LMFDB - Embedded newform 360.2.bk.a.229.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(229,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("360.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bk (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.11
Character	$\chi$	$=$	360.229
Dual form			360.2.bk.a.349.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25228 + 0.657113i) q^{2} +(-1.28051 - 1.16631i) q^{3} +(1.13640 - 1.64578i) q^{4} +(2.01086 - 0.977977i) q^{5} +(2.36996 + 0.619105i) q^{6} +(1.13221 - 0.653679i) q^{7} +(-0.341633 + 2.80772i) q^{8} +(0.279433 + 2.98696i) q^{9} +O(q^{10})$	\(q+(-1.25228 + 0.657113i) q^{2} +(-1.28051 - 1.16631i) q^{3} +(1.13640 - 1.64578i) q^{4} +(2.01086 - 0.977977i) q^{5} +(2.36996 + 0.619105i) q^{6} +(1.13221 - 0.653679i) q^{7} +(-0.341633 + 2.80772i) q^{8} +(0.279433 + 2.98696i) q^{9} +(-1.87552 + 2.54606i) q^{10} +(1.12540 - 0.649750i) q^{11} +(-3.37467 + 0.782040i) q^{12} +(1.08961 - 1.88726i) q^{13} +(-0.988296 + 1.56258i) q^{14} +(-3.71556 - 1.09298i) q^{15} +(-1.41717 - 3.74054i) q^{16} +4.74800i q^{17} +(-2.31270 - 3.55689i) q^{18} -5.58496i q^{19} +(0.675617 - 4.42081i) q^{20} +(-2.21220 - 0.483460i) q^{21} +(-0.982355 + 1.55318i) q^{22} +(-1.62707 - 0.939389i) q^{23} +(3.71214 - 3.19687i) q^{24} +(3.08712 - 3.93315i) q^{25} +(-0.124352 + 3.07938i) q^{26} +(3.12591 - 4.15075i) q^{27} +(0.210833 - 2.60620i) q^{28} +(-1.13812 + 0.657094i) q^{29} +(5.37113 - 1.07283i) q^{30} +(1.71004 - 2.96188i) q^{31} +(4.23265 + 3.75296i) q^{32} +(-2.19890 - 0.480554i) q^{33} +(-3.11998 - 5.94582i) q^{34} +(1.63742 - 2.42173i) q^{35} +(5.23342 + 2.93451i) q^{36} +7.68156 q^{37} +(3.66995 + 6.99393i) q^{38} +(-3.59640 + 1.14584i) q^{39} +(2.05891 + 5.98004i) q^{40} +(4.93913 - 8.55483i) q^{41} +(3.08798 - 0.848239i) q^{42} +(-4.10865 - 7.11638i) q^{43} +(0.209565 - 2.59054i) q^{44} +(3.48308 + 5.73308i) q^{45} +(2.65483 + 0.107208i) q^{46} +(-4.71475 + 2.72206i) q^{47} +(-2.54793 + 6.44267i) q^{48} +(-2.64541 + 4.58198i) q^{49} +(-1.28141 + 6.95399i) q^{50} +(5.53765 - 6.07988i) q^{51} +(-1.86778 - 3.93796i) q^{52} +1.66922 q^{53} +(-1.18700 + 7.25197i) q^{54} +(1.62758 - 2.40717i) q^{55} +(1.44855 + 3.40223i) q^{56} +(-6.51381 + 7.15162i) q^{57} +(0.993459 - 1.57074i) q^{58} +(-5.86091 - 3.38380i) q^{59} +(-6.02118 + 4.87293i) q^{60} +(-8.33815 + 4.81404i) q^{61} +(-0.195159 + 4.83279i) q^{62} +(2.26889 + 3.19919i) q^{63} +(-7.76657 - 1.91842i) q^{64} +(0.345358 - 4.86064i) q^{65} +(3.06942 - 0.843141i) q^{66} +(-4.04077 + 6.99882i) q^{67} +(7.81416 + 5.39565i) q^{68} +(0.987864 + 3.10057i) q^{69} +(-0.459162 + 4.10865i) q^{70} +2.53449 q^{71} +(-8.48200 - 0.235874i) q^{72} -14.6597i q^{73} +(-9.61945 + 5.04765i) q^{74} +(-8.54038 + 1.43591i) q^{75} +(-9.19160 - 6.34677i) q^{76} +(0.849457 - 1.47130i) q^{77} +(3.75075 - 3.79816i) q^{78} +(6.46769 + 11.2024i) q^{79} +(-6.50789 - 6.13574i) q^{80} +(-8.84383 + 1.66931i) q^{81} +(-0.563680 + 13.9586i) q^{82} +(1.92190 + 3.32884i) q^{83} +(-3.30962 + 3.09138i) q^{84} +(4.64344 + 9.54757i) q^{85} +(9.82144 + 6.21185i) q^{86} +(2.22376 + 0.485985i) q^{87} +(1.43984 + 3.38178i) q^{88} +10.3997 q^{89} +(-8.12906 - 4.89064i) q^{90} -2.84903i q^{91} +(-3.39503 + 1.61027i) q^{92} +(-5.64421 + 1.79829i) q^{93} +(4.11548 - 6.50691i) q^{94} +(-5.46196 - 11.2306i) q^{95} +(-1.04285 - 9.74230i) q^{96} +(6.73852 - 3.89049i) q^{97} +(0.301908 - 7.47625i) q^{98} +(2.25525 + 3.17996i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) $ 136 * q - 2 * q^4 - 8 * q^9	$ 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) $ 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.25228	+	0.657113i	−0.885495	+	0.464649i
$2$	−1.25228	+	0.657113i	−0.885495	+	0.464649i
$3$	−1.28051	−	1.16631i	−0.739305	−	0.673371i
$3$	−1.28051	−	1.16631i	−0.739305	−	0.673371i
$4$	1.13640	−	1.64578i	0.568202	−	0.822889i
$5$	2.01086	−	0.977977i	0.899284	−	0.437365i
$5$	2.01086	−	0.977977i	0.899284	−	0.437365i
$6$	2.36996	+	0.619105i	0.967532	+	0.252749i
$7$	1.13221	−	0.653679i	0.427934	−	0.247068i	−0.270532	−	0.962711i	$-0.587200\pi$
$7$	1.13221	−	0.653679i	0.427934	−	0.247068i	0.698466	+	0.715643i	$0.253866\pi$
$8$	−0.341633	+	2.80772i	−0.120785	+	0.992679i
$9$	0.279433	+	2.98696i	0.0931442	+	0.995653i
$10$	−1.87552	+	2.54606i	−0.593090	+	0.805136i
$11$	1.12540	−	0.649750i	0.339321	−	0.195907i	−0.320651	−	0.947197i	$-0.603902\pi$
$11$	1.12540	−	0.649750i	0.339321	−	0.195907i	0.659972	+	0.751290i	$0.270568\pi$
$12$	−3.37467	+	0.782040i	−0.974184	+	0.225755i
$13$	1.08961	−	1.88726i	0.302204	−	0.523433i	−0.674431	−	0.738338i	$-0.735611\pi$
$13$	1.08961	−	1.88726i	0.302204	−	0.523433i	0.976635	+	0.214905i	$0.0689442\pi$
$14$	−0.988296	+	1.56258i	−0.264133	+	0.417616i
$15$	−3.71556	−	1.09298i	−0.959354	−	0.282206i
$16$	−1.41717	−	3.74054i	−0.354293	−	0.935135i
$17$			4.74800i			1.15156i	0.817605	+	0.575780i	$0.195301\pi$
$17$			4.74800i			1.15156i	−0.817605	+	0.575780i	$0.804699\pi$
$18$	−2.31270	−	3.55689i	−0.545108	−	0.838366i
$19$		−	5.58496i		−	1.28128i	−0.767842	−	0.640639i	$-0.778670\pi$
$19$		−	5.58496i		−	1.28128i	0.767842	−	0.640639i	$-0.221330\pi$
$20$	0.675617	−	4.42081i	0.151073	−	0.988523i
$21$	−2.21220	−	0.483460i	−0.482742	−	0.105500i
$22$	−0.982355	+	1.55318i	−0.209439	+	0.331140i
$23$	−1.62707	−	0.939389i	−0.339267	−	0.195876i	0.320681	−	0.947187i	$-0.396088\pi$
$23$	−1.62707	−	0.939389i	−0.339267	−	0.195876i	−0.659948	+	0.751311i	$0.729422\pi$
$24$	3.71214	−	3.19687i	0.757738	−	0.652559i
$25$	3.08712	−	3.93315i	0.617424	−	0.786630i
$26$	−0.124352	+	3.07938i	−0.0243875	+	0.603916i
$27$	3.12591	−	4.15075i	0.601581	−	0.798812i
$28$	0.210833	−	2.60620i	0.0398436	−	0.492526i
$29$	−1.13812	+	0.657094i	−0.211344	+	0.122019i	−0.601936	−	0.798545i	$-0.705604\pi$
$29$	−1.13812	+	0.657094i	−0.211344	+	0.122019i	0.390592	+	0.920564i	$0.372270\pi$
$30$	5.37113	−	1.07283i	0.980630	−	0.195872i
$31$	1.71004	−	2.96188i	0.307133	−	0.531970i	−0.670601	−	0.741818i	$-0.733964\pi$
$31$	1.71004	−	2.96188i	0.307133	−	0.531970i	0.977734	+	0.209849i	$0.0672971\pi$
$32$	4.23265	+	3.75296i	0.748234	+	0.663435i
$33$	−2.19890	−	0.480554i	−0.382780	−	0.0836536i
$34$	−3.11998	−	5.94582i	−0.535071	−	1.01970i
$35$	1.63742	−	2.42173i	0.276775	−	0.409347i
$36$	5.23342	+	2.93451i	0.872236	+	0.489085i
$37$	7.68156			1.26284			0.631420	−	0.775441i	$-0.282472\pi$
$37$	7.68156			1.26284			0.631420	+	0.775441i	$0.282472\pi$
$38$	3.66995	+	6.99393i	0.595345	+	1.13456i
$39$	−3.59640	+	1.14584i	−0.575886	+	0.183481i
$40$	2.05891	+	5.98004i	0.325542	+	0.945527i
$41$	4.93913	−	8.55483i	0.771363	−	1.33604i	−0.165453	−	0.986218i	$-0.552909\pi$
$41$	4.93913	−	8.55483i	0.771363	−	1.33604i	0.936816	−	0.349823i	$-0.113758\pi$
$42$	3.08798	−	0.848239i	0.476485	−	0.130886i
$43$	−4.10865	−	7.11638i	−0.626563	−	1.08524i	−0.988236	−	0.152934i	$-0.951128\pi$
$43$	−4.10865	−	7.11638i	−0.626563	−	1.08524i	0.361674	−	0.932305i	$-0.382205\pi$
$44$	0.209565	−	2.59054i	0.0315932	−	0.390538i
$45$	3.48308	+	5.73308i	0.519226	+	0.854637i
$46$	2.65483	+	0.107208i	0.391433	+	0.0158070i
$47$	−4.71475	+	2.72206i	−0.687717	+	0.397054i	−0.802756	−	0.596307i	$-0.796634\pi$
$47$	−4.71475	+	2.72206i	−0.687717	+	0.397054i	0.115039	+	0.993361i	$0.463301\pi$
$48$	−2.54793	+	6.44267i	−0.367762	+	0.929920i
$49$	−2.64541	+	4.58198i	−0.377915	+	0.654568i
$50$	−1.28141	+	6.95399i	−0.181219	+	0.983443i
$51$	5.53765	−	6.07988i	0.775426	−	0.851354i
$52$	−1.86778	−	3.93796i	−0.259014	−	0.546096i
$53$	1.66922			0.229284			0.114642	−	0.993407i	$-0.463428\pi$
$53$	1.66922			0.229284			0.114642	+	0.993407i	$0.463428\pi$
$54$	−1.18700	+	7.25197i	−0.161530	+	0.986868i
$55$	1.62758	−	2.40717i	0.219463	−	0.324583i
$56$	1.44855	+	3.40223i	0.193571	+	0.454643i
$57$	−6.51381	+	7.15162i	−0.862775	+	0.947255i
$58$	0.993459	−	1.57074i	0.130448	−	0.206248i
$59$	−5.86091	−	3.38380i	−0.763025	−	0.440533i	0.0673557	−	0.997729i	$-0.478544\pi$
$59$	−5.86091	−	3.38380i	−0.763025	−	0.440533i	−0.830381	+	0.557196i	$0.811877\pi$
$60$	−6.02118	+	4.87293i	−0.777331	+	0.629092i
$61$	−8.33815	+	4.81404i	−1.06759	+	0.616374i	−0.927522	−	0.373768i	$-0.878066\pi$
$61$	−8.33815	+	4.81404i	−1.06759	+	0.616374i	−0.140069	+	0.990142i	$0.544732\pi$
$62$	−0.195159	+	4.83279i	−0.0247852	+	0.613765i
$63$	2.26889	+	3.19919i	0.285853	+	0.403060i
$64$	−7.76657	−	1.91842i	−0.970822	−	0.239802i
$65$	0.345358	−	4.86064i	0.0428363	−	0.602889i
$66$	3.06942	−	0.843141i	0.377819	−	0.103783i
$67$	−4.04077	+	6.99882i	−0.493659	+	0.855042i	−0.999973	−	0.00730655i	$-0.997674\pi$
$67$	−4.04077	+	6.99882i	−0.493659	+	0.855042i	0.506314	+	0.862349i	$0.331008\pi$
$68$	7.81416	+	5.39565i	0.947606	+	0.654319i
$69$	0.987864	+	3.10057i	0.118925	+	0.373265i
$70$	−0.459162	+	4.10865i	−0.0548803	+	0.491078i
$71$	2.53449			0.300788			0.150394	−	0.988626i	$-0.451946\pi$
$71$	2.53449			0.300788			0.150394	+	0.988626i	$0.451946\pi$
$72$	−8.48200	−	0.235874i	−0.999614	−	0.0277980i
$73$		−	14.6597i		−	1.71579i	−0.513828	−	0.857893i	$-0.671773\pi$
$73$		−	14.6597i		−	1.71579i	0.513828	−	0.857893i	$-0.328227\pi$
$74$	−9.61945	+	5.04765i	−1.11824	+	0.586778i
$75$	−8.54038	+	1.43591i	−0.986159	+	0.165805i
$76$	−9.19160	−	6.34677i	−1.05435	−	0.728025i
$77$	0.849457	−	1.47130i	0.0968046	−	0.167670i
$78$	3.75075	−	3.79816i	0.424689	−	0.430057i
$79$	6.46769	+	11.2024i	0.727672	+	1.26036i	0.957865	+	0.287220i	$0.0927310\pi$
$79$	6.46769	+	11.2024i	0.727672	+	1.26036i	−0.230193	+	0.973145i	$0.573936\pi$
$80$	−6.50789	−	6.13574i	−0.727605	−	0.685997i
$81$	−8.84383	+	1.66931i	−0.982648	+	0.185479i
$82$	−0.563680	+	13.9586i	−0.0622480	+	1.54147i
$83$	1.92190	+	3.32884i	0.210956	+	0.365387i	0.952014	−	0.306054i	$-0.0990089\pi$
$83$	1.92190	+	3.32884i	0.210956	+	0.365387i	−0.741058	+	0.671441i	$0.765676\pi$
$84$	−3.30962	+	3.09138i	−0.361109	+	0.337298i
$85$	4.64344	+	9.54757i	0.503652	+	1.03558i
$86$	9.82144	+	6.21185i	1.05907	+	0.669841i
$87$	2.22376	+	0.485985i	0.238412	+	0.0521031i
$88$	1.43984	+	3.38178i	0.153488	+	0.360499i
$89$	10.3997			1.10237			0.551185	−	0.834383i	$-0.314176\pi$
$89$	10.3997			1.10237			0.551185	+	0.834383i	$0.314176\pi$
$90$	−8.12906	−	4.89064i	−0.856879	−	0.515518i
$91$		−	2.84903i		−	0.298659i
$92$	−3.39503	+	1.61027i	−0.353957	+	0.167882i
$93$	−5.64421	+	1.79829i	−0.585277	+	0.186474i
$94$	4.11548	−	6.50691i	0.424479	−	0.671136i
$95$	−5.46196	−	11.2306i	−0.560386	−	1.15223i
$96$	−1.04285	−	9.74230i	−0.106435	−	0.994320i
$97$	6.73852	−	3.89049i	0.684193	−	0.395019i	−0.117240	−	0.993104i	$-0.537405\pi$
$97$	6.73852	−	3.89049i	0.684193	−	0.395019i	0.801433	+	0.598084i	$0.204071\pi$
$98$	0.301908	−	7.47625i	0.0304973	−	0.755215i
$99$	2.25525	+	3.17996i	0.226661	+	0.319598i
$100$	−2.96488	−	9.55037i	−0.296488	−	0.955037i
$101$	−13.3624	+	7.71476i	−1.32960	+	0.767648i	−0.985238	−	0.171188i	$-0.945240\pi$
$101$	−13.3624	+	7.71476i	−1.32960	+	0.767648i	−0.344366	+	0.938835i	$0.611906\pi$
$102$	−2.93951	+	11.2526i	−0.291055	+	1.11417i
$103$	17.0070	+	9.81899i	1.67575	+	0.967493i	0.964322	+	0.264732i	$0.0852836\pi$
$103$	17.0070	+	9.81899i	1.67575	+	0.967493i	0.711426	+	0.702761i	$0.248050\pi$
$104$	4.92666	+	3.70408i	0.483099	+	0.363215i
$105$	−4.92124	+	1.19131i	−0.480264	+	0.116260i
$106$	−2.09032	+	1.09686i	−0.203030	+	0.106537i
$107$	−10.3866			−1.00412			−0.502058	−	0.864834i	$-0.667423\pi$
$107$	−10.3866			−1.00412			−0.502058	+	0.864834i	$0.667423\pi$
$108$	−3.27891	−	9.86148i	−0.315514	−	0.948921i
$109$			5.25264i			0.503112i	0.967843	+	0.251556i	$0.0809422\pi$
$109$			5.25264i			0.503112i	−0.967843	+	0.251556i	$0.919058\pi$
$110$	−0.456402	+	4.08396i	−0.0435162	+	0.389390i
$111$	−9.83634	−	8.95909i	−0.933624	−	0.850360i
$112$	−4.04964	−	3.30868i	−0.382655	−	0.312641i
$113$	−0.414788	−	0.239478i	−0.0390199	−	0.0225282i	0.480363	−	0.877070i	$-0.340505\pi$
$113$	−0.414788	−	0.239478i	−0.0390199	−	0.0225282i	−0.519383	+	0.854542i	$0.673838\pi$
$114$	3.45768	−	13.2361i	0.323841	−	1.23968i
$115$	−4.19051	−	0.297743i	−0.390767	−	0.0277647i
$116$	−0.211934	+	2.61982i	−0.0196776	+	0.243244i
$117$	5.94165	+	2.72726i	0.549306	+	0.252136i
$118$	9.56303	+	0.386177i	0.880348	+	0.0355504i
$119$	3.10367	+	5.37572i	0.284513	+	0.492791i
$120$	4.33813	−	10.0589i	0.396015	−	0.918244i
$121$	−4.65565	+	8.06382i	−0.423241	+	0.733075i
$122$	7.27833	−	11.5076i	0.658949	−	1.04185i
$123$	−16.3022	+	5.19401i	−1.46992	+	0.468328i
$124$	−2.93130	−	6.18025i	−0.263238	−	0.555002i
$125$	2.36124	−	10.9282i	0.211196	−	0.977444i
$126$	−4.94351	−	2.51536i	−0.440403	−	0.224086i
$127$			13.9679i			1.23945i	0.784818	+	0.619727i	$0.212757\pi$
$127$			13.9679i			1.23945i	−0.784818	+	0.619727i	$0.787243\pi$
$128$	10.9865	−	2.70113i	0.971082	−	0.238748i
$129$	−3.03874	+	13.9046i	−0.267547	+	1.22423i
$130$	2.76151	+	6.31382i	0.242200	+	0.553759i
$131$	8.36098	+	4.82721i	0.730502	+	0.421756i	0.818606	−	0.574356i	$-0.194747\pi$
$131$	8.36098	+	4.82721i	0.730502	+	0.421756i	−0.0881036	+	0.996111i	$0.528081\pi$
$132$	−3.28973	+	3.07280i	−0.286334	+	0.267453i
$133$	−3.65077	−	6.32332i	−0.316562	−	0.548302i
$134$	0.461154	−	11.4197i	0.0398377	−	0.986514i
$135$	2.22643	−	11.4036i	0.191620	−	0.981469i
$136$	−13.3311	−	1.62207i	−1.14313	−	0.139092i
$137$	3.98655	−	2.30164i	0.340594	−	0.196642i	−0.319941	−	0.947438i	$-0.603663\pi$
$137$	3.98655	−	2.30164i	0.340594	−	0.196642i	0.660535	+	0.750796i	$0.270330\pi$
$138$	−3.27451	−	3.23364i	−0.278745	−	0.275266i
$139$	10.9075	+	6.29746i	0.925164	+	0.534144i	0.885279	−	0.465060i	$-0.153967\pi$
$139$	10.9075	+	6.29746i	0.925164	+	0.534144i	0.0398853	+	0.999204i	$0.487301\pi$
$140$	−2.12485	−	5.44690i	−0.179583	−	0.460347i
$141$	9.21208	+	2.01323i	0.775797	+	0.169545i
$142$	−3.17388	+	1.66544i	−0.266346	+	0.139761i
$143$		−	2.83190i		−	0.236816i
$144$	10.7768	−	5.27826i	0.898069	−	0.439855i
$145$	−1.64598	+	2.43438i	−0.136691	+	0.202164i
$146$	9.63307	+	18.3580i	0.797239	+	1.51932i
$147$	8.73150	−	2.78192i	0.720162	−	0.229449i
$148$	8.72936	−	12.6421i	0.717549	−	1.03918i
$149$	15.0467	+	8.68721i	1.23267	+	0.711684i	0.967586	−	0.252540i	$-0.0812660\pi$
$149$	15.0467	+	8.68721i	1.23267	+	0.711684i	0.265087	+	0.964225i	$0.414599\pi$
$150$	9.75139	−	7.41016i	0.796197	−	0.605037i
$151$	5.26860	+	9.12549i	0.428753	+	0.742622i	0.996763	−	0.0804000i	$-0.0256198\pi$
$151$	5.26860	+	9.12549i	0.428753	+	0.742622i	−0.568010	+	0.823022i	$0.692286\pi$
$152$	15.6810	+	1.90800i	1.27190	+	0.154760i
$153$	−14.1821	+	1.32675i	−1.14655	+	0.107261i
$154$	−0.0969444	+	2.40067i	−0.00781201	+	0.193451i
$155$	0.542006	−	7.62831i	0.0435349	−	0.612721i
$156$	−2.20117	+	7.22102i	−0.176235	+	0.578144i
$157$	−7.30815	+	12.6581i	−0.583254	+	1.01022i	0.411837	+	0.911258i	$0.364887\pi$
$157$	−7.30815	+	12.6581i	−0.583254	+	1.01022i	−0.995091	+	0.0989674i	$0.968446\pi$
$158$	−15.4606	−	9.77848i	−1.22998	−	0.777934i
$159$	−2.13745	−	1.94683i	−0.169511	−	0.154393i
$160$	12.1816	+	3.40724i	0.963038	+	0.269366i
$161$	−2.45624			−0.193579
$162$	9.97802	−	7.90184i	0.783948	−	0.620827i
$163$	13.7411			1.07628			0.538142	−	0.842854i	$-0.319126\pi$
$163$	13.7411			1.07628			0.538142	+	0.842854i	$0.319126\pi$
$164$	−8.46650	−	17.8505i	−0.661123	−	1.39389i
$165$	−4.89166	+	1.18415i	−0.380815	+	0.0921859i
$166$	−4.59418	−	2.90572i	−0.356578	−	0.225528i
$167$	−15.5309	−	8.96675i	−1.20181	−	0.693868i	−0.240856	−	0.970561i	$-0.577428\pi$
$167$	−15.5309	−	8.96675i	−1.20181	−	0.693868i	−0.960958	+	0.276693i	$0.910761\pi$
$168$	2.11318	−	6.04607i	0.163035	−	0.466464i
$169$	4.12549	+	7.14555i	0.317345	+	0.549658i
$170$	−12.0887	−	8.90496i	−0.927162	−	0.682979i
$171$	16.6820	−	1.56062i	1.27571	−	0.119344i
$172$	−16.3811	−	1.32517i	−1.24905	−	0.101043i
$173$	9.07986	+	15.7268i	0.690329	+	1.19569i	0.971730	+	0.236095i	$0.0758676\pi$
$173$	9.07986	+	15.7268i	0.690329	+	1.19569i	−0.281401	+	0.959590i	$0.590799\pi$
$174$	−3.10411	+	0.852671i	−0.235322	+	0.0646408i
$175$	0.924237	−	6.47113i	0.0698657	−	0.489171i
$176$	−4.02530	−	3.28880i	−0.303418	−	0.247902i
$177$	3.55841	+	11.1686i	0.267467	+	0.839487i
$178$	−13.0234	+	6.83381i	−0.976143	+	0.512215i
$179$		−	8.07215i		−	0.603341i	−0.953412	−	0.301670i	$-0.902456\pi$
$179$		−	8.07215i		−	0.603341i	0.953412	−	0.301670i	$-0.0975442\pi$
$180$	13.3936	+	0.782723i	0.998297	+	0.0583407i
$181$		−	17.2216i		−	1.28007i	−0.768345	−	0.640035i	$-0.778920\pi$
$181$		−	17.2216i		−	1.28007i	0.768345	−	0.640035i	$-0.221080\pi$
$182$	1.87214	+	3.56778i	0.138772	+	0.264461i
$183$	16.2918	+	3.56045i	1.20432	+	0.263196i
$184$	3.19340	−	4.24743i	0.235421	−	0.313124i
$185$	15.4465	−	7.51239i	1.13565	−	0.552322i
$186$	5.88645	−	5.96084i	0.431615	−	0.437070i
$187$	3.08501	+	5.34340i	0.225599	+	0.390748i
$188$	−0.877953	+	10.8528i	−0.0640313	+	0.791522i
$189$	0.825913	−	6.74284i	0.0600763	−	0.490470i
$190$	14.2197	+	10.4747i	1.03160	+	0.759913i
$191$	−4.67446	−	8.09640i	−0.338232	−	0.585835i	0.645868	−	0.763449i	$-0.276496\pi$
$191$	−4.67446	−	8.09640i	−0.338232	−	0.585835i	−0.984100	+	0.177614i	$0.943162\pi$
$192$	7.70774	+	11.5148i	0.556258	+	0.831010i
$193$	−13.1979	−	7.61983i	−0.950008	−	0.548487i	−0.0569247	−	0.998378i	$-0.518130\pi$
$193$	−13.1979	−	7.61983i	−0.950008	−	0.548487i	−0.893083	+	0.449891i	$0.851463\pi$
$194$	−5.88202	+	9.29995i	−0.422304	+	0.667698i
$195$	−6.11126	+	5.82133i	−0.437637	+	0.416874i
$196$	4.53467	+	9.56073i	0.323905	+	0.682909i
$197$	−24.7272			−1.76174			−0.880869	−	0.473359i	$-0.843041\pi$
$197$	−24.7272			−1.76174			−0.880869	+	0.473359i	$0.843041\pi$
$198$	−4.91380	−	2.50024i	−0.349208	−	0.177685i
$199$	11.0610			0.784093			0.392047	−	0.919945i	$-0.371767\pi$
$199$	11.0610			0.784093			0.392047	+	0.919945i	$0.371767\pi$
$200$	9.98852	+	10.0115i	0.706295	+	0.707917i
$201$	13.3371	−	4.24929i	0.940725	−	0.299722i
$202$	11.6639	−	18.4416i	0.820671	−	1.29755i
$203$	−0.859058	+	1.48793i	−0.0602940	+	0.104432i
$204$	−3.71313	−	16.0230i	−0.259971	−	1.12183i
$205$	1.56548	−	22.0329i	0.109338	−	1.53885i
$206$	−27.7497	−	1.12059i	−1.93341	−	0.0780755i
$207$	2.35126	−	5.12248i	0.163424	−	0.356037i
$208$	−8.60355	−	1.40116i	−0.596549	−	0.0971532i
$209$	−3.62883	−	6.28531i	−0.251011	−	0.434764i
$210$	5.37994	−	4.72566i	0.371251	−	0.326102i
$211$	−6.75468	−	3.89982i	−0.465011	−	0.268474i	0.249138	−	0.968468i	$-0.419853\pi$
$211$	−6.75468	−	3.89982i	−0.465011	−	0.268474i	−0.714149	+	0.699994i	$0.753186\pi$
$212$	1.89690	−	2.74716i	0.130280	−	0.188676i
$213$	−3.24545	−	2.95600i	−0.222374	−	0.202542i
$214$	13.0070	−	6.82520i	0.889139	−	0.466561i
$215$	−15.2216	−	10.2919i	−1.03810	−	0.701901i
$216$	10.5862	+	10.1947i	0.720301	+	0.693662i
$217$		−	4.47128i		−	0.303530i
$218$	−3.45158	−	6.57777i	−0.233770	−	0.445503i
$219$	−17.0978	+	18.7719i	−1.15536	+	1.26849i
$220$	−2.11208	−	5.41416i	−0.142396	−	0.365023i
$221$	8.96074	+	5.17348i	0.602764	+	0.348006i
$222$	18.2050	+	4.75569i	1.22184	+	0.319181i
$223$	−15.5471	+	8.97613i	−1.04111	+	0.601086i	−0.920148	−	0.391571i	$-0.871932\pi$
$223$	−15.5471	+	8.97613i	−1.04111	+	0.601086i	−0.120964	+	0.992657i	$0.538599\pi$
$224$	7.24546	+	1.48232i	0.484108	+	0.0990419i
$225$	12.6108	+	8.12205i	0.840720	+	0.541470i
$226$	0.676794	+	0.0273305i	0.0450197	+	0.00181800i
$227$	−1.12423	−	1.94723i	−0.0746179	−	0.129242i	0.826302	−	0.563227i	$-0.190440\pi$
$227$	−1.12423	−	1.94723i	−0.0746179	−	0.129242i	−0.900920	+	0.433985i	$0.857107\pi$
$228$	4.36766	+	18.8474i	0.289255	+	1.24820i
$229$	1.83516	+	1.05953i	0.121271	+	0.0700158i	0.559408	−	0.828892i	$-0.311028\pi$
$229$	1.83516	+	1.05953i	0.121271	+	0.0700158i	−0.438137	+	0.898908i	$0.644362\pi$
$230$	5.44334	−	2.38078i	0.358923	−	0.156984i
$231$	−2.80374	+	0.893291i	−0.184472	+	0.0587743i
$232$	−1.45612	−	3.42001i	−0.0955988	−	0.224535i
$233$		−	14.0086i		−	0.917733i	−0.888505	−	0.458867i	$-0.848256\pi$
$233$		−	14.0086i		−	0.917733i	0.888505	−	0.458867i	$-0.151744\pi$
$234$	−9.23273	+	0.489044i	−0.603562	+	0.0319698i
$235$	−6.81859	+	10.0846i	−0.444796	+	0.657847i
$236$	−12.2293	+	5.80039i	−0.796062	+	0.377573i
$237$	4.78349	−	21.8881i	0.310721	−	1.42179i
$238$	−7.41912	−	4.69243i	−0.480910	−	0.304165i
$239$	−10.6567	+	18.4580i	−0.689327	+	1.19395i	0.282728	+	0.959200i	$0.408761\pi$
$239$	−10.6567	+	18.4580i	−0.689327	+	1.19395i	−0.972056	+	0.234750i	$0.924573\pi$
$240$	1.17726	+	15.4471i	0.0759918	+	0.997108i
$241$	−6.48483	−	11.2321i	−0.417725	−	0.723521i	0.577985	−	0.816047i	$-0.303839\pi$
$241$	−6.48483	−	11.2321i	−0.417725	−	0.723521i	−0.995710	+	0.0925265i	$0.970506\pi$
$242$	0.531327	−	13.1574i	0.0341550	−	0.845792i
$243$	13.2716	+	8.17710i	0.851373	+	0.524561i
$244$	−1.55268	+	19.1934i	−0.0994002	+	1.22873i
$245$	−0.838473	+	11.8009i	−0.0535681	+	0.753930i
$246$	17.0019	−	17.2168i	1.08400	−	1.09770i
$247$	−10.5403	−	6.08544i	−0.670663	−	0.387207i
$248$	7.73192	+	5.81320i	0.490978	+	0.369138i
$249$	1.42144	−	6.50416i	0.0900798	−	0.412184i
$250$	4.22411	+	15.2367i	0.267156	+	0.963653i
$251$			27.5109i			1.73647i	0.496149	+	0.868237i	$0.334747\pi$
$251$			27.5109i			1.73647i	−0.496149	+	0.868237i	$0.665253\pi$
$252$	7.84353	−	0.0985102i	0.494096	−	0.00620556i
$253$	−2.44147			−0.153494
$254$	−9.17851	−	17.4917i	−0.575911	−	1.09753i
$255$	5.18946	−	17.6415i	0.324977	−	1.10475i
$256$	−11.9833	+	10.6020i	−0.748954	+	0.662623i
$257$	17.4308	+	10.0637i	1.08730	+	0.627755i	0.932857	−	0.360246i	$-0.117307\pi$
$257$	17.4308	+	10.0637i	1.08730	+	0.627755i	0.154447	+	0.988001i	$0.450641\pi$
$258$	−5.33154	−	19.4092i	−0.331927	−	1.20837i
$259$	8.69711	−	5.02128i	0.540412	−	0.312007i
$260$	−7.60707	−	6.09204i	−0.471771	−	0.377812i
$261$	−2.28074	−	3.21590i	−0.141174	−	0.199060i
$262$	−13.6423	−	0.550907i	−0.842824	−	0.0340352i
$263$	−6.29499	+	3.63441i	−0.388165	+	0.224107i	−0.681365	−	0.731944i	$-0.738613\pi$
$263$	−6.29499	+	3.63441i	−0.388165	+	0.224107i	0.293200	+	0.956051i	$0.405280\pi$
$264$	2.10048	−	6.00973i	0.129275	−	0.369873i
$265$	3.35656	−	1.63245i	0.206192	−	0.100281i
$266$	8.72693	+	5.51959i	0.535082	+	0.338428i
$267$	−13.3170	−	12.1293i	−0.814988	−	0.742304i
$268$	6.92656	+	14.6037i	0.423107	+	0.892064i
$269$		−	20.0503i		−	1.22249i	−0.791443	−	0.611243i	$-0.790670\pi$
$269$		−	20.0503i		−	1.22249i	0.791443	−	0.611243i	$-0.209330\pi$
$270$	4.70537	+	15.7436i	0.286360	+	0.958122i
$271$	2.71014			0.164629			0.0823145	−	0.996606i	$-0.473769\pi$
$271$	2.71014			0.164629			0.0823145	+	0.996606i	$0.473769\pi$
$272$	17.7601	−	6.72873i	1.07686	−	0.407989i
$273$	−3.32286	+	3.64822i	−0.201108	+	0.220800i
$274$	−3.47984	+	5.50191i	−0.210225	+	0.332382i
$275$	0.918681	−	6.43223i	0.0553985	−	0.387878i
$276$	6.22546	+	1.89770i	0.374729	+	0.114228i
$277$	6.00627	+	10.4032i	0.360882	+	0.625066i	0.988106	−	0.153773i	$-0.0491424\pi$
$277$	6.00627	+	10.4032i	0.360882	+	0.625066i	−0.627224	+	0.778839i	$0.715809\pi$
$278$	−17.7974	−	0.718700i	−1.06742	−	0.0431047i
$279$	9.32486	+	4.28018i	0.558265	+	0.256248i
$280$	6.24014	+	5.42477i	0.372920	+	0.324192i
$281$	−2.63275	−	4.56005i	−0.157056	−	0.272030i	0.776750	−	0.629810i	$-0.216867\pi$
$281$	−2.63275	−	4.56005i	−0.157056	−	0.272030i	−0.933806	+	0.357780i	$0.883534\pi$
$282$	−12.8590	+	3.53225i	−0.765743	+	0.210343i
$283$	−1.31473	+	2.27718i	−0.0781527	+	0.135364i	−0.902453	−	0.430788i	$-0.858236\pi$
$283$	−1.31473	+	2.27718i	−0.0781527	+	0.135364i	0.824300	+	0.566153i	$0.191569\pi$
$284$	2.88020	−	4.17120i	0.170909	−	0.247515i
$285$	−6.10423	+	20.7513i	−0.361584	+	1.22920i
$286$	1.86088	+	3.54633i	0.110036	+	0.209699i
$287$		−	12.9144i		−	0.762315i
$288$	−10.0272	+	13.6914i	−0.590857	+	0.806776i
$289$	−5.54352			−0.326090
$290$	0.461560	−	4.13012i	0.0271038	−	0.242529i
$291$	−13.1663	−	2.87740i	−0.771822	−	0.168676i
$292$	−24.1266	−	16.6593i	−1.41190	−	0.974913i
$293$	7.27501	−	12.6007i	0.425011	−	0.736140i	−0.571411	−	0.820664i	$-0.693604\pi$
$293$	7.27501	−	12.6007i	0.425011	−	0.736140i	0.996421	+	0.0845239i	$0.0269369\pi$
$294$	−9.10623	+	9.22132i	−0.531086	+	0.537798i
$295$	−15.0947	−	1.07251i	−0.878850	−	0.0624439i
$296$	−2.62427	+	21.5677i	−0.152533	+	1.25359i
$297$	0.820948	−	6.70231i	0.0476363	−	0.388908i
$298$	−24.5511	−	0.991431i	−1.42221	−	0.0574320i
$299$	−3.54575	+	2.04714i	−0.205056	+	0.118389i
$300$	−7.34214	+	15.6874i	−0.423899	+	0.905710i
$301$	−9.30367	−	5.37148i	−0.536254	−	0.309607i
$302$	−12.5942	−	7.96559i	−0.724717	−	0.458368i
$303$	26.1085	+	5.70582i	1.49989	+	0.327791i
$304$	−20.8908	+	7.91484i	−1.19817	+	0.453947i
$305$	−12.0588	+	17.8349i	−0.690488	+	1.02122i
$306$	16.8881	−	10.9807i	0.965428	−	0.627724i
$307$	23.7833			1.35738			0.678691	−	0.734424i	$-0.262547\pi$
$307$	23.7833			1.35738			0.678691	+	0.734424i	$0.262547\pi$
$308$	−1.45611	−	3.07001i	−0.0829696	−	0.174930i
$309$	−10.3257	−	32.4088i	−0.587407	−	1.84367i
$310$	4.33392	+	9.90893i	0.246150	+	0.562790i
$311$	−9.10950	+	15.7781i	−0.516553	+	0.894695i	0.483263	+	0.875475i	$0.339452\pi$
$311$	−9.10950	+	15.7781i	−0.516553	+	0.894695i	−0.999815	+	0.0192198i	$0.993882\pi$
$312$	−1.98855	−	10.4891i	−0.112579	−	0.593831i
$313$	−8.34962	+	4.82065i	−0.471948	+	0.272479i	−0.717055	−	0.697017i	$-0.754510\pi$
$313$	−8.34962	+	4.82065i	−0.471948	+	0.272479i	0.245107	+	0.969496i	$0.421177\pi$
$314$	0.834044	−	20.6537i	0.0470678	−	1.16556i
$315$	7.69115	+	4.21421i	0.433347	+	0.237444i
$316$	25.7865	+	2.08604i	1.45061	+	0.117349i
$317$	−8.21914	−	14.2360i	−0.461633	−	0.799571i	0.537410	−	0.843321i	$-0.319403\pi$
$317$	−8.21914	−	14.2360i	−0.461633	−	0.799571i	−0.999043	+	0.0437499i	$0.986070\pi$
$318$	3.95597	+	1.03342i	0.221840	+	0.0579513i
$319$	−0.853894	+	1.47899i	−0.0478089	+	0.0828074i
$320$	−17.4937	+	3.73786i	−0.977926	+	0.208953i
$321$	13.3003	+	12.1141i	0.742348	+	0.676142i
$322$	3.07589	−	1.61403i	0.171413	−	0.0899461i
$323$	26.5174			1.47547
$324$	−7.30286	+	16.4520i	−0.405715	+	0.914000i
$325$	−4.05913	−	10.1118i	−0.225160	−	0.560903i
$326$	−17.2077	+	9.02945i	−0.953045	+	0.500095i
$327$	6.12622	−	6.72608i	0.338781	−	0.371953i
$328$	22.3322	+	16.7903i	1.23309	+	0.927090i
$329$	−3.55871	+	6.16387i	−0.196198	+	0.339825i
$330$	5.34760	−	4.69726i	0.294376	−	0.258576i
$331$	−26.5877	+	15.3504i	−1.46139	+	0.843734i	−0.999076	−	0.0429819i	$-0.986314\pi$
$331$	−26.5877	+	15.3504i	−1.46139	+	0.843734i	−0.462315	+	0.886716i	$0.652981\pi$
$332$	7.66258	+	0.619876i	0.420539	+	0.0340201i
$333$	2.14648	+	22.9445i	0.117626	+	1.25735i
$334$	25.3411	+	1.02333i	1.38661	+	0.0559943i
$335$	−1.28074	+	18.0254i	−0.0699744	+	0.984835i
$336$	1.32666	+	8.95996i	0.0723755	+	0.488806i
$337$	−4.15837	−	2.40084i	−0.226521	−	0.130782i	0.382445	−	0.923978i	$-0.375082\pi$
$337$	−4.15837	−	2.40084i	−0.226521	−	0.130782i	−0.608966	+	0.793196i	$0.708415\pi$
$338$	−9.86170	−	6.23731i	−0.536406	−	0.339265i
$339$	0.251836	+	0.790427i	0.0136778	+	0.0429301i
$340$	20.9900	+	3.20783i	1.13834	+	0.173969i
$341$		−	4.44440i		−	0.240678i
$342$	−19.8651	+	12.9163i	−1.07418	+	0.698435i
$343$			16.0685i			0.867618i
$344$	21.3845	−	9.10474i	1.15297	−	0.490895i
$345$	5.01875	+	5.26871i	0.270200	+	0.283658i
$346$	−21.7048	−	13.7278i	−1.16686	−	0.738012i
$347$	−11.0199	+	19.0870i	−0.591578	+	1.02464i	0.402442	+	0.915446i	$0.368162\pi$
$347$	−11.0199	+	19.0870i	−0.591578	+	1.02464i	−0.994020	+	0.109198i	$0.965172\pi$
$348$	3.32691	−	3.10753i	0.178341	−	0.166581i
$349$	−22.3432	+	12.8998i	−1.19600	+	0.690512i	−0.959661	−	0.281158i	$-0.909281\pi$
$349$	−22.3432	+	12.8998i	−1.19600	+	0.690512i	−0.236340	+	0.971670i	$0.575948\pi$
$350$	3.09486	+	8.71098i	0.165427	+	0.465622i
$351$	−4.42753	−	10.4221i	−0.236324	−	0.556292i
$352$	7.20191	+	1.47341i	0.383863	+	0.0785331i
$353$	−0.0526051	+	0.0303716i	−0.00279989	+	0.00161652i	−0.501399	−	0.865216i	$-0.667181\pi$
$353$	−0.0526051	+	0.0303716i	−0.00279989	+	0.00161652i	0.498599	+	0.866833i	$0.333848\pi$
$354$	−11.7952	−	11.6480i	−0.626907	−	0.619083i
$355$	5.09650	−	2.47867i	0.270494	−	0.131554i
$356$	11.8183	−	17.1157i	0.626369	−	0.907128i
$357$	2.29547	−	10.5035i	0.121489	−	0.555906i
$358$	5.30432	+	10.1086i	0.280342	+	0.534255i
$359$	1.84501			0.0973760			0.0486880	−	0.998814i	$-0.484496\pi$
$359$	1.84501			0.0973760			0.0486880	+	0.998814i	$0.484496\pi$
$360$	−17.2868	+	7.82090i	−0.911095	+	0.412197i
$361$	−12.1918			−0.641672
$362$	11.3165	+	21.5662i	0.594784	+	1.13350i
$363$	15.3666	−	4.89590i	0.806535	−	0.256968i
$364$	−4.68887	−	3.23765i	−0.245764	−	0.169699i
$365$	−14.3368	−	29.4786i	−0.750424	−	1.54298i
$366$	−22.7415	+	6.24688i	−1.18872	+	0.326530i
$367$	11.4440	−	6.60720i	0.597372	−	0.344893i	−0.170635	−	0.985334i	$-0.554582\pi$
$367$	11.4440	−	6.60720i	0.597372	−	0.344893i	0.768007	+	0.640441i	$0.221249\pi$
$368$	−1.20799	+	7.41739i	−0.0629706	+	0.386658i
$369$	26.9331	+	12.3625i	1.40208	+	0.643565i
$370$	−14.4069	+	19.5577i	−0.748979	+	1.01676i
$371$	1.88990	−	1.09113i	0.0981185	−	0.0566487i
$372$	−3.45453	+	11.3327i	−0.179109	+	0.587573i
$373$	0.587436	−	1.01747i	0.0304163	−	0.0526825i	−0.850417	−	0.526110i	$-0.823650\pi$
$373$	0.587436	−	1.01747i	0.0304163	−	0.0526825i	0.880833	+	0.473427i	$0.156983\pi$
$374$	−7.37452	−	4.66423i	−0.381327	−	0.241181i
$375$	−15.7692	+	11.2397i	−0.814320	+	0.580416i
$376$	−6.03208	−	14.1676i	−0.311081	−	0.730640i
$377$			2.86391i			0.147499i
$378$	3.39654	+	8.98664i	0.174699	+	0.462223i
$379$		−	3.73649i		−	0.191930i	−0.995385	−	0.0959652i	$-0.969406\pi$
$379$		−	3.73649i		−	0.191930i	0.995385	−	0.0959652i	$-0.0305937\pi$
$380$	−24.6900	−	3.77330i	−1.26657	−	0.193566i
$381$	16.2910	−	17.8861i	0.834611	−	0.916334i
$382$	11.1740	+	7.06730i	0.571711	+	0.361595i
$383$	23.5310	+	13.5856i	1.20238	+	0.694193i	0.961083	−	0.276259i	$-0.0890948\pi$
$383$	23.5310	+	13.5856i	1.20238	+	0.694193i	0.241294	+	0.970452i	$0.422428\pi$
$384$	−17.2188	−	9.35490i	−0.878692	−	0.477390i
$385$	0.269239	−	3.78933i	0.0137217	−	0.193122i
$386$	21.5346	+	0.869615i	1.09608	+	0.0442623i
$387$	20.1083	−	14.2609i	1.02216	−	0.724922i
$388$	1.25481	−	15.5113i	0.0637032	−	0.787466i
$389$	5.93814	−	3.42839i	0.301076	−	0.173826i	−0.341850	−	0.939754i	$-0.611054\pi$
$389$	5.93814	−	3.42839i	0.301076	−	0.173826i	0.642926	+	0.765928i	$0.277720\pi$
$390$	3.82773	−	11.3057i	0.193825	−	0.572487i
$391$	4.46022	−	7.72533i	0.225563	−	0.390687i
$392$	−11.9612	−	8.99291i	−0.604129	−	0.454211i
$393$	−5.07632	−	15.9328i	−0.256066	−	0.803705i
$394$	30.9653	−	16.2486i	1.56001	−	0.818591i
$395$	23.9613	+	16.2011i	1.20562	+	0.815168i
$396$	7.79639	−	0.0979181i	0.391783	−	0.00492057i
$397$	16.2588			0.816004			0.408002	−	0.912981i	$-0.366226\pi$
$397$	16.2588			0.816004			0.408002	+	0.912981i	$0.366226\pi$
$398$	−13.8514	+	7.26833i	−0.694310	+	0.364328i
$399$	−2.70010	+	12.3550i	−0.135174	+	0.618526i
$400$	−19.0871	−	5.97355i	−0.954354	−	0.298677i
$401$	−8.07734	+	13.9904i	−0.403363	+	0.698646i	−0.994129	−	0.108197i	$-0.965492\pi$
$401$	−8.07734	+	13.9904i	−0.403363	+	0.698646i	0.590766	+	0.806843i	$0.298826\pi$
$402$	−13.9095	+	14.0853i	−0.693742	+	0.702509i
$403$	−3.72657	−	6.45461i	−0.185634	−	0.321527i
$404$	−2.48826	+	30.7586i	−0.123796	+	1.53030i
$405$	−16.1512	+	12.0058i	−0.802558	+	0.596574i
$406$	0.0980402	−	2.42780i	0.00486565	−	0.120490i
$407$	8.64483	−	4.99109i	0.428508	−	0.247399i
$408$	15.1788	+	17.6253i	0.751461	+	0.872580i
$409$	−0.502385	+	0.870157i	−0.0248414	+	0.0430265i	−0.878179	−	0.478332i	$-0.841241\pi$
$409$	−0.502385	+	0.870157i	−0.0248414	+	0.0430265i	0.853337	+	0.521359i	$0.174575\pi$
$410$	12.5177	+	28.6201i	0.618206	+	1.41344i
$411$	−7.78926	−	1.70228i	−0.384216	−	0.0839675i
$412$	35.4867	−	16.8314i	1.74830	−	0.829223i
$413$	−8.84767			−0.435365
$414$	0.421620	+	7.95982i	0.0207215	+	0.391204i
$415$	7.12021	+	4.81425i	0.349517	+	0.236322i
$416$	11.6948	−	3.89886i	0.573383	−	0.191157i
$417$	−6.62243	−	20.7856i	−0.324302	−	1.01787i
$418$	8.67447	+	5.48642i	0.424282	+	0.268349i
$419$	−30.9697	−	17.8804i	−1.51297	−	0.873514i	−0.999885	−	0.0151767i	$-0.995169\pi$
$419$	−30.9697	−	17.8804i	−1.51297	−	0.873514i	−0.513086	−	0.858337i	$-0.671498\pi$
$420$	−3.63188	+	9.45308i	−0.177218	+	0.461263i
$421$	18.9979	−	10.9684i	0.925900	−	0.534568i	0.0403871	−	0.999184i	$-0.487141\pi$
$421$	18.9979	−	10.9684i	0.925900	−	0.534568i	0.885512	+	0.464616i	$0.153808\pi$
$422$	11.0214	+	0.445067i	0.536511	+	0.0216655i
$423$	−9.44814	−	13.3221i	−0.459384	−	0.647744i
$424$	−0.570258	+	4.68669i	−0.0276942	+	0.227606i
$425$	18.6746	+	14.6577i	0.905852	+	0.711001i
$426$	6.00663	+	1.56911i	0.291022	+	0.0760238i
$427$	−6.29367	+	10.9010i	−0.304572	+	0.527534i
$428$	−11.8034	+	17.0941i	−0.570541	+	0.826275i
$429$	−3.30288	+	3.62629i	−0.159465	+	0.175079i
$430$	25.8246	+	2.88602i	1.24537	+	0.139176i
$431$	11.7024			0.563684			0.281842	−	0.959461i	$-0.409055\pi$
$431$	11.7024			0.563684			0.281842	+	0.959461i	$0.409055\pi$
$432$	−19.9560	−	5.81026i	−0.960132	−	0.279546i
$433$		−	18.5776i		−	0.892781i	−0.894838	−	0.446391i	$-0.852709\pi$
$433$		−	18.5776i		−	0.892781i	0.894838	−	0.446391i	$-0.147291\pi$
$434$	2.93814	+	5.59929i	0.141035	+	0.268774i
$435$	4.94695	−	1.19753i	0.237188	−	0.0574174i
$436$	8.64468	+	5.96912i	0.414005	+	0.285869i
$437$	−5.24645	+	9.08711i	−0.250972	+	0.434696i
$438$	9.07588	−	34.7429i	0.433663	−	1.66008i
$439$	−14.4599	−	25.0453i	−0.690135	−	1.19535i	−0.971793	−	0.235834i	$-0.924218\pi$
$439$	−14.4599	−	25.0453i	−0.690135	−	1.19535i	0.281658	−	0.959515i	$-0.409116\pi$
$440$	6.20263	+	5.39216i	0.295699	+	0.257061i
$441$	−14.4254	−	6.62136i	−0.686923	−	0.315303i
$442$	−14.6209	−	0.590425i	−0.695446	−	0.0280837i
$443$	−8.60211	−	14.8993i	−0.408699	−	0.707887i	0.586046	−	0.810278i	$-0.300684\pi$
$443$	−8.60211	−	14.8993i	−0.408699	−	0.707887i	−0.994744	+	0.102391i	$0.967351\pi$
$444$	−25.9227	+	6.00728i	−1.23024	+	0.285093i
$445$	20.9124	−	10.1707i	0.991344	−	0.482138i
$446$	13.5710	−	21.4568i	0.642605	−	1.01601i
$447$	−9.13550	−	28.6732i	−0.432095	−	1.35620i
$448$	−10.0474	+	2.90481i	−0.474695	+	0.137239i
$449$	−12.6078			−0.595001			−0.297500	−	0.954722i	$-0.596153\pi$
$449$	−12.6078			−0.595001			−0.297500	+	0.954722i	$0.596153\pi$
$450$	−21.1293	−	1.88435i	−0.996047	−	0.0888289i
$451$		−	12.8368i		−	0.604462i
$452$	−0.865494	+	0.410505i	−0.0407094	+	0.0193085i
$453$	3.89665	−	17.8302i	0.183080	−	0.837734i
$454$	2.68740	+	1.69972i	0.126126	+	0.0797719i
$455$	−2.78629	−	5.72900i	−0.130623	−	0.268580i
$456$	−17.8544	−	20.7322i	−0.836109	−	0.970872i
$457$	−3.27554	+	1.89113i	−0.153223	+	0.0884635i	−0.574651	−	0.818398i	$-0.694862\pi$
$457$	−3.27554	+	1.89113i	−0.153223	+	0.0884635i	0.421428	+	0.906862i	$0.361529\pi$
$458$	−2.99437	−	0.120919i	−0.139918	−	0.00565019i
$459$	19.7078	+	14.8418i	0.919879	+	0.692757i
$460$	−5.25213	+	6.55829i	−0.244882	+	0.305782i
$461$	−0.962364	+	0.555621i	−0.0448217	+	0.0258778i	−0.522243	−	0.852796i	$-0.674905\pi$
$461$	−0.962364	+	0.555621i	−0.0448217	+	0.0258778i	0.477422	+	0.878674i	$0.341571\pi$
$462$	2.92407	−	2.96102i	0.136040	−	0.137759i
$463$	19.6806	+	11.3626i	0.914634	+	0.528064i	0.881919	−	0.471400i	$-0.156251\pi$
$463$	19.6806	+	11.3626i	0.914634	+	0.528064i	0.0327149	+	0.999465i	$0.489585\pi$
$464$	4.07080	+	3.32597i	0.188982	+	0.154404i
$465$	−9.59104	+	9.13602i	−0.444774	+	0.423673i
$466$	9.20523	+	17.5427i	0.426424	+	0.812648i
$467$	−3.30323			−0.152855			−0.0764276	−	0.997075i	$-0.524351\pi$
$467$	−3.30323			−0.152855			−0.0764276	+	0.997075i	$0.524351\pi$
$468$	11.2406	−	6.67937i	0.519597	−	0.308754i
$469$			10.5655i			0.487869i
$470$	1.91205	−	17.1093i	0.0881962	−	0.789194i
$471$	24.1215	−	7.68527i	1.11146	−	0.354119i
$472$	11.5030	−	15.2998i	0.529470	−	0.704229i
$473$	−9.24774	−	5.33919i	−0.425212	−	0.245496i
$474$	8.39272	+	30.5533i	0.385491	+	1.40336i
$475$	−21.9665	−	17.2414i	−1.00789	−	0.791092i
$476$	12.3743	+	1.00103i	0.567173	+	0.0458823i
$477$	0.466433	+	4.98588i	0.0213565	+	0.228288i
$478$	1.21620	−	30.1173i	0.0556279	−	1.37753i
$479$	−2.16563	−	3.75098i	−0.0989502	−	0.171387i	0.812300	−	0.583240i	$-0.198215\pi$
$479$	−2.16563	−	3.75098i	−0.0989502	−	0.171387i	−0.911250	+	0.411853i	$0.864882\pi$
$480$	−11.6248	−	18.5705i	−0.530596	−	0.847625i
$481$	8.36992	−	14.4971i	0.381636	−	0.661012i
$482$	15.5016	+	9.80440i	0.706076	+	0.446578i
$483$	3.14525	+	2.86474i	0.143114	+	0.130350i
$484$	7.98056	+	16.8259i	0.362753	+	0.764815i
$485$	9.74542	−	14.4134i	0.442517	−	0.654477i
$486$	−21.9930	−	1.51907i	−0.997623	−	0.0689065i
$487$		−	2.96062i		−	0.134158i	−0.997748	−	0.0670792i	$-0.978632\pi$
$487$		−	2.96062i		−	0.134158i	0.997748	−	0.0670792i	$-0.0213680\pi$
$488$	−10.6679	−	25.0558i	−0.482912	−	1.13422i
$489$	−17.5957	−	16.0264i	−0.795703	−	0.724739i
$490$	−6.70450	−	15.3289i	−0.302879	−	0.692491i
$491$	−12.6421	−	7.29891i	−0.570529	−	0.329395i	0.186831	−	0.982392i	$-0.440178\pi$
$491$	−12.6421	−	7.29891i	−0.570529	−	0.329395i	−0.757361	+	0.652997i	$0.773512\pi$
$492$	−9.97774	+	32.7324i	−0.449831	+	1.47569i
$493$	−3.11988	−	5.40380i	−0.140513	−	0.243375i
$494$	17.1982	+	0.694503i	0.773784	+	0.0312472i
$495$	7.64492	+	4.18888i	0.343614	+	0.188276i
$496$	−13.5025	−	2.19899i	−0.606278	−	0.0987376i
$497$	2.86956	−	1.65674i	0.128717	−	0.0743150i
$498$	2.49394	+	9.07907i	0.111756	+	0.406843i
$499$	19.8379	+	11.4534i	0.888068	+	0.512726i	0.873310	−	0.487165i	$-0.161969\pi$
$499$	19.8379	+	11.4534i	0.888068	+	0.512726i	0.0147578	+	0.999891i	$0.495302\pi$
$500$	−15.3020	−	16.3049i	−0.684326	−	0.729176i
$501$	9.42946	+	29.5959i	0.421277	+	1.32225i
$502$	−18.0778	−	34.4514i	−0.806851	−	1.53764i
$503$			28.6551i			1.27767i	0.769345	+	0.638833i	$0.220583\pi$
$503$			28.6551i			1.27767i	−0.769345	+	0.638833i	$0.779417\pi$
$504$	−9.75756	+	5.27745i	−0.434636	+	0.235076i
$505$	−19.3250	+	28.5814i	−0.859951	+	1.27186i
$506$	3.05740	−	1.60432i	0.135918	−	0.0713209i
$507$	3.05120	−	13.9616i	0.135509	−	0.620056i
$508$	22.9881	+	15.8732i	1.01993	+	0.704260i
$509$	33.6466	+	19.4259i	1.49136	+	0.861038i	0.999951	−	0.00989035i	$-0.00314825\pi$
$509$	33.6466	+	19.4259i	1.49136	+	0.861038i	0.491410	+	0.870928i	$0.336482\pi$
$510$	5.09381	+	25.5021i	0.225558	+	1.12925i
$511$	−9.58273	−	16.5978i	−0.423915	−	0.734243i
$512$	8.03969	−	21.1510i	0.355307	−	0.934749i
$513$	−23.1818	−	17.4581i	−1.02350	−	0.770792i
$514$	−28.4412	−	1.14852i	−1.25449	−	0.0506591i
$515$	43.8014	+	3.11217i	1.93012	+	0.137139i
$516$	19.4306	+	20.8023i	0.855386	+	0.915772i
$517$	−3.53732	+	6.12682i	−0.155571	+	0.269457i
$518$	−7.59165	+	12.0030i	−0.333558	+	0.527383i
$519$	6.71544	−	30.7283i	0.294775	−	1.34882i
$520$	13.5293	+	2.63022i	0.593301	+	0.115343i
$521$	33.5911			1.47165			0.735826	−	0.677171i	$-0.236794\pi$
$521$	33.5911			1.47165			0.735826	+	0.677171i	$0.236794\pi$
$522$	4.96934	+	2.52850i	0.217502	+	0.110670i
$523$	−31.5892			−1.38130			−0.690650	−	0.723189i	$-0.742676\pi$
$523$	−31.5892			−1.38130			−0.690650	+	0.723189i	$0.742676\pi$
$524$	17.4460	−	8.27465i	0.762131	−	0.361480i
$525$	−8.73085	+	7.20842i	−0.381045	+	0.314601i
$526$	5.49486	−	8.68781i	0.239587	−	0.378807i
$527$	14.0630	+	8.11929i	0.612595	+	0.353682i
$528$	1.31869	+	8.90610i	0.0573886	+	0.387588i
$529$	−9.73510	−	16.8617i	−0.423265	−	0.733117i
$530$	−3.13064	+	4.24993i	−0.135986	+	0.184605i
$531$	8.46953	−	18.4518i	0.367546	−	0.800741i
$532$	−14.5555	−	1.17749i	−0.631063	−	0.0510507i
$533$	−10.7635	−	18.6429i	−0.466218	−	0.807514i
$534$	24.6470	+	6.43853i	1.06658	+	0.278622i
$535$	−20.8861	+	10.1579i	−0.902985	+	0.439165i
$536$	−18.2703	−	13.7364i	−0.789156	−	0.593321i
$537$	−9.41464	+	10.3365i	−0.406272	+	0.446053i
$538$	13.1753	+	25.1085i	0.568027	+	1.08251i
$539$			6.87541i			0.296145i
$540$	−16.2377	−	16.6234i	−0.698761	−	0.715355i
$541$			5.71420i			0.245673i	0.992427	+	0.122836i	$0.0391990\pi$
$541$			5.71420i			0.245673i	−0.992427	+	0.122836i	$0.960801\pi$
$542$	−3.39384	+	1.78087i	−0.145778	+	0.0764947i
$543$	−20.0857	+	22.0525i	−0.861962	+	0.946363i
$544$	−17.8190	+	20.0966i	−0.763985	+	0.861636i
$545$	5.13696	+	10.5623i	0.220043	+	0.452440i
$546$	1.76385	−	6.75209i	0.0754858	−	0.288963i
$547$	11.0398	+	19.1216i	0.472029	+	0.817579i	0.999488	−	0.0320021i	$-0.0101883\pi$
$547$	11.0398	+	19.1216i	0.472029	+	0.817579i	−0.527458	+	0.849581i	$0.676855\pi$
$548$	0.742352	−	9.17657i	0.0317117	−	0.392004i
$549$	−16.7093	−	23.5605i	−0.713134	−	1.00554i
$550$	3.07626	+	8.65862i	0.131172	+	0.369205i
$551$	3.66984	+	6.35636i	0.156341	+	0.270790i
$552$	−9.04302	+	1.71439i	−0.384896	+	0.0729693i
$553$	14.6455	+	8.45559i	0.622791	+	0.359568i
$554$	−14.3576	−	9.08086i	−0.609995	−	0.385809i
$555$	−28.5413	−	8.39577i	−1.21151	−	0.356381i
$556$	22.7596	−	10.7949i	0.965221	−	0.457806i
$557$	−11.8720			−0.503034			−0.251517	−	0.967853i	$-0.580929\pi$
$557$	−11.8720			−0.503034			−0.251517	+	0.967853i	$0.580929\pi$
$558$	−14.4899	+	0.767508i	−0.613406	+	0.0324912i
$559$	−17.9073			−0.757400
$560$	−11.3791	−	2.69285i	−0.480854	−	0.113794i
$561$	2.28167	−	10.4404i	0.0963322	−	0.440794i
$562$	6.29340	+	3.98044i	0.265471	+	0.167905i
$563$	−3.22361	+	5.58346i	−0.135859	+	0.235315i	−0.925925	−	0.377707i	$-0.876713\pi$
$563$	−3.22361	+	5.58346i	−0.135859	+	0.235315i	0.790066	+	0.613021i	$0.210046\pi$
$564$	13.7820	−	12.8732i	0.580326	−	0.542059i
$565$	−1.06828	−	0.0759036i	−0.0449431	−	0.00319329i
$566$	0.150044	−	3.71560i	0.00630683	−	0.156178i
$567$	−8.92185	+	7.67103i	−0.374683	+	0.322153i
$568$	−0.865863	+	7.11613i	−0.0363308	+	0.298586i
$569$	6.39879	+	11.0830i	0.268251	+	0.464625i	0.968410	−	0.249362i	$-0.0802209\pi$
$569$	6.39879	+	11.0830i	0.268251	+	0.464625i	−0.700159	+	0.713987i	$0.746888\pi$
$570$	−5.99173	−	29.9975i	−0.250966	−	1.25646i
$571$	−16.4227	−	9.48165i	−0.687269	−	0.396795i	0.115319	−	0.993328i	$-0.463211\pi$
$571$	−16.4227	−	9.48165i	−0.687269	−	0.396795i	−0.802588	+	0.596534i	$0.796544\pi$
$572$	−4.66069	−	3.21819i	−0.194873	−	0.134559i
$573$	−3.45722	+	15.8194i	−0.144427	+	0.660866i
$574$	8.48625	+	16.1725i	0.354209	+	0.675026i
$575$	−8.71772	+	3.49950i	−0.363554	+	0.145939i
$576$	3.56000	−	23.7345i	0.148333	−	0.988937i
$577$		−	10.1998i		−	0.424624i	−0.977202	−	0.212312i	$-0.931901\pi$
$577$		−	10.1998i		−	0.424624i	0.977202	−	0.212312i	$-0.0680994\pi$
$578$	6.94204	−	3.64272i	0.288751	−	0.151517i
$579$	8.01304	+	25.1502i	0.333011	+	1.04521i
$580$	2.13595	+	5.47536i	0.0886906	+	0.227352i
$581$	4.35198	+	2.51262i	0.180551	+	0.104241i
$582$	18.3787	−	5.04845i	0.761820	−	0.209265i
$583$	1.87854	−	1.08457i	0.0778010	−	0.0449184i
$584$	41.1603	+	5.00823i	1.70322	+	0.207242i
$585$	14.6150	−	0.326653i	0.604258	−	0.0135055i
$586$	−0.830263	+	20.5601i	−0.0342978	+	0.849329i
$587$	−21.5066	−	37.2505i	−0.887671	−	1.53749i	−0.842621	−	0.538507i	$-0.818989\pi$
$587$	−21.5066	−	37.2505i	−0.887671	−	1.53749i	−0.0450502	−	0.998985i	$-0.514345\pi$
$588$	5.34409	−	17.5315i	0.220387	−	0.722986i
$589$	−16.5420	−	9.55052i	−0.681601	−	0.393522i
$590$	19.6076	−	8.57588i	0.807232	−	0.353063i
$591$	31.6635	+	28.8396i	1.30246	+	1.18630i
$592$	−10.8861	−	28.7332i	−0.447415	−	1.18093i
$593$			14.6922i			0.603335i	0.953413	+	0.301667i	$0.0975432\pi$
$593$			14.6922i			0.603335i	−0.953413	+	0.301667i	$0.902457\pi$
$594$	3.37612	+	8.93262i	0.138524	+	0.366510i
$595$	11.4984	+	7.77450i	0.471388	+	0.318723i
$596$	31.3964	−	14.8913i	1.28604	−	0.609973i
$597$	−14.1638	−	12.9006i	−0.579684	−	0.527985i
$598$	3.09507	−	4.89355i	0.126567	−	0.200112i
$599$	11.9688	−	20.7306i	0.489034	−	0.847031i	−0.510887	−	0.859648i	$-0.670683\pi$
$599$	11.9688	−	20.7306i	0.489034	−	0.847031i	0.999920	+	0.0126170i	$0.00401623\pi$
$600$	−1.11396	−	24.4696i	−0.0454772	−	0.998965i
$601$	4.45287	+	7.71260i	0.181636	+	0.314603i	0.942438	−	0.334381i	$-0.108527\pi$
$601$	4.45287	+	7.71260i	0.181636	+	0.314603i	−0.760802	+	0.648985i	$0.775194\pi$
$602$	15.1805	+	0.613021i	0.618709	+	0.0249849i
$603$	−22.0343	−	10.1139i	−0.897307	−	0.411871i
$604$	21.0058	+	1.69929i	0.854714	+	0.0691433i
$605$	−1.47563	+	20.7683i	−0.0599928	+	0.844353i
$606$	−36.4445	+	10.0110i	−1.48046	+	0.406668i
$607$	−20.8881	−	12.0597i	−0.847821	−	0.489490i	0.0120937	−	0.999927i	$-0.496150\pi$
$607$	−20.8881	−	12.0597i	−0.847821	−	0.489490i	−0.859915	+	0.510437i	$0.829484\pi$
$608$	20.9601	−	23.6392i	0.850045	−	0.958695i
$609$	2.83543	−	0.903388i	0.114897	−	0.0366071i
$610$	3.38151	−	30.2583i	0.136913	−	1.22512i
$611$			11.8640i			0.479965i
$612$	−13.9330	+	24.8483i	−0.563210	+	1.00443i
$613$	−0.542323			−0.0219042			−0.0109521	−	0.999940i	$-0.503486\pi$
$613$	−0.542323			−0.0219042			−0.0109521	+	0.999940i	$0.503486\pi$
$614$	−29.7833	+	15.6283i	−1.20196	+	0.630707i
$615$	−27.7019	+	26.3876i	−1.11705	+	1.06405i
$616$	3.84080	+	2.88768i	0.154750	+	0.116348i
$617$	−6.87191	−	3.96750i	−0.276653	−	0.159726i	0.355254	−	0.934770i	$-0.384394\pi$
$617$	−6.87191	−	3.96750i	−0.276653	−	0.159726i	−0.631907	+	0.775044i	$0.717728\pi$
$618$	34.2269	+	33.7997i	1.37681	+	1.35962i
$619$	36.5733	−	21.1156i	1.47000	−	0.848707i	0.470570	−	0.882363i	$-0.344048\pi$
$619$	36.5733	−	21.1156i	1.47000	−	0.848707i	0.999433	+	0.0336559i	$0.0107150\pi$
$620$	−11.9386	−	9.56087i	−0.479465	−	0.383974i
$621$	−8.98523	+	3.81711i	−0.360565	+	0.153175i
$622$	1.03962	−	25.7446i	0.0416851	−	1.03226i
$623$	11.7746	−	6.79810i	0.471741	−	0.272360i
$624$	9.38278	+	11.8286i	0.375612	+	0.473524i
$625$	−5.93937	−	24.2842i	−0.237575	−	0.971369i
$626$	7.28833	−	11.5234i	0.291300	−	0.460569i
$627$	−2.68387	+	12.2808i	−0.107184	+	0.490447i
$628$	12.5274	+	26.4123i	0.499897	+	1.05396i
$629$			36.4721i			1.45424i
$630$	−12.4007	−	0.223404i	−0.494055	−	0.00890065i
$631$	−20.8270			−0.829112			−0.414556	−	0.910024i	$-0.636063\pi$
$631$	−20.8270			−0.829112			−0.414556	+	0.910024i	$0.636063\pi$
$632$	−33.6627	+	14.3324i	−1.33903	+	0.570111i
$633$	4.10106	+	12.8718i	0.163002	+	0.511609i
$634$	19.6473	+	12.4265i	0.780294	+	0.493519i
$635$	13.6603	+	28.0876i	0.542093	+	1.11462i
$636$	−5.63306	+	1.30539i	−0.223365	+	0.0517622i
$637$	5.76494	+	9.98516i	0.228415	+	0.395627i
$638$	0.0974509	−	2.41321i	0.00385812	−	0.0955399i
$639$	0.708218	+	7.57040i	0.0280167	+	0.299481i
$640$	19.4507	−	16.1762i	0.768858	−	0.639419i
$641$	−7.80074	−	13.5113i	−0.308111	−	0.533663i	0.669838	−	0.742507i	$-0.266363\pi$
$641$	−7.80074	−	13.5113i	−0.308111	−	0.533663i	−0.977949	+	0.208844i	$0.933030\pi$
$642$	−24.6159	−	6.43043i	−0.971514	−	0.253789i
$643$	−2.58179	+	4.47180i	−0.101816	+	0.176351i	−0.912433	−	0.409226i	$-0.865799\pi$
$643$	−2.58179	+	4.47180i	−0.101816	+	0.176351i	0.810617	+	0.585577i	$0.199132\pi$
$644$	−2.79128	+	4.04242i	−0.109992	+	0.159294i
$645$	7.48788	+	30.9320i	0.294835	+	1.21795i
$646$	−33.2072	+	17.4249i	−1.30652	+	0.685575i
$647$			23.3690i			0.918732i	0.888247	+	0.459366i	$0.151923\pi$
$647$			23.3690i			0.918732i	−0.888247	+	0.459366i	$0.848077\pi$
$648$	−1.66560	−	25.4013i	−0.0654311	−	0.997857i
$649$	−8.79449			−0.345214
$650$	11.7278	+	9.99552i	0.460001	+	0.392056i
$651$	−5.21491	+	5.72554i	−0.204388	+	0.224401i
$652$	15.6154	−	22.6148i	0.611547	−	0.885663i
$653$	5.82035	−	10.0811i	0.227768	−	0.394506i	−0.729378	−	0.684111i	$-0.760191\pi$
$653$	5.82035	−	10.0811i	0.227768	−	0.394506i	0.957146	+	0.289605i	$0.0935239\pi$
$654$	−3.25194	+	12.4485i	−0.127161	+	0.486777i
$655$	21.5337	+	1.53001i	0.841390	+	0.0597823i
$656$	−38.9993	−	6.35137i	−1.52267	−	0.247979i
$657$	43.7879	−	4.09639i	1.70833	−	0.159816i
$658$	0.406139	−	10.0574i	0.0158329	−	0.392077i
$659$	9.92811	−	5.73200i	0.386744	−	0.223287i	−0.294004	−	0.955804i	$-0.594988\pi$
$659$	9.92811	−	5.73200i	0.386744	−	0.223287i	0.680748	+	0.732517i	$0.261655\pi$
$660$	−3.61005	+	9.39625i	−0.140521	+	0.365749i
$661$	29.9208	+	17.2748i	1.16378	+	0.671911i	0.952208	−	0.305450i	$-0.0988070\pi$
$661$	29.9208	+	17.2748i	1.16378	+	0.671911i	0.211576	+	0.977362i	$0.432140\pi$
$662$	23.2082	−	36.6941i	0.902013	−	1.42616i
$663$	−5.44045	−	17.0757i	−0.211290	−	0.663167i
$664$	−10.0030	+	4.25893i	−0.388192	+	0.165278i
$665$	−13.5253	−	9.14495i	−0.524487	−	0.354626i
$666$	−17.7651	−	27.3224i	−0.688384	−	1.05872i
$667$	2.46907			0.0956027
$668$	−32.4066	+	15.3705i	−1.25385	+	0.594702i
$669$	30.3773	+	6.63873i	1.17445	+	0.256668i
$670$	−10.2409	−	23.4145i	−0.395641	−	0.904580i
$671$	−6.25584	+	10.8354i	−0.241504	+	0.418297i
$672$	−7.54906	−	10.3486i	−0.291211	−	0.399206i
$673$	−23.4711	+	13.5511i	−0.904746	+	0.522355i	−0.878737	−	0.477306i	$-0.841613\pi$
$673$	−23.4711	+	13.5511i	−0.904746	+	0.522355i	−0.0260090	+	0.999662i	$0.508280\pi$
$674$	6.78506	+	0.273996i	0.261351	+	0.0105539i
$675$	−6.67546	−	25.1085i	−0.256939	−	0.966428i
$676$	16.4482	+	1.33060i	0.632624	+	0.0511770i
$677$	21.3333	+	36.9503i	0.819905	+	1.42012i	0.905752	+	0.423808i	$0.139307\pi$
$677$	21.3333	+	36.9503i	0.819905	+	1.42012i	−0.0858476	+	0.996308i	$0.527360\pi$
$678$	−0.834768	−	0.824350i	−0.0320591	−	0.0316590i
$679$	5.08626	−	8.80967i	0.195193	−	0.338084i
$680$	−28.3932	+	9.77571i	−1.08883	+	0.374881i
$681$	−0.831479	+	3.80466i	−0.0318623	+	0.145795i
$682$	2.92048	+	5.56563i	0.111831	+	0.213119i
$683$	−11.6809			−0.446956			−0.223478	−	0.974709i	$-0.571741\pi$
$683$	−11.6809			−0.446956			−0.223478	+	0.974709i	$0.571741\pi$
$684$	16.3891	−	29.2284i	0.626653	−	1.11758i
$685$	5.76545	−	8.52703i	0.220287	−	0.325801i
$686$	−10.5588	−	20.1222i	−0.403138	−	0.768271i
$687$	−1.11421	−	3.49712i	−0.0425097	−	0.133423i
$688$	−20.7965	+	25.4537i	−0.792858	+	0.970412i
$689$	1.81880	−	3.15025i	0.0692907	−	0.120015i
$690$	−9.74701	−	3.30001i	−0.371062	−	0.125629i
$691$	2.63092	−	1.51896i	0.100085	−	0.0577840i	−0.449122	−	0.893470i	$-0.648263\pi$
$691$	2.63092	−	1.51896i	0.100085	−	0.0577840i	0.549207	+	0.835686i	$0.314930\pi$
$692$	36.2012	+	2.92855i	1.37616	+	0.111327i
$693$	4.63208	+	2.12616i	0.175958	+	0.0807662i
$694$	1.25765	−	31.1435i	0.0477396	−	1.18219i
$695$	28.0923	+	1.99601i	1.06560	+	0.0757129i
$696$	−2.12422	+	6.07765i	−0.0805183	+	0.230373i
$697$	40.6184	+	23.4510i	1.53853	+	0.888271i
$698$	19.5032	−	30.8362i	0.738207	−	1.16717i
$699$	−16.3384	+	17.9382i	−0.617975	+	0.678485i
$700$	−9.59973	−	8.87490i	−0.362836	−	0.335440i
$701$		−	13.9946i		−	0.528568i	−0.964445	−	0.264284i	$-0.914864\pi$
$701$		−	13.9946i		−	0.528568i	0.964445	−	0.264284i	$-0.0851356\pi$
$702$	12.3930	+	10.1420i	0.467744	+	0.382786i
$703$		−	42.9012i		−	1.61805i
$704$	−9.98700	+	2.88735i	−0.376399	+	0.108821i
$705$	20.4931	−	4.96088i	0.771815	−	0.186837i
$706$	0.0459187	−	0.0726012i	0.00172817	−	0.00273238i
$707$	−10.0860	+	17.4694i	−0.379322	+	0.657004i
$708$	22.4249	+	6.83574i	0.842780	+	0.256903i
$709$	−38.9397	+	22.4819i	−1.46241	+	0.844324i	−0.999123	−	0.0418834i	$-0.986664\pi$
$709$	−38.9397	+	22.4819i	−1.46241	+	0.844324i	−0.463289	+	0.886207i	$0.653331\pi$
$710$	−4.75347	+	6.45296i	−0.178395	+	0.242175i
$711$	−31.6537	+	22.4490i	−1.18711	+	0.841904i
$712$	−3.55289	+	29.1995i	−0.133150	+	1.09430i
$713$	−5.56472	+	3.21279i	−0.208400	+	0.120320i
$714$	4.02744	+	14.6617i	0.150723	+	0.548701i
$715$	−2.76954	−	5.69456i	−0.103575	−	0.212965i
$716$	−13.2850	−	9.17322i	−0.496482	−	0.342819i
$717$	35.1739	−	11.2067i	1.31359	−	0.418521i
$718$	−2.31047	+	1.21238i	−0.0862260	+	0.0452457i
$719$	0.765821			0.0285603			0.0142801	−	0.999898i	$-0.495454\pi$
$719$	0.765821			0.0285603			0.0142801	+	0.999898i	$0.495454\pi$
$720$	16.5087	−	21.1533i	0.615242	−	0.788338i
$721$	25.6739			0.956145
$722$	15.2675	−	8.01137i	0.568197	−	0.298152i
$723$	−4.79617	+	21.9461i	−0.178371	+	0.816186i
$724$	−28.3429	−	19.5707i	−1.05336	−	0.727339i
$725$	−0.929065	+	6.50493i	−0.0345046	+	0.241587i
$726$	−16.0261	+	16.2286i	−0.594783	+	0.602300i
$727$	11.7407	−	6.77850i	0.435439	−	0.251401i	−0.266222	−	0.963912i	$-0.585775\pi$
$727$	11.7407	−	6.77850i	0.435439	−	0.251401i	0.701661	+	0.712511i	$0.252442\pi$
$728$	7.99928	+	0.973321i	0.296473	+	0.0360737i
$729$	−7.45741	−	25.9497i	−0.276200	−	0.961100i
$730$	37.3245	+	27.4945i	1.38144	+	1.01762i
$731$	33.7886	−	19.5079i	1.24972	−	0.721524i
$732$	24.3738	−	22.7666i	0.900881	−	0.841476i
$733$	−20.1595	+	34.9172i	−0.744607	+	1.28970i	0.205771	+	0.978600i	$0.434030\pi$
$733$	−20.1595	+	34.9172i	−0.744607	+	1.28970i	−0.950378	+	0.311097i	$0.899304\pi$
$734$	−9.98941	+	15.7941i	−0.368716	+	0.582970i
$735$	14.8372	−	14.1333i	0.547277	−	0.521313i
$736$	−3.36133	−	10.0824i	−0.123900	−	0.371643i
$737$			10.5020i			0.386845i
$738$	−41.8513	+	2.21680i	−1.54057	+	0.0816016i
$739$		−	52.8497i		−	1.94411i	−0.234758	−	0.972054i	$-0.575430\pi$
$739$		−	52.8497i		−	1.94411i	0.234758	−	0.972054i	$-0.424570\pi$
$740$	5.18980	−	33.9587i	0.190781	−	1.24835i
$741$	6.39947	+	20.0858i	0.235091	+	0.737869i
$742$	−1.64968	+	2.60828i	−0.0605616	+	0.0957528i
$743$	−4.94812	−	2.85680i	−0.181529	−	0.104806i	0.406482	−	0.913659i	$-0.366755\pi$
$743$	−4.94812	−	2.85680i	−0.181529	−	0.104806i	−0.588011	+	0.808853i	$0.700089\pi$
$744$	−3.12084	−	16.4617i	−0.114415	−	0.603516i
$745$	38.7527	+	2.75345i	1.41979	+	0.100879i
$746$	−0.0670413	+	1.66017i	−0.00245456	+	0.0607830i
$747$	−9.40605	+	6.67083i	−0.344149	+	0.244073i
$748$	12.2999	+	0.995016i	0.449728	+	0.0363814i
$749$	−11.7598	+	6.78954i	−0.429695	+	0.248084i
$750$	12.3617	−	24.4374i	0.451386	−	0.892329i
$751$	−8.59815	+	14.8924i	−0.313751	+	0.543433i	−0.979171	−	0.203036i	$-0.934919\pi$
$751$	−8.59815	+	14.8924i	−0.313751	+	0.543433i	0.665420	+	0.746469i	$0.268252\pi$
$752$	16.8636	+	13.7781i	0.614952	+	0.502435i
$753$	32.0863	−	35.2281i	1.16929	−	1.28378i
$754$	−1.88192	−	3.58642i	−0.0685353	−	0.130610i
$755$	19.5189	+	13.1975i	0.710367	+	0.480307i
$756$	−10.1586	−	9.02186i	−0.369467	−	0.328122i
$757$	3.23350			0.117524			0.0587619	−	0.998272i	$-0.481285\pi$
$757$	3.23350			0.117524			0.0587619	+	0.998272i	$0.481285\pi$
$758$	2.45529	+	4.67912i	0.0891803	+	0.169953i
$759$	3.12634	+	2.84752i	0.113479	+	0.103358i
$760$	33.3983	−	11.4989i	1.21148	−	0.417110i
$761$	−20.4297	+	35.3853i	−0.740576	+	1.28272i	0.211657	+	0.977344i	$0.432114\pi$
$761$	−20.4297	+	35.3853i	−0.740576	+	1.28272i	−0.952233	+	0.305371i	$0.901219\pi$
$762$	−8.64761	+	33.1034i	−0.313270	+	1.19921i
$763$	3.43354	+	5.94707i	0.124303	+	0.215298i
$764$	−18.6370	−	1.50766i	−0.674261	−	0.0545453i
$765$	−27.2207	+	16.5377i	−0.984165	+	0.597920i
$766$	−38.3946	−	1.55046i	−1.38726	−	0.0560205i
$767$	−12.7722	+	7.37406i	−0.461179	+	0.266262i
$768$	27.7099	+	0.400257i	0.999896	+	0.0144430i
$769$	25.8491	−	44.7720i	0.932144	−	1.61452i	0.152495	−	0.988304i	$-0.451269\pi$
$769$	25.8491	−	44.7720i	0.932144	−	1.61452i	0.779649	−	0.626217i	$-0.215398\pi$
$770$	2.15286	+	4.92222i	0.0775836	+	0.177385i
$771$	−10.5830	−	33.2164i	−0.381138	−	1.19626i
$772$	−27.5387	+	13.0617i	−0.991141	+	0.470100i
$773$	−1.05635			−0.0379943			−0.0189971	−	0.999820i	$-0.506047\pi$
$773$	−1.05635			−0.0379943			−0.0189971	+	0.999820i	$0.506047\pi$
$774$	−15.8101	+	31.0720i	−0.568283	+	1.11686i
$775$	−6.37042	−	15.8695i	−0.228832	−	0.570051i
$776$	8.62130	+	20.2490i	0.309487	+	0.726897i
$777$	−16.9931	−	3.71372i	−0.609626	−	0.133229i
$778$	−5.18337	+	8.19532i	−0.185833	+	0.293817i
$779$	−47.7784	−	27.5849i	−1.71184	−	0.988330i
$780$	2.63575	+	16.6732i	0.0943749	+	0.596995i
$781$	2.85231	−	1.64678i	0.102064	−	0.0589265i
$782$	−0.509024	+	12.6051i	−0.0182027	+	0.450759i
$783$	−0.830228	+	6.77807i	−0.0296699	+	0.242228i
$784$	20.8881	+	3.40180i	0.746002	+	0.121493i
$785$	−2.31635	+	32.6008i	−0.0826741	+	1.16357i
$786$	16.8266	+	16.6166i	0.600186	+	0.592696i
$787$	−4.90026	+	8.48751i	−0.174676	+	0.302547i	−0.940049	−	0.341040i	$-0.889221\pi$
$787$	−4.90026	+	8.48751i	−0.174676	+	0.302547i	0.765373	+	0.643587i	$0.222554\pi$
$788$	−28.1001	+	40.6955i	−1.00102	+	1.44972i
$789$	12.2997	+	2.68800i	0.437880	+	0.0956954i
$790$	−40.6522	−	4.54308i	−1.44634	−	0.161635i
$791$	−0.626167			−0.0222639
$792$	−9.69891	+	5.24573i	−0.344636	+	0.186399i
$793$			20.9817i			0.745083i
$794$	−20.3605	+	10.6838i	−0.722567	+	0.379155i
$795$	−6.20207	−	1.82441i	−0.219965	−	0.0647053i
$796$	12.5698	−	18.2039i	0.445523	−	0.645222i
$797$	−8.52322	+	14.7627i	−0.301908	+	0.522920i	−0.976568	−	0.215209i	$-0.930957\pi$
$797$	−8.52322	+	14.7627i	−0.301908	+	0.522920i	0.674660	+	0.738129i	$0.264290\pi$
$798$	−4.73738	−	17.2462i	−0.167702	−	0.610510i
$799$	−12.9244	−	22.3856i	−0.457231	−	0.791947i
$800$	27.8276	−	5.06183i	0.983856	−	0.178963i
$801$	2.90603	+	31.0636i	0.102679	+	1.09758i
$802$	0.921829	−	22.8276i	0.0325509	−	0.806070i
$803$	−9.52513	−	16.4980i	−0.336135	−	0.582202i
$804$	8.16293	−	26.7788i	0.287884	−	0.944415i
$805$	−4.93915	+	2.40214i	−0.174082	+	0.0846644i
$806$	8.90811	+	5.63419i	0.313775	+	0.198456i
$807$	−23.3849	+	25.6746i	−0.823186	+	0.903790i
$808$	−17.0959	−	40.1534i	−0.601431	−	1.41259i
$809$	−5.72585			−0.201310			−0.100655	−	0.994921i	$-0.532094\pi$
$809$	−5.72585			−0.201310			−0.100655	+	0.994921i	$0.532094\pi$
$810$	12.3366	−	25.6478i	0.433464	−	0.901171i
$811$			54.0055i			1.89639i	0.317689	+	0.948195i	$0.397093\pi$
$811$			54.0055i			1.89639i	−0.317689	+	0.948195i	$0.602907\pi$
$812$	1.47257	+	3.10471i	0.0516770	+	0.108954i
$813$	−3.47037	−	3.16086i	−0.121711	−	0.110856i
$814$	−7.54602	+	11.9309i	−0.264488	+	0.418177i
$815$	27.6314	−	13.4385i	0.967886	−	0.470729i
$816$	−30.5898	−	12.0976i	−1.07086	−	0.423500i
$817$	−39.7447	+	22.9466i	−1.39049	+	0.802801i
$818$	0.0573348	−	1.41980i	0.00200467	−	0.0496422i
$819$	8.50993	−	0.796112i	0.297361	−	0.0278184i
$820$	−34.4823	−	27.6148i	−1.20417	−	0.964349i
$821$	−17.6578	+	10.1948i	−0.616263	+	0.355800i	−0.775413	−	0.631455i	$-0.782458\pi$
$821$	−17.6578	+	10.1948i	−0.616263	+	0.355800i	0.159150	+	0.987254i	$0.449125\pi$
$822$	10.8729	−	2.98669i	0.379237	−	0.104173i
$823$	−2.41832	−	1.39622i	−0.0842974	−	0.0486691i	0.457259	−	0.889334i	$-0.348831\pi$
$823$	−2.41832	−	1.39622i	−0.0842974	−	0.0486691i	−0.541556	+	0.840665i	$0.682165\pi$
$824$	−33.3791	+	44.3963i	−1.16282	+	1.54662i
$825$	−8.67837	+	7.16509i	−0.302142	+	0.249456i
$826$	11.0798	−	5.81392i	0.385514	−	0.202292i
$827$	−21.1112			−0.734108			−0.367054	−	0.930200i	$-0.619634\pi$
$827$	−21.1112			−0.734108			−0.367054	+	0.930200i	$0.619634\pi$
$828$	−5.75849	−	9.69086i	−0.200121	−	0.336781i
$829$			15.7409i			0.546704i	0.961914	+	0.273352i	$0.0881324\pi$
$829$			15.7409i			0.546704i	−0.961914	+	0.273352i	$0.911868\pi$
$830$	−12.0800	−	1.35000i	−0.419302	−	0.0468590i
$831$	4.44222	−	20.3266i	0.154099	−	0.705121i
$832$	−12.0831	+	12.5673i	−0.418907	+	0.435691i
$833$	−21.7552	−	12.5604i	−0.753775	−	0.435192i
$834$	21.9516	+	21.6776i	0.760122	+	0.750635i
$835$	−39.9997	−	2.84205i	−1.38425	−	0.0983532i
$836$	−14.4680	−	1.17041i	−0.500388	−	0.0404796i
$837$	−6.94858	−	16.3565i	−0.240178	−	0.565364i
$838$	50.5322	+	2.04060i	1.74561	+	0.0704915i
$839$	−16.6856	−	28.9004i	−0.576052	−	0.997751i	−0.995926	−	0.0901690i	$-0.971259\pi$
$839$	−16.6856	−	28.9004i	−0.576052	−	0.997751i	0.419875	−	0.907582i	$-0.362074\pi$
$840$	−1.66361	−	14.2244i	−0.0574000	−	0.490790i
$841$	−13.6365	+	23.6190i	−0.470223	+	0.814449i
$842$	−16.5831	+	26.2193i	−0.571492	+	0.903576i
$843$	−1.94717	+	8.90981i	−0.0670642	+	0.306870i
$844$	−14.0943	+	6.68493i	−0.485145	+	0.230105i
$845$	15.2840	+	10.3341i	0.525785	+	0.355503i
$846$	20.5859	+	10.4745i	0.707756	+	0.360121i
$847$			12.1732i			0.418276i
$848$	−2.36556	−	6.24376i	−0.0812337	−	0.214412i
$849$	4.33944	−	1.38258i	0.148929	−	0.0474499i
$850$	−33.0176	−	6.08414i	−1.13249	−	0.208684i
$851$	−12.4984	−	7.21597i	−0.428441	−	0.247360i
$852$	−8.55306	+	1.98207i	−0.293023	+	0.0679046i
$853$	−8.28860	−	14.3563i	−0.283796	−	0.491549i	0.688520	−	0.725217i	$-0.258261\pi$
$853$	−8.28860	−	14.3563i	−0.283796	−	0.491549i	−0.972317	+	0.233668i	$0.924927\pi$
$854$	0.718267	−	17.7867i	0.0245786	−	0.608648i
$855$	32.0190	−	19.4528i	1.09503	−	0.665273i
$856$	3.54842	−	29.1628i	0.121282	−	0.996764i
$857$	−8.20098	+	4.73484i	−0.280140	+	0.161739i	−0.633487	−	0.773753i	$-0.718377\pi$
$857$	−8.20098	+	4.73484i	−0.280140	+	0.161739i	0.353347	+	0.935492i	$0.385044\pi$
$858$	1.75325	−	6.71150i	0.0598548	−	0.229127i
$859$	−7.21262	−	4.16421i	−0.246091	−	0.142081i	0.371882	−	0.928280i	$-0.378713\pi$
$859$	−7.21262	−	4.16421i	−0.246091	−	0.142081i	−0.617973	+	0.786199i	$0.712046\pi$
$860$	−34.2360	+	13.3556i	−1.16744	+	0.455422i
$861$	−15.0623	+	16.5371i	−0.513321	+	0.563584i
$862$	−14.6546	+	7.68979i	−0.499139	+	0.261915i
$863$		−	16.9671i		−	0.577568i	−0.957394	−	0.288784i	$-0.906749\pi$
$863$		−	16.9671i		−	0.577568i	0.957394	−	0.288784i	$-0.0932510\pi$
$864$	28.8084	−	5.83727i	0.980083	−	0.198588i
$865$	33.6388	+	22.7445i	1.14375	+	0.773335i
$866$	12.2076	+	23.2643i	0.414830	+	0.790553i
$867$	7.09856	+	6.46548i	0.241080	+	0.219579i
$868$	−7.35873	−	5.08118i	−0.249772	−	0.172467i
$869$	14.5575	+	8.40477i	0.493829	+	0.285112i
$870$	−5.40804	+	4.75035i	−0.183350	+	0.161052i
$871$	8.80576	+	15.2520i	0.298372	+	0.516795i
$872$	−14.7479	−	1.79447i	−0.499428	−	0.0607685i
$873$	13.5037	+	19.0406i	0.457031	+	0.644425i
$874$	0.598752	−	14.8271i	0.0202531	−	0.501535i
$875$	−4.47010	−	13.9164i	−0.151117	−	0.470461i
$876$	11.4645	+	49.4716i	0.387348	+	1.67149i
$877$	4.17126	−	7.22484i	0.140854	−	0.243966i	−0.786965	−	0.616998i	$-0.788349\pi$
$877$	4.17126	−	7.22484i	0.140854	−	0.243966i	0.927818	+	0.373032i	$0.121682\pi$
$878$	34.5655	+	21.8619i	1.16653	+	0.737805i
$879$	−24.0121	+	7.65043i	−0.809908	+	0.258043i
$880$	−11.3107	−	2.67666i	−0.381283	−	0.0902302i
$881$	−21.8620			−0.736550			−0.368275	−	0.929717i	$-0.620051\pi$
$881$	−21.8620			−0.736550			−0.368275	+	0.929717i	$0.620051\pi$
$882$	22.4156	−	1.18732i	0.754772	−	0.0399792i
$883$	−2.50414			−0.0842711			−0.0421355	−	0.999112i	$-0.513416\pi$
$883$	−2.50414			−0.0842711			−0.0421355	+	0.999112i	$0.513416\pi$
$884$	18.6974	−	8.86821i	0.628862	−	0.298270i
$885$	18.0782	+	18.9785i	0.607690	+	0.637957i
$886$	20.5628	+	13.0055i	0.690820	+	0.436929i
$887$	20.4540	+	11.8091i	0.686778	+	0.396511i	0.802404	−	0.596782i	$-0.203554\pi$
$887$	20.4540	+	11.8091i	0.686778	+	0.396511i	−0.115626	+	0.993293i	$0.536887\pi$
$888$	28.5150	−	24.5570i	0.956902	−	0.824078i
$889$	9.13055	+	15.8146i	0.306229	+	0.530404i
$890$	−19.5049	+	26.4784i	−0.653805	+	0.887558i
$891$	−8.86822	+	7.62492i	−0.297097	+	0.255444i
$892$	−2.89509	+	35.7876i	−0.0969348	+	1.19826i
$893$	15.2026	+	26.3317i	0.508736	+	0.881157i
$894$	30.2818	+	29.9038i	1.01277	+	1.00013i
$895$	−7.89438	−	16.2320i	−0.263880	−	0.542575i
$896$	10.6733	−	10.2399i	0.356572	−	0.342091i
$897$	6.92799	+	1.51406i	0.231319	+	0.0505530i
$898$	15.7885	−	8.28478i	0.526870	−	0.276467i
$899$			4.49464i			0.149905i
$900$	27.6981	−	11.5246i	0.923269	−	0.384155i
$901$			7.92544i			0.264035i
$902$	8.43524	+	16.0753i	0.280863	+	0.535248i
$903$	5.64866	+	17.7292i	0.187976	+	0.589992i
$904$	0.814091	−	1.08279i	0.0270763	−	0.0360132i
$905$	−16.8423	−	34.6302i	−0.559858	−	1.15115i
$906$	6.83674	+	24.8889i	0.227136	+	0.826877i
$907$	2.57114	+	4.45335i	0.0853735	+	0.147871i	0.905550	−	0.424239i	$-0.139458\pi$
$907$	2.57114	+	4.45335i	0.0853735	+	0.147871i	−0.820177	+	0.572110i	$0.806125\pi$
$908$	−4.48228	−	0.362601i	−0.148750	−	0.0120333i
$909$	−26.7776	−	37.7571i	−0.888155	−	1.25232i
$910$	7.25381	+	5.34340i	0.240461	+	0.177132i
$911$	−15.6515	−	27.1092i	−0.518558	−	0.898168i	−0.999767	−	0.0215626i	$-0.993136\pi$
$911$	−15.6515	−	27.1092i	−0.518558	−	0.898168i	0.481210	−	0.876605i	$-0.340197\pi$
$912$	35.9821	+	14.2301i	1.19149	+	0.471205i
$913$	4.32582	+	2.49751i	0.143164	+	0.0826557i
$914$	2.85920	−	4.52063i	0.0945739	−	0.149529i
$915$	36.2426	−	8.77343i	1.19814	−	0.290041i
$916$	3.82924	−	1.81621i	0.126522	−	0.0600094i
$917$	12.6218			0.416809
$918$	−34.4324	−	5.63586i	−1.13644	−	0.186011i
$919$	13.2617			0.437464			0.218732	−	0.975785i	$-0.429808\pi$
$919$	13.2617			0.437464			0.218732	+	0.975785i	$0.429808\pi$
$920$	2.26759	−	11.6641i	0.0747604	−	0.384553i
$921$	−30.4548	−	27.7387i	−1.00352	−	0.914021i
$922$	0.840042	−	1.32817i	0.0276653	−	0.0437411i
$923$	2.76161	−	4.78325i	0.0908995	−	0.157442i
$924$	−1.71602	+	5.62947i	−0.0564529	+	0.185196i
$925$	23.7139	−	30.2127i	0.779708	−	0.993389i
$926$	−32.1121	−	1.29676i	−1.05527	−	0.0426141i
$927$	−24.5766	+	53.5429i	−0.807201	+	1.75858i
$928$	−7.28331	−	1.49007i	−0.239086	−	0.0489138i
$929$	−10.7193	−	18.5664i	−0.351690	−	0.609145i	0.634856	−	0.772631i	$-0.281060\pi$
$929$	−10.7193	−	18.5664i	−0.351690	−	0.609145i	−0.986546	+	0.163486i	$0.947726\pi$
$930$	6.00726	−	17.7432i	0.196986	−	0.581824i
$931$	25.5902	+	14.7745i	0.838684	+	0.484214i
$932$	−23.0550	−	15.9194i	−0.755193	−	0.521458i
$933$	30.0671	−	9.57958i	0.984351	−	0.313622i
$934$	4.13656	−	2.17060i	0.135352	−	0.0710240i
$935$	11.4293	+	7.72776i	0.373777	+	0.252725i
$936$	−9.68725	+	15.7508i	−0.316638	+	0.514830i
$937$			17.1401i			0.559942i	0.960009	+	0.279971i	$0.0903248\pi$
$937$			17.1401i			0.559942i	−0.960009	+	0.279971i	$0.909675\pi$
$938$	−6.94272	−	13.2309i	−0.226688	−	0.432005i
$939$	16.3142	+	3.56534i	0.532393	+	0.116351i
$940$	8.84835	+	22.6821i	0.288601	+	0.739808i
$941$	−22.1713	−	12.8006i	−0.722763	−	0.417288i	0.0930055	−	0.995666i	$-0.470353\pi$
$941$	−22.1713	−	12.8006i	−0.722763	−	0.417288i	−0.815769	+	0.578378i	$0.803686\pi$
$942$	−25.1567	+	25.4746i	−0.819649	+	0.830008i
$943$	−16.0726	+	9.27954i	−0.523397	+	0.302183i
$944$	−4.35132	+	26.7184i	−0.141623	+	0.869609i
$945$	−4.93355	−	14.3666i	−0.160488	−	0.467347i
$946$	15.0892	+	0.609336i	0.490592	+	0.0198112i
$947$	−4.44609	−	7.70086i	−0.144479	−	0.250244i	0.784700	−	0.619876i	$-0.212817\pi$
$947$	−4.44609	−	7.70086i	−0.144479	−	0.250244i	−0.929178	+	0.369632i	$0.879484\pi$
$948$	−30.5870	−	32.7463i	−0.993421	−	1.06355i
$949$	−27.6667	−	15.9734i	−0.898099	−	0.518518i
$950$	38.8378	+	7.15662i	1.26006	+	0.232192i
$951$	−6.07885	+	27.8154i	−0.197120	+	0.901977i
$952$	−16.1538	+	6.87772i	−0.523548	+	0.222908i
$953$		−	29.9732i		−	0.970927i	−0.874257	−	0.485463i	$-0.838651\pi$
$953$		−	29.9732i		−	0.970927i	0.874257	−	0.485463i	$-0.161349\pi$
$954$	−3.86039	−	5.93721i	−0.124985	−	0.192224i
$955$	−17.3178	−	11.7092i	−0.560390	−	0.378902i
$956$	18.2674	+	38.5144i	0.590811	+	1.24565i
$957$	2.81838	−	0.897958i	0.0911054	−	0.0290269i
$958$	5.17679	+	3.27421i	0.167255	+	0.105785i
$959$	3.00906	−	5.21185i	0.0971678	−	0.168300i
$960$	26.7604	+	15.6167i	0.863688	+	0.504026i
$961$	9.65151	+	16.7169i	0.311339	+	0.539255i
$962$	−0.955220	+	23.6544i	−0.0307975	+	0.762650i
$963$	−2.90237	−	31.0245i	−0.0935275	−	0.999750i
$964$	−25.8549	−	2.09157i	−0.832729	−	0.0673648i
$965$	−33.9912	−	2.41514i	−1.09422	−	0.0777461i
$966$	−5.82118	−	1.52067i	−0.187293	−	0.0489267i
$967$	−13.3045	−	7.68136i	−0.427844	−	0.247016i	0.270584	−	0.962696i	$-0.412783\pi$
$967$	−13.3045	−	7.68136i	−0.427844	−	0.247016i	−0.698428	+	0.715681i	$0.746117\pi$
$968$	−21.0504	−	15.8266i	−0.676586	−	0.508687i
$969$	−33.9559	−	30.9276i	−1.09082	−	0.993536i
$970$	−2.73278	+	24.4534i	−0.0877443	+	0.785151i
$971$		−	28.0124i		−	0.898962i	−0.893290	−	0.449481i	$-0.851609\pi$
$971$		−	28.0124i		−	0.898962i	0.893290	−	0.449481i	$-0.148391\pi$
$972$	28.5396	−	12.5496i	0.915407	−	0.402528i
$973$	16.4661			0.527879
$974$	1.94546	+	3.70752i	0.0623366	+	0.118797i
$975$	−6.59577	+	17.6826i	−0.211234	+	0.566295i
$976$	29.8237	+	24.3669i	0.954632	+	0.779965i
$977$	−39.3939	−	22.7441i	−1.26032	−	0.727647i	−0.287185	−	0.957875i	$-0.592720\pi$
$977$	−39.3939	−	22.7441i	−1.26032	−	0.727647i	−0.973137	+	0.230228i	$0.926053\pi$
$978$	32.5658	+	8.50718i	1.04134	+	0.272029i
$979$	11.7039	−	6.75723i	0.374057	−	0.215962i
$980$	18.4688	+	14.7905i	0.589963	+	0.472465i
$981$	−15.6894	+	1.46776i	−0.500925	+	0.0468619i
$982$	20.6276	+	0.832990i	0.658254	+	0.0265818i
$983$	28.9059	−	16.6888i	0.921954	−	0.532290i	0.0376958	−	0.999289i	$-0.487998\pi$
$983$	28.9059	−	16.6888i	0.921954	−	0.532290i	0.884258	+	0.466999i	$0.154665\pi$
$984$	−9.01395	−	47.5465i	−0.287354	−	1.51573i
$985$	−49.7229	+	24.1826i	−1.58430	+	0.770522i
$986$	7.45787	+	4.71695i	0.237507	+	0.150218i
$987$	11.7460	−	3.74235i	0.373879	−	0.119120i
$988$	−21.9933	+	10.4315i	−0.699701	+	0.331869i
$989$			15.4385i			0.490915i
$990$	−12.3261	−	0.222062i	−0.391750	−	0.00705758i
$991$	19.2664			0.612017			0.306008	−	0.952029i	$-0.401006\pi$
$991$	19.2664			0.612017			0.306008	+	0.952029i	$0.401006\pi$
$992$	18.3538	−	6.11889i	0.582734	−	0.194275i
$993$	51.9492	+	11.3531i	1.64856	+	0.360280i
$994$	−2.50482	+	3.96033i	−0.0794482	+	0.125614i
$995$	22.2421	−	10.8174i	0.705123	−	0.342935i
$996$	−9.08908	−	9.73072i	−0.287998	−	0.308330i
$997$	11.6049	+	20.1002i	0.367530	+	0.636581i	0.989179	−	0.146715i	$-0.0468701\pi$
$997$	11.6049	+	20.1002i	0.367530	+	0.636581i	−0.621649	+	0.783296i	$0.713537\pi$
$998$	−32.3688	−	1.30713i	−1.02462	−	0.0413764i
$999$	24.0118	−	31.8842i	0.759701	−	1.00877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bk.a.229.11	✓	136
5.4	even	2	inner	360.2.bk.a.229.58	yes	136
8.5	even	2	inner	360.2.bk.a.229.13	yes	136
9.7	even	3	inner	360.2.bk.a.349.56	yes	136
40.29	even	2	inner	360.2.bk.a.229.56	yes	136
45.34	even	6	inner	360.2.bk.a.349.13	yes	136
72.61	even	6	inner	360.2.bk.a.349.58	yes	136
360.349	even	6	inner	360.2.bk.a.349.11	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bk.a.229.11	✓	136	1.1	even	1	trivial
360.2.bk.a.229.13	yes	136	8.5	even	2	inner
360.2.bk.a.229.56	yes	136	40.29	even	2	inner
360.2.bk.a.229.58	yes	136	5.4	even	2	inner
360.2.bk.a.349.11	yes	136	360.349	even	6	inner
360.2.bk.a.349.13	yes	136	45.34	even	6	inner
360.2.bk.a.349.56	yes	136	9.7	even	3	inner
360.2.bk.a.349.58	yes	136	72.61	even	6	inner

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25228 + 0.657113i) q^{2} +(-1.28051 - 1.16631i) q^{3} +(1.13640 - 1.64578i) q^{4} +(2.01086 - 0.977977i) q^{5} +(2.36996 + 0.619105i) q^{6} +(1.13221 - 0.653679i) q^{7} +(-0.341633 + 2.80772i) q^{8} +(0.279433 + 2.98696i) q^{9} +O(q^{10})\)	\(q+(-1.25228 + 0.657113i) q^{2} +(-1.28051 - 1.16631i) q^{3} +(1.13640 - 1.64578i) q^{4} +(2.01086 - 0.977977i) q^{5} +(2.36996 + 0.619105i) q^{6} +(1.13221 - 0.653679i) q^{7} +(-0.341633 + 2.80772i) q^{8} +(0.279433 + 2.98696i) q^{9} +(-1.87552 + 2.54606i) q^{10} +(1.12540 - 0.649750i) q^{11} +(-3.37467 + 0.782040i) q^{12} +(1.08961 - 1.88726i) q^{13} +(-0.988296 + 1.56258i) q^{14} +(-3.71556 - 1.09298i) q^{15} +(-1.41717 - 3.74054i) q^{16} +4.74800i q^{17} +(-2.31270 - 3.55689i) q^{18} -5.58496i q^{19} +(0.675617 - 4.42081i) q^{20} +(-2.21220 - 0.483460i) q^{21} +(-0.982355 + 1.55318i) q^{22} +(-1.62707 - 0.939389i) q^{23} +(3.71214 - 3.19687i) q^{24} +(3.08712 - 3.93315i) q^{25} +(-0.124352 + 3.07938i) q^{26} +(3.12591 - 4.15075i) q^{27} +(0.210833 - 2.60620i) q^{28} +(-1.13812 + 0.657094i) q^{29} +(5.37113 - 1.07283i) q^{30} +(1.71004 - 2.96188i) q^{31} +(4.23265 + 3.75296i) q^{32} +(-2.19890 - 0.480554i) q^{33} +(-3.11998 - 5.94582i) q^{34} +(1.63742 - 2.42173i) q^{35} +(5.23342 + 2.93451i) q^{36} +7.68156 q^{37} +(3.66995 + 6.99393i) q^{38} +(-3.59640 + 1.14584i) q^{39} +(2.05891 + 5.98004i) q^{40} +(4.93913 - 8.55483i) q^{41} +(3.08798 - 0.848239i) q^{42} +(-4.10865 - 7.11638i) q^{43} +(0.209565 - 2.59054i) q^{44} +(3.48308 + 5.73308i) q^{45} +(2.65483 + 0.107208i) q^{46} +(-4.71475 + 2.72206i) q^{47} +(-2.54793 + 6.44267i) q^{48} +(-2.64541 + 4.58198i) q^{49} +(-1.28141 + 6.95399i) q^{50} +(5.53765 - 6.07988i) q^{51} +(-1.86778 - 3.93796i) q^{52} +1.66922 q^{53} +(-1.18700 + 7.25197i) q^{54} +(1.62758 - 2.40717i) q^{55} +(1.44855 + 3.40223i) q^{56} +(-6.51381 + 7.15162i) q^{57} +(0.993459 - 1.57074i) q^{58} +(-5.86091 - 3.38380i) q^{59} +(-6.02118 + 4.87293i) q^{60} +(-8.33815 + 4.81404i) q^{61} +(-0.195159 + 4.83279i) q^{62} +(2.26889 + 3.19919i) q^{63} +(-7.76657 - 1.91842i) q^{64} +(0.345358 - 4.86064i) q^{65} +(3.06942 - 0.843141i) q^{66} +(-4.04077 + 6.99882i) q^{67} +(7.81416 + 5.39565i) q^{68} +(0.987864 + 3.10057i) q^{69} +(-0.459162 + 4.10865i) q^{70} +2.53449 q^{71} +(-8.48200 - 0.235874i) q^{72} -14.6597i q^{73} +(-9.61945 + 5.04765i) q^{74} +(-8.54038 + 1.43591i) q^{75} +(-9.19160 - 6.34677i) q^{76} +(0.849457 - 1.47130i) q^{77} +(3.75075 - 3.79816i) q^{78} +(6.46769 + 11.2024i) q^{79} +(-6.50789 - 6.13574i) q^{80} +(-8.84383 + 1.66931i) q^{81} +(-0.563680 + 13.9586i) q^{82} +(1.92190 + 3.32884i) q^{83} +(-3.30962 + 3.09138i) q^{84} +(4.64344 + 9.54757i) q^{85} +(9.82144 + 6.21185i) q^{86} +(2.22376 + 0.485985i) q^{87} +(1.43984 + 3.38178i) q^{88} +10.3997 q^{89} +(-8.12906 - 4.89064i) q^{90} -2.84903i q^{91} +(-3.39503 + 1.61027i) q^{92} +(-5.64421 + 1.79829i) q^{93} +(4.11548 - 6.50691i) q^{94} +(-5.46196 - 11.2306i) q^{95} +(-1.04285 - 9.74230i) q^{96} +(6.73852 - 3.89049i) q^{97} +(0.301908 - 7.47625i) q^{98} +(2.25525 + 3.17996i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) 136 * q - 2 * q^4 - 8 * q^9	\( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

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