LMFDB - Embedded newform 360.2.bk.a.229.13

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			229.13
Character	$\chi$	$=$	360.229
Dual form			360.2.bk.a.349.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19522 + 0.755949i) q^{2} +(1.28051 + 1.16631i) q^{3} +(0.857083 - 1.80704i) q^{4} +(-2.01086 + 0.977977i) q^{5} +(-2.41216 - 0.425992i) q^{6} +(1.13221 - 0.653679i) q^{7} +(0.341633 + 2.80772i) q^{8} +(0.279433 + 2.98696i) q^{9} +O(q^{10})$	\(q+(-1.19522 + 0.755949i) q^{2} +(1.28051 + 1.16631i) q^{3} +(0.857083 - 1.80704i) q^{4} +(-2.01086 + 0.977977i) q^{5} +(-2.41216 - 0.425992i) q^{6} +(1.13221 - 0.653679i) q^{7} +(0.341633 + 2.80772i) q^{8} +(0.279433 + 2.98696i) q^{9} +(1.66411 - 2.68900i) q^{10} +(-1.12540 + 0.649750i) q^{11} +(3.20508 - 1.31432i) q^{12} +(-1.08961 + 1.88726i) q^{13} +(-0.859083 + 1.63718i) q^{14} +(-3.71556 - 1.09298i) q^{15} +(-2.53082 - 3.09757i) q^{16} +4.74800i q^{17} +(-2.59197 - 3.35882i) q^{18} +5.58496i q^{19} +(0.0437727 + 4.47192i) q^{20} +(2.21220 + 0.483460i) q^{21} +(0.853919 - 1.62734i) q^{22} +(-1.62707 - 0.939389i) q^{23} +(-2.83721 + 3.99377i) 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} +(5.26713 - 1.50243i) q^{30} +(1.71004 - 2.96188i) q^{31} +(5.36648 + 1.78910i) q^{32} +(-2.19890 - 0.480554i) q^{33} +(-3.58925 - 5.67489i) q^{34} +(-1.63742 + 2.42173i) q^{35} +(5.63706 + 2.05512i) q^{36} -7.68156 q^{37} +(-4.22194 - 6.67523i) q^{38} +(-3.59640 + 1.14584i) q^{39} +(-3.43286 - 5.31182i) q^{40} +(4.93913 - 8.55483i) q^{41} +(-3.00953 + 1.09447i) 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} +(0.371993 - 6.91821i) q^{48} +(-2.64541 + 4.58198i) q^{49} +(-0.716516 + 7.03467i) q^{50} +(-5.53765 + 6.07988i) q^{51} +(2.47648 + 3.58652i) q^{52} -1.66922 q^{53} +(0.598383 - 7.32407i) q^{54} +(1.62758 - 2.40717i) q^{55} +(2.22215 + 2.95560i) q^{56} +(-6.51381 + 7.15162i) q^{57} +(-0.863571 + 1.64573i) q^{58} +(5.86091 + 3.38380i) q^{59} +(-5.15960 + 5.77741i) 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} +(2.99144 - 1.08789i) q^{66} +(4.04077 - 6.99882i) q^{67} +(8.57985 + 4.06943i) q^{68} +(-0.987864 - 3.10057i) q^{69} +(0.126373 - 4.13230i) q^{70} +2.53449 q^{71} +(-8.29108 + 1.80501i) q^{72} -14.6597i q^{73} +(9.18112 - 5.80686i) q^{74} +(8.54038 - 1.43591i) q^{75} +(10.0923 + 4.78678i) q^{76} +(-0.849457 + 1.47130i) q^{77} +(3.43228 - 4.08822i) q^{78} +(6.46769 + 11.2024i) q^{79} +(8.11848 + 3.75371i) q^{80} +(-8.84383 + 1.66931i) q^{81} +(0.563680 + 13.9586i) q^{82} +(-1.92190 - 3.32884i) q^{83} +(2.76967 - 3.58318i) q^{84} +(-4.64344 - 9.54757i) q^{85} +(-10.2903 - 5.39969i) q^{86} +(2.22376 + 0.485985i) q^{87} +(-2.20879 - 2.93783i) q^{88} +10.3997 q^{89} +(8.49694 + 4.21924i) q^{90} +2.84903i q^{91} +(-3.09205 + 2.13505i) q^{92} +(5.64421 - 1.79829i) q^{93} +(3.57741 - 6.81756i) q^{94} +(-5.46196 - 11.2306i) q^{95} +(4.78520 + 8.54996i) 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 $

$2$	−1.19522	+	0.755949i	−0.845145	+	0.534536i
$2$	−1.19522	+	0.755949i	−0.845145	+	0.534536i
$3$	1.28051	+	1.16631i	0.739305	+	0.673371i
$3$	1.28051	+	1.16631i	0.739305	+	0.673371i
$4$	0.857083	−	1.80704i	0.428542	−	0.903522i
$5$	−2.01086	+	0.977977i	−0.899284	+	0.437365i
$5$	−2.01086	+	0.977977i	−0.899284	+	0.437365i
$6$	−2.41216	−	0.425992i	−0.984761	−	0.173911i
$7$	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
$10$	1.66411	−	2.68900i	0.526239	−	0.850337i
$11$	−1.12540	+	0.649750i	−0.339321	+	0.195907i	−0.659972	−	0.751290i	$-0.729432\pi$
$11$	−1.12540	+	0.649750i	−0.339321	+	0.195907i	0.320651	+	0.947197i	$0.396098\pi$
$12$	3.20508	−	1.31432i	0.925228	−	0.379411i
$13$	−1.08961	+	1.88726i	−0.302204	+	0.523433i	−0.976635	−	0.214905i	$-0.931056\pi$
$13$	−1.08961	+	1.88726i	−0.302204	+	0.523433i	0.674431	+	0.738338i	$0.264389\pi$
$14$	−0.859083	+	1.63718i	−0.229600	+	0.437554i
$15$	−3.71556	−	1.09298i	−0.959354	−	0.282206i
$16$	−2.53082	−	3.09757i	−0.632704	−	0.774394i
$17$			4.74800i			1.15156i	0.817605	+	0.575780i	$0.195301\pi$
$17$			4.74800i			1.15156i	−0.817605	+	0.575780i	$0.804699\pi$
$18$	−2.59197	−	3.35882i	−0.610933	−	0.791682i
$19$			5.58496i			1.28128i	0.767842	+	0.640639i	$0.221330\pi$
$19$			5.58496i			1.28128i	−0.767842	+	0.640639i	$0.778670\pi$
$20$	0.0437727	+	4.47192i	0.00978787	+	0.999952i
$21$	2.21220	+	0.483460i	0.482742	+	0.105500i
$22$	0.853919	−	1.62734i	0.182056	−	0.346949i
$23$	−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	$0.729422\pi$
$24$	−2.83721	+	3.99377i	−0.579143	+	0.815226i
$25$	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	−0.390592	−	0.920564i	$-0.627730\pi$
$29$	1.13812	−	0.657094i	0.211344	−	0.122019i	0.601936	+	0.798545i	$0.294396\pi$
$30$	5.26713	−	1.50243i	0.961643	−	0.274305i
$31$	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	$0.0672971\pi$
$32$	5.36648	+	1.78910i	0.948669	+	0.316272i
$33$	−2.19890	−	0.480554i	−0.382780	−	0.0836536i
$34$	−3.58925	−	5.67489i	−0.615551	−	0.973235i
$35$	−1.63742	+	2.42173i	−0.276775	+	0.409347i
$36$	5.63706	+	2.05512i	0.939510	+	0.342521i
$37$	−7.68156			−1.26284			−0.631420	−	0.775441i	$-0.717528\pi$
$37$	−7.68156			−1.26284			−0.631420	+	0.775441i	$0.717528\pi$
$38$	−4.22194	−	6.67523i	−0.684889	−	1.08287i
$39$	−3.59640	+	1.14584i	−0.575886	+	0.183481i
$40$	−3.43286	−	5.31182i	−0.542783	−	0.839873i
$41$	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	$-0.113758\pi$
$42$	−3.00953	+	1.09447i	−0.464380	+	0.168880i
$43$	4.10865	+	7.11638i	0.626563	+	1.08524i	0.988236	+	0.152934i	$0.0488721\pi$
$43$	4.10865	+	7.11638i	0.626563	+	1.08524i	−0.361674	+	0.932305i	$0.617795\pi$
$44$	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	$0.463301\pi$
$48$	0.371993	−	6.91821i	0.0536925	−	0.998558i
$49$	−2.64541	+	4.58198i	−0.377915	+	0.654568i
$50$	−0.716516	+	7.03467i	−0.101331	+	0.994853i
$51$	−5.53765	+	6.07988i	−0.775426	+	0.851354i
$52$	2.47648	+	3.58652i	0.343426	+	0.497361i
$53$	−1.66922			−0.229284			−0.114642	−	0.993407i	$-0.536572\pi$
$53$	−1.66922			−0.229284			−0.114642	+	0.993407i	$0.536572\pi$
$54$	0.598383	−	7.32407i	0.0814297	−	0.996679i
$55$	1.62758	−	2.40717i	0.219463	−	0.324583i
$56$	2.22215	+	2.95560i	0.296947	+	0.394958i
$57$	−6.51381	+	7.15162i	−0.862775	+	0.947255i
$58$	−0.863571	+	1.64573i	−0.113392	+	0.216095i
$59$	5.86091	+	3.38380i	0.763025	+	0.440533i	0.830381	−	0.557196i	$-0.188123\pi$
$59$	5.86091	+	3.38380i	0.763025	+	0.440533i	−0.0673557	+	0.997729i	$0.521456\pi$
$60$	−5.15960	+	5.77741i	−0.666102	+	0.745861i
$61$	8.33815	−	4.81404i	1.06759	−	0.616374i	0.140069	−	0.990142i	$-0.455268\pi$
$61$	8.33815	−	4.81404i	1.06759	−	0.616374i	0.927522	+	0.373768i	$0.121934\pi$
$62$	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
$66$	2.99144	−	1.08789i	0.368220	−	0.133910i
$67$	4.04077	−	6.99882i	0.493659	−	0.855042i	−0.506314	−	0.862349i	$-0.668992\pi$
$67$	4.04077	−	6.99882i	0.493659	−	0.855042i	0.999973	+	0.00730655i	$0.00232577\pi$
$68$	8.57985	+	4.06943i	1.04046	+	0.493491i
$69$	−0.987864	−	3.10057i	−0.118925	−	0.373265i
$70$	0.126373	−	4.13230i	0.0151045	−	0.493904i
$71$	2.53449			0.300788			0.150394	−	0.988626i	$-0.451946\pi$
$71$	2.53449			0.300788			0.150394	+	0.988626i	$0.451946\pi$
$72$	−8.29108	+	1.80501i	−0.977113	+	0.212723i
$73$		−	14.6597i		−	1.71579i	−0.513828	−	0.857893i	$-0.671773\pi$
$73$		−	14.6597i		−	1.71579i	0.513828	−	0.857893i	$-0.328227\pi$
$74$	9.18112	−	5.80686i	1.06728	−	0.675034i
$75$	8.54038	−	1.43591i	0.986159	−	0.165805i
$76$	10.0923	+	4.78678i	1.15766	+	0.549081i
$77$	−0.849457	+	1.47130i	−0.0968046	+	0.167670i
$78$	3.43228	−	4.08822i	0.388630	−	0.462900i
$79$	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	$0.573936\pi$
$80$	8.11848	+	3.75371i	0.907673	+	0.419678i
$81$	−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	0.741058	−	0.671441i	$-0.234324\pi$
$83$	−1.92190	−	3.32884i	−0.210956	−	0.365387i	−0.952014	+	0.306054i	$0.900991\pi$
$84$	2.76967	−	3.58318i	0.302196	−	0.390957i
$85$	−4.64344	−	9.54757i	−0.503652	−	1.03558i
$86$	−10.2903	−	5.39969i	−1.10964	−	0.582264i
$87$	2.22376	+	0.485985i	0.238412	+	0.0521031i
$88$	−2.20879	−	2.93783i	−0.235458	−	0.313174i
$89$	10.3997			1.10237			0.551185	−	0.834383i	$-0.314176\pi$
$89$	10.3997			1.10237			0.551185	+	0.834383i	$0.314176\pi$
$90$	8.49694	+	4.21924i	0.895656	+	0.444747i
$91$			2.84903i			0.298659i
$92$	−3.09205	+	2.13505i	−0.322369	+	0.222594i
$93$	5.64421	−	1.79829i	0.585277	−	0.186474i
$94$	3.57741	−	6.81756i	0.368981	−	0.703178i
$95$	−5.46196	−	11.2306i	−0.560386	−	1.15223i
$96$	4.78520	+	8.54996i	0.488387	+	0.872627i
$97$	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
$100$	−4.46146	−	8.94960i	−0.446146	−	0.894960i
$101$	13.3624	−	7.71476i	1.32960	−	0.767648i	0.344366	−	0.938835i	$-0.388094\pi$
$101$	13.3624	−	7.71476i	1.32960	−	0.767648i	0.985238	+	0.171188i	$0.0547605\pi$
$102$	2.02261	−	11.4530i	0.200268	−	1.13401i
$103$	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	$0.248050\pi$
$104$	−5.67116	−	2.41458i	−0.556103	−	0.236769i
$105$	−4.92124	+	1.19131i	−0.480264	+	0.116260i
$106$	1.99507	−	1.26184i	0.193779	−	0.122561i
$107$	10.3866			1.00412			0.502058	−	0.864834i	$-0.332577\pi$
$107$	10.3866			1.00412			0.502058	+	0.864834i	$0.332577\pi$
$108$	4.82142	+	9.20619i	0.463941	+	0.885866i
$109$		−	5.25264i		−	0.503112i	−0.967843	−	0.251556i	$-0.919058\pi$
$109$		−	5.25264i		−	0.503112i	0.967843	−	0.251556i	$-0.0809422\pi$
$110$	−0.125614	+	4.10746i	−0.0119768	+	0.391631i
$111$	−9.83634	−	8.95909i	−0.933624	−	0.850360i
$112$	−4.89023	−	1.85275i	−0.462083	−	0.175068i
$113$	−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	$0.673838\pi$
$114$	2.37915	−	13.4718i	0.222828	−	1.26175i
$115$	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
$120$	1.79942	−	10.8057i	0.164264	−	0.986416i
$121$	−4.65565	+	8.06382i	−0.423241	+	0.733075i
$122$	−6.32673	+	12.0570i	−0.572796	+	1.09159i
$123$	16.3022	−	5.19401i	1.46992	−	0.468328i
$124$	−3.88660	−	5.62870i	−0.349027	−	0.505472i
$125$	−2.36124	+	10.9282i	−0.211196	+	0.977444i
$126$	−5.13024	−	2.10856i	−0.457038	−	0.187846i
$127$			13.9679i			1.23945i	0.784818	+	0.619727i	$0.212757\pi$
$127$			13.9679i			1.23945i	−0.784818	+	0.619727i	$0.787243\pi$
$128$	7.83251	−	8.16405i	0.692303	−	0.721607i
$129$	−3.03874	+	13.9046i	−0.267547	+	1.22423i
$130$	3.26162	+	6.07059i	0.286063	+	0.532426i
$131$	−8.36098	−	4.82721i	−0.730502	−	0.421756i	0.0881036	−	0.996111i	$-0.471919\pi$
$131$	−8.36098	−	4.82721i	−0.730502	−	0.421756i	−0.818606	+	0.574356i	$0.805253\pi$
$132$	−2.75302	+	3.56164i	−0.239620	+	0.310001i
$133$	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	$0.270330\pi$
$138$	3.52458	+	2.95908i	0.300032	+	0.251893i
$139$	−10.9075	−	6.29746i	−0.925164	−	0.534144i	−0.0398853	−	0.999204i	$-0.512699\pi$
$139$	−10.9075	−	6.29746i	−0.925164	−	0.534144i	−0.885279	+	0.465060i	$0.846033\pi$
$140$	2.97276	+	5.03452i	0.251244	+	0.425495i
$141$	−9.21208	−	2.01323i	−0.775797	−	0.169545i
$142$	−3.02926	+	1.91594i	−0.254210	+	0.160782i
$143$		−	2.83190i		−	0.236816i
$144$	8.54513	−	8.42500i	0.712094	−	0.702084i
$145$	−1.64598	+	2.43438i	−0.136691	+	0.202164i
$146$	11.0820	+	17.5215i	0.917150	+	1.45009i
$147$	−8.73150	+	2.78192i	−0.720162	+	0.229449i
$148$	−6.58374	+	13.8809i	−0.541180	+	1.14100i
$149$	−15.0467	−	8.68721i	−1.23267	−	0.711684i	−0.265087	−	0.964225i	$-0.585401\pi$
$149$	−15.0467	−	8.68721i	−1.23267	−	0.711684i	−0.967586	+	0.252540i	$0.918734\pi$
$150$	−9.12213	+	8.17231i	−0.744819	+	0.667267i
$151$	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
$156$	−1.01183	+	7.48094i	−0.0810115	+	0.598955i
$157$	7.30815	−	12.6581i	0.583254	−	1.01022i	−0.411837	−	0.911258i	$-0.635113\pi$
$157$	7.30815	−	12.6581i	0.583254	−	1.01022i	0.995091	−	0.0989674i	$-0.0315540\pi$
$158$	−16.1987	−	8.50001i	−1.28870	−	0.676224i
$159$	−2.13745	−	1.94683i	−0.169511	−	0.154393i
$160$	−12.5409	+	1.65066i	−0.991449	+	0.130496i
$161$	−2.45624			−0.193579
$162$	9.30838	−	8.68067i	0.731336	−	0.682018i
$163$	−13.7411			−1.07628			−0.538142	−	0.842854i	$-0.680874\pi$
$163$	−13.7411			−1.07628			−0.538142	+	0.842854i	$0.680874\pi$
$164$	−11.2257	−	16.2574i	−0.876581	−	1.26949i
$165$	4.89166	−	1.18415i	0.380815	−	0.0921859i
$166$	4.81352	+	2.52582i	0.373602	+	0.196041i
$167$	−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	$0.910761\pi$
$168$	−0.601660	+	6.37640i	−0.0464190	+	0.491950i
$169$	4.12549	+	7.14555i	0.317345	+	0.549658i
$170$	12.7674	+	7.90121i	0.979214	+	0.605995i
$171$	−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	$-0.924132\pi$
$173$	−9.07986	−	15.7268i	−0.690329	−	1.19569i	0.281401	−	0.959590i	$-0.409201\pi$
$174$	−3.02525	+	1.10019i	−0.229344	+	0.0834050i
$175$	0.924237	−	6.47113i	0.0698657	−	0.489171i
$176$	4.86083	+	1.84161i	0.366399	+	0.138817i
$177$	3.55841	+	11.1686i	0.267467	+	0.839487i
$178$	−12.4299	+	7.86167i	−0.931663	+	0.589257i
$179$			8.07215i			0.603341i	0.953412	+	0.301670i	$0.0975442\pi$
$179$			8.07215i			0.603341i	−0.953412	+	0.301670i	$0.902456\pi$
$180$	−13.3452	+	1.38035i	−0.994693	+	0.102885i
$181$			17.2216i			1.28007i	0.768345	+	0.640035i	$0.221080\pi$
$181$			17.2216i			1.28007i	−0.768345	+	0.640035i	$0.778920\pi$
$182$	−2.15372	−	3.40521i	−0.159644	−	0.252411i
$183$	16.2918	+	3.56045i	1.20432	+	0.263196i
$184$	2.08168	−	4.88928i	0.153463	−	0.360442i
$185$	15.4465	−	7.51239i	1.13565	−	0.552322i
$186$	−5.38664	+	6.41608i	−0.394968	+	0.470450i
$187$	−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
$190$	15.0180	+	9.29400i	1.08952	+	0.674258i
$191$	−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	$0.943162\pi$
$192$	−12.1827	−	6.60169i	−0.879209	−	0.476436i
$193$	−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	$0.851463\pi$
$194$	−5.11298	+	9.74395i	−0.367091	+	0.699575i
$195$	6.11126	−	5.82133i	0.437637	−	0.416874i
$196$	6.01250	+	8.70750i	0.429464	+	0.621965i
$197$	24.7272			1.76174			0.880869	−	0.473359i	$-0.156959\pi$
$197$	24.7272			1.76174			0.880869	+	0.473359i	$0.156959\pi$
$198$	5.09940	+	2.09589i	0.362398	+	0.148948i
$199$	11.0610			0.784093			0.392047	−	0.919945i	$-0.371767\pi$
$199$	11.0610			0.784093			0.392047	+	0.919945i	$0.371767\pi$
$200$	12.0978	+	7.32408i	0.855447	+	0.517890i
$201$	13.3371	−	4.24929i	0.940725	−	0.299722i
$202$	−10.1389	+	19.3221i	−0.713374	+	1.35950i
$203$	0.859058	−	1.48793i	0.0602940	−	0.104432i
$204$	6.24039	+	15.2177i	0.436915	+	1.06546i
$205$	−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
$210$	4.98137	−	5.14408i	0.343747	−	0.354975i
$211$	6.75468	+	3.89982i	0.465011	+	0.268474i	0.714149	−	0.699994i	$-0.246814\pi$
$211$	6.75468	+	3.89982i	0.465011	+	0.268474i	−0.249138	+	0.968468i	$0.580147\pi$
$212$	−1.43066	+	3.01635i	−0.0982579	+	0.207163i
$213$	3.24545	+	2.95600i	0.222374	+	0.202542i
$214$	−12.4143	+	7.85177i	−0.848623	+	0.536736i
$215$	−15.2216	−	10.2919i	−1.03810	−	0.701901i
$216$	−12.7220	−	7.35864i	−0.865625	−	0.500692i
$217$		−	4.47128i		−	0.303530i
$218$	3.97073	+	6.27804i	0.268932	+	0.425203i
$219$	17.0978	−	18.7719i	1.15536	−	1.26849i
$220$	−2.95489	−	5.00426i	−0.199219	−	0.337387i
$221$	−8.96074	−	5.17348i	−0.602764	−	0.348006i
$222$	18.5292	+	3.27228i	1.24360	+	0.219621i
$223$	−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	0.900920	−	0.433985i	$-0.142893\pi$
$227$	1.12423	+	1.94723i	0.0746179	+	0.129242i	−0.826302	+	0.563227i	$0.809560\pi$
$228$	7.34042	+	17.9003i	0.486131	+	1.18547i
$229$	−1.83516	−	1.05953i	−0.121271	−	0.0700158i	0.438137	−	0.898908i	$-0.355638\pi$
$229$	−1.83516	−	1.05953i	−0.121271	−	0.0700158i	−0.559408	+	0.828892i	$0.688972\pi$
$230$	−5.23364	+	2.81194i	−0.345096	+	0.185414i
$231$	−2.80374	+	0.893291i	−0.184472	+	0.0587743i
$232$	2.23376	+	2.97104i	0.146653	+	0.195058i
$233$		−	14.0086i		−	0.917733i	−0.888505	−	0.458867i	$-0.848256\pi$
$233$		−	14.0086i		−	0.917733i	0.888505	−	0.458867i	$-0.151744\pi$
$234$	9.16323	−	1.23191i	0.599019	−	0.0805328i
$235$	6.81859	−	10.0846i	0.444796	−	0.657847i
$236$	11.1380	−	7.69072i	0.725019	−	0.500623i
$237$	−4.78349	+	21.8881i	−0.310721	+	1.42179i
$238$	−7.77332	−	4.07893i	−0.503870	−	0.264398i
$239$	−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	$0.924573\pi$
$240$	6.01783	+	14.2754i	0.388449	+	0.921470i
$241$	−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
$246$	−15.5583	+	18.5316i	−0.991960	+	1.18153i
$247$	−10.5403	−	6.08544i	−0.670663	−	0.387207i
$248$	8.90034	+	3.78945i	0.565172	+	0.240630i
$249$	1.42144	−	6.50416i	0.0900798	−	0.412184i
$250$	−5.43893	−	14.8465i	−0.343988	−	0.938974i
$251$		−	27.5109i		−	1.73647i	−0.496149	−	0.868237i	$-0.665253\pi$
$251$		−	27.5109i		−	1.73647i	0.496149	−	0.868237i	$-0.334747\pi$
$252$	7.72571	−	1.35801i	0.486674	−	0.0855464i
$253$	2.44147			0.153494
$254$	−10.5590	−	16.6947i	−0.662533	−	1.04752i
$255$	5.18946	−	17.6415i	0.324977	−	1.10475i
$256$	−3.18994	+	15.6788i	−0.199371	+	0.979924i
$257$	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	$0.450641\pi$
$258$	−6.87920	−	18.9161i	−0.428280	−	1.17767i
$259$	−8.69711	+	5.02128i	−0.540412	+	0.312007i
$260$	−8.48740	−	4.79005i	−0.526366	−	0.297066i
$261$	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	$0.405280\pi$
$264$	0.598043	−	6.33807i	0.0368070	−	0.390081i
$265$	3.35656	−	1.63245i	0.206192	−	0.100281i
$266$	−9.14357	−	4.79794i	−0.560628	−	0.294181i
$267$	13.3170	+	12.1293i	0.814988	+	0.742304i
$268$	−9.18390	−	13.3004i	−0.560996	−	0.812453i
$269$			20.0503i			1.22249i	0.791443	+	0.611243i	$0.209330\pi$
$269$			20.0503i			1.22249i	−0.791443	+	0.611243i	$0.790670\pi$
$270$	5.95950	+	15.3129i	0.362684	+	0.931912i
$271$	2.71014			0.164629			0.0823145	−	0.996606i	$-0.473769\pi$
$271$	2.71014			0.164629			0.0823145	+	0.996606i	$0.473769\pi$
$272$	14.7073	−	12.0163i	0.891761	−	0.728596i
$273$	−3.32286	+	3.64822i	−0.201108	+	0.220800i
$274$	−3.02487	+	5.76458i	−0.182739	+	0.348251i
$275$	−0.918681	+	6.43223i	−0.0553985	+	0.387878i
$276$	−6.44955	−	0.872333i	−0.388217	−	0.0525083i
$277$	−6.00627	−	10.4032i	−0.360882	−	0.625066i	0.627224	−	0.778839i	$-0.284191\pi$
$277$	−6.00627	−	10.4032i	−0.360882	−	0.625066i	−0.988106	+	0.153773i	$0.950858\pi$
$278$	17.7974	−	0.718700i	1.06742	−	0.0431047i
$279$	9.32486	+	4.28018i	0.558265	+	0.256248i
$280$	−7.35893	−	3.77009i	−0.439780	−	0.225306i
$281$	−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	$0.883534\pi$
$282$	12.5323	−	4.55761i	0.746289	−	0.271402i
$283$	1.31473	−	2.27718i	0.0781527	−	0.135364i	−0.824300	−	0.566153i	$-0.808431\pi$
$283$	1.31473	−	2.27718i	0.0781527	−	0.135364i	0.902453	+	0.430788i	$0.141764\pi$
$284$	2.17227	−	4.57993i	0.128900	−	0.271769i
$285$	6.10423	−	20.7513i	0.361584	−	1.22920i
$286$	2.14077	+	3.38474i	0.126587	+	0.200144i
$287$		−	12.9144i		−	0.762315i
$288$	−3.84441	+	16.5294i	−0.226534	+	0.974003i
$289$	−5.54352			−0.326090
$290$	0.127033	−	4.15389i	0.00745966	−	0.243925i
$291$	13.1663	+	2.87740i	0.771822	+	0.168676i
$292$	−26.4907	−	12.5646i	−1.55025	−	0.735286i
$293$	−7.27501	+	12.6007i	−0.425011	+	0.736140i	−0.996421	−	0.0845239i	$-0.973063\pi$
$293$	−7.27501	+	12.6007i	−0.425011	+	0.736140i	0.571411	+	0.820664i	$0.306396\pi$
$294$	8.33304	−	9.92556i	0.485993	−	0.578870i
$295$	−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
$300$	4.72507	−	16.6635i	0.272802	−	0.962070i
$301$	9.30367	+	5.37148i	0.536254	+	0.309607i
$302$	−13.1955	−	6.92414i	−0.759317	−	0.398439i
$303$	26.1085	+	5.70582i	1.49989	+	0.327791i
$304$	17.2998	−	14.1345i	0.992213	−	0.810670i
$305$	−12.0588	+	17.8349i	−0.690488	+	1.02122i
$306$	15.9477	−	12.3067i	0.911669	−	0.703526i
$307$	−23.7833			−1.35738			−0.678691	−	0.734424i	$-0.737453\pi$
$307$	−23.7833			−1.35738			−0.678691	+	0.734424i	$0.737453\pi$
$308$	1.93065	+	2.79603i	0.110009	+	0.159319i
$309$	10.3257	+	32.4088i	0.587407	+	1.84367i
$310$	−5.11880	−	9.52721i	−0.290728	−	0.541109i
$311$	−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	$0.993882\pi$
$312$	−4.44585	−	9.70624i	−0.251697	−	0.549507i
$313$	−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	0.999043	−	0.0437499i	$-0.0139305\pi$
$317$	8.21914	+	14.2360i	0.461633	+	0.799571i	−0.537410	+	0.843321i	$0.680597\pi$
$318$	4.02642	+	0.711073i	0.225790	+	0.0398750i
$319$	−0.853894	+	1.47899i	−0.0478089	+	0.0828074i
$320$	13.7413	−	11.4532i	0.768164	−	0.640253i
$321$	13.3003	+	12.1141i	0.742348	+	0.676142i
$322$	2.93573	−	1.85679i	0.163602	−	0.103475i
$323$	−26.5174			−1.47547
$324$	−4.56339	+	17.4119i	−0.253522	+	0.967330i
$325$	4.05913	+	10.1118i	0.225160	+	0.560903i
$326$	16.4236	−	10.3876i	0.909617	−	0.575313i
$327$	6.12622	−	6.72608i	0.338781	−	0.371953i
$328$	25.7069	+	10.9451i	1.41943	+	0.604342i
$329$	−3.55871	+	6.16387i	−0.196198	+	0.339825i
$330$	−4.95143	+	5.11316i	−0.272567	+	0.281470i
$331$	26.5877	−	15.3504i	1.46139	−	0.843734i	0.462315	−	0.886716i	$-0.347019\pi$
$331$	26.5877	−	15.3504i	1.46139	−	0.843734i	0.999076	+	0.0429819i	$0.0136858\pi$
$332$	−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
$336$	−4.10112	−	8.07600i	−0.223734	−	0.440582i
$337$	−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	$0.708415\pi$
$338$	−10.3325	−	5.42183i	−0.562015	−	0.294908i
$339$	−0.251836	−	0.790427i	−0.0136778	−	0.0429301i
$340$	−21.2327	+	0.207833i	−1.15150	+	0.0112713i
$341$			4.44440i			0.240678i
$342$	18.7589	−	14.4760i	1.01436	−	0.782775i
$343$			16.0685i			0.867618i
$344$	−18.5772	+	13.9671i	−1.00161	+	0.753056i
$345$	5.01875	+	5.26871i	0.270200	+	0.283658i
$346$	22.7410	+	11.9330i	1.22257	+	0.641522i
$347$	11.0199	−	19.0870i	0.591578	−	1.02464i	−0.402442	−	0.915446i	$-0.631838\pi$
$347$	11.0199	−	19.0870i	0.591578	−	1.02464i	0.994020	−	0.109198i	$-0.0348282\pi$
$348$	2.78414	−	3.60190i	0.149246	−	0.193082i
$349$	22.3432	−	12.8998i	1.19600	−	0.690512i	0.236340	−	0.971670i	$-0.424052\pi$
$349$	22.3432	−	12.8998i	1.19600	−	0.690512i	0.959661	+	0.281158i	$0.0907186\pi$
$350$	3.78718	+	8.43307i	0.202433	+	0.450766i
$351$	−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	$0.333848\pi$
$354$	−12.6960	−	10.6590i	−0.674784	−	0.566518i
$355$	−5.09650	+	2.47867i	−0.270494	+	0.131554i
$356$	8.91344	−	18.7928i	0.472412	−	0.996016i
$357$	−2.29547	+	10.5035i	−0.121489	+	0.555906i
$358$	−6.10213	−	9.64796i	−0.322508	−	0.509911i
$359$	1.84501			0.0973760			0.0486880	−	0.998814i	$-0.484496\pi$
$359$	1.84501			0.0973760			0.0486880	+	0.998814i	$0.484496\pi$
$360$	14.9069	−	11.7381i	0.785665	−	0.618653i
$361$	−12.1918			−0.641672
$362$	−13.0186	−	20.5835i	−0.684244	−	1.08185i
$363$	−15.3666	+	4.89590i	−0.806535	+	0.256968i
$364$	5.14832	+	2.44186i	0.269845	+	0.127988i
$365$	14.3368	+	29.4786i	0.750424	+	1.54298i
$366$	−22.1637	+	8.06025i	−1.15852	+	0.421316i
$367$	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
$370$	−12.7830	+	20.6557i	−0.664555	+	1.07384i
$371$	−1.88990	+	1.09113i	−0.0981185	+	0.0566487i
$372$	1.58798	−	11.7406i	0.0823327	−	0.608723i
$373$	−0.587436	+	1.01747i	−0.0304163	+	0.0526825i	−0.880833	−	0.473427i	$-0.843017\pi$
$373$	−0.587436	+	1.01747i	−0.0304163	+	0.0526825i	0.850417	+	0.526110i	$0.176350\pi$
$374$	7.72660	+	4.05441i	0.399533	+	0.209648i
$375$	−15.7692	+	11.2397i	−0.814320	+	0.580416i
$376$	−9.25350	−	12.3078i	−0.477213	−	0.634724i
$377$			2.86391i			0.147499i
$378$	−4.11010	−	8.68350i	−0.211401	−	0.446631i
$379$			3.73649i			0.191930i	0.995385	+	0.0959652i	$0.0305937\pi$
$379$			3.73649i			0.191930i	−0.995385	+	0.0959652i	$0.969406\pi$
$380$	−24.9755	+	0.244469i	−1.28122	+	0.0125410i
$381$	−16.2910	+	17.8861i	−0.834611	+	0.916334i
$382$	11.7075	+	6.14330i	0.599005	+	0.314319i
$383$	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	$0.422428\pi$
$384$	19.5515	−	1.31903i	0.997732	−	0.0673117i
$385$	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	−0.642926	−	0.765928i	$-0.722280\pi$
$389$	−5.93814	+	3.42839i	−0.301076	+	0.173826i	0.341850	+	0.939754i	$0.388946\pi$
$390$	−2.90365	+	11.5775i	−0.147032	+	0.586252i
$391$	4.46022	−	7.72533i	0.225563	−	0.390687i
$392$	−13.7687	−	5.86221i	−0.695423	−	0.296086i
$393$	−5.07632	−	15.9328i	−0.256066	−	0.803705i
$394$	−29.5543	+	18.6925i	−1.48893	+	0.941714i
$395$	−23.9613	−	16.2011i	−1.20562	−	0.815168i
$396$	−7.67927	+	1.34984i	−0.385898	+	0.0678322i
$397$	−16.2588			−0.816004			−0.408002	−	0.912981i	$-0.633774\pi$
$397$	−16.2588			−0.816004			−0.408002	+	0.912981i	$0.633774\pi$
$398$	−13.2203	+	8.36154i	−0.662673	+	0.419126i
$399$	−2.70010	+	12.3550i	−0.135174	+	0.618526i
$400$	−19.9962	+	0.391496i	−0.999808	+	0.0195748i
$401$	−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	$0.298826\pi$
$402$	−12.7284	+	15.1610i	−0.634837	+	0.756160i
$403$	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
$408$	−18.9624	−	13.4711i	−0.938781	−	0.666918i
$409$	−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	$0.174575\pi$
$410$	−14.7847	−	27.5175i	−0.730163	−	1.35899i
$411$	7.78926	+	1.70228i	0.384216	+	0.0839675i
$412$	32.3197	−	22.3167i	1.59228	−	1.09946i
$413$	8.84767			0.435365
$414$	1.06207	+	7.89990i	0.0521980	+	0.388259i
$415$	7.12021	+	4.81425i	0.349517	+	0.236322i
$416$	−9.22390	+	8.17854i	−0.452239	+	0.400986i
$417$	−6.62243	−	20.7856i	−0.324302	−	1.01787i
$418$	9.08861	+	4.76910i	0.444538	+	0.233264i
$419$	30.9697	+	17.8804i	1.51297	+	0.873514i	0.999885	+	0.0151767i	$0.00483108\pi$
$419$	30.9697	+	17.8804i	1.51297	+	0.873514i	0.513086	+	0.858337i	$0.328502\pi$
$420$	−2.06516	+	9.91395i	−0.100769	+	0.483751i
$421$	−18.9979	+	10.9684i	−0.925900	+	0.534568i	−0.885512	−	0.464616i	$-0.846192\pi$
$421$	−18.9979	+	10.9684i	−0.925900	+	0.534568i	−0.0403871	+	0.999184i	$0.512859\pi$
$422$	−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
$426$	−6.11359	−	1.07967i	−0.296205	−	0.0523102i
$427$	6.29367	−	10.9010i	0.304572	−	0.527534i
$428$	8.90222	−	18.7691i	0.430305	−	0.907240i
$429$	3.30288	−	3.62629i	0.159465	−	0.175079i
$430$	25.9732	+	0.794309i	1.25254	+	0.0383050i
$431$	11.7024			0.563684			0.281842	−	0.959461i	$-0.409055\pi$
$431$	11.7024			0.563684			0.281842	+	0.959461i	$0.409055\pi$
$432$	20.7683	−	0.822047i	0.999218	−	0.0395507i
$433$		−	18.5776i		−	0.892781i	−0.894838	−	0.446391i	$-0.852709\pi$
$433$		−	18.5776i		−	0.892781i	0.894838	−	0.446391i	$-0.147291\pi$
$434$	3.38006	+	5.34415i	0.162248	+	0.256527i
$435$	−4.94695	+	1.19753i	−0.237188	+	0.0574174i
$436$	−9.49175	−	4.50195i	−0.454573	−	0.215604i
$437$	5.24645	−	9.08711i	0.250972	−	0.434696i
$438$	−6.24491	+	35.3615i	−0.298393	+	1.68964i
$439$	−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	$-0.409116\pi$
$440$	7.31470	+	3.74743i	0.348715	+	0.178651i
$441$	−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	0.994744	−	0.102391i	$-0.0326494\pi$
$443$	8.60211	+	14.8993i	0.408699	+	0.707887i	−0.586046	+	0.810278i	$0.699316\pi$
$444$	−24.6200	+	10.0960i	−1.16842	+	0.479136i
$445$	−20.9124	+	10.1707i	−0.991344	+	0.482138i
$446$	11.7967	−	22.4812i	0.558589	−	1.06452i
$447$	−9.13550	−	28.6732i	−0.432095	−	1.35620i
$448$	−7.53933	+	7.24889i	−0.356200	+	0.342478i
$449$	−12.6078			−0.595001			−0.297500	−	0.954722i	$-0.596153\pi$
$449$	−12.6078			−0.595001			−0.297500	+	0.954722i	$0.596153\pi$
$450$	−21.2125	−	0.174488i	−0.999966	−	0.00822543i
$451$			12.8368i			0.604462i
$452$	−0.788255	+	0.544287i	−0.0370764	+	0.0256011i
$453$	−3.89665	+	17.8302i	−0.183080	+	0.837734i
$454$	−2.81570	−	1.47749i	−0.132147	−	0.0693423i
$455$	−2.78629	−	5.72900i	−0.130623	−	0.268580i
$456$	−22.3051	−	15.8457i	−1.04453	−	0.742043i
$457$	−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
$460$	4.12965	−	7.31725i	0.192546	−	0.341168i
$461$	0.962364	−	0.555621i	0.0448217	−	0.0258778i	−0.477422	−	0.878674i	$-0.658429\pi$
$461$	0.962364	−	0.555621i	0.0448217	−	0.0258778i	0.522243	+	0.852796i	$0.325095\pi$
$462$	2.67579	−	3.18716i	0.124489	−	0.148280i
$463$	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	$0.489585\pi$
$464$	−4.91577	−	1.86243i	−0.228209	−	0.0864611i
$465$	−9.59104	+	9.13602i	−0.444774	+	0.423673i
$466$	10.5898	+	16.7433i	0.490562	+	0.775618i
$467$	3.30323			0.152855			0.0764276	−	0.997075i	$-0.475649\pi$
$467$	3.30323			0.152855			0.0764276	+	0.997075i	$0.475649\pi$
$468$	−10.0208	+	8.39934i	−0.463211	+	0.388259i
$469$		−	10.5655i		−	0.487869i
$470$	−0.526246	+	17.2078i	−0.0242739	+	0.793736i
$471$	24.1215	−	7.68527i	1.11146	−	0.354119i
$472$	−7.49847	+	17.6118i	−0.345145	+	0.810649i
$473$	−9.24774	−	5.33919i	−0.425212	−	0.245496i
$474$	−10.8290	−	29.7771i	−0.497393	−	1.36771i
$475$	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	$0.864882\pi$
$480$	−17.9840	−	12.5130i	−0.820855	−	0.571136i
$481$	8.36992	−	14.4971i	0.381636	−	0.661012i
$482$	16.2416	+	8.52254i	0.739786	+	0.388191i
$483$	−3.14525	−	2.86474i	−0.143114	−	0.130350i
$484$	10.5814	+	15.3243i	0.480973	+	0.696561i
$485$	−9.74542	+	14.4134i	−0.442517	+	0.654477i
$486$	22.0439	−	0.259236i	0.999931	−	0.0117592i
$487$		−	2.96062i		−	0.134158i	−0.997748	−	0.0670792i	$-0.978632\pi$
$487$		−	2.96062i		−	0.134158i	0.997748	−	0.0670792i	$-0.0213680\pi$
$488$	16.3650	+	21.7666i	0.740811	+	0.985326i
$489$	−17.5957	−	16.0264i	−0.795703	−	0.724739i
$490$	7.91869	+	14.7384i	0.357730	+	0.665814i
$491$	12.6421	+	7.29891i	0.570529	+	0.329395i	0.757361	−	0.652997i	$-0.226488\pi$
$491$	12.6421	+	7.29891i	0.570529	+	0.329395i	−0.186831	+	0.982392i	$0.559822\pi$
$492$	4.58657	−	33.9106i	0.206778	−	1.52881i
$493$	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
$498$	3.21789	+	8.84841i	0.144197	+	0.396507i
$499$	−19.8379	−	11.4534i	−0.888068	−	0.512726i	−0.0147578	−	0.999891i	$-0.504698\pi$
$499$	−19.8379	−	11.4534i	−0.888068	−	0.512726i	−0.873310	+	0.487165i	$0.838031\pi$
$500$	17.7239	+	13.6332i	0.792636	+	0.609695i
$501$	−9.42946	−	29.5959i	−0.421277	−	1.32225i
$502$	20.7968	+	32.8815i	0.928209	+	1.46757i
$503$			28.6551i			1.27767i	0.769345	+	0.638833i	$0.220583\pi$
$503$			28.6551i			1.27767i	−0.769345	+	0.638833i	$0.779417\pi$
$504$	−8.20731	+	7.46335i	−0.365583	+	0.332444i
$505$	−19.3250	+	28.5814i	−0.859951	+	1.27186i
$506$	−2.91809	+	1.84563i	−0.129725	+	0.0820481i
$507$	−3.05120	+	13.9616i	−0.135509	+	0.620056i
$508$	25.2407	+	11.9717i	1.11987	+	0.531157i
$509$	−33.6466	−	19.4259i	−1.49136	−	0.861038i	−0.491410	−	0.870928i	$-0.663518\pi$
$509$	−33.6466	−	19.4259i	−1.49136	−	0.861038i	−0.999951	+	0.00989035i	$0.996852\pi$
$510$	7.13354	+	25.0084i	0.315878	+	1.10739i
$511$	−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
$516$	22.5218	+	17.4085i	0.991465	+	0.766368i
$517$	3.53732	−	6.12682i	0.155571	−	0.269457i
$518$	6.59910	−	12.5761i	0.289948	−	0.552561i
$519$	6.71544	−	30.7283i	0.294775	−	1.34882i
$520$	13.7653	−	0.690887i	0.603649	−	0.0302974i
$521$	33.5911			1.47165			0.735826	−	0.677171i	$-0.236794\pi$
$521$	33.5911			1.47165			0.735826	+	0.677171i	$0.236794\pi$
$522$	−5.15704	−	2.11958i	−0.225717	−	0.0927714i
$523$	31.5892			1.38130			0.690650	−	0.723189i	$-0.257324\pi$
$523$	31.5892			1.38130			0.690650	+	0.723189i	$0.257324\pi$
$524$	−15.8890	+	10.9713i	−0.694116	+	0.479285i
$525$	8.73085	−	7.20842i	0.381045	−	0.314601i
$526$	4.77644	−	9.10259i	0.208263	−	0.396892i
$527$	14.0630	+	8.11929i	0.612595	+	0.353682i
$528$	4.07647	+	8.02746i	0.177405	+	0.349350i
$529$	−9.73510	−	16.8617i	−0.423265	−	0.733117i
$530$	−2.77776	+	4.48852i	−0.120658	+	0.194969i
$531$	−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
$534$	−25.0859	−	4.43021i	−1.08557	−	0.191714i
$535$	−20.8861	+	10.1579i	−0.902985	+	0.439165i
$536$	21.0312	+	8.95433i	0.908409	+	0.386768i
$537$	−9.41464	+	10.3365i	−0.406272	+	0.446053i
$538$	−15.1570	−	23.9644i	−0.653463	−	1.03318i
$539$		−	6.87541i		−	0.296145i
$540$	−18.6986	−	13.7971i	−0.804662	−	0.593734i
$541$		−	5.71420i		−	0.245673i	−0.992427	−	0.122836i	$-0.960801\pi$
$541$		−	5.71420i		−	0.245673i	0.992427	−	0.122836i	$-0.0391990\pi$
$542$	−3.23920	+	2.04872i	−0.139135	+	0.0880002i
$543$	−20.0857	+	22.0525i	−0.861962	+	0.946363i
$544$	−8.49467	+	25.4801i	−0.364206	+	1.09245i
$545$	5.13696	+	10.5623i	0.220043	+	0.452440i
$546$	1.21366	−	6.87232i	0.0519400	−	0.294108i
$547$	−11.0398	−	19.1216i	−0.472029	−	0.817579i	0.527458	−	0.849581i	$-0.323145\pi$
$547$	−11.0398	−	19.1216i	−0.472029	−	0.817579i	−0.999488	+	0.0320021i	$0.989812\pi$
$548$	−0.742352	−	9.17657i	−0.0317117	−	0.392004i
$549$	16.7093	+	23.5605i	0.713134	+	1.00554i
$550$	−3.76441	−	8.38238i	−0.160515	−	0.357426i
$551$	3.66984	+	6.35636i	0.156341	+	0.270790i
$552$	8.36805	−	3.83290i	0.356168	−	0.163139i
$553$	14.6455	+	8.45559i	0.622791	+	0.359568i
$554$	15.0431	+	7.89360i	0.639118	+	0.335367i
$555$	28.5413	+	8.39577i	1.21151	+	0.356381i
$556$	−20.7285	+	14.3129i	−0.879082	+	0.607003i
$557$	11.8720			0.503034			0.251517	−	0.967853i	$-0.419071\pi$
$557$	11.8720			0.503034			0.251517	+	0.967853i	$0.419071\pi$
$558$	−14.3808	+	1.93337i	−0.608788	+	0.0818462i
$559$	−17.9073			−0.757400
$560$	11.6455	−	1.05691i	0.492113	−	0.0446625i
$561$	2.28167	−	10.4404i	0.0963322	−	0.440794i
$562$	6.59386	+	3.46002i	0.278145	+	0.145952i
$563$	3.22361	−	5.58346i	0.135859	−	0.235315i	−0.790066	−	0.613021i	$-0.789954\pi$
$563$	3.22361	−	5.58346i	0.135859	−	0.235315i	0.925925	+	0.377707i	$0.123287\pi$
$564$	−11.5335	+	14.9211i	−0.485649	+	0.628293i
$565$	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	$0.746888\pi$
$570$	8.39101	+	29.4167i	0.351461	+	1.23213i
$571$	16.4227	+	9.48165i	0.687269	+	0.396795i	0.802588	−	0.596534i	$-0.203456\pi$
$571$	16.4227	+	9.48165i	0.687269	+	0.396795i	−0.115319	+	0.993328i	$0.536789\pi$
$572$	−5.11738	−	2.42718i	−0.213968	−	0.101485i
$573$	3.45722	−	15.8194i	0.144427	−	0.660866i
$574$	9.76266	+	15.4356i	0.407485	+	0.644267i
$575$	−8.71772	+	3.49950i	−0.363554	+	0.145939i
$576$	−7.90046	−	22.6624i	−0.329186	−	0.944265i
$577$		−	10.1998i		−	0.424624i	−0.977202	−	0.212312i	$-0.931901\pi$
$577$		−	10.1998i		−	0.424624i	0.977202	−	0.212312i	$-0.0680994\pi$
$578$	6.62571	−	4.19062i	0.275593	−	0.174307i
$579$	−8.01304	−	25.1502i	−0.333011	−	1.04521i
$580$	2.98829	+	5.06082i	0.124082	+	0.210139i
$581$	−4.35198	−	2.51262i	−0.180551	−	0.104241i
$582$	−17.9117	+	6.51394i	−0.742465	+	0.270011i
$583$	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	$0.181011\pi$
$587$	21.5066	+	37.2505i	0.887671	+	1.53749i	0.0450502	+	0.998985i	$0.485655\pi$
$588$	−2.45657	+	18.1625i	−0.101307	+	0.749010i
$589$	16.5420	+	9.55052i	0.681601	+	0.393522i
$590$	18.8522	−	10.1290i	0.776135	−	0.417003i
$591$	31.6635	+	28.8396i	1.30246	+	1.18630i
$592$	19.4406	+	23.7942i	0.799004	+	0.977936i
$593$			14.6922i			0.603335i	0.953413	+	0.301667i	$0.0975432\pi$
$593$			14.6922i			0.603335i	−0.953413	+	0.301667i	$0.902457\pi$
$594$	4.08539	+	8.63130i	0.167626	+	0.354147i
$595$	−11.4984	−	7.77450i	−0.471388	−	0.318723i
$596$	−28.5945	+	19.7444i	−1.17127	+	0.808761i
$597$	14.1638	+	12.9006i	0.579684	+	0.527985i
$598$	−2.69041	+	5.12718i	−0.110019	+	0.209666i
$599$	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	$0.00401623\pi$
$600$	6.94930	+	23.4884i	0.283704	+	0.958912i
$601$	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
$606$	−35.5186	+	12.9170i	−1.44285	+	0.524718i
$607$	−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	$0.829484\pi$
$608$	−9.99208	+	29.9716i	−0.405232	+	1.21551i
$609$	2.83543	−	0.903388i	0.114897	−	0.0366071i
$610$	0.930679	−	30.4324i	0.0376821	−	1.23217i
$611$		−	11.8640i		−	0.479965i
$612$	−9.75774	+	26.7648i	−0.394433	+	1.08190i
$613$	0.542323			0.0219042			0.0109521	−	0.999940i	$-0.496514\pi$
$613$	0.542323			0.0219042			0.0109521	+	0.999940i	$0.496514\pi$
$614$	28.4261	−	17.9789i	1.14719	−	0.725570i
$615$	−27.7019	+	26.3876i	−1.11705	+	1.06405i
$616$	−4.42120	−	1.88239i	−0.178135	−	0.0758437i
$617$	−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	$0.717728\pi$
$618$	−36.8408	−	30.9298i	−1.48195	−	1.24418i
$619$	−36.5733	+	21.1156i	−1.47000	+	0.848707i	−0.999433	−	0.0336559i	$-0.989285\pi$
$619$	−36.5733	+	21.1156i	−1.47000	+	0.848707i	−0.470570	+	0.882363i	$0.655952\pi$
$620$	13.3202	+	7.51753i	0.534950	+	0.301911i
$621$	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
$624$	12.6512	+	8.24022i	0.506452	+	0.329873i
$625$	−5.93937	−	24.2842i	−0.237575	−	0.971369i
$626$	6.33543	−	12.0736i	0.253215	−	0.482558i
$627$	2.68387	−	12.2808i	0.107184	−	0.490447i
$628$	−16.6100	−	24.0552i	−0.662812	−	0.959906i
$629$		−	36.4721i		−	1.45424i
$630$	12.3783	−	0.777228i	0.493164	−	0.0309655i
$631$	−20.8270			−0.829112			−0.414556	−	0.910024i	$-0.636063\pi$
$631$	−20.8270			−0.829112			−0.414556	+	0.910024i	$0.636063\pi$
$632$	−29.2435	+	21.9866i	−1.16325	+	0.874578i
$633$	4.10106	+	12.8718i	0.163002	+	0.511609i
$634$	−20.5853	−	10.8018i	−0.817547	−	0.428995i
$635$	−13.6603	−	28.0876i	−0.542093	−	1.11462i
$636$	−5.34998	+	2.19388i	−0.212140	+	0.0869930i
$637$	−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
$640$	−7.76583	+	24.0768i	−0.306971	+	0.951719i
$641$	−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	$0.933030\pi$
$642$	−25.0543	−	4.42463i	−0.988814	−	0.174626i
$643$	2.58179	−	4.47180i	0.101816	−	0.176351i	−0.810617	−	0.585577i	$-0.800868\pi$
$643$	2.58179	−	4.47180i	0.101816	−	0.176351i	0.912433	+	0.409226i	$0.134201\pi$
$644$	−2.10520	+	4.43853i	−0.0829565	+	0.174902i
$645$	−7.48788	−	30.9320i	−0.294835	−	1.21795i
$646$	31.6940	−	20.0458i	1.24698	−	0.788691i
$647$			23.3690i			0.918732i	0.888247	+	0.459366i	$0.151923\pi$
$647$			23.3690i			0.918732i	−0.888247	+	0.459366i	$0.848077\pi$
$648$	−7.70829	−	24.2607i	−0.302810	−	0.953051i
$649$	−8.79449			−0.345214
$650$	−12.4956	−	9.01732i	−0.490116	−	0.353689i
$651$	5.21491	−	5.72554i	0.204388	−	0.224401i
$652$	−11.7773	+	24.8307i	−0.461233	+	0.972447i
$653$	−5.82035	+	10.0811i	−0.227768	+	0.394506i	−0.957146	−	0.289605i	$-0.906476\pi$
$653$	−5.82035	+	10.0811i	−0.227768	+	0.394506i	0.729378	+	0.684111i	$0.239809\pi$
$654$	−2.23758	+	12.6702i	−0.0874964	+	0.495445i
$655$	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	−0.680748	−	0.732517i	$-0.738345\pi$
$659$	−9.92811	+	5.73200i	−0.386744	+	0.223287i	0.294004	+	0.955804i	$0.405012\pi$
$660$	2.05275	−	9.85435i	0.0799030	−	0.383580i
$661$	−29.9208	−	17.2748i	−1.16378	−	0.671911i	−0.211576	−	0.977362i	$-0.567860\pi$
$661$	−29.9208	−	17.2748i	−1.16378	−	0.671911i	−0.952208	+	0.305450i	$0.901193\pi$
$662$	−20.1739	+	38.4460i	−0.784081	+	1.49424i
$663$	−5.44045	−	17.0757i	−0.211290	−	0.663167i
$664$	8.68985	−	6.53341i	0.337232	−	0.253545i
$665$	−13.5253	−	9.14495i	−0.524487	−	0.354626i
$666$	19.9104	+	25.8010i	0.771511	+	0.999768i
$667$	−2.46907			−0.0956027
$668$	−29.5146	+	20.3797i	−1.14195	+	0.788514i
$669$	−30.3773	−	6.63873i	−1.17445	−	0.256668i
$670$	−12.0955	−	22.5125i	−0.467292	−	0.869733i
$671$	−6.25584	+	10.8354i	−0.241504	+	0.418297i
$672$	11.0068	+	6.55233i	0.424595	+	0.252762i
$673$	−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	$-0.860693\pi$
$677$	−21.3333	−	36.9503i	−0.819905	−	1.42012i	0.0858476	−	0.996308i	$-0.472640\pi$
$678$	0.898520	+	0.754356i	0.0345075	+	0.0289709i
$679$	5.08626	−	8.80967i	0.195193	−	0.338084i
$680$	25.2205	−	16.2992i	0.967164	−	0.625047i
$681$	−0.831479	+	3.80466i	−0.0318623	+	0.145795i
$682$	−3.35974	−	5.31202i	−0.128651	−	0.203408i
$683$	11.6809			0.446956			0.223478	−	0.974709i	$-0.428259\pi$
$683$	11.6809			0.446956			0.223478	+	0.974709i	$0.428259\pi$
$684$	−11.4778	+	31.4828i	−0.438864	+	1.20377i
$685$	−5.76545	+	8.52703i	−0.220287	+	0.325801i
$686$	−12.1470	−	19.2053i	−0.463773	−	0.733263i
$687$	−1.11421	−	3.49712i	−0.0425097	−	0.133423i
$688$	11.6453	−	30.7371i	0.443973	−	1.17184i
$689$	1.81880	−	3.15025i	0.0692907	−	0.120015i
$690$	−9.98136	−	2.50333i	−0.379984	−	0.0953001i
$691$	−2.63092	+	1.51896i	−0.100085	+	0.0577840i	−0.549207	−	0.835686i	$-0.685070\pi$
$691$	−2.63092	+	1.51896i	−0.100085	+	0.0577840i	0.449122	+	0.893470i	$0.351737\pi$
$692$	−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
$696$	−0.604803	+	6.40971i	−0.0229250	+	0.242959i
$697$	40.6184	+	23.4510i	1.53853	+	0.888271i
$698$	−16.9533	+	32.3084i	−0.641692	+	1.22289i
$699$	16.3384	−	17.9382i	0.617975	−	0.678485i
$700$	−10.9015	−	7.21643i	−0.412036	−	0.272755i
$701$			13.9946i			0.528568i	0.964445	+	0.264284i	$0.0851356\pi$
$701$			13.9946i			0.528568i	−0.964445	+	0.264284i	$0.914864\pi$
$702$	13.1704	+	9.10970i	0.497086	+	0.343824i
$703$		−	42.9012i		−	1.61805i
$704$	7.49401	−	7.20532i	0.282441	−	0.271561i
$705$	20.4931	−	4.96088i	0.771815	−	0.186837i
$706$	0.0399152	−	0.0760674i	0.00150223	−	0.00286283i
$707$	10.0860	−	17.4694i	0.379322	−	0.657004i
$708$	23.2321	+	3.14225i	0.873115	+	0.118093i
$709$	38.9397	−	22.4819i	1.46241	−	0.844324i	0.463289	−	0.886207i	$-0.346669\pi$
$709$	38.9397	−	22.4819i	1.46241	−	0.844324i	0.999123	+	0.0418834i	$0.0133358\pi$
$710$	4.21767	−	6.81524i	0.158286	−	0.255771i
$711$	−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
$714$	−5.19655	−	14.2892i	−0.194476	−	0.534762i
$715$	2.76954	+	5.69456i	0.103575	+	0.212965i
$716$	14.5867	+	6.91850i	0.545132	+	0.258557i
$717$	−35.1739	+	11.2067i	−1.31359	+	0.418521i
$718$	−2.20519	+	1.39473i	−0.0822969	+	0.0520510i
$719$	0.765821			0.0285603			0.0142801	−	0.999898i	$-0.495454\pi$
$719$	0.765821			0.0285603			0.0142801	+	0.999898i	$0.495454\pi$
$720$	−8.94361	+	25.2985i	−0.333309	+	0.942818i
$721$	25.6739			0.956145
$722$	14.5718	−	9.21635i	0.542306	−	0.342997i
$723$	4.79617	−	21.9461i	0.178371	−	0.816186i
$724$	31.1202	+	14.7603i	1.15657	+	0.548564i
$725$	0.929065	−	6.50493i	0.0345046	−	0.241587i
$726$	14.6653	−	17.4680i	0.544281	−	0.648298i
$727$	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
$730$	−39.4199	−	24.3954i	−1.45900	−	0.902913i
$731$	−33.7886	+	19.5079i	−1.24972	+	0.721524i
$732$	20.3973	−	26.3884i	0.753906	−	0.975343i
$733$	20.1595	−	34.9172i	0.744607	−	1.28970i	−0.205771	−	0.978600i	$-0.565970\pi$
$733$	20.1595	−	34.9172i	0.744607	−	1.28970i	0.950378	−	0.311097i	$-0.100696\pi$
$734$	−8.68336	+	16.5481i	−0.320509	+	0.610802i
$735$	14.8372	−	14.1333i	0.547277	−	0.521313i
$736$	−7.05097	−	7.95221i	−0.259902	−	0.293122i
$737$			10.5020i			0.386845i
$738$	−41.5363	+	5.58418i	−1.52897	+	0.205556i
$739$			52.8497i			1.94411i	0.234758	+	0.972054i	$0.424570\pi$
$739$			52.8497i			1.94411i	−0.234758	+	0.972054i	$0.575430\pi$
$740$	−0.336242	−	34.3513i	−0.0123605	−	1.26278i
$741$	−6.39947	−	20.0858i	−0.235091	−	0.737869i
$742$	1.43399	−	2.73280i	0.0526436	−	0.100324i
$743$	−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	$0.700089\pi$
$744$	6.97733	+	15.2330i	0.255801	+	0.558469i
$745$	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
$750$	10.3510	−	25.3546i	0.377965	−	0.925820i
$751$	−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	$0.268252\pi$
$752$	20.3640	+	7.71525i	0.742597	+	0.281346i
$753$	32.0863	−	35.2281i	1.16929	−	1.28378i
$754$	−2.16497	−	3.42300i	−0.0788436	−	0.124658i
$755$	−19.5189	−	13.1975i	−0.710367	−	0.480307i
$756$	11.4767	+	7.27164i	0.417405	+	0.264467i
$757$	−3.23350			−0.117524			−0.0587619	−	0.998272i	$-0.518715\pi$
$757$	−3.23350			−0.117524			−0.0587619	+	0.998272i	$0.518715\pi$
$758$	−2.82459	−	4.46591i	−0.102594	−	0.162209i
$759$	3.12634	+	2.84752i	0.113479	+	0.103358i
$760$	29.6663	−	19.1724i	1.07611	−	0.695456i
$761$	−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	$0.901219\pi$
$762$	5.95023	−	33.6929i	0.215554	−	1.22057i
$763$	−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
$768$	−22.3711	+	16.3564i	−0.807248	+	0.590212i
$769$	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	$-0.215398\pi$
$770$	2.54274	+	4.73260i	0.0916340	+	0.170551i
$771$	10.5830	+	33.2164i	0.381138	+	1.19626i
$772$	−25.0811	+	17.3184i	−0.902689	+	0.623304i
$773$	1.05635			0.0379943			0.0189971	−	0.999820i	$-0.493953\pi$
$773$	1.05635			0.0379943			0.0189971	+	0.999820i	$0.493953\pi$
$774$	13.2532	−	32.2457i	0.476376	−	1.15905i
$775$	−6.37042	−	15.8695i	−0.228832	−	0.570051i
$776$	13.2255	+	17.5908i	0.474768	+	0.631472i
$777$	−16.9931	−	3.71372i	−0.609626	−	0.133229i
$778$	4.50568	−	8.58659i	0.161536	−	0.307844i
$779$	47.7784	+	27.5849i	1.71184	+	0.988330i
$780$	−5.28153	−	16.0327i	−0.189109	−	0.574062i
$781$	−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
$786$	18.1117	+	15.2057i	0.646023	+	0.542371i
$787$	4.90026	−	8.48751i	0.174676	−	0.302547i	−0.765373	−	0.643587i	$-0.777446\pi$
$787$	4.90026	−	8.48751i	0.174676	−	0.302547i	0.940049	+	0.341040i	$0.110779\pi$
$788$	21.1933	−	44.6831i	0.754979	−	1.59177i
$789$	−12.2997	−	2.68800i	−0.437880	−	0.0956954i
$790$	40.8862	+	1.25037i	1.45466	+	0.0444863i
$791$	−0.626167			−0.0222639
$792$	8.15797	−	7.41849i	0.289881	−	0.263604i
$793$			20.9817i			0.745083i
$794$	19.4327	−	12.2908i	0.689642	−	0.436184i
$795$	6.20207	+	1.82441i	0.219965	+	0.0647053i
$796$	9.48019	−	19.9877i	0.336017	−	0.708445i
$797$	8.52322	−	14.7627i	0.301908	−	0.522920i	−0.674660	−	0.738129i	$-0.735710\pi$
$797$	8.52322	−	14.7627i	0.301908	−	0.522920i	0.976568	+	0.215209i	$0.0690431\pi$
$798$	−6.11257	−	16.8081i	−0.216383	−	0.595000i
$799$	−12.9244	−	22.3856i	−0.457231	−	0.791947i
$800$	23.6038	−	15.5840i	0.834520	−	0.550978i
$801$	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
$804$	3.75233	−	27.7427i	0.132335	−	0.978409i
$805$	4.93915	−	2.40214i	0.174082	−	0.0846644i
$806$	−9.33341	−	4.89756i	−0.328755	−	0.172509i
$807$	−23.3849	+	25.6746i	−0.823186	+	0.903790i
$808$	26.2259	+	34.8821i	0.922624	+	1.22715i
$809$	−5.72585			−0.201310			−0.100655	−	0.994921i	$-0.532094\pi$
$809$	−5.72585			−0.201310			−0.100655	+	0.994921i	$0.532094\pi$
$810$	−10.2284	+	26.5590i	−0.359388	+	0.933188i
$811$		−	54.0055i		−	1.89639i	−0.317689	−	0.948195i	$-0.602907\pi$
$811$		−	54.0055i		−	1.89639i	0.317689	−	0.948195i	$-0.397093\pi$
$812$	−1.95247	−	2.82764i	−0.0685184	−	0.0992306i
$813$	3.47037	+	3.16086i	0.121711	+	0.110856i
$814$	−6.55943	+	12.5005i	−0.229908	+	0.438142i
$815$	27.6314	−	13.4385i	0.967886	−	0.470729i
$816$	32.8477	+	1.76622i	1.14990	+	0.0618302i
$817$	−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
$820$	38.4727	+	21.7130i	1.34353	+	0.758249i
$821$	17.6578	−	10.1948i	0.616263	−	0.355800i	−0.159150	−	0.987254i	$-0.550875\pi$
$821$	17.6578	−	10.1948i	0.616263	−	0.355800i	0.775413	+	0.631455i	$0.217542\pi$
$822$	−10.5967	+	3.85368i	−0.369602	+	0.134413i
$823$	−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	$0.682165\pi$
$824$	−21.7588	+	51.1053i	−0.758004	+	1.78034i
$825$	−8.67837	+	7.16509i	−0.302142	+	0.249456i
$826$	−10.5749	+	6.68839i	−0.367947	+	0.232719i
$827$	21.1112			0.734108			0.367054	−	0.930200i	$-0.380366\pi$
$827$	21.1112			0.734108			0.367054	+	0.930200i	$0.380366\pi$
$828$	−7.24133	−	8.63922i	−0.251654	−	0.300234i
$829$		−	15.7409i		−	0.546704i	−0.961914	−	0.273352i	$-0.911868\pi$
$829$		−	15.7409i		−	0.546704i	0.961914	−	0.273352i	$-0.0881324\pi$
$830$	−12.1495	−	0.371554i	−0.421716	−	0.0128968i
$831$	4.44222	−	20.3266i	0.154099	−	0.705121i
$832$	4.84200	−	16.7479i	0.167866	−	0.580629i
$833$	−21.7552	−	12.5604i	−0.753775	−	0.435192i
$834$	23.6281	+	19.8370i	0.818173	+	0.686900i
$835$	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	$-0.362074\pi$
$840$	−5.02612	−	13.4105i	−0.173418	−	0.462705i
$841$	−13.6365	+	23.6190i	−0.470223	+	0.814449i
$842$	14.4150	−	27.4711i	0.496774	−	0.946715i
$843$	1.94717	−	8.90981i	0.0670642	−	0.306870i
$844$	12.8365	−	8.86353i	0.441849	−	0.305095i
$845$	−15.2840	−	10.3341i	−0.525785	−	0.355503i
$846$	21.3634	+	8.78052i	0.734489	+	0.301880i
$847$			12.1732i			0.418276i
$848$	4.22448	+	5.17052i	0.145069	+	0.177556i
$849$	4.33944	−	1.38258i	0.148929	−	0.0474499i
$850$	−33.4006	−	3.40202i	−1.14563	−	0.116688i
$851$	12.4984	+	7.21597i	0.428441	+	0.247360i
$852$	8.12324	−	3.33112i	0.278298	−	0.114122i
$853$	8.28860	+	14.3563i	0.283796	+	0.491549i	0.972317	−	0.233668i	$-0.0750728\pi$
$853$	8.28860	+	14.3563i	0.283796	+	0.491549i	−0.688520	+	0.725217i	$0.741739\pi$
$854$	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	$0.385044\pi$
$858$	−1.20637	+	6.83101i	−0.0411848	+	0.233207i
$859$	7.21262	+	4.16421i	0.246091	+	0.142081i	0.617973	−	0.786199i	$-0.287954\pi$
$859$	7.21262	+	4.16421i	0.246091	+	0.142081i	−0.371882	+	0.928280i	$0.621287\pi$
$860$	−31.6441	+	18.6850i	−1.07905	+	0.637155i
$861$	15.0623	−	16.5371i	0.513321	−	0.563584i
$862$	−13.9869	+	8.84640i	−0.476395	+	0.301310i
$863$		−	16.9671i		−	0.577568i	−0.957394	−	0.288784i	$-0.906749\pi$
$863$		−	16.9671i		−	0.577568i	0.957394	−	0.288784i	$-0.0932510\pi$
$864$	−24.2012	+	16.6823i	−0.823343	+	0.567544i
$865$	33.6388	+	22.7445i	1.14375	+	0.773335i
$866$	14.0437	+	22.2042i	0.477224	+	0.754530i
$867$	−7.09856	−	6.46548i	−0.241080	−	0.219579i
$868$	−8.07980	−	3.83226i	−0.274246	−	0.130075i
$869$	−14.5575	−	8.40477i	−0.493829	−	0.285112i
$870$	5.00740	−	5.17095i	0.169767	−	0.175312i
$871$	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
$876$	−19.2675	−	46.9855i	−0.650988	−	1.58749i
$877$	−4.17126	+	7.22484i	−0.140854	+	0.243966i	−0.927818	−	0.373032i	$-0.878318\pi$
$877$	−4.17126	+	7.22484i	−0.140854	+	0.243966i	0.786965	+	0.616998i	$0.211651\pi$
$878$	36.2157	+	19.0036i	1.22222	+	0.641341i
$879$	−24.0121	+	7.65043i	−0.809908	+	0.258043i
$880$	−11.5755	+	1.05055i	−0.390210	+	0.0354142i
$881$	−21.8620			−0.736550			−0.368275	−	0.929717i	$-0.620051\pi$
$881$	−21.8620			−0.736550			−0.368275	+	0.929717i	$0.620051\pi$
$882$	22.2469	−	2.99089i	0.749091	−	0.100709i
$883$	2.50414			0.0842711			0.0421355	−	0.999112i	$-0.486584\pi$
$883$	2.50414			0.0842711			0.0421355	+	0.999112i	$0.486584\pi$
$884$	−17.0288	+	11.7583i	−0.572741	+	0.395476i
$885$	−18.0782	−	18.9785i	−0.607690	−	0.637957i
$886$	−21.5445	−	11.3051i	−0.723801	−	0.379803i
$887$	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	$0.536887\pi$
$888$	21.7942	−	30.6784i	0.731366	−	1.02950i
$889$	9.13055	+	15.8146i	0.306229	+	0.530404i
$890$	17.3063	−	27.9649i	0.580110	−	0.937386i
$891$	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
$894$	32.5944	+	27.3648i	1.09012	+	0.915214i
$895$	−7.89438	−	16.2320i	−0.263880	−	0.542575i
$896$	3.53134	−	14.3633i	0.117974	−	0.479846i
$897$	6.92799	+	1.51406i	0.231319	+	0.0505530i
$898$	15.0691	−	9.53088i	0.502862	−	0.318050i
$899$		−	4.49464i		−	0.149905i
$900$	25.4854	−	15.8270i	0.849514	−	0.527567i
$901$		−	7.92544i		−	0.264035i
$902$	−9.70397	−	15.3428i	−0.323107	−	0.510858i
$903$	5.64866	+	17.7292i	0.187976	+	0.589992i
$904$	0.530681	−	1.24642i	0.0176502	−	0.0414553i
$905$	−16.8423	−	34.6302i	−0.559858	−	1.15115i
$906$	−8.82134	−	24.2566i	−0.293070	−	0.805870i
$907$	−2.57114	−	4.45335i	−0.0853735	−	0.147871i	0.820177	−	0.572110i	$-0.193875\pi$
$907$	−2.57114	−	4.45335i	−0.0853735	−	0.147871i	−0.905550	+	0.424239i	$0.860542\pi$
$908$	4.48228	−	0.362601i	0.148750	−	0.0120333i
$909$	26.7776	+	37.7571i	0.888155	+	1.25232i
$910$	7.66105	+	4.74111i	0.253961	+	0.157166i
$911$	−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	$-0.340197\pi$
$912$	38.6379	+	2.07756i	1.27943	+	0.0687950i
$913$	4.32582	+	2.49751i	0.143164	+	0.0826557i
$914$	2.48538	−	4.73645i	0.0822090	−	0.156668i
$915$	−36.2426	+	8.77343i	−1.19814	+	0.290041i
$916$	−3.48751	+	2.40811i	−0.115231	+	0.0795663i
$917$	−12.6218			−0.416809
$918$	34.7747	+	2.84113i	1.14774	+	0.0937711i
$919$	13.2617			0.437464			0.218732	−	0.975785i	$-0.429808\pi$
$919$	13.2617			0.437464			0.218732	+	0.975785i	$0.429808\pi$
$920$	0.595635	+	11.8675i	0.0196375	+	0.391260i
$921$	−30.4548	−	27.7387i	−1.00352	−	0.914021i
$922$	−0.730212	+	1.39158i	−0.0240482	+	0.0458294i
$923$	−2.76161	+	4.78325i	−0.0908995	+	0.157442i
$924$	−0.788820	+	5.83210i	−0.0259503	+	0.191862i
$925$	−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	$0.947726\pi$
$930$	4.55701	−	18.1698i	0.149430	−	0.595813i
$931$	−25.5902	−	14.7745i	−0.838684	−	0.484214i
$932$	−25.3141	−	12.0065i	−0.829192	−	0.393287i
$933$	−30.0671	+	9.57958i	−0.984351	+	0.313622i
$934$	−3.94807	+	2.49707i	−0.129185	+	0.0817067i
$935$	11.4293	+	7.72776i	0.373777	+	0.252725i
$936$	5.62753	−	17.6142i	0.183942	−	0.575739i
$937$			17.1401i			0.559942i	0.960009	+	0.279971i	$0.0903248\pi$
$937$			17.1401i			0.559942i	−0.960009	+	0.279971i	$0.909675\pi$
$938$	7.98696	+	12.6280i	0.260784	+	0.412320i
$939$	−16.3142	−	3.56534i	−0.532393	−	0.116351i
$940$	−12.3792	−	20.9648i	−0.403766	−	0.683798i
$941$	22.1713	+	12.8006i	0.722763	+	0.417288i	0.815769	−	0.578378i	$-0.196314\pi$
$941$	22.1713	+	12.8006i	0.722763	+	0.417288i	−0.0930055	+	0.995666i	$0.529647\pi$
$942$	−23.0207	+	27.4201i	−0.750054	+	0.893397i
$943$	−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	0.929178	−	0.369632i	$-0.120516\pi$
$947$	4.44609	+	7.70086i	0.144479	+	0.250244i	−0.784700	+	0.619876i	$0.787183\pi$
$948$	35.4530	+	27.4039i	1.15146	+	0.890038i
$949$	27.6667	+	15.9734i	0.898099	+	0.518518i
$950$	−39.2884	−	4.00171i	−1.27468	−	0.129833i
$951$	−6.07885	+	27.8154i	−0.197120	+	0.901977i
$952$	−14.0332	+	10.5508i	−0.454818	+	0.341952i
$953$		−	29.9732i		−	0.970927i	−0.874257	−	0.485463i	$-0.838651\pi$
$953$		−	29.9732i		−	0.970927i	0.874257	−	0.485463i	$-0.161349\pi$
$954$	4.32655	+	5.60660i	0.140077	+	0.181520i
$955$	17.3178	+	11.7092i	0.560390	+	0.378902i
$956$	24.2207	+	35.0773i	0.783355	+	1.13448i
$957$	−2.81838	+	0.897958i	−0.0911054	+	0.0290269i
$958$	5.42394	+	2.84613i	0.175240	+	0.0919542i
$959$	3.00906	−	5.21185i	0.0971678	−	0.168300i
$960$	30.9540	+	1.36069i	0.999035	+	0.0439162i
$961$	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
$966$	5.92484	+	1.04634i	0.190629	+	0.0336654i
$967$	−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	$0.746117\pi$
$968$	−24.2315	−	10.3169i	−0.778829	−	0.331597i
$969$	−33.9559	−	30.9276i	−1.09082	−	0.993536i
$970$	0.752133	−	24.5941i	0.0241495	−	0.789669i
$971$			28.0124i			0.898962i	0.893290	+	0.449481i	$0.148391\pi$
$971$			28.0124i			0.898962i	−0.893290	+	0.449481i	$0.851609\pi$
$972$	−26.1512	+	16.9739i	−0.838801	+	0.544438i
$973$	−16.4661			−0.527879
$974$	2.23808	+	3.53858i	0.0717126	+	0.113383i
$975$	−6.59577	+	17.6826i	−0.211234	+	0.566295i
$976$	−36.0142	−	13.6446i	−1.15279	−	0.436754i
$977$	−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	$0.926053\pi$
$978$	33.1457	+	5.85359i	1.05988	+	0.187177i
$979$	−11.7039	+	6.75723i	−0.374057	+	0.215962i
$980$	−20.6060	−	11.6295i	−0.658236	−	0.371490i
$981$	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	$0.154665\pi$
$984$	20.1527	+	43.9977i	0.642445	+	1.40259i
$985$	−49.7229	+	24.1826i	−1.58430	+	0.770522i
$986$	−7.81393	−	4.10024i	−0.248846	−	0.130578i
$987$	−11.7460	+	3.74235i	−0.373879	+	0.119120i
$988$	−20.0306	+	13.8310i	−0.637258	+	0.440024i
$989$		−	15.4385i		−	0.490915i
$990$	−12.3039	+	0.772556i	−0.391044	+	0.0245534i
$991$	19.2664			0.612017			0.306008	−	0.952029i	$-0.401006\pi$
$991$	19.2664			0.612017			0.306008	+	0.952029i	$0.401006\pi$
$992$	14.4760	−	12.8354i	0.459614	−	0.407525i
$993$	51.9492	+	11.3531i	1.64856	+	0.360280i
$994$	−2.17733	+	4.14940i	−0.0690608	+	0.131611i
$995$	−22.2421	+	10.8174i	−0.705123	+	0.342935i
$996$	−10.5350	−	8.14320i	−0.333815	−	0.258027i
$997$	−11.6049	−	20.1002i	−0.367530	−	0.636581i	0.621649	−	0.783296i	$-0.286463\pi$
$997$	−11.6049	−	20.1002i	−0.367530	−	0.636581i	−0.989179	+	0.146715i	$0.953130\pi$
$998$	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.229.13	yes	136
5.4	even	2	inner	360.2.bk.a.229.56	yes	136
8.5	even	2	inner	360.2.bk.a.229.11	✓	136
9.7	even	3	inner	360.2.bk.a.349.58	yes	136
40.29	even	2	inner	360.2.bk.a.229.58	yes	136
45.34	even	6	inner	360.2.bk.a.349.11	yes	136
72.61	even	6	inner	360.2.bk.a.349.56	yes	136
360.349	even	6	inner	360.2.bk.a.349.13	yes	136

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

\(f(q)\)	\(=\)	\(q+(-1.19522 + 0.755949i) q^{2} +(1.28051 + 1.16631i) q^{3} +(0.857083 - 1.80704i) q^{4} +(-2.01086 + 0.977977i) q^{5} +(-2.41216 - 0.425992i) q^{6} +(1.13221 - 0.653679i) q^{7} +(0.341633 + 2.80772i) q^{8} +(0.279433 + 2.98696i) q^{9} +O(q^{10})\)	\(q+(-1.19522 + 0.755949i) q^{2} +(1.28051 + 1.16631i) q^{3} +(0.857083 - 1.80704i) q^{4} +(-2.01086 + 0.977977i) q^{5} +(-2.41216 - 0.425992i) q^{6} +(1.13221 - 0.653679i) q^{7} +(0.341633 + 2.80772i) q^{8} +(0.279433 + 2.98696i) q^{9} +(1.66411 - 2.68900i) q^{10} +(-1.12540 + 0.649750i) q^{11} +(3.20508 - 1.31432i) q^{12} +(-1.08961 + 1.88726i) q^{13} +(-0.859083 + 1.63718i) q^{14} +(-3.71556 - 1.09298i) q^{15} +(-2.53082 - 3.09757i) q^{16} +4.74800i q^{17} +(-2.59197 - 3.35882i) q^{18} +5.58496i q^{19} +(0.0437727 + 4.47192i) q^{20} +(2.21220 + 0.483460i) q^{21} +(0.853919 - 1.62734i) q^{22} +(-1.62707 - 0.939389i) q^{23} +(-2.83721 + 3.99377i) 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} +(5.26713 - 1.50243i) q^{30} +(1.71004 - 2.96188i) q^{31} +(5.36648 + 1.78910i) q^{32} +(-2.19890 - 0.480554i) q^{33} +(-3.58925 - 5.67489i) q^{34} +(-1.63742 + 2.42173i) q^{35} +(5.63706 + 2.05512i) q^{36} -7.68156 q^{37} +(-4.22194 - 6.67523i) q^{38} +(-3.59640 + 1.14584i) q^{39} +(-3.43286 - 5.31182i) q^{40} +(4.93913 - 8.55483i) q^{41} +(-3.00953 + 1.09447i) 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} +(0.371993 - 6.91821i) q^{48} +(-2.64541 + 4.58198i) q^{49} +(-0.716516 + 7.03467i) q^{50} +(-5.53765 + 6.07988i) q^{51} +(2.47648 + 3.58652i) q^{52} -1.66922 q^{53} +(0.598383 - 7.32407i) q^{54} +(1.62758 - 2.40717i) q^{55} +(2.22215 + 2.95560i) q^{56} +(-6.51381 + 7.15162i) q^{57} +(-0.863571 + 1.64573i) q^{58} +(5.86091 + 3.38380i) q^{59} +(-5.15960 + 5.77741i) 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} +(2.99144 - 1.08789i) q^{66} +(4.04077 - 6.99882i) q^{67} +(8.57985 + 4.06943i) q^{68} +(-0.987864 - 3.10057i) q^{69} +(0.126373 - 4.13230i) q^{70} +2.53449 q^{71} +(-8.29108 + 1.80501i) q^{72} -14.6597i q^{73} +(9.18112 - 5.80686i) q^{74} +(8.54038 - 1.43591i) q^{75} +(10.0923 + 4.78678i) q^{76} +(-0.849457 + 1.47130i) q^{77} +(3.43228 - 4.08822i) q^{78} +(6.46769 + 11.2024i) q^{79} +(8.11848 + 3.75371i) q^{80} +(-8.84383 + 1.66931i) q^{81} +(0.563680 + 13.9586i) q^{82} +(-1.92190 - 3.32884i) q^{83} +(2.76967 - 3.58318i) q^{84} +(-4.64344 - 9.54757i) q^{85} +(-10.2903 - 5.39969i) q^{86} +(2.22376 + 0.485985i) q^{87} +(-2.20879 - 2.93783i) q^{88} +10.3997 q^{89} +(8.49694 + 4.21924i) q^{90} +2.84903i q^{91} +(-3.09205 + 2.13505i) q^{92} +(5.64421 - 1.79829i) q^{93} +(3.57741 - 6.81756i) q^{94} +(-5.46196 - 11.2306i) q^{95} +(4.78520 + 8.54996i) 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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