−17.1925	+	29.7783i	−0.748917	+	1.29716i
$528$	1.82441	+	3.47464i	0.0793971	+	0.151214i
$529$	1.64720			0.0716173
$530$	5.10485			0.221740
$531$	−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
$534$	0.579633	−	14.4461i	0.0250832	−	0.625143i
$535$	−9.62128	−	16.6645i	−0.415964	−	0.720471i
$536$	3.51789	−	2.03106i	0.151950	−	0.0877282i
$537$	19.3799	−	10.1757i	0.836305	−	0.439113i
$538$	7.51872			0.324155
$539$	3.56740	−	15.4542i	0.153659	−	0.665661i
$540$	−14.6197	+	6.23790i	−0.629130	+	0.268436i
$541$	1.91892	−	1.10789i	0.0825009	−	0.0476319i	−0.458182	−	0.888858i	$-0.651499\pi$
$541$	1.91892	−	1.10789i	0.0825009	−	0.0476319i	0.540683	+	0.841226i	$0.318166\pi$
$542$	−0.0247852			−0.00106462
$543$	−0.124366	+	3.09956i	−0.00533708	+	0.133015i
$544$	3.59543			0.154153
$545$	−31.8730			−1.36529
$546$	13.3599	−	9.72174i	0.571752	−	0.416052i
$547$	35.2174			1.50579			0.752895	−	0.658141i	$-0.228657\pi$
$547$	35.2174			1.50579			0.752895	+	0.658141i	$0.228657\pi$
$548$	−8.97465			−0.383378
$549$	−26.0795	−	17.9879i	−1.11304	−	0.767706i
$550$	9.87269			0.420973
$551$	6.30348	−	3.63931i	0.268537	−	0.155040i
$552$	0.320879	−	7.99721i	0.0136575	−	0.340384i
$553$	15.2560	−	2.28026i	0.648752	−	0.0969665i
$554$	6.18124			0.262616
$555$	−3.31529	−	6.31408i	−0.140726	−	0.268018i
$556$	−18.0789	+	10.4379i	−0.766716	+	0.442664i
$557$	4.07382	+	7.05607i	0.172613	+	0.298975i	0.939333	−	0.343007i	$-0.111446\pi$
$557$	4.07382	+	7.05607i	0.172613	+	0.298975i	−0.766719	+	0.641982i	$0.778112\pi$
$558$	−16.2899	+	23.6176i	−0.689606	+	0.999812i
$559$	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
$562$	29.5748			1.24754
$563$	−21.8949			−0.922761			−0.461380	−	0.887202i	$-0.652646\pi$
$563$	−21.8949			−0.922761			−0.461380	+	0.887202i	$0.652646\pi$
$564$	−4.85016	+	2.54664i	−0.204229	+	0.107233i
$565$	−12.8134	+	22.1934i	−0.539063	+	0.933684i
$566$	18.3623	−	10.6015i	0.771824	−	0.445613i
$567$	12.1533	−	20.4767i	0.510392	−	0.859942i
$568$	−3.81286	−	6.60406i	−0.159984	−	0.277100i
$569$			39.3854i			1.65112i	0.564314	+	0.825560i	$0.309141\pi$
$569$			39.3854i			1.65112i	−0.564314	+	0.825560i	$0.690859\pi$
$570$	0.175805	−	4.38155i	0.00736366	−	0.183523i
$571$	−10.0406	+	17.3909i	−0.420187	+	0.727786i	−0.995958	−	0.0898257i	$-0.971369\pi$
$571$	−10.0406	+	17.3909i	−0.420187	+	0.727786i	0.575770	+	0.817612i	$0.304702\pi$
$572$	−0.0228937	+	8.16944i	−0.000957235	+	0.341581i
$573$	14.2919	+	9.03416i	0.597053	+	0.377407i
$574$	−16.8228	+	13.3819i	−0.702172	+	0.558550i
$575$	−17.4370	−	10.0672i	−0.727172	−	0.419833i
$576$	2.99036	+	0.240356i	0.124598	+	0.0100148i
$577$	10.1331	−	17.5510i	0.421847	−	0.730660i	−0.574274	−	0.818663i	$-0.694715\pi$
$577$	10.1331	−	17.5510i	0.421847	−	0.730660i	0.996120	+	0.0880038i	$0.0280488\pi$
$578$	−4.07291			−0.169411
$579$	−15.9974	+	8.39962i	−0.664827	+	0.349076i
$580$	26.9018			1.11704
$581$	9.33546	+	3.67717i	0.387300	+	0.152555i
$582$	12.8813	+	24.5328i	0.533946	+	1.01692i
$583$		−	3.78121i		−	0.156602i
$584$	5.74190	−	9.94525i	0.237601	−	0.411538i
$585$	−32.9738	−	2.74337i	−1.36330	−	0.113424i
$586$	10.1781	−	5.87631i	0.420452	−	0.242748i
$587$	−5.90203	−	3.40754i	−0.243603	−	0.140644i	0.373229	−	0.927739i	$-0.378251\pi$
$587$	−5.90203	−	3.40754i	−0.243603	−	0.140644i	−0.616831	+	0.787095i	$0.711584\pi$
$588$	−8.52881	−	8.61739i	−0.351722	−	0.355375i
$589$	−3.95759	−	6.85474i	−0.163070	−	0.282445i
$590$	−16.5095	−	28.5954i	−0.679687	−	1.17725i
$591$	−6.98547	+	11.0509i	−0.287344	+	0.454574i
$592$			1.34601i			0.0553206i
$593$	−30.3893	+	17.5453i	−1.24794	+	0.720498i	−0.970698	−	0.240302i	$-0.922754\pi$
$593$	−30.3893	+	17.5453i	−1.24794	+	0.720498i	−0.277242	+	0.960800i	$0.589420\pi$
$594$	4.62047	+	10.8289i	0.189580	+	0.444316i
$595$	4.30150	+	28.7790i	0.176344	+	1.17982i
$596$	0.851501	−	1.47484i	0.0348788	−	0.0604119i
$597$	0.849821	−	21.1799i	0.0347808	−	0.866836i
$598$	8.37086	−	14.4054i	0.342310	−	0.589080i
$599$	−3.02800	−	1.74821i	−0.123721	−	0.0714301i	0.436863	−	0.899528i	$-0.356090\pi$
$599$	−3.02800	−	1.74821i	−0.123721	−	0.0714301i	−0.560583	+	0.828098i	$0.689423\pi$
$600$	4.03250	−	6.37935i	0.164626	−	0.260436i
$601$	−30.2974	−	17.4922i	−1.23586	−	0.713521i	−0.267611	−	0.963527i	$-0.586234\pi$
$601$	−30.2974	−	17.4922i	−1.23586	−	0.713521i	−0.968244	+	0.250006i	$0.919567\pi$
$602$	−24.5987	+	3.67668i	−1.00257	+	0.149850i
$603$	11.0079	−	5.22803i	0.448277	−	0.212902i
$604$	−19.2492	−	11.1135i	−0.783239	−	0.452203i
$605$			17.9443i			0.729539i
$606$	5.74900	+	10.9492i	0.233537	+	0.444779i
$607$	−15.1664	−	8.75631i	−0.615584	−	0.355408i	0.159564	−	0.987188i	$-0.448991\pi$
$607$	−15.1664	−	8.75631i	−0.615584	−	0.355408i	−0.775148	+	0.631780i	$0.782325\pi$
$608$	−0.413821	+	0.716759i	−0.0167826	+	0.0290684i
$609$	−32.5201	+	23.8039i	−1.31778	+	0.964581i
$610$	32.3040			1.30795
$611$	−11.4035	−	0.0319568i	−0.461337	−	0.00129283i
$612$	10.7516	+	0.864184i	0.434608	+	0.0349326i
$613$	11.5436	−	6.66471i	0.466242	−	0.269185i	−0.248423	−	0.968652i	$-0.579912\pi$
$613$	11.5436	−	6.66471i	0.466242	−	0.269185i	0.714665	+	0.699467i	$0.246579\pi$
$614$	−12.2431			−0.494090
$615$	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	$0.602799\pi$
$618$	2.72064	−	1.42851i	0.109440	−	0.0574631i
$619$	3.67239	−	6.36076i	0.147606	−	0.255661i	−0.782736	−	0.622353i	$-0.786177\pi$
$619$	3.67239	−	6.36076i	0.147606	−	0.255661i	0.930342	+	0.366693i	$0.119510\pi$
$620$		−	29.2545i		−	1.17489i
$621$	2.88172	−	23.8374i	0.115640	−	0.956562i
$622$	−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
$626$	12.0523	−	6.95841i	0.481707	−	0.278114i
$627$	−3.24546	−	0.130220i	−0.129611	−	0.00520050i
$628$	10.2785	+	5.93431i	0.410158	+	0.236805i
$629$			4.83947i			0.192962i
$630$	1.65371	+	24.2234i	0.0658852	+	0.965083i
$631$	−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
$633$	−6.22371	+	9.84581i	−0.247370	+	0.391336i
$634$	−11.8204	−	20.4735i	−0.469448	−	0.813108i
$635$		−	0.262636i		−	0.0104224i
$636$	−2.44327	−	1.54443i	−0.0968819	−	0.0612408i
$637$	−7.31219	−	24.1564i	−0.289719	−	0.957112i
$638$		−	19.9264i		−	0.788895i
$639$	−9.81447	−	20.6649i	−0.388254	−	0.817492i
$640$	−2.64914	+	1.52948i	−0.104716	+	0.0604581i
$641$		−	20.7741i		−	0.820526i	−0.911967	−	0.410263i	$-0.865437\pi$
$641$		−	20.7741i		−	0.820526i	0.911967	−	0.410263i	$-0.134563\pi$
$642$	−0.436820	+	10.8868i	−0.0172399	+	0.429667i
$643$	0.127258	+	0.220417i	0.00501857	+	0.00869242i	0.868524	−	0.495647i	$-0.165069\pi$
$643$	0.127258	+	0.220417i	0.00501857	+	0.00869242i	−0.863505	+	0.504340i	$0.831736\pi$
$644$	−11.3751	−	4.48059i	−0.448243	−	0.176560i
$645$	42.1016	+	26.6132i	1.65775	+	1.04789i
$646$	−1.48786	+	2.57705i	−0.0585392	+	0.101393i
$647$	12.2158	+	21.1583i	0.480251	+	0.831819i	0.999743	−	0.0226559i	$-0.00721223\pi$
$647$	12.2158	+	21.1583i	0.480251	+	0.831819i	−0.519492	+	0.854475i	$0.673879\pi$
$648$	8.88446	+	1.43750i	0.349014	+	0.0564704i
$649$	−21.1809	+	12.2288i	−0.831422	+	0.480022i
$650$	13.6275	−	7.81700i	0.534514	−	0.306608i
$651$	25.8856	+	35.3641i	1.01454	+	1.38603i
$652$	8.32458	+	4.80620i	0.326016	+	0.188225i
$653$			0.782789i			0.0306329i	0.999883	+	0.0153164i	$0.00487557\pi$
$653$			0.782789i			0.0306329i	−0.999883	+	0.0153164i	$0.995124\pi$
$654$	15.2550	+	9.64292i	0.596516	+	0.377068i
$655$	−5.45942	−	3.15200i	−0.213317	−	0.123159i
$656$	−7.03626	−	4.06239i	−0.274720	−	0.158610i
$657$	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	$0.0137263\pi$
$660$	−10.1475	−	6.41442i	−0.394991	−	0.249681i
$661$	6.51294	+	11.2807i	0.253324	+	0.438770i	0.964439	−	0.264306i	$-0.0851428\pi$
$661$	6.51294	+	11.2807i	0.253324	+	0.438770i	−0.711115	+	0.703076i	$0.751809\pi$
$662$	13.0461	+	7.53219i	0.507053	+	0.292747i
$663$	18.9458	+	12.0504i	0.735795	+	0.468000i
$664$			3.79233i			0.147171i
$665$	−6.23227	−	2.45485i	−0.241677	−	0.0951949i
$666$	−0.323522	+	4.02504i	−0.0125362	+	0.155967i
$667$	−20.3191	+	35.1937i	−0.786759	+	1.36271i
$668$	−21.5888	−	12.4643i	−0.835296	−	0.482258i
$669$	11.5449	−	18.2638i	0.446351	−	0.706120i
$670$	−6.21292	+	10.7611i	−0.240026	+	0.415738i
$671$		−	23.9279i		−	0.923725i
$672$	1.84905	−	4.19297i	0.0713285	−	0.161747i
$673$	−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	$0.953246\pi$
$674$	−9.93070			−0.382516
$675$	13.5919	−	18.1073i	0.523153	−	0.696950i
$676$	6.43680	+	11.2946i	0.247569	+	0.434407i
$677$	−12.3401	−	21.3737i	−0.474268	−	0.821457i	0.525298	−	0.850919i	$-0.323954\pi$
$677$	−12.3401	−	21.3737i	−0.474268	−	0.821457i	−0.999566	+	0.0294618i	$0.990621\pi$
$678$	12.8472	−	6.74557i	0.493392	−	0.259062i
$679$	41.8611	−	6.25683i	1.60648	−	0.240115i
$680$	−9.52479	+	5.49914i	−0.365259	+	0.210882i
$681$	−1.48931	+	37.1177i	−0.0570703	+	1.42235i
$682$	−21.6691			−0.829752
$683$	−16.2437			−0.621546			−0.310773	−	0.950484i	$-0.600588\pi$
$683$	−16.2437			−0.621546			−0.310773	+	0.950484i	$0.600588\pi$
$684$	−1.40975	+	2.04390i	−0.0539031	+	0.0781504i
$685$	23.7751	−	13.7266i	0.908400	−	0.524465i
$686$	−16.7158	+	7.97393i	−0.638210	+	0.304446i
$687$	18.9161	+	36.0264i	0.721694	+	1.37449i
$688$	−4.70036	−	8.14127i	−0.179200	−	0.310383i
$689$	−2.99389	−	5.21929i	−0.114058	−	0.198839i
$690$	11.3815	+	21.6765i	0.433288	+	0.825211i
$691$	−16.1544			−0.614541			−0.307271	−	0.951622i	$-0.599416\pi$
$691$	−16.1544			−0.614541			−0.307271	+	0.951622i	$0.599416\pi$
$692$	−2.01276	+	3.48621i	−0.0765138	+	0.132526i
$693$	17.9425	−	1.22492i	0.681579	−	0.0465307i
$694$		−	3.36902i		−	0.127886i
$695$	31.9290	−	55.3027i	1.21114	−	2.09775i
$696$	−12.8757	−	8.13894i	−0.488051	−	0.308506i
$697$	−25.2984	−	14.6060i	−0.958243	−	0.553242i
$698$	15.4110	−	26.6927i	0.583317	−	1.01033i
$699$	19.7840	−	10.3879i	0.748301	−	0.392905i
$700$	−7.17662	−	9.02197i	−0.271251	−	0.340998i
$701$			36.9386i			1.39515i	0.716510	+	0.697577i	$0.245738\pi$
$701$			36.9386i			1.39515i	−0.716510	+	0.697577i	$0.754262\pi$
$702$	14.9519	+	11.2890i	0.564322	+	0.426076i
$703$	−0.964763	−	0.557006i	−0.0363867	−	0.0210079i
$704$	1.13290	+	1.96224i	0.0426979	+	0.0739549i
$705$	8.95372	−	14.1646i	0.337217	−	0.533471i
$706$	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
$709$	−2.33135	−	1.34600i	−0.0875556	−	0.0505502i	0.455583	−	0.890193i	$-0.349431\pi$
$709$	−2.33135	−	1.34600i	−0.0875556	−	0.0505502i	−0.543139	+	0.839643i	$0.682764\pi$
$710$	20.2016	+	11.6634i	0.758152	+	0.437719i
$711$	7.50371	+	15.7995i	0.281411	+	0.592528i
$712$		−	8.34716i		−	0.312823i
$713$	38.2716	+	22.0961i	1.43328	+	0.827506i
$714$	6.64811	−	15.0755i	0.248799	−	0.564188i
$715$	−12.4344	−	21.6770i	−0.465019	−	0.810674i
$716$	10.9445	−	6.31879i	0.409014	−	0.236144i
$717$	−39.8748	−	1.59993i	−1.48915	−	0.0597505i
$718$	−5.20022	−	9.00705i	−0.194071	−	0.336140i
$719$	9.62506	−	16.6711i	0.358954	−	0.621727i	−0.628832	−	0.777541i	$-0.716467\pi$
$719$	9.62506	−	16.6711i	0.358954	−	0.621727i	0.987786	+	0.155814i	$0.0498001\pi$
$720$	−8.28949	+	3.93696i	−0.308931	+	0.146722i
$721$	−0.693871	−	4.64232i	−0.0258411	−	0.172889i
$722$	9.15750	+	15.8613i	0.340807	+	0.590295i
$723$	−48.0752	−	1.92896i	−1.78794	−	0.0717390i
$724$			1.79097i			0.0665610i
$725$	−33.1857	+	19.1598i	−1.23249	+	0.711577i
$726$	5.42891	−	8.58845i	0.201486	−	0.318747i
$727$			29.4029i			1.09049i	0.838276	+	0.545246i	$0.183564\pi$
$727$			29.4029i			1.09049i	−0.838276	+	0.545246i	$0.816436\pi$
$728$	7.48213	−	5.91758i	0.277306	−	0.219320i
$729$	26.2222	+	6.43408i	0.971192	+	0.238299i
$730$			35.1285i			1.30016i
$731$	−16.8998	−	29.2713i	−0.625062	−	1.08264i
$732$	−15.4612	−	9.77332i	−0.571464	−	0.361232i
$733$	−13.5812	−	23.5234i	−0.501635	−	0.868857i	−0.999998	−	0.00188874i	$-0.999399\pi$
$733$	−13.5812	−	23.5234i	−0.501635	−	0.868857i	0.498363	−	0.866968i	$-0.333935\pi$
$734$	−19.6101	+	11.3219i	−0.723821	+	0.417898i
$735$	35.7742	+	9.78400i	1.31955	+	0.360888i
$736$		−	4.62091i		−	0.170329i
$737$	7.97085	+	4.60197i	0.293610	+	0.169516i
$738$	−20.0645	−	13.8392i	−0.738584	−	0.509428i
$739$	15.9336	−	9.19930i	0.586129	−	0.338402i	−0.177437	−	0.984132i	$-0.556780\pi$
$739$	15.9336	−	9.19930i	0.586129	−	0.338402i	0.763565	+	0.645731i	$0.223447\pi$
$740$	−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	$0.961089\pi$
$744$	−8.85073	+	14.0017i	−0.324484	+	0.513328i
$745$			5.20942i			0.190858i
$746$	−8.39025	+	14.5323i	−0.307189	+	0.532067i
$747$	−0.911511	+	11.3404i	−0.0333504	+	0.414924i
$748$	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
$751$	11.4802			0.418917			0.209459	−	0.977818i	$-0.432830\pi$
$751$	11.4802			0.418917			0.209459	+	0.977818i	$0.432830\pi$
$752$	−2.73905	+	1.58139i	−0.0998827	+	0.0576673i
$753$	10.7631	+	20.4987i	0.392230	+	0.747015i
$754$	−15.7774	−	27.5049i	−0.574577	−	1.00167i
$755$	67.9918			2.47447
$756$	6.53711	−	12.0941i	0.237752	−	0.439857i
$757$	−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	$0.246365\pi$
$758$	−3.91399	−	2.25974i	−0.142163	−	0.0820776i
$759$	16.0560	−	8.43042i	0.582796	−	0.306005i
$760$		−	2.53173i		−	0.0918353i
$761$	−29.4337	−	16.9936i	−1.06697	−	0.616016i	−0.139619	−	0.990205i	$-0.544588\pi$
$761$	−29.4337	−	16.9936i	−1.06697	−	0.616016i	−0.927352	+	0.374189i	$0.877921\pi$
$762$	−0.0794587	+	0.125702i	−0.00287848	+	0.00455372i
$763$	21.5743	−	17.1615i	0.781041	−	0.621287i
$764$	8.45391	+	4.88087i	0.305852	+	0.176584i
$765$	−29.8043	+	14.1550i	−1.07758	+	0.511777i
$766$	2.99527	+	1.72932i	0.108223	+	0.0624828i
$767$	−19.5539	+	33.6502i	−0.706051	+	1.21504i
$768$	1.73066	+	0.0694407i	0.0624498	+	0.00250573i
$769$	19.7746	−	34.2506i	0.713090	−	1.23511i	−0.250602	−	0.968090i	$-0.580628\pi$
$769$	19.7746	−	34.2506i	0.713090	−	1.23511i	0.963692	−	0.267018i	$-0.0860382\pi$
$770$	−14.3511	+	11.4157i	−0.517177	+	0.411394i
$771$	−4.69226	−	0.188272i	−0.168988	−	0.00678044i
$772$	−9.03423	+	5.21591i	−0.325149	+	0.187725i
$773$			8.09302i			0.291086i	0.989352	+	0.145543i	$0.0464929\pi$
$773$			8.09302i			0.291086i	−0.989352	+	0.145543i	$0.953507\pi$
$774$	−12.0990	−	25.4751i	−0.434888	−	0.915682i
$775$	20.8354	+	36.0880i	0.748429	+	1.29632i
$776$	7.99888	+	13.8545i	0.287143	+	0.497347i
$777$	5.64378	+	2.48883i	0.202469	+	0.0892863i
$778$	3.12443	+	1.80389i	0.112016	+	0.0646726i
$779$	5.82350	−	3.36220i	0.208649	−	0.120463i
$780$	−19.0856	−	0.819367i	−0.683376	−	0.0293380i
$781$	8.63918	−	14.9635i	0.309134	−	0.535436i
$782$		−	16.6141i		−	0.594120i
$783$	−36.5466	−	27.4331i	−1.30607	−	0.980379i
$784$	−5.11962	−	4.77383i	−0.182844	−	0.170494i
$785$	−36.3057			−1.29581
$786$	1.65936	+	3.16031i	0.0591874	+	0.112724i
$787$	−7.98791			−0.284738			−0.142369	−	0.989814i	$-0.545472\pi$
$787$	−7.98791			−0.284738			−0.142369	+	0.989814i	$0.545472\pi$
$788$	−3.77403	+	6.53681i	−0.134444	+	0.232864i
$789$	22.5524	−	11.8414i	0.802886	−	0.421566i
$790$	−15.4452	−	8.91731i	−0.549517	−	0.317264i
$791$	−3.27653	−	21.9215i	−0.116500	−	0.779439i
$792$	2.91614	+	6.14011i	0.103621	+	0.218179i
$793$	−18.9456	−	33.0282i	−0.672778	−	1.17286i
$794$	15.1719	−	26.2786i	0.538432	−	0.932592i
$795$	8.83475	+	0.354484i	0.313336	+	0.0125723i
$796$		−	12.2381i		−	0.433767i
$797$	12.1440	+	21.0340i	0.430162	+	0.745063i	0.996887	−	0.0788442i	$-0.0251230\pi$
$797$	12.1440	+	21.0340i	0.430162	+	0.745063i	−0.566725	+	0.823907i	$0.691790\pi$
$798$	2.24018	+	3.06046i	0.0793014	+	0.108339i
$799$	−9.84804	+	5.68577i	−0.348398	+	0.201148i
$800$	2.17863	−	3.77350i	0.0770262	−	0.133413i
$801$	2.00629	−	24.9610i	0.0708889	−	0.881953i
$802$	33.2182			1.17298
$803$	26.0200			0.918227
$804$	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
$807$	13.0123	+	0.522105i	0.458056	+	0.0183790i
$808$	3.56996	+	6.18335i	0.125591	+	0.217529i
$809$	17.1927	−	9.92621i	0.604463	−	0.348987i	−0.166332	−	0.986070i	$-0.553192\pi$
$809$	17.1927	−	9.92621i	0.604463	−	0.348987i	0.770795	+	0.637083i	$0.219859\pi$
$810$	−25.7348	+	9.78047i	−0.904229	+	0.343651i
$811$	−44.1058			−1.54876			−0.774382	−	0.632719i	$-0.781939\pi$
$811$	−44.1058			−1.54876			−0.774382	+	0.632719i	$0.781939\pi$
$812$	−18.2094	+	14.4849i	−0.639025	+	0.508319i
$813$	−0.0428947	−	0.00172110i	−0.00150438	−	6.03617e-5i
$814$	−2.64120	+	1.52490i	−0.0925739	+	0.0534476i
$815$	−29.4040			−1.02998
$816$	6.22246	+	0.249669i	0.217829	+	0.00874017i
$817$	7.78043			0.272203
$818$	15.4590			0.540513
$819$	23.7966	−	15.8973i	0.831519	−	0.555496i
$820$	24.8534			0.867918
$821$	48.6744			1.69875			0.849375	−	0.527790i	$-0.176979\pi$
$821$	48.6744			1.69875			0.849375	+	0.527790i	$0.176979\pi$
$822$	−15.5320	−	0.623206i	−0.541742	−	0.0217368i
$823$	1.25808			0.0438537			0.0219269	−	0.999760i	$-0.493020\pi$
$823$	1.25808			0.0438537			0.0219269	+	0.999760i	$0.493020\pi$
$824$	1.53644	−	0.887062i	0.0535243	−	0.0309023i
$825$	17.0863	+	0.685567i	0.594867	+	0.0238684i
$826$	26.5718	+	10.4664i	0.924550	+	0.364174i
$827$	−45.8818			−1.59547			−0.797734	−	0.603010i	$-0.793968\pi$
$827$	−45.8818			−1.59547			−0.797734	+	0.603010i	$0.793968\pi$
$828$	1.11066	−	13.8182i	0.0385983	−	0.480214i
$829$	9.08503	−	5.24525i	0.315536	−	0.182175i	−0.333865	−	0.942621i	$-0.608353\pi$
$829$	9.08503	−	5.24525i	0.315536	−	0.182175i	0.649401	+	0.760446i	$0.275020\pi$
$830$	−5.80030	−	10.0464i	−0.201331	−	0.348716i
$831$	10.6976	+	0.429230i	0.371096	+	0.0148898i
$832$	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
$835$	76.2557			2.63894
$836$	−1.87527			−0.0648577
$837$	−29.8322	+	39.7428i	−1.03115	+	1.37371i
$838$	6.78747	−	11.7562i	0.234469	−	0.406113i
$839$	−25.7265	+	14.8532i	−0.888179	+	0.512790i	−0.873346	−	0.487100i	$-0.838055\pi$
$839$	−25.7265	+	14.8532i	−0.888179	+	0.512790i	−0.0148325	+	0.999890i	$0.504722\pi$
$840$	1.51470	+	13.9359i	0.0522620	+	0.480833i
$841$	24.1709	+	41.8653i	0.833481	+	1.44363i
$842$			22.2151i			0.765584i
$843$	51.1838	+	2.05369i	1.76287	+	0.0707330i
$844$	−3.36247	+	5.82397i	−0.115741	+	0.200469i
$845$	−34.3268	−	20.0760i	−1.18088	−	0.690634i
$846$	−8.57082	+	4.07057i	−0.294671	+	0.139949i
$847$	−9.66181	−	12.1462i	−0.331984	−	0.417348i
$848$	−1.44524	−	0.834408i	−0.0496296	−	0.0286537i
$849$	32.5150	−	17.0724i	1.11591	−	0.585924i
$850$	7.83310	−	13.5673i	0.268673	−	0.465356i
$851$	6.21978			0.213211
$852$	−6.14016	−	11.6941i	−0.210358	−	0.400635i
$853$	32.2400			1.10388			0.551939	−	0.833885i	$-0.313888\pi$
$853$	32.2400			1.10388			0.551939	+	0.833885i	$0.313888\pi$
$854$	−21.8660	+	17.3936i	−0.748240	+	0.595195i
$855$	0.608516	−	7.57076i	0.0208108	−	0.258915i
$856$			6.29055i			0.215006i
$857$	−12.4374	+	21.5422i	−0.424853	+	0.735867i	−0.996407	−	0.0846975i	$-0.973008\pi$
$857$	−12.4374	+	21.5422i	−0.424853	+	0.735867i	0.571554	+	0.820565i	$0.306341\pi$
$858$	−0.606913	+	14.1369i	−0.0207197	+	0.482627i
$859$	−36.6844	+	21.1798i	−1.25166	+	0.722644i	−0.971438	−	0.237293i	$-0.923740\pi$
$859$	−36.6844	+	21.1798i	−1.25166	+	0.722644i	−0.280218	+	0.959937i	$0.590407\pi$
$860$	24.9038	+	14.3782i	0.849214	+	0.490294i
$861$	−30.0438	+	21.9913i	−1.02389	+	0.749462i
$862$	4.40288	+	7.62602i	0.149963	+	0.259743i
$863$	21.7601	+	37.6895i	0.740721	+	1.28297i	0.952167	+	0.305577i	$0.0988493\pi$
$863$	21.7601	+	37.6895i	0.740721	+	1.28297i	−0.211446	+	0.977390i	$0.567817\pi$
$864$	5.15859	+	0.623627i	0.175499	+	0.0212162i
$865$		−	12.3139i		−	0.418686i
$866$	−3.16975	+	1.83006i	−0.107712	+	0.0621878i
$867$	−7.04881	−	0.282826i	−0.239390	−	0.00960526i
$868$	15.7516	+	19.8019i	0.534645	+	0.672120i
$869$	−6.60514	+	11.4404i	−0.224064	+	0.388090i
$870$	46.5579	+	1.86808i	1.57846	+	0.0633339i
$871$	14.6461	+	0.0410437i	0.496264	+	0.00139071i
$872$	9.02357	+	5.20976i	0.305577	+	0.176425i
$873$	20.5895	+	43.3524i	0.696849	+	1.46726i
$874$	3.31208	+	1.91223i	0.112033	+	0.0646821i
$875$	−4.83995	−	1.90642i	−0.163620	−	0.0644488i
$876$	10.6279	−	16.8131i	0.359082	−	0.568062i
$877$	1.76857	+	1.02108i	0.0597203	+	0.0344795i	0.529563	−	0.848271i	$-0.322356\pi$
$877$	1.76857	+	1.02108i	0.0597203	+	0.0344795i	−0.469843	+	0.882750i	$0.655689\pi$
$878$			17.7844i			0.600196i
$879$	18.0228	−	9.46312i	0.607895	−	0.319183i
$880$	−6.00243	−	3.46551i	−0.202342	−	0.116822i
$881$	9.47062	−	16.4036i	0.319073	−	0.552651i	−0.661222	−	0.750191i	$-0.729962\pi$
$881$	9.47062	−	16.4036i	0.319073	−	0.552651i	0.980295	+	0.197539i	$0.0632950\pi$
$882$	−14.1621	−	15.5060i	−0.476861	−	0.522114i
$883$	10.7657			0.362296			0.181148	−	0.983456i	$-0.442019\pi$
$883$	10.7657			0.362296			0.181148	+	0.983456i	$0.442019\pi$
$884$	11.2085	+	6.51318i	0.376983	+	0.219062i
$885$	−26.5867	−	50.6352i	−0.893702	−	1.70208i
$886$	20.0861	−	11.5967i	0.674805	−	0.389599i
$887$	18.6812			0.627254			0.313627	−	0.949546i	$-0.398456\pi$
$887$	18.6812			0.627254			0.313627	+	0.949546i	$0.398456\pi$
$888$	−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
$891$	7.24449	+	19.0620i	0.242700	+	0.638602i
$892$	6.23733	−	10.8034i	0.208841	−	0.361724i
$893$		−	2.61765i		−	0.0875962i
$894$	1.57607	−	2.49332i	0.0527117	−	0.0833891i
$895$	−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
$899$	72.8377	−	42.0529i	2.42927	−	1.40254i
$900$	7.42186	−	10.7604i	0.247395	−	0.358682i
$901$	−5.19624	−	3.00005i	−0.173112	−	0.0999462i
$902$		−	18.4091i		−	0.612957i
$903$	−42.8273	+	4.65493i	−1.42520	+	0.154906i
$904$	7.25521	−	4.18880i	0.241305	−	0.139317i
$905$	−2.73926	−	4.74454i	−0.0910561	−	0.157714i
$906$	−32.5420	−	20.5704i	−1.08114	−	0.683406i
$907$	15.5213	+	26.8836i	0.515375	+	0.892656i	0.999841	+	0.0178455i	$0.00568070\pi$
$907$	15.5213	+	26.8836i	0.515375	+	0.892656i	−0.484466	+	0.874810i	$0.660986\pi$
$908$			21.4471i			0.711748i
$909$	9.18924	+	19.3485i	0.304788	+	0.641748i
$910$	−10.7704	+	27.1203i	−0.357035	+	0.899028i
$911$		−	11.8527i		−	0.392697i	−0.980534	−	0.196349i	$-0.937092\pi$
$911$		−	11.8527i		−	0.392697i	0.980534	−	0.196349i	$-0.0629084\pi$
$912$	−0.765955	+	1.21173i	−0.0253633	+	0.0401243i
$913$	−7.44148	+	4.29634i	−0.246277	+	0.142188i
$914$			15.3575i			0.507981i
$915$	55.9071	+	2.24321i	1.84823	+	0.0741583i
$916$	11.7463	+	20.3453i	0.388110	+	0.672226i
$917$	5.39253	−	0.806002i	0.178077	−	0.0266165i
$918$	18.5473	+	2.24221i	0.612154	+	0.0740038i
$919$	4.54584	−	7.87363i	0.149953	−	0.259727i	−0.781257	−	0.624210i	$-0.785421\pi$
$919$	4.54584	−	7.87363i	0.149953	−	0.259727i	0.931210	+	0.364483i	$0.118754\pi$
$920$	7.06760	+	12.2414i	0.233012	+	0.403588i
$921$	−21.1886	−	0.850168i	−0.698188	−	0.0280140i
$922$	1.90360	−	1.09904i	0.0626918	−	0.0361951i
$923$	0.0770504	−	27.4948i	0.00253614	−	0.905002i
$924$	10.3224	−	1.12195i	0.339583	−	0.0369095i
$925$	5.07916	+	2.93245i	0.167002	+	0.0964184i
$926$		−	9.47072i		−	0.311227i
$927$	4.80770	−	2.28334i	0.157906	−	0.0749947i
$928$	−7.61619	−	4.39721i	−0.250014	−	0.144346i
$929$	2.76571	+	1.59678i	0.0907399	+	0.0523887i	0.544683	−	0.838642i	$-0.316650\pi$
$929$	2.76571	+	1.59678i	0.0907399	+	0.0523887i	−0.453943	+	0.891030i	$0.649983\pi$
$930$	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
$933$	−8.91232	+	14.0992i	−0.291776	+	0.461586i
$934$	−7.74149	−	13.4087i	−0.253309	−	0.438745i
$935$	−21.5813	−	12.4600i	−0.705784	−	0.407485i
$936$	8.88683	+	6.16638i	0.290475	+	0.201554i
$937$		−	50.2345i		−	1.64109i	−0.571581	−	0.820545i	$-0.693670\pi$
$937$		−	50.2345i		−	1.64109i	0.571581	−	0.820545i	$-0.306330\pi$
$938$	−1.58872	−	10.6293i	−0.0518734	−	0.347058i
$939$	21.3416	−	11.2057i	0.696458	−	0.365684i
$940$	4.83741	−	8.37864i	0.157779	−	0.273281i
$941$	23.4013	+	13.5107i	0.762861	+	0.440438i	0.830322	−	0.557284i	$-0.188157\pi$
$941$	23.4013	+	13.5107i	0.762861	+	0.440438i	−0.0674613	+	0.997722i	$0.521490\pi$
$942$	17.3765	+	10.9840i	0.566158	+	0.357878i
$943$	−18.7719	+	32.5139i	−0.611298	+	1.05880i
$944$			10.7942i			0.351322i
$945$	1.17991	+	42.0372i	0.0383825	+	1.36747i
$946$	10.6501	−	18.4465i	0.346265	−	0.599748i
$947$	−28.3520			−0.921317			−0.460658	−	0.887578i	$-0.652387\pi$
$947$	−28.3520			−0.921317			−0.460658	+	0.887578i	$0.652387\pi$
$948$	4.69450	+	8.94083i	0.152470	+	0.290385i
$949$	35.9160	−	20.6021i	1.16588	−	0.668773i
$950$	1.80312	+	3.12310i	0.0585011	+	0.101327i
$951$	−19.0354	−	36.2535i	−0.617265	−	1.17560i
$952$	3.48625	−	8.85075i	0.112990	−	0.286854i
$953$	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	$0.232957\pi$
$954$	−4.12122	−	2.84255i	−0.133429	−	0.0920309i
$955$	−29.8608			−0.966273
$956$	−23.0402			−0.745175
$957$	1.38371	−	34.4859i	0.0447289	−	1.11477i
$958$	35.7766	−	20.6556i	1.15589	−	0.667353i
$959$	−8.70212	+	22.0926i	−0.281006	+	0.713407i
$960$	−4.69096	+	2.46305i	−0.151400	+	0.0794947i
$961$	−30.2306	−	52.3609i	−0.975180	−	1.68906i
$962$	−2.43832	+	4.19609i	−0.0786146	+	0.135287i
$963$	−1.51197	+	18.8110i	−0.0487227	+	0.606175i
$964$	−27.7786			−0.894688
$965$	15.9553	−	27.6354i	0.513619	−	0.889614i
$966$	−19.3754	−	8.54427i	−0.623392	−	0.274907i
$967$			40.5538i			1.30412i	0.758167	+	0.652061i	$0.226095\pi$
$967$			40.5538i			1.30412i	−0.758167	+	0.652061i	$0.773905\pi$
$968$	2.93307	−	5.08022i	0.0942723	−	0.163284i
$969$	−2.75393	+	4.35668i	−0.0884691	+	0.139957i
$970$	−42.3803	−	24.4683i	−1.36075	−	0.785630i
$971$	−12.1157	+	20.9850i	−0.388812	+	0.673442i	−0.992290	−	0.123938i	$-0.960448\pi$
$971$	−12.1157	+	20.9850i	−0.388812	+	0.673442i	0.603478	+	0.797380i	$0.293781\pi$
$972$	15.2761	+	3.10477i	0.489982	+	0.0995855i
$973$	8.16462	+	54.6252i	0.261746	+	1.75120i
$974$			2.53448i			0.0812099i
$975$	24.1274	−	12.5823i	0.772694	−	0.402955i
$976$	−9.14560	−	5.28021i	−0.292744	−	0.169016i
$977$	−6.91109	−	11.9704i	−0.221105	−	0.382966i	0.734039	−	0.679108i	$-0.237633\pi$
$977$	−6.91109	−	11.9704i	−0.221105	−	0.382966i	−0.955144	+	0.296142i	$0.904300\pi$
$978$	14.0733	+	8.89595i	0.450013	+	0.284461i
$979$	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
$982$	−22.3657	−	12.9129i	−0.713719	−	0.412066i
$983$	6.38037	+	3.68371i	0.203502	+	0.117492i	0.598288	−	0.801281i	$-0.295848\pi$
$983$	6.38037	+	3.68371i	0.203502	+	0.117492i	−0.394786	+	0.918773i	$0.629181\pi$
$984$	−11.8953	−	7.51920i	−0.379207	−	0.239703i
$985$		−	23.0892i		−	0.735684i
$986$	−27.3835	−	15.8099i	−0.872067	−	0.503488i
$987$	1.56610	+	14.4088i	0.0498496	+	0.458637i
$988$	−2.58848	+	1.48480i	−0.0823506	+	0.0472379i
$989$	−37.6201	+	21.7200i	−1.19625	+	0.690654i
$990$	−17.1165	−	11.8058i	−0.543997	−	0.375214i
$991$	30.4130	+	52.6768i	0.966100	+	1.67333i	0.706629	+	0.707584i	$0.250215\pi$
$991$	30.4130	+	52.6768i	0.966100	+	1.67333i	0.259471	+	0.965751i	$0.416452\pi$
$992$	−4.78177	+	8.28226i	−0.151821	+	0.262962i
$993$	22.0554	+	13.9416i	0.699906	+	0.442423i
$994$	−19.9541	+	2.98246i	−0.632905	+	0.0945980i
$995$	18.7179	+	32.4204i	0.593397	+	1.02779i
$996$	−0.263342	+	6.56323i	−0.00834432	+	0.207964i
$997$			41.1210i			1.30231i	0.758943	+	0.651157i	$0.225716\pi$
$997$			41.1210i			1.30231i	−0.758943	+	0.651157i	$0.774284\pi$
$998$	−24.8498	+	14.3470i	−0.786606	+	0.454147i
$999$	−0.839407	+	6.94351i	−0.0265577	+	0.219683i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.11	✓	34	3.2	odd	2
546.2.bi.e.257.11	yes	34	91.75	odd	6
546.2.bi.f.17.17	yes	34	1.1	even	1	trivial
546.2.bi.f.257.17	yes	34	273.257	even	6	inner
546.2.bn.e.101.12	yes	34	39.23	odd	6
546.2.bn.e.173.12	yes	34	7.5	odd	6
546.2.bn.f.101.6	yes	34	13.10	even	6
546.2.bn.f.173.6	yes	34	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.73066 + 0.0694407i) q^{3} +1.00000 q^{4} +(-2.64914 + 1.52948i) q^{5} +(1.73066 + 0.0694407i) q^{6} +(0.969634 - 2.46167i) q^{7} +1.00000 q^{8} +(2.99036 + 0.240356i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.73066 + 0.0694407i) q^{3} +1.00000 q^{4} +(-2.64914 + 1.52948i) q^{5} +(1.73066 + 0.0694407i) q^{6} +(0.969634 - 2.46167i) q^{7} +1.00000 q^{8} +(2.99036 + 0.240356i) q^{9} +(-2.64914 + 1.52948i) q^{10} +(1.13290 + 1.96224i) q^{11} +(1.73066 + 0.0694407i) q^{12} +(3.11743 + 1.81152i) q^{13} +(0.969634 - 2.46167i) q^{14} +(-4.69096 + 2.46305i) q^{15} +1.00000 q^{16} +3.59543 q^{17} +(2.99036 + 0.240356i) q^{18} +(-0.413821 + 0.716759i) q^{19} +(-2.64914 + 1.52948i) q^{20} +(1.84905 - 4.19297i) q^{21} +(1.13290 + 1.96224i) q^{22} -4.62091i q^{23} +(1.73066 + 0.0694407i) q^{24} +(2.17863 - 3.77350i) q^{25} +(3.11743 + 1.81152i) q^{26} +(5.15859 + 0.623627i) q^{27} +(0.969634 - 2.46167i) q^{28} +(-7.61619 - 4.39721i) q^{29} +(-4.69096 + 2.46305i) q^{30} +(-4.78177 + 8.28226i) q^{31} +1.00000 q^{32} +(1.82441 + 3.47464i) q^{33} +3.59543 q^{34} +(1.19638 + 8.00434i) q^{35} +(2.99036 + 0.240356i) q^{36} +1.34601i q^{37} +(-0.413821 + 0.716759i) q^{38} +(5.26942 + 3.35160i) q^{39} +(-2.64914 + 1.52948i) q^{40} +(-7.03626 - 4.06239i) q^{41} +(1.84905 - 4.19297i) q^{42} +(-4.70036 - 8.14127i) q^{43} +(1.13290 + 1.96224i) q^{44} +(-8.28949 + 3.93696i) q^{45} -4.62091i q^{46} +(-2.73905 + 1.58139i) q^{47} +(1.73066 + 0.0694407i) q^{48} +(-5.11962 - 4.77383i) q^{49} +(2.17863 - 3.77350i) q^{50} +(6.22246 + 0.249669i) q^{51} +(3.11743 + 1.81152i) q^{52} +(-1.44524 - 0.834408i) q^{53} +(5.15859 + 0.623627i) q^{54} +(-6.00243 - 3.46551i) q^{55} +(0.969634 - 2.46167i) q^{56} +(-0.765955 + 1.21173i) q^{57} +(-7.61619 - 4.39721i) q^{58} +10.7942i q^{59} +(-4.69096 + 2.46305i) q^{60} +(-9.14560 - 5.28021i) q^{61} +(-4.78177 + 8.28226i) q^{62} +(3.49123 - 7.12821i) q^{63} +1.00000 q^{64} +(-11.0292 - 0.0309078i) q^{65} +(1.82441 + 3.47464i) q^{66} +(3.51789 - 2.03106i) q^{67} +3.59543 q^{68} +(0.320879 - 7.99721i) q^{69} +(1.19638 + 8.00434i) q^{70} +(-3.81286 - 6.60406i) q^{71} +(2.99036 + 0.240356i) q^{72} +(5.74190 - 9.94525i) q^{73} +1.34601i q^{74} +(4.03250 - 6.37935i) 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} +(-2.64914 + 1.52948i) q^{80} +(8.88446 + 1.43750i) q^{81} +(-7.03626 - 4.06239i) q^{82} +3.79233i q^{83} +(1.84905 - 4.19297i) q^{84} +(-9.52479 + 5.49914i) q^{85} +(-4.70036 - 8.14127i) q^{86} +(-12.8757 - 8.13894i) q^{87} +(1.13290 + 1.96224i) q^{88} -8.34716i q^{89} +(-8.28949 + 3.93696i) q^{90} +(7.48213 - 5.91758i) q^{91} -4.62091i q^{92} +(-8.85073 + 14.0017i) q^{93} +(-2.73905 + 1.58139i) q^{94} -2.53173i q^{95} +(1.73066 + 0.0694407i) q^{96} +(7.99888 + 13.8545i) q^{97} +(-5.11962 - 4.77383i) q^{98} +(2.91614 + 6.14011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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