LMFDB - Embedded newform 640.2.bm.a.101.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.20
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.726334 + 1.21344i) q^{2} +(-1.23992 + 0.662750i) q^{3} +(-0.944879 - 1.76273i) q^{4} +(0.634393 + 0.773010i) q^{5} +(0.0963861 - 1.98595i) q^{6} +(0.491409 - 0.328349i) q^{7} +(2.82526 + 0.133772i) q^{8} +(-0.568550 + 0.850895i) q^{9} +(-1.39878 + 0.208335i) q^{10} +(1.28844 - 0.390843i) q^{11} +(2.33982 + 1.55942i) q^{12} +(-3.74579 - 3.07409i) q^{13} +(0.0415053 + 0.834787i) q^{14} +(-1.29891 - 0.538026i) q^{15} +(-2.21441 + 3.33113i) q^{16} +(-4.56638 + 1.89146i) q^{17} +(-0.619554 - 1.30794i) q^{18} +(0.748461 + 7.59925i) q^{19} +(0.763181 - 1.84866i) q^{20} +(-0.391694 + 0.732807i) q^{21} +(-0.461569 + 1.84732i) q^{22} +(-3.22825 + 0.642139i) q^{23} +(-3.59175 + 1.70658i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(6.45092 - 2.31248i) q^{26} +(0.554440 - 5.62933i) q^{27} +(-1.04311 - 0.555969i) q^{28} +(1.38269 - 4.55813i) q^{29} +(1.59630 - 1.18536i) q^{30} +(-0.603170 - 0.603170i) q^{31} +(-2.43373 - 5.10656i) q^{32} +(-1.33852 + 1.33852i) q^{33} +(1.02155 - 6.91487i) q^{34} +(0.565564 + 0.171562i) q^{35} +(2.03711 + 0.198205i) q^{36} +(-10.1492 - 0.999604i) q^{37} +(-9.76487 - 4.61138i) q^{38} +(6.68183 + 1.32910i) q^{39} +(1.68892 + 2.26882i) q^{40} +(-2.10509 - 10.5830i) q^{41} +(-0.604718 - 1.00756i) q^{42} +(-2.32716 - 1.24389i) q^{43} +(-1.90636 - 1.90186i) q^{44} +(-1.01844 + 0.100307i) q^{45} +(1.56559 - 4.38370i) q^{46} +(3.11554 + 7.52159i) q^{47} +(0.537981 - 5.59793i) q^{48} +(-2.54511 + 6.14445i) q^{49} +(-1.04842 - 0.949108i) q^{50} +(4.40838 - 5.37163i) q^{51} +(-1.87946 + 9.50745i) q^{52} +(-2.45787 - 8.10252i) q^{53} +(6.42815 + 4.76155i) q^{54} +(1.11950 + 0.748026i) q^{55} +(1.43228 - 0.861935i) q^{56} +(-5.96444 - 8.92641i) q^{57} +(4.52673 + 4.98854i) q^{58} +(3.24067 - 2.65955i) q^{59} +(0.278920 + 2.79799i) q^{60} +(-3.50675 - 6.56066i) q^{61} +(1.17001 - 0.293809i) q^{62} +0.604820i q^{63} +(7.96421 + 0.755884i) q^{64} -4.84572i q^{65} +(-0.652005 - 2.59644i) q^{66} +(-2.96125 - 5.54011i) q^{67} +(7.64880 + 6.26209i) q^{68} +(3.57719 - 2.93573i) q^{69} +(-0.618968 + 0.561667i) q^{70} +(-0.235938 - 0.353105i) q^{71} +(-1.72013 + 2.32795i) q^{72} +(5.36398 + 3.58409i) q^{73} +(8.58463 - 11.5894i) q^{74} +(-0.408120 - 1.34539i) q^{75} +(12.6882 - 8.49970i) q^{76} +(0.504816 - 0.615120i) q^{77} +(-6.46602 + 7.14264i) q^{78} +(-5.03667 + 12.1596i) q^{79} +(-3.97980 + 0.401484i) q^{80} +(1.86851 + 4.51097i) q^{81} +(14.3708 + 5.13238i) q^{82} +(-5.72577 + 0.563939i) q^{83} +(1.66184 - 0.00196549i) q^{84} +(-4.35900 - 2.32993i) q^{85} +(3.19968 - 1.92039i) q^{86} +(1.30648 + 6.56810i) q^{87} +(3.69245 - 0.931876i) q^{88} +(-11.5169 - 2.29086i) q^{89} +(0.618007 - 1.30867i) q^{90} +(-2.85009 - 0.280709i) q^{91} +(4.18222 + 5.08378i) q^{92} +(1.14763 + 0.348131i) q^{93} +(-11.3899 - 1.68265i) q^{94} +(-5.39948 + 5.39948i) q^{95} +(6.40200 + 4.71877i) q^{96} +(11.4138 + 11.4138i) q^{97} +(-5.60733 - 7.55127i) q^{98} +(-0.399974 + 1.31854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.726334	+	1.21344i	−0.513595	+	0.858032i
$2$	−0.726334	+	1.21344i	−0.513595	+	0.858032i
$3$	−1.23992	+	0.662750i	−0.715868	+	0.382639i	−0.788761	−	0.614701i	$-0.789277\pi$
$3$	−1.23992	+	0.662750i	−0.715868	+	0.382639i	0.0728930	+	0.997340i	$0.476777\pi$
$4$	−0.944879	−	1.76273i	−0.472439	−	0.881363i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	0.0963861	−	1.98595i	0.0393495	−	0.810759i
$7$	0.491409	−	0.328349i	0.185735	−	0.124104i	−0.459226	−	0.888319i	$-0.651873\pi$
$7$	0.491409	−	0.328349i	0.185735	−	0.124104i	0.644962	+	0.764215i	$0.276873\pi$
$8$	2.82526	+	0.133772i	0.998881	+	0.0472957i
$9$	−0.568550	+	0.850895i	−0.189517	+	0.283632i
$10$	−1.39878	+	0.208335i	−0.442334	+	0.0658815i
$11$	1.28844	−	0.390843i	0.388478	−	0.117843i	−0.0900029	−	0.995941i	$-0.528688\pi$
$11$	1.28844	−	0.390843i	0.388478	−	0.117843i	0.478481	+	0.878098i	$0.341188\pi$
$12$	2.33982	+	1.55942i	0.675448	+	0.450165i
$13$	−3.74579	−	3.07409i	−1.03890	−	0.852599i	−0.0496356	−	0.998767i	$-0.515806\pi$
$13$	−3.74579	−	3.07409i	−1.03890	−	0.852599i	−0.989260	+	0.146168i	$0.953306\pi$
$14$	0.0415053	+	0.834787i	0.0110928	+	0.223106i
$15$	−1.29891	−	0.538026i	−0.335377	−	0.138918i
$16$	−2.21441	+	3.33113i	−0.553602	+	0.832781i
$17$	−4.56638	+	1.89146i	−1.10751	+	0.458746i	−0.860080	−	0.510159i	$-0.829586\pi$
$17$	−4.56638	+	1.89146i	−1.10751	+	0.458746i	−0.247431	+	0.968905i	$0.579586\pi$
$18$	−0.619554	−	1.30794i	−0.146030	−	0.308283i
$19$	0.748461	+	7.59925i	0.171709	+	1.74339i	0.566003	+	0.824403i	$0.308489\pi$
$19$	0.748461	+	7.59925i	0.171709	+	1.74339i	−0.394295	+	0.918984i	$0.629011\pi$
$20$	0.763181	−	1.84866i	0.170652	−	0.413374i
$21$	−0.391694	+	0.732807i	−0.0854746	+	0.159912i
$22$	−0.461569	+	1.84732i	−0.0984069	+	0.393850i
$23$	−3.22825	+	0.642139i	−0.673137	+	0.133895i	−0.519812	−	0.854281i	$-0.673998\pi$
$23$	−3.22825	+	0.642139i	−0.673137	+	0.133895i	−0.153325	+	0.988176i	$0.548998\pi$
$24$	−3.59175	+	1.70658i	−0.733164	+	0.348354i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	6.45092	−	2.31248i	1.26513	−	0.453515i
$27$	0.554440	−	5.62933i	0.106702	−	1.08336i
$28$	−1.04311	−	0.555969i	−0.197129	−	0.105068i
$29$	1.38269	−	4.55813i	0.256760	−	0.846424i	−0.729889	−	0.683565i	$-0.760428\pi$
$29$	1.38269	−	4.55813i	0.256760	−	0.846424i	0.986649	−	0.162859i	$-0.0520715\pi$
$30$	1.59630	−	1.18536i	0.291444	−	0.216417i
$31$	−0.603170	−	0.603170i	−0.108332	−	0.108332i	0.650863	−	0.759195i	$-0.274407\pi$
$31$	−0.603170	−	0.603170i	−0.108332	−	0.108332i	−0.759195	+	0.650863i	$0.774407\pi$
$32$	−2.43373	−	5.10656i	−0.430226	−	0.902721i
$33$	−1.33852	+	1.33852i	−0.233007	+	0.233007i
$34$	1.02155	−	6.91487i	0.175194	−	1.18589i
$35$	0.565564	+	0.171562i	0.0955977	+	0.0289992i
$36$	2.03711	+	0.198205i	0.339518	+	0.0330342i
$37$	−10.1492	−	0.999604i	−1.66851	−	0.164334i	−0.780814	−	0.624763i	$-0.785195\pi$
$37$	−10.1492	−	0.999604i	−1.66851	−	0.164334i	−0.887696	+	0.460430i	$0.847695\pi$
$38$	−9.76487	−	4.61138i	−1.58407	−	0.748064i
$39$	6.68183	+	1.32910i	1.06995	+	0.212826i
$40$	1.68892	+	2.26882i	0.267042	+	0.358732i
$41$	−2.10509	−	10.5830i	−0.328759	−	1.65278i	−0.692600	−	0.721322i	$-0.743535\pi$
$41$	−2.10509	−	10.5830i	−0.328759	−	1.65278i	0.363841	−	0.931461i	$-0.381465\pi$
$42$	−0.604718	−	1.00756i	−0.0933101	−	0.155470i
$43$	−2.32716	−	1.24389i	−0.354888	−	0.189692i	0.284312	−	0.958732i	$-0.408235\pi$
$43$	−2.32716	−	1.24389i	−0.354888	−	0.189692i	−0.639201	+	0.769040i	$0.720735\pi$
$44$	−1.90636	−	1.90186i	−0.287395	−	0.286716i
$45$	−1.01844	+	0.100307i	−0.151819	+	0.0149529i
$46$	1.56559	−	4.38370i	0.230834	−	0.646341i
$47$	3.11554	+	7.52159i	0.454449	+	1.09714i	0.970613	+	0.240647i	$0.0773595\pi$
$47$	3.11554	+	7.52159i	0.454449	+	1.09714i	−0.516164	+	0.856490i	$0.672641\pi$
$48$	0.537981	−	5.59793i	0.0776508	−	0.807991i
$49$	−2.54511	+	6.14445i	−0.363588	+	0.877779i
$50$	−1.04842	−	0.949108i	−0.148270	−	0.134224i
$51$	4.40838	−	5.37163i	0.617297	−	0.752179i
$52$	−1.87946	+	9.50745i	−0.260634	+	1.31845i
$53$	−2.45787	−	8.10252i	−0.337615	−	1.11297i	−0.947307	−	0.320328i	$-0.896207\pi$
$53$	−2.45787	−	8.10252i	−0.337615	−	1.11297i	0.609692	−	0.792639i	$-0.291293\pi$
$54$	6.42815	+	4.76155i	0.874760	+	0.647965i
$55$	1.11950	+	0.748026i	0.150953	+	0.100864i
$56$	1.43228	−	0.861935i	0.191397	−	0.115181i
$57$	−5.96444	−	8.92641i	−0.790009	−	1.18233i
$58$	4.52673	+	4.98854i	0.594389	+	0.655028i
$59$	3.24067	−	2.65955i	0.421899	−	0.346244i	−0.399365	−	0.916792i	$-0.630769\pi$
$59$	3.24067	−	2.65955i	0.421899	−	0.346244i	0.821264	+	0.570548i	$0.193269\pi$
$60$	0.278920	+	2.79799i	0.0360084	+	0.361219i
$61$	−3.50675	−	6.56066i	−0.448993	−	0.840007i	−0.999985	−	0.00549634i	$-0.998250\pi$
$61$	−3.50675	−	6.56066i	−0.448993	−	0.840007i	0.550992	−	0.834511i	$-0.314250\pi$
$62$	1.17001	−	0.293809i	0.148592	−	0.0373137i
$63$			0.604820i			0.0762002i
$64$	7.96421	+	0.755884i	0.995526	+	0.0944855i
$65$		−	4.84572i		−	0.601037i
$66$	−0.652005	−	2.59644i	−0.0802563	−	0.319599i
$67$	−2.96125	−	5.54011i	−0.361775	−	0.676833i	0.633520	−	0.773726i	$-0.281609\pi$
$67$	−2.96125	−	5.54011i	−0.361775	−	0.676833i	−0.995295	+	0.0968935i	$0.969109\pi$
$68$	7.64880	+	6.26209i	0.927554	+	0.759390i
$69$	3.57719	−	2.93573i	0.430643	−	0.353420i
$70$	−0.618968	+	0.561667i	−0.0739808	+	0.0671320i
$71$	−0.235938	−	0.353105i	−0.0280006	−	0.0419059i	0.817205	−	0.576347i	$-0.195522\pi$
$71$	−0.235938	−	0.353105i	−0.0280006	−	0.0419059i	−0.845206	+	0.534441i	$0.820522\pi$
$72$	−1.72013	+	2.32795i	−0.202719	+	0.274351i
$73$	5.36398	+	3.58409i	0.627806	+	0.419487i	0.828360	−	0.560196i	$-0.189274\pi$
$73$	5.36398	+	3.58409i	0.627806	+	0.419487i	−0.200554	+	0.979683i	$0.564274\pi$
$74$	8.58463	−	11.5894i	0.997943	−	1.34723i
$75$	−0.408120	−	1.34539i	−0.0471256	−	0.155352i
$76$	12.6882	−	8.49970i	1.45544	−	0.974983i
$77$	0.504816	−	0.615120i	0.0575291	−	0.0700994i
$78$	−6.46602	+	7.14264i	−0.732133	+	0.808745i
$79$	−5.03667	+	12.1596i	−0.566670	+	1.36806i	0.337677	+	0.941262i	$0.390359\pi$
$79$	−5.03667	+	12.1596i	−0.566670	+	1.36806i	−0.904346	+	0.426799i	$0.859641\pi$
$80$	−3.97980	+	0.401484i	−0.444955	+	0.0448872i
$81$	1.86851	+	4.51097i	0.207612	+	0.501219i
$82$	14.3708	+	5.13238i	1.58699	+	0.566776i
$83$	−5.72577	+	0.563939i	−0.628485	+	0.0619003i	−0.407245	−	0.913319i	$-0.633510\pi$
$83$	−5.72577	+	0.563939i	−0.628485	+	0.0619003i	−0.221240	+	0.975219i	$0.571010\pi$
$84$	1.66184	−	0.00196549i	0.181322	−	0.000214452i
$85$	−4.35900	−	2.32993i	−0.472800	−	0.252717i
$86$	3.19968	−	1.92039i	0.345031	−	0.207081i
$87$	1.30648	+	6.56810i	0.140069	+	0.704174i
$88$	3.69245	−	0.931876i	0.393617	−	0.0993383i
$89$	−11.5169	−	2.29086i	−1.22079	−	0.242831i	−0.457693	−	0.889111i	$-0.651324\pi$
$89$	−11.5169	−	2.29086i	−1.22079	−	0.242831i	−0.763101	+	0.646280i	$0.776324\pi$
$90$	0.618007	−	1.30867i	0.0651436	−	0.137946i
$91$	−2.85009	−	0.280709i	−0.298770	−	0.0294263i
$92$	4.18222	+	5.08378i	0.436027	+	0.530021i
$93$	1.14763	+	0.348131i	0.119004	+	0.0360995i
$94$	−11.3899	−	1.68265i	−1.17478	−	0.173552i
$95$	−5.39948	+	5.39948i	−0.553975	+	0.553975i
$96$	6.40200	+	4.71877i	0.653401	+	0.481607i
$97$	11.4138	+	11.4138i	1.15890	+	1.15890i	0.984713	+	0.174187i	$0.0557297\pi$
$97$	11.4138	+	11.4138i	1.15890	+	1.15890i	0.174187	+	0.984713i	$0.444270\pi$
$98$	−5.60733	−	7.55127i	−0.566425	−	0.762793i
$99$	−0.399974	+	1.31854i	−0.0401989	+	0.132518i
$100$	1.91319	−	0.582833i	0.191319	−	0.0582833i
$101$	−0.171550	+	1.74177i	−0.0170698	+	0.173313i	−0.999940	−	0.0109883i	$-0.996502\pi$
$101$	−0.171550	+	1.74177i	−0.0170698	+	0.173313i	0.982870	+	0.184301i	$0.0590022\pi$
$102$	3.31620	+	9.25091i	0.328353	+	0.915976i
$103$	1.21993	−	6.13301i	0.120204	−	0.604304i	−0.872981	−	0.487754i	$-0.837816\pi$
$103$	1.21993	−	6.13301i	0.120204	−	0.604304i	0.993185	−	0.116550i	$-0.0371836\pi$
$104$	−10.1716	−	9.18619i	−0.997408	−	0.900780i
$105$	−0.814956	+	0.162105i	−0.0795315	+	0.0158198i
$106$	11.6172	+	2.90265i	1.12836	+	0.281930i
$107$	−6.23973	+	11.6737i	−0.603218	+	1.12854i	0.376170	+	0.926551i	$0.377241\pi$
$107$	−6.23973	+	11.6737i	−0.603218	+	1.12854i	−0.979388	+	0.201990i	$0.935259\pi$
$108$	−10.4468	+	4.34171i	−1.00525	+	0.417781i
$109$	0.538861	+	5.47115i	0.0516136	+	0.524041i	0.985879	+	0.167462i	$0.0535571\pi$
$109$	0.538861	+	5.47115i	0.0516136	+	0.524041i	−0.934265	+	0.356579i	$0.883943\pi$
$110$	−1.72082	+	0.815131i	−0.164073	+	0.0777197i
$111$	13.2466	−	5.48693i	1.25731	−	0.520796i
$112$	0.00559200	+	2.36404i	0.000528394	+	0.223381i
$113$	−5.90100	−	2.44427i	−0.555119	−	0.229938i	0.0874455	−	0.996169i	$-0.472130\pi$
$113$	−5.90100	−	2.44427i	−0.555119	−	0.229938i	−0.642565	+	0.766231i	$0.722130\pi$
$114$	15.1638	−	0.753941i	1.42022	−	0.0706130i
$115$	−2.54436	−	2.08810i	−0.237263	−	0.194717i
$116$	−9.34122	+	1.86957i	−0.867310	+	0.173585i
$117$	4.74540	−	1.43950i	0.438712	−	0.133082i
$118$	0.873399	+	5.86408i	0.0804029	+	0.539833i
$119$	−1.62290	+	2.42885i	−0.148771	+	0.222652i
$120$	−3.59779	−	1.69382i	−0.328431	−	0.154624i
$121$	−7.63886	+	5.10412i	−0.694442	+	0.464011i
$122$	10.5080	+	0.509999i	0.951354	+	0.0461731i
$123$	9.62401	+	11.7269i	0.867768	+	1.05738i
$124$	−0.493301	+	1.63315i	−0.0442997	+	0.146661i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−0.733914	−	0.439301i	−0.0653822	−	0.0391361i
$127$	−14.5570			−1.29173			−0.645863	−	0.763453i	$-0.723502\pi$
$127$	−14.5570			−1.29173			−0.645863	+	0.763453i	$0.723502\pi$
$128$	−6.70189	+	9.11508i	−0.592369	+	0.805667i
$129$	3.70988			0.326637
$130$	5.87999	+	3.51961i	0.515710	+	0.308690i
$131$	10.1374	−	5.41853i	0.885705	−	0.473419i	0.0351968	−	0.999380i	$-0.488794\pi$
$131$	10.1374	−	5.41853i	0.885705	−	0.473419i	0.850509	+	0.525961i	$0.176294\pi$
$132$	3.62419	+	1.09471i	0.315446	+	0.0952821i
$133$	2.86300	+	3.48858i	0.248254	+	0.302498i
$134$	8.87346	+	0.430665i	0.766550	+	0.0372038i
$135$	4.70326	−	3.14262i	0.404792	−	0.270474i
$136$	−13.1543	+	4.73301i	−1.12797	+	0.405852i
$137$	−10.9878	+	16.4444i	−0.938753	+	1.40494i	−0.0245452	+	0.999699i	$0.507814\pi$
$137$	−10.9878	+	16.4444i	−0.938753	+	1.40494i	−0.914208	+	0.405245i	$0.867186\pi$
$138$	0.964095	+	6.47303i	0.0820693	+	0.551021i
$139$	0.602019	−	0.182620i	0.0510625	−	0.0154897i	−0.264650	−	0.964345i	$-0.585256\pi$
$139$	0.602019	−	0.182620i	0.0510625	−	0.0154897i	0.315713	+	0.948855i	$0.397756\pi$
$140$	−0.231973	−	1.15904i	−0.0196053	−	0.0979567i
$141$	−8.84796	−	7.26133i	−0.745132	−	0.611514i
$142$	0.599842	−	0.0298239i	0.0503376	−	0.00250277i
$143$	−6.02769	−	2.49675i	−0.504061	−	0.208789i
$144$	−1.57544	−	3.77814i	−0.131286	−	0.314845i
$145$	4.40066	−	1.82281i	0.365455	−	0.151376i
$146$	−8.24512	+	3.90562i	−0.682371	+	0.323232i
$147$	−0.916501	−	9.30540i	−0.0755918	−	0.767496i
$148$	7.82769	+	18.8347i	0.643432	+	1.54820i
$149$	0.110393	−	0.206530i	0.00904372	−	0.0169196i	−0.877359	−	0.479835i	$-0.840697\pi$
$149$	0.110393	−	0.206530i	0.00904372	−	0.0169196i	0.886403	+	0.462915i	$0.153197\pi$
$150$	1.92898	+	0.481973i	0.157501	+	0.0393529i
$151$	15.2347	−	3.03037i	1.23978	−	0.246608i	0.468708	−	0.883353i	$-0.344719\pi$
$151$	15.2347	−	3.03037i	1.23978	−	0.246608i	0.771075	+	0.636745i	$0.219719\pi$
$152$	1.09803	+	21.5700i	0.0890618	+	1.74956i
$153$	0.986785	−	4.96090i	0.0797768	−	0.401065i
$154$	0.379747	+	1.05935i	0.0306009	+	0.0853645i
$155$	0.0836097	−	0.848903i	0.00671569	−	0.0681856i
$156$	−3.97068	−	13.0341i	−0.317909	−	1.04356i
$157$	6.02513	−	19.8622i	0.480858	−	1.58518i	−0.295798	−	0.955251i	$-0.595585\pi$
$157$	6.02513	−	19.8622i	0.480858	−	1.58518i	0.776655	−	0.629926i	$-0.216915\pi$
$158$	−11.0967	−	14.9436i	−0.882802	−	1.18885i
$159$	8.41751	+	8.41751i	0.667552	+	0.667552i
$160$	2.40349	−	5.12086i	0.190012	−	0.404840i
$161$	−1.37555	+	1.37555i	−0.108408	+	0.108408i
$162$	−6.83096	−	1.00915i	−0.536691	−	0.0792862i
$163$	6.48829	+	1.96820i	0.508202	+	0.154161i	0.533965	−	0.845507i	$-0.320701\pi$
$163$	6.48829	+	1.96820i	0.508202	+	0.154161i	−0.0257627	+	0.999668i	$0.508201\pi$
$164$	−16.6658	+	13.7103i	−1.30138	+	1.07060i
$165$	−1.88384	−	0.185542i	−0.146657	−	0.0144445i
$166$	3.47451	−	7.35749i	0.269674	−	0.571052i
$167$	5.35572	+	1.06532i	0.414438	+	0.0824369i	0.397905	−	0.917426i	$-0.369737\pi$
$167$	5.35572	+	1.06532i	0.414438	+	0.0824369i	0.0165328	+	0.999863i	$0.494737\pi$
$168$	−1.20467	+	2.01798i	−0.0929421	+	0.155690i
$169$	2.04474	+	10.2796i	0.157288	+	0.790738i
$170$	5.99333	−	3.59708i	0.459667	−	0.275884i
$171$	−6.89170	−	3.68369i	−0.527021	−	0.281699i
$172$	0.00624176	+	5.27747i	0.000475929	+	0.402403i
$173$	−10.0213	+	0.987010i	−0.761904	+	0.0750410i	−0.471503	−	0.881864i	$-0.656288\pi$
$173$	−10.0213	+	0.987010i	−0.761904	+	0.0750410i	−0.290400	+	0.956905i	$0.593788\pi$
$174$	−8.91894	−	3.18530i	−0.676143	−	0.241477i
$175$	0.226171	+	0.546024i	0.0170969	+	0.0412756i
$176$	−1.55117	+	5.15742i	−0.116924	+	0.388755i
$177$	−2.25555	+	5.44538i	−0.169538	+	0.409300i
$178$	11.1450	−	12.3112i	0.835351	−	0.922763i
$179$	−9.21358	+	11.2268i	−0.688655	+	0.839128i	−0.993566	−	0.113252i	$-0.963873\pi$
$179$	−9.21358	+	11.2268i	−0.688655	+	0.839128i	0.304911	+	0.952381i	$0.401373\pi$
$180$	1.13911	+	1.70044i	0.0849044	+	0.126744i
$181$	5.61121	+	18.4977i	0.417078	+	1.37492i	0.874221	+	0.485528i	$0.161373\pi$
$181$	5.61121	+	18.4977i	0.417078	+	1.37492i	−0.457143	+	0.889393i	$0.651127\pi$
$182$	2.41074	−	3.25453i	0.178696	−	0.241242i
$183$	8.69617	+	5.81059i	0.642839	+	0.429531i
$184$	−9.20656	+	1.38236i	−0.678716	+	0.101909i
$185$	−5.66585	−	8.47954i	−0.416562	−	0.623428i
$186$	−1.25600	+	1.13973i	−0.0920944	+	0.0835687i
$187$	−5.14423	+	4.22176i	−0.376183	+	0.308726i
$188$	10.3147	−	12.5988i	0.752276	−	0.918865i
$189$	−1.57593	−	2.94835i	−0.114632	−	0.214461i
$190$	−2.63013	−	10.4738i	−0.190809	−	0.759847i
$191$		−	6.12680i		−	0.443319i	−0.975124	−	0.221660i	$-0.928853\pi$
$191$		−	6.12680i		−	0.443319i	0.975124	−	0.221660i	$-0.0711474\pi$
$192$	−10.3759	+	4.34105i	−0.748819	+	0.313288i
$193$			23.1401i			1.66566i	0.553529	+	0.832830i	$0.313281\pi$
$193$			23.1401i			1.66566i	−0.553529	+	0.832830i	$0.686719\pi$
$194$	−22.1403	+	5.55977i	−1.58958	+	0.399168i
$195$	3.21150	+	6.00830i	0.229980	+	0.430263i
$196$	13.2358	−	1.31942i	0.945415	−	0.0942444i
$197$	4.98435	−	4.09055i	0.355120	−	0.291440i	−0.439871	−	0.898061i	$-0.644976\pi$
$197$	4.98435	−	4.09055i	0.355120	−	0.291440i	0.794991	+	0.606622i	$0.207476\pi$
$198$	−1.30945	−	1.44304i	−0.0930587	−	0.102553i
$199$	13.9108	+	20.8189i	0.986107	+	1.47581i	0.876244	+	0.481867i	$0.160041\pi$
$199$	13.9108	+	20.8189i	0.986107	+	1.47581i	0.109863	+	0.993947i	$0.464959\pi$
$200$	−0.682383	+	2.74488i	−0.0482518	+	0.194092i
$201$	7.34343	+	4.90672i	0.517965	+	0.346093i
$202$	−1.98894	−	1.47328i	−0.139941	−	0.103659i
$203$	−0.817189	−	2.69391i	−0.0573555	−	0.189076i
$204$	−13.6341	−	2.69523i	−0.954578	−	0.188704i
$205$	6.84530	−	8.34102i	0.478097	−	0.582562i
$206$	6.55597	+	5.93493i	0.456776	+	0.413506i
$207$	1.28903	−	3.11199i	0.0895937	−	0.216298i
$208$	18.5349	−	5.67041i	1.28516	−	0.393172i
$209$	3.93445	+	9.49861i	0.272152	+	0.657032i
$210$	0.395225	−	1.10664i	0.0272731	−	0.0763656i
$211$	−10.0208	+	0.986962i	−0.689860	+	0.0679453i	−0.436871	−	0.899524i	$-0.643913\pi$
$211$	−10.0208	+	0.986962i	−0.689860	+	0.0679453i	−0.252989	+	0.967469i	$0.581413\pi$
$212$	−11.9601	+	11.9885i	−0.821426	+	0.823371i
$213$	0.526564	+	0.281454i	0.0360796	+	0.0192849i
$214$	−9.63324	−	16.0506i	−0.658515	−	1.09719i
$215$	−0.514792	−	2.58803i	−0.0351085	−	0.176503i
$216$	2.31949	−	15.8302i	0.157821	−	1.07711i
$217$	−0.494453	−	0.0983528i	−0.0335657	−	0.00667662i
$218$	−7.03031	−	3.32000i	−0.476153	−	0.224859i
$219$	−9.02626	−	0.889009i	−0.609938	−	0.0600736i
$220$	0.260773	−	2.68017i	0.0175813	−	0.180697i
$221$	22.9192	+	6.95247i	1.54171	+	0.467674i
$222$	−2.96340	+	20.0593i	−0.198890	+	1.34629i
$223$	−5.90855	+	5.90855i	−0.395666	+	0.395666i	−0.876701	−	0.481035i	$-0.840261\pi$
$223$	−5.90855	+	5.90855i	−0.395666	+	0.395666i	0.481035	+	0.876701i	$0.340261\pi$
$224$	−2.87269	−	1.71030i	−0.191940	−	0.114274i
$225$	−0.723627	−	0.723627i	−0.0482418	−	0.0482418i
$226$	7.25208	−	5.38516i	0.482401	−	0.358215i
$227$	7.16123	−	23.6074i	0.475308	−	1.56688i	−0.311853	−	0.950130i	$-0.600950\pi$
$227$	7.16123	−	23.6074i	0.475308	−	1.56688i	0.787160	−	0.616749i	$-0.211550\pi$
$228$	−10.0991	+	18.9480i	−0.668832	+	1.25486i
$229$	1.46390	−	14.8632i	0.0967371	−	0.982188i	−0.817206	−	0.576346i	$-0.804478\pi$
$229$	1.46390	−	14.8632i	0.0967371	−	0.982188i	0.913943	−	0.405843i	$-0.133022\pi$
$230$	4.38185	−	1.57077i	0.288930	−	0.103574i
$231$	−0.218260	+	1.09727i	−0.0143604	+	0.0721948i
$232$	4.51623	−	12.6930i	0.296505	−	0.833333i
$233$	14.0156	−	2.78789i	0.918196	−	0.182640i	0.286700	−	0.958020i	$-0.407442\pi$
$233$	14.0156	−	2.78789i	0.918196	−	0.182640i	0.631495	+	0.775380i	$0.282442\pi$
$234$	−1.69999	+	6.80382i	−0.111132	+	0.444780i
$235$	−3.83779	+	7.17999i	−0.250350	+	0.468371i
$236$	−7.75010	−	3.19946i	−0.504488	−	0.208267i
$237$	−1.81372	−	18.4150i	−0.117814	−	1.19618i
$238$	−1.76849	−	3.73345i	−0.114634	−	0.242004i
$239$	13.0068	−	5.38757i	0.841337	−	0.348493i	0.0799563	−	0.996798i	$-0.474522\pi$
$239$	13.0068	−	5.38757i	0.841337	−	0.348493i	0.761381	+	0.648305i	$0.224522\pi$
$240$	4.66855	−	3.13542i	0.301353	−	0.202391i
$241$	6.13208	+	2.53999i	0.395002	+	0.163615i	0.571338	−	0.820715i	$-0.306424\pi$
$241$	6.13208	+	2.53999i	0.395002	+	0.163615i	−0.176336	+	0.984330i	$0.556424\pi$
$242$	−0.645192	−	12.9766i	−0.0414745	−	0.834168i
$243$	7.81130	+	6.41057i	0.501095	+	0.411238i
$244$	−8.25120	+	12.3805i	−0.528229	+	0.792578i
$245$	−6.36433	+	1.93060i	−0.406602	+	0.123341i
$246$	−21.2201	+	3.16053i	−1.35295	+	0.201508i
$247$	20.5572	−	30.7660i	1.30802	−	1.95760i
$248$	−1.62343	−	1.78480i	−0.103088	−	0.113335i
$249$	6.72574	−	4.49399i	0.426226	−	0.284795i
$250$	0.0685569	−	1.41255i	0.00433592	−	0.0893376i
$251$	−11.8746	−	14.4692i	−0.749518	−	0.913290i	0.248956	−	0.968515i	$-0.419912\pi$
$251$	−11.8746	−	14.4692i	−0.749518	−	0.913290i	−0.998474	+	0.0552248i	$0.982412\pi$
$252$	1.06613	−	0.571482i	0.0671600	−	0.0360000i
$253$	−3.90842	+	2.08909i	−0.245720	+	0.131340i
$254$	10.5733	−	17.6641i	0.663425	−	1.10834i
$255$	6.94897			0.435162
$256$	−6.19280	−	14.7529i	−0.387050	−	0.922059i
$257$	−21.2827			−1.32758			−0.663790	−	0.747919i	$-0.731053\pi$
$257$	−21.2827			−1.32758			−0.663790	+	0.747919i	$0.731053\pi$
$258$	−2.69461	+	4.50172i	−0.167759	+	0.280265i
$259$	−5.31560	+	2.84125i	−0.330295	+	0.176547i
$260$	−8.54167	+	4.57862i	−0.529732	+	0.283954i
$261$	3.09236	+	3.76805i	0.191412	+	0.233237i
$262$	−0.788036	+	16.2368i	−0.0486850	+	1.00311i
$263$	20.8170	−	13.9095i	1.28363	−	0.857694i	0.288617	−	0.957445i	$-0.406805\pi$
$263$	20.8170	−	13.9095i	1.28363	−	0.857694i	0.995012	+	0.0997511i	$0.0318047\pi$
$264$	−3.96074	+	3.60262i	−0.243767	+	0.221726i
$265$	4.70408	−	7.04015i	0.288969	−	0.432473i
$266$	−6.31268	+	0.940214i	−0.387056	+	0.0576482i
$267$	15.7983	−	4.79237i	0.966843	−	0.293289i
$268$	−6.96768	+	10.4546i	−0.425619	+	0.638617i
$269$	−1.59688	−	1.31052i	−0.0973634	−	0.0799040i	0.584452	−	0.811428i	$-0.301309\pi$
$269$	−1.59688	−	1.31052i	−0.0973634	−	0.0799040i	−0.681816	+	0.731524i	$0.738809\pi$
$270$	0.397246	+	7.98972i	0.0241756	+	0.486239i
$271$	25.1857	+	10.4323i	1.52993	+	0.633716i	0.979550	−	0.201202i	$-0.0644846\pi$
$271$	25.1857	+	10.4323i	1.52993	+	0.633716i	0.550375	+	0.834917i	$0.314485\pi$
$272$	3.81115	−	19.3997i	0.231085	−	1.17628i
$273$	3.71992	−	1.54084i	0.225140	−	0.0932559i
$274$	−11.9735	−	25.2772i	−0.723348	−	1.52705i
$275$	0.131971	+	1.33993i	0.00795817	+	0.0808007i
$276$	−8.55489	−	3.53170i	−0.514944	−	0.212584i
$277$	−7.88475	+	14.7513i	−0.473749	+	0.886321i	0.525617	+	0.850721i	$0.323834\pi$
$277$	−7.88475	+	14.7513i	−0.473749	+	0.886321i	−0.999366	+	0.0356004i	$0.988666\pi$
$278$	−0.215667	+	0.863157i	−0.0129349	+	0.0517687i
$279$	0.856166	−	0.170302i	0.0512573	−	0.0101957i
$280$	1.57491	+	0.560364i	0.0941192	+	0.0334881i
$281$	−1.05912	+	5.32455i	−0.0631817	+	0.317636i	−0.999432	−	0.0336977i	$-0.989272\pi$
$281$	−1.05912	+	5.32455i	−0.0631817	+	0.317636i	0.936250	+	0.351333i	$0.114272\pi$
$282$	15.2378	−	5.46233i	0.907396	−	0.325277i
$283$	−1.97428	+	20.0452i	−0.117359	+	1.19156i	0.738464	+	0.674293i	$0.235551\pi$
$283$	−1.97428	+	20.0452i	−0.117359	+	1.19156i	−0.855823	+	0.517269i	$0.826949\pi$
$284$	−0.399496	+	0.749535i	−0.0237057	+	0.0444767i
$285$	3.11641	−	10.2734i	0.184600	−	0.608545i
$286$	7.40778	−	5.50078i	0.438031	−	0.325268i
$287$	−4.50937	−	4.50937i	−0.266179	−	0.266179i
$288$	5.72884	+	0.832489i	0.337575	+	0.0490549i
$289$	5.25344	−	5.25344i	0.309026	−	0.309026i
$290$	−0.984470	+	6.66391i	−0.0578101	+	0.391318i
$291$	−21.7168	−	6.58771i	−1.27306	−	0.386178i
$292$	1.24947	−	12.8418i	0.0731196	−	0.751507i
$293$	20.8283	+	2.05141i	1.21680	+	0.119844i	0.685967	−	0.727632i	$-0.259379\pi$
$293$	20.8283	+	2.05141i	1.21680	+	0.119844i	0.530833	+	0.847477i	$0.321879\pi$
$294$	11.9572	+	5.64670i	0.697360	+	0.329322i
$295$	4.11172	+	0.817872i	0.239394	+	0.0476183i
$296$	−28.5403	−	4.18182i	−1.65887	−	0.243063i
$297$	−1.48582	−	7.46972i	−0.0862160	−	0.433437i
$298$	0.170430	+	0.283965i	0.00987276	+	0.0164496i
$299$	14.0663	+	7.51862i	0.813478	+	0.434813i
$300$	−1.98593	+	1.99063i	−0.114658	+	0.114929i
$301$	−1.55202	+	0.152860i	−0.0894568	+	0.00881072i
$302$	−7.38830	+	20.6875i	−0.425149	+	1.19043i
$303$	−0.941654	−	2.27335i	−0.0540966	−	0.130601i
$304$	−26.9714	−	14.3346i	−1.54692	−	0.822147i
$305$	2.84680	−	6.87279i	0.163008	−	0.393535i
$306$	5.30303	+	4.80068i	0.303154	+	0.274436i
$307$	−15.5953	+	19.0029i	−0.890069	+	1.08455i	0.105857	+	0.994381i	$0.466241\pi$
$307$	−15.5953	+	19.0029i	−0.890069	+	1.08455i	−0.995926	+	0.0901710i	$0.971259\pi$
$308$	−1.56128	−	0.308638i	−0.0889620	−	0.0175863i
$309$	2.55204	+	8.41295i	0.145181	+	0.478596i
$310$	0.969366	+	0.718042i	0.0550563	+	0.0407821i
$311$	−2.05946	−	1.37609i	−0.116781	−	0.0780307i	0.495808	−	0.868432i	$-0.334872\pi$
$311$	−2.05946	−	1.37609i	−0.116781	−	0.0780307i	−0.612589	+	0.790401i	$0.709872\pi$
$312$	18.7001	+	4.64890i	1.05869	+	0.263192i
$313$	−3.03218	−	4.53798i	−0.171389	−	0.256502i	0.735824	−	0.677172i	$-0.236795\pi$
$313$	−3.03218	−	4.53798i	−0.171389	−	0.256502i	−0.907213	+	0.420671i	$0.861795\pi$
$314$	19.7254	+	21.7377i	1.11317	+	1.22673i
$315$	−0.467532	+	0.383694i	−0.0263425	+	0.0216187i
$316$	26.1931	−	2.61108i	1.47348	−	0.146885i
$317$	2.02093	+	3.78089i	0.113507	+	0.212356i	0.932260	−	0.361790i	$-0.117834\pi$
$317$	2.02093	+	3.78089i	0.113507	+	0.212356i	−0.818753	+	0.574146i	$0.805334\pi$
$318$	−16.3281	+	4.10023i	−0.915633	+	0.229930i
$319$		−	6.41327i		−	0.359074i
$320$	4.46814	+	6.63595i	0.249776	+	0.370961i
$321$		−	18.6098i		−	1.03870i
$322$	−0.670039	−	2.66825i	−0.0373398	−	0.148696i
$323$	−17.7914	−	33.2854i	−0.989941	−	1.85205i
$324$	6.18610	−	7.55599i	0.343672	−	0.419777i
$325$	3.74579	−	3.07409i	0.207779	−	0.170520i
$326$	−7.10096	+	6.44359i	−0.393286	+	0.356877i
$327$	−4.29415	−	6.42665i	−0.237467	−	0.355395i
$328$	−4.53171	−	30.1813i	−0.250222	−	1.66648i
$329$	4.00071	+	2.67319i	0.220566	+	0.147378i
$330$	1.59344	−	2.15117i	0.0877162	−	0.118418i
$331$	−3.55835	−	11.7303i	−0.195585	−	0.644757i	−0.998796	−	0.0490620i	$-0.984377\pi$
$331$	−3.55835	−	11.7303i	−0.195585	−	0.644757i	0.803211	−	0.595695i	$-0.203123\pi$
$332$	6.40423	+	9.56011i	0.351478	+	0.524679i
$333$	6.62086	−	8.06754i	0.362821	−	0.442098i
$334$	−5.18274	+	5.72508i	−0.283587	+	0.313262i
$335$	2.40397	−	5.80369i	0.131343	−	0.317089i
$336$	−1.57370	−	2.92752i	−0.0858526	−	0.159709i
$337$	−3.53957	−	8.54527i	−0.192812	−	0.465490i	0.797676	−	0.603086i	$-0.206063\pi$
$337$	−3.53957	−	8.54527i	−0.192812	−	0.465490i	−0.990488	+	0.137596i	$0.956063\pi$
$338$	−13.9588	−	4.98524i	−0.759261	−	0.271161i
$339$	8.93670	−	0.880188i	0.485375	−	0.0478053i
$340$	0.0116914	+	9.88523i	0.000634057	+	0.536102i
$341$	−1.01289	−	0.541401i	−0.0548510	−	0.0293185i
$342$	9.47561	−	5.68708i	0.512383	−	0.307522i
$343$	1.57394	+	7.91272i	0.0849846	+	0.427246i
$344$	−6.40843	−	3.82563i	−0.345520	−	0.206264i
$345$	4.53869	+	0.902802i	0.244355	+	0.0486052i
$346$	6.08111	−	12.8771i	0.326923	−	0.692279i
$347$	−2.51178	−	0.247389i	−0.134839	−	0.0132805i	0.0303723	−	0.999539i	$-0.490331\pi$
$347$	−2.51178	−	0.247389i	−0.134839	−	0.0132805i	−0.165212	+	0.986258i	$0.552831\pi$
$348$	10.3433	−	8.50901i	0.554459	−	0.456131i
$349$	−17.0359	−	5.16779i	−0.911911	−	0.276625i	−0.200740	−	0.979644i	$-0.564335\pi$
$349$	−17.0359	−	5.16779i	−0.911911	−	0.276625i	−0.711171	+	0.703019i	$0.751835\pi$
$350$	−0.826844	−	0.122151i	−0.0441966	−	0.00652924i
$351$	−19.3819	+	19.3819i	−1.03453	+	1.03453i
$352$	−5.13156	−	5.62827i	−0.273513	−	0.299988i
$353$	16.7796	+	16.7796i	0.893086	+	0.893086i	0.994812	−	0.101726i	$-0.0324365\pi$
$353$	16.7796	+	16.7796i	0.893086	+	0.893086i	−0.101726	+	0.994812i	$0.532437\pi$
$354$	−4.96937	−	6.69214i	−0.264119	−	0.355683i
$355$	0.123277	−	0.406390i	0.00654287	−	0.0215689i
$356$	6.84395	+	22.4658i	0.362729	+	1.19068i
$357$	0.402549	−	4.08715i	0.0213052	−	0.216315i
$358$	−6.93090	−	19.3345i	−0.366309	−	1.02186i
$359$	−2.90687	+	14.6138i	−0.153419	+	0.771289i	0.825077	+	0.565021i	$0.191132\pi$
$359$	−2.90687	+	14.6138i	−0.153419	+	0.771289i	−0.978496	+	0.206268i	$0.933868\pi$
$360$	−2.89076	+	0.147155i	−0.152357	+	0.00775577i
$361$	−38.5535	+	7.66876i	−2.02913	+	0.403619i
$362$	−26.5214	−	6.62661i	−1.39394	−	0.348287i
$363$	6.08881	−	11.3914i	0.319579	−	0.597891i
$364$	2.19818	+	5.28916i	0.115216	+	0.277227i
$365$	0.632328	+	6.42013i	0.0330976	+	0.336045i
$366$	−13.3671	+	6.33186i	−0.698711	+	0.330972i
$367$	−30.6534	+	12.6971i	−1.60010	+	0.662781i	−0.991429	−	0.130644i	$-0.958295\pi$
$367$	−30.6534	+	12.6971i	−1.60010	+	0.662781i	−0.608667	+	0.793426i	$0.708295\pi$
$368$	5.00962	−	12.1757i	0.261144	−	0.634701i
$369$	10.2018	+	4.22574i	0.531087	+	0.219983i
$370$	14.4047	−	0.716198i	0.748866	−	0.0372334i
$371$	−3.86827	−	3.17461i	−0.200831	−	0.164818i
$372$	−0.470715	−	2.35190i	−0.0244054	−	0.121941i
$373$	6.64563	−	2.01593i	0.344098	−	0.104381i	−0.113506	−	0.993537i	$-0.536208\pi$
$373$	6.64563	−	2.01593i	0.344098	−	0.104381i	0.457603	+	0.889156i	$0.348708\pi$
$374$	−1.38643	−	9.30862i	−0.0716906	−	0.481337i
$375$	0.781092	−	1.16899i	0.0403354	−	0.0603663i
$376$	7.79605	+	21.6672i	0.402050	+	1.11740i
$377$	−19.1914	+	12.8233i	−0.988407	+	0.660433i
$378$	4.72230	+	0.229192i	0.242889	+	0.0117884i
$379$	14.7373	+	17.9574i	0.757003	+	0.922410i	0.998852	−	0.0479035i	$-0.0152540\pi$
$379$	14.7373	+	17.9574i	0.757003	+	0.922410i	−0.241849	+	0.970314i	$0.577754\pi$
$380$	14.6197	+	4.41595i	0.749973	+	0.226533i
$381$	18.0495	−	9.64767i	0.924705	−	0.494265i
$382$	7.43451	+	4.45010i	0.380382	+	0.227687i
$383$	4.42976			0.226350			0.113175	−	0.993575i	$-0.463898\pi$
$383$	4.42976			0.226350			0.113175	+	0.993575i	$0.463898\pi$
$384$	2.26878	−	15.7436i	0.115778	−	0.803414i
$385$	0.795746			0.0405550
$386$	−28.0791	−	16.8074i	−1.42919	−	0.855475i
$387$	2.38153	−	1.27295i	0.121060	−	0.0647078i
$388$	9.33478	−	30.9042i	0.473901	−	1.56892i
$389$	−10.6539	−	12.9818i	−0.540173	−	0.658203i	0.429369	−	0.903129i	$-0.358736\pi$
$389$	−10.6539	−	12.9818i	−0.540173	−	0.658203i	−0.969542	+	0.244927i	$0.921236\pi$
$390$	−9.62334	−	0.467060i	−0.487297	−	0.0236505i
$391$	13.5269	−	9.03836i	0.684083	−	0.457089i
$392$	−8.01257	+	17.0192i	−0.404696	+	0.859600i
$393$	−8.97837	+	13.4371i	−0.452899	+	0.677811i
$394$	1.34334	+	9.01932i	0.0676765	+	0.454387i
$395$	−12.5947	+	3.82057i	−0.633709	+	0.192234i
$396$	2.70215	−	0.540813i	0.135788	−	0.0271769i
$397$	16.6773	+	13.6867i	0.837008	+	0.686914i	0.951882	−	0.306466i	$-0.0991465\pi$
$397$	16.6773	+	13.6867i	0.837008	+	0.686914i	−0.114874	+	0.993380i	$0.536646\pi$
$398$	−35.3664	+	1.75840i	−1.77276	+	0.0881408i
$399$	−5.86195	−	2.42810i	−0.293465	−	0.121557i
$400$	−2.83511	−	2.82173i	−0.141755	−	0.141086i
$401$	−20.7786	+	8.60678i	−1.03763	+	0.429802i	−0.835462	−	0.549548i	$-0.814800\pi$
$401$	−20.7786	+	8.60678i	−1.03763	+	0.429802i	−0.202172	+	0.979350i	$0.564800\pi$
$402$	−11.2878	+	5.34690i	−0.562984	+	0.266679i
$403$	0.405149	+	4.11355i	0.0201819	+	0.204910i
$404$	3.23237	−	1.34337i	0.160816	−	0.0668352i
$405$	−2.30166	+	4.30610i	−0.114370	+	0.213972i
$406$	3.86246	+	0.965068i	0.191691	+	0.0478955i
$407$	−13.4672	+	2.67879i	−0.667545	+	0.132783i
$408$	13.1734	−	14.5865i	0.652181	−	0.722141i
$409$	6.32571	−	31.8015i	0.312786	−	1.57248i	−0.429921	−	0.902867i	$-0.641458\pi$
$409$	6.32571	−	31.8015i	0.312786	−	1.57248i	0.742707	−	0.669617i	$-0.233542\pi$
$410$	5.14937	+	14.3647i	0.254309	+	0.709424i
$411$	2.72545	−	27.6720i	0.134437	−	1.36496i
$412$	−11.9635	+	3.64455i	−0.589400	+	0.179554i
$413$	0.719234	−	2.37100i	0.0353912	−	0.116669i
$414$	2.83995	+	3.82450i	0.139576	+	0.187964i
$415$	−4.06832	−	4.06832i	−0.199706	−	0.199706i
$416$	−6.58181	+	26.6096i	−0.322700	+	1.30464i
$417$	−0.625422	+	0.625422i	−0.0306271	+	0.0306271i
$418$	−14.3837	−	2.12493i	−0.703531	−	0.103934i
$419$	9.97678	+	3.02642i	0.487398	+	0.147850i	0.524413	−	0.851464i	$-0.324285\pi$
$419$	9.97678	+	3.02642i	0.487398	+	0.147850i	−0.0370150	+	0.999315i	$0.511785\pi$
$420$	1.05578	+	1.28337i	0.0515168	+	0.0626223i
$421$	15.9144	+	1.56743i	0.775621	+	0.0763920i	0.478079	−	0.878317i	$-0.341333\pi$
$421$	15.9144	+	1.56743i	0.775621	+	0.0763920i	0.297542	+	0.954709i	$0.403833\pi$
$422$	6.08082	−	12.8765i	0.296010	−	0.626818i
$423$	−8.17142	−	1.62540i	−0.397308	−	0.0790295i
$424$	−5.86024	−	23.2205i	−0.284599	−	1.12769i
$425$	−0.964257	−	4.84765i	−0.0467733	−	0.235145i
$426$	−0.723990	+	0.434525i	−0.0350774	+	0.0210528i
$427$	−3.87743	−	2.07253i	−0.187642	−	0.100297i
$428$	26.4734	−	0.0313105i	1.27964	−	0.00151345i
$429$	9.12857	−	0.899086i	0.440732	−	0.0434083i
$430$	3.51434	+	1.25511i	0.169476	+	0.0605266i
$431$	−2.46621	−	5.95395i	−0.118793	−	0.286792i	0.853287	−	0.521442i	$-0.174606\pi$
$431$	−2.46621	−	5.95395i	−0.118793	−	0.286792i	−0.972080	+	0.234650i	$0.924606\pi$
$432$	17.5242	+	14.3125i	0.843135	+	0.688612i
$433$	4.00850	−	9.67736i	0.192636	−	0.465064i	−0.797820	−	0.602896i	$-0.794013\pi$
$433$	4.00850	−	9.67736i	0.192636	−	0.465064i	0.990456	+	0.137832i	$0.0440133\pi$
$434$	0.478483	−	0.528553i	0.0229679	−	0.0253713i
$435$	−4.24839	+	5.17668i	−0.203695	+	0.248203i
$436$	9.13498	−	6.11944i	0.437486	−	0.293068i
$437$	−7.29599	−	24.0517i	−0.349015	−	1.15055i
$438$	7.63483	−	10.3071i	0.364806	−	0.492493i
$439$	−20.1395	−	13.4568i	−0.961208	−	0.642259i	−0.0272453	−	0.999629i	$-0.508674\pi$
$439$	−20.1395	−	13.4568i	−0.961208	−	0.642259i	−0.933963	+	0.357370i	$0.883674\pi$
$440$	3.06282	+	2.26313i	0.146014	+	0.107890i
$441$	−3.78126	−	5.65905i	−0.180060	−	0.269479i
$442$	−25.0834	+	22.7613i	−1.19310	+	1.08265i
$443$	−12.0142	+	9.85976i	−0.570810	+	0.468452i	−0.874975	−	0.484168i	$-0.839122\pi$
$443$	−12.0142	+	9.85976i	−0.570810	+	0.468452i	0.304165	+	0.952619i	$0.401622\pi$
$444$	−22.1884	−	18.1657i	−1.05301	−	0.862105i
$445$	−5.53541	−	10.3560i	−0.262404	−	0.490923i
$446$	−2.87810	−	11.4613i	−0.136282	−	0.542706i
$447$			0.329243i			0.0155727i
$448$	4.16188	−	2.24359i	0.196630	−	0.106000i
$449$		−	8.05817i		−	0.380289i	−0.981756	−	0.190144i	$-0.939104\pi$
$449$		−	8.05817i		−	0.380289i	0.981756	−	0.190144i	$-0.0608956\pi$
$450$	1.40367	−	0.352484i	0.0661698	−	0.0166163i
$451$	−6.84854	−	12.8127i	−0.322485	−	0.603328i
$452$	1.26714	+	12.7114i	0.0596014	+	0.597893i
$453$	−16.8814	+	13.8542i	−0.793159	+	0.650928i
$454$	23.4448	+	25.8366i	1.10032	+	1.21257i
$455$	−1.59109	−	2.38123i	−0.0745913	−	0.111634i
$456$	−15.6570	−	26.0173i	−0.733206	−	1.21837i
$457$	10.7006	+	7.14990i	0.500552	+	0.334458i	0.780081	−	0.625679i	$-0.215178\pi$
$457$	10.7006	+	7.14990i	0.500552	+	0.334458i	−0.279528	+	0.960137i	$0.590178\pi$
$458$	16.9723	+	12.5720i	0.793066	+	0.587451i
$459$	8.11585	+	26.7544i	0.378815	+	1.24879i
$460$	−1.27664	+	6.45802i	−0.0595237	+	0.301107i
$461$	−1.75665	+	2.14048i	−0.0818153	+	0.0996923i	−0.812309	−	0.583227i	$-0.801790\pi$
$461$	−1.75665	+	2.14048i	−0.0818153	+	0.0996923i	0.730494	+	0.682919i	$0.239290\pi$
$462$	−1.17294	−	1.06183i	−0.0545700	−	0.0494006i
$463$	5.36924	−	12.9625i	0.249530	−	0.602418i	−0.748634	−	0.662983i	$-0.769290\pi$
$463$	5.36924	−	12.9625i	0.249530	−	0.602418i	0.998164	+	0.0605646i	$0.0192901\pi$
$464$	12.1219	+	14.6995i	0.562743	+	0.682407i
$465$	0.458942	+	1.10798i	0.0212829	+	0.0513815i
$466$	−6.79710	+	19.0321i	−0.314870	+	0.881645i
$467$	33.9940	−	3.34812i	1.57306	−	0.154932i	0.726475	−	0.687193i	$-0.241157\pi$
$467$	33.9940	−	3.34812i	1.57306	−	0.154932i	0.846581	+	0.532260i	$0.178657\pi$
$468$	−7.02127	−	7.00468i	−0.324558	−	0.323792i
$469$	−3.27428	−	1.75014i	−0.151192	−	0.0808138i
$470$	−5.92499	−	9.87200i	−0.273299	−	0.455361i
$471$	5.69301	+	28.6207i	0.262320	+	1.31877i
$472$	9.51152	−	7.08041i	0.437803	−	0.325902i
$473$	−3.48456	−	0.693122i	−0.160220	−	0.0318698i
$474$	23.6628	+	11.1746i	1.08687	+	0.513265i
$475$	−7.59925	−	0.748461i	−0.348677	−	0.0343417i
$476$	5.81484	+	0.565768i	0.266523	+	0.0259320i
$477$	8.29182	+	2.51530i	0.379656	+	0.115167i
$478$	−2.90974	+	19.6961i	−0.133088	+	0.900879i
$479$	−10.6020	+	10.6020i	−0.484418	+	0.484418i	−0.906539	−	0.422122i	$-0.861286\pi$
$479$	−10.6020	+	10.6020i	−0.484418	+	0.484418i	0.422122	+	0.906539i	$0.361286\pi$
$480$	0.413728	+	7.94237i	0.0188840	+	0.362518i
$481$	34.9437	+	34.9437i	1.59330	+	1.59330i
$482$	−7.53607	+	5.59604i	−0.343259	+	0.254893i
$483$	0.793921	−	2.61721i	0.0361247	−	0.119087i
$484$	16.2150	+	8.64244i	0.737044	+	0.392838i
$485$	−1.58215	+	16.0639i	−0.0718419	+	0.729423i
$486$	−13.4525	+	4.82234i	−0.610216	+	0.218746i
$487$	4.98252	−	25.0488i	0.225779	−	1.13507i	−0.687013	−	0.726645i	$-0.741078\pi$
$487$	4.98252	−	25.0488i	0.225779	−	1.13507i	0.912792	−	0.408424i	$-0.133922\pi$
$488$	−9.02985	−	19.0047i	−0.408762	−	0.860302i
$489$	−9.34938	+	1.85971i	−0.422794	+	0.0840989i
$490$	2.27996	−	9.12499i	0.102998	−	0.412225i
$491$	−17.9055	+	33.4989i	−0.808065	+	1.51178i	0.0502952	+	0.998734i	$0.483984\pi$
$491$	−17.9055	+	33.4989i	−0.808065	+	1.51178i	−0.858360	+	0.513048i	$0.828516\pi$
$492$	11.5778	−	28.0450i	0.521966	−	1.26437i
$493$	2.30760	+	23.4295i	0.103929	+	1.05521i
$494$	22.4014	+	47.2914i	1.00789	+	2.12774i
$495$	−1.27298	+	0.527287i	−0.0572163	+	0.0236998i
$496$	3.34490	−	0.673571i	0.150190	−	0.0302442i
$497$	−0.231884	−	0.0960493i	−0.0104014	−	0.00430840i
$498$	0.568068	+	11.4254i	0.0254557	+	0.511986i
$499$	−16.0546	−	13.1756i	−0.718701	−	0.589822i	0.202328	−	0.979318i	$-0.435149\pi$
$499$	−16.0546	−	13.1756i	−0.718701	−	0.589822i	−0.921028	+	0.389496i	$0.872649\pi$
$500$	1.66425	+	1.10917i	0.0744276	+	0.0496037i
$501$	−7.34670	+	2.22860i	−0.328227	+	0.0995664i
$502$	26.1825	−	3.89963i	1.16858	−	0.174049i
$503$	9.07823	−	13.5865i	0.404778	−	0.605793i	−0.571946	−	0.820291i	$-0.693811\pi$
$503$	9.07823	−	13.5865i	0.404778	−	0.605793i	0.976725	+	0.214498i	$0.0688114\pi$
$504$	−0.0809082	+	1.70878i	−0.00360394	+	0.0761149i
$505$	−1.45524	+	0.972360i	−0.0647573	+	0.0432695i
$506$	0.303824	−	6.26001i	0.0135066	−	0.278291i
$507$	−9.34811	−	11.3907i	−0.415164	−	0.505879i
$508$	13.7546	+	25.6600i	0.610263	+	1.13848i
$509$	22.7993	−	12.1865i	1.01056	−	0.540157i	0.118923	−	0.992903i	$-0.462056\pi$
$509$	22.7993	−	12.1865i	1.01056	−	0.540157i	0.891639	+	0.452746i	$0.149556\pi$
$510$	−5.04727	+	8.43217i	−0.223497	+	0.373383i
$511$	3.81274			0.168666
$512$	22.3999	+	3.20096i	0.989943	+	0.141464i
$513$	43.1936			1.90704
$514$	15.4584	−	25.8253i	0.681839	−	1.13911i
$515$	5.51480	−	2.94772i	0.243011	−	0.129892i
$516$	−3.50539	−	6.53950i	−0.154316	−	0.287885i
$517$	6.95393	+	8.47339i	0.305834	+	0.372659i
$518$	0.413213	−	8.51386i	0.0181555	−	0.374078i
$519$	11.7714	−	7.86542i	0.516708	−	0.345254i
$520$	0.648223	−	13.6904i	0.0284265	−	0.600365i
$521$	−6.34831	+	9.50092i	−0.278125	+	0.416243i	−0.944064	−	0.329763i	$-0.893031\pi$
$521$	−6.34831	+	9.50092i	−0.278125	+	0.416243i	0.665939	+	0.746006i	$0.268031\pi$
$522$	−6.81840	+	1.01553i	−0.298433	+	0.0444488i
$523$	14.8417	−	4.50218i	0.648982	−	0.196867i	0.0514050	−	0.998678i	$-0.483630\pi$
$523$	14.8417	−	4.50218i	0.648982	−	0.196867i	0.597577	+	0.801811i	$0.296130\pi$
$524$	−19.1300	−	12.7495i	−0.835697	−	0.556966i
$525$	−0.642311	−	0.527131i	−0.0280328	−	0.0230059i
$526$	1.75824	+	35.3631i	0.0766629	+	1.54190i
$527$	3.89518	+	1.61343i	0.169677	+	0.0702823i
$528$	−1.49475	−	7.42283i	−0.0650508	−	0.323037i
$529$	−11.2400	+	4.65575i	−0.488694	+	0.202424i
$530$	5.12608	+	10.8216i	0.222663	+	0.470061i
$531$	0.420515	+	4.26956i	0.0182488	+	0.185283i
$532$	3.44422	−	8.34298i	0.149326	−	0.361714i
$533$	−24.6478	+	46.1128i	−1.06762	+	1.99737i
$534$	−5.65960	+	22.6512i	−0.244915	+	0.980214i
$535$	−12.9824	+	2.58235i	−0.561276	+	0.111645i
$536$	−7.62520	−	16.0484i	−0.329358	−	0.693186i
$537$	3.98354	−	20.0266i	0.171902	−	0.864211i
$538$	2.75011	−	0.985840i	0.118566	−	0.0425026i
$539$	−0.877703	+	8.91146i	−0.0378053	+	0.383844i
$540$	−9.98359	−	5.32117i	−0.429625	−	0.228987i
$541$	3.31703	−	10.9348i	0.142610	−	0.470124i	−0.856316	−	0.516453i	$-0.827252\pi$
$541$	3.31703	−	10.9348i	0.142610	−	0.470124i	0.998926	+	0.0463290i	$0.0147522\pi$
$542$	−30.9522	+	22.9841i	−1.32951	+	0.987252i
$543$	−19.2168	−	19.2168i	−0.824671	−	0.824671i
$544$	20.7722	+	18.7152i	0.890600	+	0.802409i
$545$	−3.88741	+	3.88741i	−0.166518	+	0.166518i
$546$	−0.832182	+	5.63307i	−0.0356141	+	0.241073i
$547$	−28.9711	−	8.78830i	−1.23872	−	0.375760i	−0.398075	−	0.917353i	$-0.630322\pi$
$547$	−28.9711	−	8.78830i	−1.23872	−	0.375760i	−0.840641	+	0.541592i	$0.817822\pi$
$548$	39.3692	+	3.83052i	1.68177	+	0.163632i
$549$	7.57620	+	0.746190i	0.323344	+	0.0318466i
$550$	−1.72178	−	0.813095i	−0.0734169	−	0.0346705i
$551$	35.6733	+	7.09585i	1.51973	+	0.302294i
$552$	10.4992	−	7.81566i	0.446877	−	0.332657i
$553$	1.51753	+	7.62912i	0.0645318	+	0.324423i
$554$	−12.1729	−	20.2821i	−0.517177	−	0.861702i
$555$	12.6450	+	6.75890i	0.536751	+	0.286899i
$556$	−0.890744	−	0.888640i	−0.0377760	−	0.0376867i
$557$	−4.82162	+	0.474888i	−0.204298	+	0.0201216i	−0.199649	−	0.979868i	$-0.563980\pi$
$557$	−4.82162	+	0.474888i	−0.204298	+	0.0201216i	−0.00464977	+	0.999989i	$0.501480\pi$
$558$	−0.415211	+	1.16260i	−0.0175773	+	0.0492169i
$559$	4.89321	+	11.8133i	0.206961	+	0.499648i
$560$	−1.82388	+	1.50406i	−0.0770731	+	0.0635579i
$561$	3.58045	−	8.64398i	0.151167	−	0.364949i
$562$	−5.69175	−	5.15257i	−0.240092	−	0.217348i
$563$	−13.3910	+	16.3170i	−0.564364	+	0.687680i	−0.974511	−	0.224340i	$-0.927978\pi$
$563$	−13.3910	+	16.3170i	−0.564364	+	0.687680i	0.410147	+	0.912020i	$0.365478\pi$
$564$	−4.43949	+	22.4576i	−0.186936	+	0.945636i
$565$	−1.85410	−	6.11216i	−0.0780028	−	0.257141i
$566$	−22.8897	−	16.9552i	−0.962124	−	0.712678i
$567$	2.39937	+	1.60321i	0.100764	+	0.0673285i
$568$	−0.619350	−	1.02918i	−0.0259873	−	0.0431833i
$569$	−11.4756	−	17.1745i	−0.481083	−	0.719991i	0.508955	−	0.860793i	$-0.330032\pi$
$569$	−11.4756	−	17.1745i	−0.481083	−	0.719991i	−0.990038	+	0.140802i	$0.955032\pi$
$570$	10.2026	+	11.2435i	0.427342	+	0.470939i
$571$	−24.9432	+	20.4704i	−1.04384	+	0.856658i	−0.989883	−	0.141885i	$-0.954684\pi$
$571$	−24.9432	+	20.4704i	−1.04384	+	0.856658i	−0.0539577	+	0.998543i	$0.517184\pi$
$572$	1.29435	+	12.9843i	0.0541195	+	0.542901i
$573$	4.06054	+	7.59673i	0.169631	+	0.317358i
$574$	8.74715	−	2.19655i	0.365099	−	0.0916821i
$575$		−	3.29150i		−	0.137265i
$576$	−5.17123	+	6.34695i	−0.215468	+	0.264456i
$577$		−	7.32481i		−	0.304936i	−0.988308	−	0.152468i	$-0.951278\pi$
$577$		−	7.32481i		−	0.304936i	0.988308	−	0.152468i	$-0.0487220\pi$
$578$	2.55899	+	10.1905i	0.106440	+	0.423869i
$579$	−15.3361	−	28.6918i	−0.637346	−	1.19239i
$580$	−7.37120	−	6.03482i	−0.306073	−	0.250582i
$581$	−2.62852	+	2.15717i	−0.109050	+	0.0894947i
$582$	23.7674	−	21.5671i	0.985191	−	0.893986i
$583$	−6.33362	−	9.47893i	−0.262312	−	0.392577i
$584$	14.6752	+	10.8436i	0.607263	+	0.448710i
$585$	4.12320	+	2.75503i	0.170473	+	0.113907i
$586$	−17.6175	+	23.7839i	−0.727773	+	0.982503i
$587$	−0.422961	−	1.39432i	−0.0174575	−	0.0575496i	0.947779	−	0.318928i	$-0.103323\pi$
$587$	−0.422961	−	1.39432i	−0.0174575	−	0.0575496i	−0.965236	+	0.261379i	$0.915823\pi$
$588$	−15.5369	+	10.4080i	−0.640730	+	0.429219i
$589$	4.13219	−	5.03509i	0.170264	−	0.207467i
$590$	−3.97892	+	4.39528i	−0.163810	+	0.180951i
$591$	−3.46918	+	8.37533i	−0.142703	+	0.344515i
$592$	25.8042	−	31.5946i	1.06054	−	1.29853i
$593$	−0.180918	−	0.436774i	−0.00742940	−	0.0179361i	0.920121	−	0.391633i	$-0.128090\pi$
$593$	−0.180918	−	0.436774i	−0.00742940	−	0.0179361i	−0.927551	+	0.373697i	$0.878090\pi$
$594$	10.1433	+	3.62255i	0.416183	+	0.148635i
$595$	−2.90708	+	0.286323i	−0.119179	+	0.0117381i
$596$	−0.468364		0.000553942i	−0.0191849		2.26903e-5i
$597$	−31.0460	−	16.5944i	−1.27063	−	0.679164i
$598$	−19.3403	+	11.6077i	−0.790882	+	0.474672i
$599$	2.23503	+	11.2363i	0.0913209	+	0.459101i	0.999205	+	0.0398790i	$0.0126972\pi$
$599$	2.23503	+	11.2363i	0.0913209	+	0.459101i	−0.907884	+	0.419222i	$0.862303\pi$
$600$	−0.973069	−	3.85568i	−0.0397254	−	0.157407i
$601$	−33.7223	−	6.70779i	−1.37556	−	0.273616i	−0.548700	−	0.836019i	$-0.684877\pi$
$601$	−33.7223	−	6.70779i	−1.37556	−	0.273616i	−0.826863	+	0.562403i	$0.809877\pi$
$602$	0.941795	−	1.99431i	0.0383847	−	0.0812820i
$603$	6.39768	+	0.630116i	0.260534	+	0.0256603i
$604$	−19.7367	−	23.9913i	−0.803074	−	0.976192i
$605$	−8.79158	−	2.66690i	−0.357429	−	0.108425i
$606$	3.44254	+	0.508572i	0.139843	+	0.0206593i
$607$	−25.1820	+	25.1820i	−1.02211	+	1.02211i	−0.0223575	+	0.999750i	$0.507117\pi$
$607$	−25.1820	+	25.1820i	−1.02211	+	1.02211i	−0.999750	+	0.0223575i	$0.992883\pi$
$608$	36.9845	−	22.3166i	1.49992	−	0.905056i
$609$	2.79864	+	2.79864i	0.113407	+	0.113407i
$610$	6.27200	+	8.44637i	0.253946	+	0.341984i
$611$	11.4519	−	37.7518i	0.463293	−	1.52727i
$612$	−9.67711	+	2.94802i	−0.391174	+	0.119167i
$613$	−3.80816	+	38.6649i	−0.153810	+	1.56166i	0.540102	+	0.841600i	$0.318386\pi$
$613$	−3.80816	+	38.6649i	−0.153810	+	1.56166i	−0.693912	+	0.720060i	$0.744114\pi$
$614$	−11.7315	−	32.7264i	−0.473446	−	1.32073i
$615$	−2.95960	+	14.8789i	−0.119343	+	0.599976i
$616$	1.50852	−	1.67034i	0.0607801	−	0.0673001i
$617$	24.3552	−	4.84455i	0.980503	−	0.195034i	0.321282	−	0.946983i	$-0.395886\pi$
$617$	24.3552	−	4.84455i	0.980503	−	0.195034i	0.659221	+	0.751949i	$0.270886\pi$
$618$	−12.0623	−	3.01386i	−0.485215	−	0.121235i
$619$	−12.9475	+	24.2231i	−0.520404	+	0.973608i	0.475194	+	0.879881i	$0.342378\pi$
$619$	−12.9475	+	24.2231i	−0.520404	+	0.973608i	−0.995598	+	0.0937266i	$0.970122\pi$
$620$	−1.57539	+	0.654730i	−0.0632690	+	0.0262946i
$621$	1.82494	+	18.5289i	0.0732322	+	0.743539i
$622$	3.16565	−	1.49953i	0.126931	−	0.0601258i
$623$	−6.41173	+	2.65582i	−0.256880	+	0.106403i
$624$	−19.2237	+	19.3149i	−0.769564	+	0.773213i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	7.70894	−	0.383286i	0.308111	−	0.0153192i
$627$	−11.1736	−	9.16994i	−0.446231	−	0.366212i
$628$	−40.7046	+	8.14672i	−1.62429	+	0.325089i
$629$	48.2356	−	14.6321i	1.92328	−	0.583421i
$630$	−0.126005	−	0.846013i	−0.00502018	−	0.0337059i
$631$	−24.3975	+	36.5134i	−0.971249	+	1.45358i	−0.0817428	+	0.996653i	$0.526049\pi$
$631$	−24.3975	+	36.5134i	−0.971249	+	1.45358i	−0.889506	+	0.456923i	$0.848951\pi$
$632$	−15.8565	+	33.6803i	−0.630739	+	1.33973i
$633$	11.7709	−	7.86504i	0.467850	−	0.312607i
$634$	−6.05576	−	0.293911i	−0.240505	−	0.0116727i
$635$	−9.23487	−	11.2527i	−0.366475	−	0.446551i
$636$	6.88424	−	22.7913i	0.272978	−	0.903734i
$637$	28.4221	−	15.1919i	1.12612	−	0.601925i
$638$	7.78213	+	4.65818i	0.308097	+	0.184419i
$639$	0.434598			0.0171924
$640$	−11.2977	+	0.601909i	−0.446580	+	0.0237926i
$641$	−5.81435			−0.229653			−0.114826	−	0.993386i	$-0.536631\pi$
$641$	−5.81435			−0.229653			−0.114826	+	0.993386i	$0.536631\pi$
$642$	22.5820	+	13.5170i	0.891239	+	0.533472i
$643$	−0.960553	+	0.513426i	−0.0378805	+	0.0202476i	−0.490228	−	0.871594i	$-0.663087\pi$
$643$	−0.960553	+	0.513426i	−0.0378805	+	0.0202476i	0.452348	+	0.891842i	$0.350587\pi$
$644$	3.72443	+	1.12499i	0.146763	+	0.0443307i
$645$	2.35352	+	2.86777i	0.0926698	+	0.112919i
$646$	53.3124	+	2.58747i	2.09755	+	0.101803i
$647$	10.6920	−	7.14418i	0.420347	−	0.280867i	−0.327355	−	0.944901i	$-0.606157\pi$
$647$	10.6920	−	7.14418i	0.420347	−	0.280867i	0.747702	+	0.664035i	$0.231157\pi$
$648$	4.67557	+	12.9946i	0.183674	+	0.510477i
$649$	3.13593	−	4.69325i	0.123096	−	0.184226i
$650$	1.00953	+	6.77811i	0.0395972	+	0.265859i
$651$	0.678265	−	0.205749i	0.0265833	−	0.00806396i
$652$	−2.66125	−	13.2968i	−0.104223	−	0.520743i
$653$	2.90325	+	2.38264i	0.113613	+	0.0932398i	0.689484	−	0.724300i	$-0.257837\pi$
$653$	2.90325	+	2.38264i	0.113613	+	0.0932398i	−0.575871	+	0.817540i	$0.695337\pi$
$654$	10.9174	−	0.542807i	0.426902	−	0.0212254i
$655$	10.6197	+	4.39881i	0.414944	+	0.171876i
$656$	39.9147	+	16.4227i	1.55841	+	0.641200i
$657$	−6.09938	+	2.52644i	−0.237959	+	0.0985660i
$658$	−6.14961	+	2.91300i	−0.239737	+	0.113561i
$659$	−3.85041	−	39.0939i	−0.149991	−	1.52288i	−0.715777	−	0.698329i	$-0.753927\pi$
$659$	−3.85041	−	39.0939i	−0.149991	−	1.52288i	0.565786	−	0.824552i	$-0.308573\pi$
$660$	1.45294	+	3.49602i	0.0565558	+	0.136082i
$661$	4.01025	−	7.50266i	0.155981	−	0.291820i	−0.791777	−	0.610810i	$-0.790844\pi$
$661$	4.01025	−	7.50266i	0.155981	−	0.291820i	0.947758	+	0.318991i	$0.103344\pi$
$662$	16.8186	+	4.20227i	0.653674	+	0.163326i
$663$	−33.0258	+	6.56923i	−1.28261	+	0.255128i
$664$	−16.2522	+	0.827326i	−0.630709	+	0.0321065i
$665$	−0.880439	+	4.42626i	−0.0341420	+	0.171643i
$666$	4.98053	+	13.8937i	0.192992	+	0.538372i
$667$	−1.53673	+	15.6027i	−0.0595024	+	0.604138i
$668$	−3.18264	−	10.4473i	−0.123140	−	0.404217i
$669$	3.41023	−	11.2420i	0.131847	−	0.434642i
$670$	5.29635	+	7.13249i	0.204616	+	0.275552i
$671$	−7.08240	−	7.08240i	−0.273413	−	0.273413i
$672$	4.69540	+	0.216755i	0.181129	+	0.00836152i
$673$	1.14048	−	1.14048i	0.0439622	−	0.0439622i	−0.684784	−	0.728746i	$-0.740103\pi$
$673$	1.14048	−	1.14048i	0.0439622	−	0.0439622i	0.728746	+	0.684784i	$0.240103\pi$
$674$	12.9401	+	1.91166i	0.498434	+	0.0736344i
$675$	5.41299	+	1.64201i	0.208346	+	0.0632011i
$676$	16.1881	−	13.3173i	0.622618	−	0.512203i
$677$	9.22446	+	0.908530i	0.354525	+	0.0349176i	0.273712	−	0.961812i	$-0.411748\pi$
$677$	9.22446	+	0.908530i	0.354525	+	0.0349176i	0.0808127	+	0.996729i	$0.474248\pi$
$678$	−5.42297	+	11.4835i	−0.208268	+	0.441020i
$679$	9.35658	+	1.86114i	0.359073	+	0.0714240i
$680$	−12.0036	−	7.16579i	−0.460319	−	0.274795i
$681$	6.76648	+	34.0174i	0.259292	+	1.30355i
$682$	1.39265	−	0.835844i	0.0533275	−	0.0320061i
$683$	12.2020	+	6.52210i	0.466896	+	0.249561i	0.688030	−	0.725682i	$-0.258476\pi$
$683$	12.2020	+	6.52210i	0.466896	+	0.249561i	−0.221134	+	0.975243i	$0.570976\pi$
$684$	0.0184845	+	15.6288i	0.000706772	+	0.597583i
$685$	−19.6823	+	1.93854i	−0.752023	+	0.0740678i
$686$	−10.7448	−	3.83739i	−0.410239	−	0.146512i
$687$	8.03548	+	19.3994i	0.306573	+	0.740132i
$688$	9.29684	−	4.99757i	0.354439	−	0.190531i
$689$	−15.7012	+	37.9061i	−0.598168	+	1.44411i
$690$	−4.39210	+	4.85170i	−0.167204	+	0.184701i
$691$	−15.7599	+	19.2035i	−0.599536	+	0.730537i	−0.981035	−	0.193833i	$-0.937908\pi$
$691$	−15.7599	+	19.2035i	−0.599536	+	0.730537i	0.381499	+	0.924369i	$0.375408\pi$
$692$	11.2087	+	16.7322i	0.426092	+	0.636061i
$693$	0.236389	+	0.779271i	0.00897969	+	0.0296021i
$694$	2.12458	−	2.86821i	0.0806480	−	0.108876i
$695$	0.523084	+	0.349513i	0.0198417	+	0.0132578i
$696$	2.81251	+	18.7314i	0.106608	+	0.710010i
$697$	29.6299	+	44.3443i	1.12231	+	1.67966i
$698$	18.6446	−	16.9185i	0.705707	−	0.640376i
$699$	−15.5306	+	12.7456i	−0.587421	+	0.482084i
$700$	0.748787	−	0.914604i	0.0283015	−	0.0345688i
$701$	−0.359935	−	0.673391i	−0.0135946	−	0.0254336i	0.875032	−	0.484065i	$-0.160840\pi$
$701$	−0.359935	−	0.673391i	−0.0135946	−	0.0254336i	−0.888627	+	0.458631i	$0.848340\pi$
$702$	−9.44106	−	37.5965i	−0.356330	−	1.41899i
$703$		−	77.8741i		−	2.93708i
$704$	10.5568	−	2.13884i	0.397874	−	0.0806107i
$705$		−	11.4461i		−	0.431085i
$706$	−32.5486	+	8.17345i	−1.22498	+	0.307612i
$707$	0.487609	+	0.912252i	0.0183384	+	0.0343088i
$708$	11.7299	−	1.16931i	0.440838	−	0.0439453i
$709$	8.81970	−	7.23814i	0.331231	−	0.271834i	−0.454047	−	0.890978i	$-0.650020\pi$
$709$	8.81970	−	7.23814i	0.331231	−	0.271834i	0.785278	+	0.619144i	$0.212520\pi$
$710$	0.403590	+	0.444764i	0.0151465	+	0.0166917i
$711$	−7.48294	−	11.1990i	−0.280632	−	0.419996i
$712$	−32.2319	−	8.01293i	−1.20794	−	0.300297i
$713$	2.33450	+	1.55986i	0.0874278	+	0.0584174i
$714$	4.66713	+	3.45711i	0.174663	+	0.129379i
$715$	−1.89391	−	6.24339i	−0.0708283	−	0.233490i
$716$	28.4954	+	5.63307i	1.06492	+	0.210518i
$717$	−12.5567	+	15.3004i	−0.468939	+	0.571403i
$718$	−15.6217	−	14.1418i	−0.582995	−	0.527769i
$719$	−2.48667	+	6.00336i	−0.0927373	+	0.223888i	−0.963441	−	0.267920i	$-0.913664\pi$
$719$	−2.48667	+	6.00336i	−0.0927373	+	0.223888i	0.870704	+	0.491808i	$0.163664\pi$
$720$	1.92109	−	3.61466i	0.0715950	−	0.134710i
$721$	−1.41428	−	3.41438i	−0.0526706	−	0.127158i
$722$	18.6971	−	52.3524i	0.695833	−	1.94836i
$723$	−9.28667	+	0.914657i	−0.345375	+	0.0340165i
$724$	27.3044	−	27.3691i	1.01476	−	1.01716i
$725$	4.20080	+	2.24537i	0.156014	+	0.0833911i
$726$	9.40023	+	15.6623i	0.348875	+	0.581284i
$727$	1.25204	+	6.29444i	0.0464356	+	0.233448i	0.997033	−	0.0769800i	$-0.0245278\pi$
$727$	1.25204	+	6.29444i	0.0464356	+	0.233448i	−0.950597	+	0.310428i	$0.899528\pi$
$728$	−8.01470	−	1.17434i	−0.297044	−	0.0435239i
$729$	−28.3005	−	5.62931i	−1.04817	−	0.208493i
$730$	−8.24974	−	3.89587i	−0.305336	−	0.144193i
$731$	12.9795	+	1.27837i	0.480063	+	0.0472821i
$732$	2.02566	−	20.8193i	0.0748705	−	0.769502i
$733$	30.9333	+	9.38351i	1.14255	+	0.346588i	0.804156	−	0.594418i	$-0.202618\pi$
$733$	30.9333	+	9.38351i	1.14255	+	0.346588i	0.338390	+	0.941006i	$0.390118\pi$
$734$	6.85747	−	46.4184i	0.253114	−	1.71334i
$735$	6.61175	−	6.61175i	0.243878	−	0.243878i
$736$	11.1358	+	14.9225i	0.410471	+	0.550050i
$737$	−5.98069	−	5.98069i	−0.220302	−	0.220302i
$738$	−12.5376	+	9.31004i	−0.461517	+	0.342707i
$739$	−2.77793	+	9.15759i	−0.102188	+	0.336867i	−0.993094	−	0.117319i	$-0.962570\pi$
$739$	−2.77793	+	9.15759i	−0.102188	+	0.336867i	0.890907	+	0.454186i	$0.150070\pi$
$740$	−9.59357	+	17.9995i	−0.352667	+	0.661674i
$741$	−5.09906	+	51.7717i	−0.187319	+	1.90188i
$742$	6.66186	−	2.38810i	0.244565	−	0.0876698i
$743$	6.68800	−	33.6228i	0.245359	−	1.23350i	−0.639920	−	0.768442i	$-0.721032\pi$
$743$	6.68800	−	33.6228i	0.245359	−	1.23350i	0.885279	−	0.465061i	$-0.153968\pi$
$744$	3.19579	+	1.13708i	0.117163	+	0.0416874i
$745$	0.229682	−	0.0456866i	0.00841491	−	0.00167383i
$746$	−2.38073	+	9.52832i	−0.0871648	+	0.348857i
$747$	2.77553	−	5.19266i	0.101551	−	0.189989i
$748$	12.3025	+	5.07881i	0.449823	+	0.185700i
$749$	0.766793	+	7.78538i	0.0280180	+	0.284471i
$750$	0.851164	+	1.79688i	0.0310801	+	0.0656130i
$751$	−2.68562	+	1.11242i	−0.0979998	+	0.0405928i	−0.431145	−	0.902283i	$-0.641890\pi$
$751$	−2.68562	+	1.11242i	−0.0979998	+	0.0405928i	0.333145	+	0.942876i	$0.391890\pi$
$752$	−31.9544	−	6.27759i	−1.16526	−	0.228920i
$753$	24.3130	+	10.0708i	0.886016	+	0.367000i
$754$	−1.62094	−	32.6016i	−0.0590312	−	1.18728i
$755$	12.0073	+	9.85414i	0.436991	+	0.358629i
$756$	−3.70807	+	5.56376i	−0.134861	+	0.202352i
$757$	−10.2986	+	3.12406i	−0.374310	+	0.113546i	−0.471834	−	0.881687i	$-0.656408\pi$
$757$	−10.2986	+	3.12406i	−0.374310	+	0.113546i	0.0975236	+	0.995233i	$0.468908\pi$
$758$	−32.4944	+	4.83973i	−1.18025	+	0.175787i
$759$	3.46157	−	5.18061i	0.125647	−	0.188044i
$760$	−15.9772	+	14.5326i	−0.579556	+	0.527154i
$761$	−1.44077	+	0.962691i	−0.0522278	+	0.0348975i	−0.581410	−	0.813611i	$-0.697499\pi$
$761$	−1.44077	+	0.962691i	−0.0522278	+	0.0348975i	0.529182	+	0.848508i	$0.322499\pi$
$762$	−1.40309	+	28.9095i	−0.0508287	+	1.04728i
$763$	2.06125	+	2.51164i	0.0746222	+	0.0909274i
$764$	−10.7999	+	5.78908i	−0.390725	+	0.209442i
$765$	4.46084	−	2.38437i	0.161282	−	0.0862070i
$766$	−3.21749	+	5.37526i	−0.116252	+	0.194216i
$767$	−20.3146			−0.733517
$768$	17.4561	+	14.1882i	0.629892	+	0.511971i
$769$	5.34066			0.192589			0.0962945	−	0.995353i	$-0.469301\pi$
$769$	5.34066			0.192589			0.0962945	+	0.995353i	$0.469301\pi$
$770$	−0.577977	+	0.965590i	−0.0208288	+	0.0347975i
$771$	26.3888	−	14.1051i	0.950371	−	0.507984i
$772$	40.7896	−	21.8646i	1.46805	−	0.786923i
$773$	−29.0006	−	35.3373i	−1.04308	−	1.27099i	−0.961640	−	0.274316i	$-0.911549\pi$
$773$	−29.0006	−	35.3373i	−1.04308	−	1.27099i	−0.0814384	−	0.996678i	$-0.525951\pi$
$774$	−0.185130	+	3.81443i	−0.00665436	+	0.137107i
$775$	0.709253	−	0.473907i	0.0254771	−	0.0170233i
$776$	30.7202	+	33.7739i	1.10279	+	1.21241i
$777$	4.70788	−	7.04583i	0.168894	−	0.252768i
$778$	23.4909	−	3.49874i	0.842190	−	0.125436i
$779$	78.8471	−	23.9180i	2.82499	−	0.856951i
$780$	7.55650	−	11.3381i	0.270566	−	0.405970i
$781$	−0.441999	−	0.362739i	−0.0158160	−	0.0129798i
$782$	1.14250	+	22.9789i	0.0408558	+	0.821724i
$783$	−24.8926	−	10.3108i	−0.889589	−	0.368480i
$784$	−14.8320	−	22.0844i	−0.529715	−	0.788729i
$785$	19.1760	−	7.94296i	0.684421	−	0.283496i
$786$	−9.78382	−	20.6545i	−0.348977	−	0.736723i
$787$	−3.69636	−	37.5298i	−0.131761	−	1.33779i	−0.802746	−	0.596321i	$-0.796628\pi$
$787$	−3.69636	−	37.5298i	−0.131761	−	1.33779i	0.670985	−	0.741471i	$-0.265872\pi$
$788$	−11.9201	−	4.92097i	−0.424637	−	0.175302i
$789$	−16.5929	+	31.0430i	−0.590721	+	1.10516i
$790$	4.51194	−	18.0580i	0.160528	−	0.642474i
$791$	−3.70238	+	0.736449i	−0.131641	+	0.0261851i
$792$	−1.30641	+	3.67171i	−0.0464214	+	0.130468i
$793$	−7.03253	+	35.3549i	−0.249733	+	1.25549i
$794$	−28.7212	+	10.2958i	−1.01928	+	0.365384i
$795$	−1.16681	+	11.8468i	−0.0413826	+	0.420164i
$796$	23.5541	−	44.1922i	0.834852	−	1.56635i
$797$	5.34921	−	17.6340i	0.189479	−	0.624627i	−0.809802	−	0.586703i	$-0.800426\pi$
$797$	5.34921	−	17.6340i	0.189479	−	0.624627i	0.999281	−	0.0379240i	$-0.0120745\pi$
$798$	7.20409	−	5.34952i	0.255022	−	0.189371i
$799$	−28.4535	−	28.4535i	−1.00661	−	1.00661i
$800$	5.48324	−	1.39072i	0.193862	−	0.0491695i
$801$	8.49724	−	8.49724i	0.300235	−	0.300235i
$802$	4.64838	−	31.4650i	0.164140	−	1.11107i
$803$	8.31195	+	2.52140i	0.293322	+	0.0889784i
$804$	1.71056	−	17.5807i	0.0603267	−	0.620024i
$805$	−1.93595	−	0.190674i	−0.0682332	−	0.00672038i
$806$	−5.28582	−	2.49618i	−0.186185	−	0.0879243i
$807$	2.84855	+	0.566612i	0.100274	+	0.0199457i
$808$	−0.717674	+	4.89802i	−0.0252477	+	0.172312i
$809$	−6.70560	−	33.7113i	−0.235756	−	1.18523i	−0.899382	−	0.437163i	$-0.855983\pi$
$809$	−6.70560	−	33.7113i	−0.235756	−	1.18523i	0.663626	−	0.748065i	$-0.269017\pi$
$810$	−3.55343	−	5.92060i	−0.124855	−	0.208029i
$811$	2.08001	+	1.11179i	0.0730392	+	0.0390403i	0.507512	−	0.861645i	$-0.330565\pi$
$811$	2.08001	+	1.11179i	0.0730392	+	0.0390403i	−0.434473	+	0.900685i	$0.643065\pi$
$812$	−3.97649	+	3.98590i	−0.139547	+	0.139878i
$813$	−38.1423	+	3.75669i	−1.33771	+	0.131753i
$814$	6.53113	−	18.2874i	0.228916	−	0.640972i
$815$	2.59469	+	6.26413i	0.0908880	+	0.219423i
$816$	8.13162	+	26.5799i	0.284664	+	0.930481i
$817$	7.71086	−	18.6157i	0.269769	−	0.651279i
$818$	33.9947	+	30.7744i	1.18860	+	1.07600i
$819$	1.85927	−	2.26553i	0.0649682	−	0.0791640i
$820$	−21.1709	−	4.18513i	−0.739321	−	0.146151i
$821$	−4.69423	−	15.4748i	−0.163830	−	0.540074i	0.836135	−	0.548524i	$-0.184810\pi$
$821$	−4.69423	−	15.4748i	−0.163830	−	0.540074i	−0.999964	+	0.00845035i	$0.997310\pi$
$822$	31.5987	+	23.4063i	1.10213	+	0.816387i
$823$	−12.0134	−	8.02713i	−0.418762	−	0.279808i	0.328285	−	0.944579i	$-0.393529\pi$
$823$	−12.0134	−	8.02713i	−0.418762	−	0.279808i	−0.747048	+	0.664771i	$0.768529\pi$
$824$	4.26706	−	17.1642i	0.148650	−	0.597942i
$825$	−1.05167	−	1.57394i	−0.0366145	−	0.0547975i
$826$	2.35466	+	2.59488i	0.0819291	+	0.0902875i
$827$	15.9764	−	13.1115i	0.555553	−	0.455930i	−0.314243	−	0.949343i	$-0.601751\pi$
$827$	15.9764	−	13.1115i	0.555553	−	0.455930i	0.869795	+	0.493412i	$0.164251\pi$
$828$	−6.70356	+	0.668250i	−0.232965	+	0.0232233i
$829$	−16.1096	−	30.1389i	−0.559509	−	1.04677i	−0.989581	−	0.143974i	$-0.954012\pi$
$829$	−16.1096	−	30.1389i	−0.559509	−	1.04677i	0.430072	−	0.902795i	$-0.358488\pi$
$830$	7.89162	−	1.98171i	0.273922	−	0.0687861i
$831$		−	23.5161i		−	0.815764i
$832$	−27.5086	−	27.3141i	−0.953689	−	0.946946i
$833$		−	32.8719i		−	1.13894i
$834$	−0.304648	−	1.21318i	−0.0105491	−	0.0420089i
$835$	2.57413	+	4.81586i	0.0890815	+	0.166660i
$836$	13.0259	−	15.9104i	0.450509	−	0.550273i
$837$	−3.72986	+	3.06102i	−0.128923	+	0.105804i
$838$	−10.9189	+	9.90805i	−0.377186	+	0.342268i
$839$	−4.48307	−	6.70939i	−0.154773	−	0.231634i	0.745977	−	0.665971i	$-0.231983\pi$
$839$	−4.48307	−	6.70939i	−0.154773	−	0.231634i	−0.900750	+	0.434337i	$0.856983\pi$
$840$	−2.32415	+	0.348970i	−0.0801907	+	0.0120406i
$841$	5.24789	+	3.50653i	0.180962	+	0.120915i
$842$	−13.4612	+	18.1727i	−0.463902	+	0.626274i
$843$	−2.21562	−	7.30394i	−0.0763102	−	0.251561i
$844$	11.2082	+	16.7314i	0.385801	+	0.575917i
$845$	−6.64906	+	8.10191i	−0.228735	+	0.278714i
$846$	7.90750	−	8.73496i	0.271866	−	0.300314i
$847$	−2.07787	+	5.01642i	−0.0713964	+	0.172366i
$848$	32.4333	+	9.75480i	1.11376	+	0.334981i
$849$	−10.8370	−	26.1628i	−0.371925	−	0.897907i
$850$	6.58271	+	2.35094i	0.225785	+	0.0806366i
$851$	33.4059	−	3.29019i	1.14514	−	0.112786i
$852$	−0.00141232	−	1.19413i	−4.83852e−5	−	0.0409102i
$853$	−33.6761	−	18.0002i	−1.15305	−	0.616317i	−0.219798	−	0.975545i	$-0.570540\pi$
$853$	−33.6761	−	18.0002i	−1.15305	−	0.616317i	−0.933250	+	0.359229i	$0.883040\pi$
$854$	5.33121	−	3.19969i	0.182430	−	0.109491i
$855$	−1.52452	−	7.66426i	−0.0521374	−	0.262112i
$856$	−19.1905	+	32.1466i	−0.655918	+	1.09875i
$857$	3.73615	+	0.743167i	0.127625	+	0.0253861i	0.258489	−	0.966014i	$-0.416775\pi$
$857$	3.73615	+	0.743167i	0.127625	+	0.0253861i	−0.130865	+	0.991400i	$0.541775\pi$
$858$	−5.53940	+	11.7300i	−0.189112	+	0.400456i
$859$	−12.6528	−	1.24619i	−0.431707	−	0.0425194i	−0.120170	−	0.992753i	$-0.538344\pi$
$859$	−12.6528	−	1.24619i	−0.431707	−	0.0425194i	−0.311537	+	0.950234i	$0.600844\pi$
$860$	−4.07558	+	3.35282i	−0.138976	+	0.114330i
$861$	8.57983	+	2.60266i	0.292400	+	0.0886985i
$862$	9.01606	+	1.33196i	0.307088	+	0.0453667i
$863$	−4.81256	+	4.81256i	−0.163821	+	0.163821i	−0.784257	−	0.620436i	$-0.786956\pi$
$863$	−4.81256	+	4.81256i	−0.163821	+	0.163821i	0.620436	+	0.784257i	$0.286956\pi$
$864$	−30.0959	+	10.8690i	−1.02388	+	0.369769i
$865$	−7.12040	−	7.12040i	−0.242101	−	0.242101i
$866$	8.83141	+	11.8931i	0.300103	+	0.404143i
$867$	−3.03212	+	9.99556i	−0.102976	+	0.339467i
$868$	0.293829	+	0.964517i	0.00997321	+	0.0327378i
$869$	−1.73694	+	17.6354i	−0.0589215	+	0.598240i
$870$	−3.19584	−	8.91516i	−0.108349	−	0.302252i
$871$	−5.93858	+	29.8553i	−0.201221	+	1.01161i
$872$	0.790536	+	15.5295i	0.0267709	+	0.525896i
$873$	−16.2013	+	3.22264i	−0.548331	+	0.109070i
$874$	34.4846	+	8.61628i	1.16646	+	0.291450i
$875$	−0.278601	+	0.521226i	−0.00941844	+	0.0176207i
$876$	6.96164	+	16.7508i	0.235212	+	0.565958i
$877$	1.03468	+	10.5053i	0.0349386	+	0.354738i	0.996721	+	0.0809211i	$0.0257862\pi$
$877$	1.03468	+	10.5053i	0.0349386	+	0.354738i	−0.961782	+	0.273817i	$0.911714\pi$
$878$	30.9571	−	14.6640i	1.04475	−	0.494887i
$879$	−27.1849	+	11.2604i	−0.916925	+	0.379803i
$880$	−4.97080	+	2.07276i	−0.167566	+	0.0698728i
$881$	14.7980	+	6.12955i	0.498559	+	0.206510i	0.617770	−	0.786359i	$-0.288036\pi$
$881$	14.7980	+	6.12955i	0.498559	+	0.206510i	−0.119211	+	0.992869i	$0.538036\pi$
$882$	9.61338	−	0.477974i	0.323699	−	0.0160942i
$883$	26.7526	+	21.9553i	0.900295	+	0.738853i	0.965879	−	0.258994i	$-0.0833909\pi$
$883$	26.7526	+	21.9553i	0.900295	+	0.738853i	−0.0655835	+	0.997847i	$0.520891\pi$
$884$	−9.40059	−	46.9696i	−0.316176	−	1.57976i
$885$	−5.64024	+	1.71095i	−0.189595	+	0.0575129i
$886$	−3.23796	−	21.7400i	−0.108781	−	0.730368i
$887$	−6.26280	+	9.37294i	−0.210284	+	0.314713i	−0.921586	−	0.388174i	$-0.873106\pi$
$887$	−6.26280	+	9.37294i	−0.210284	+	0.314713i	0.711302	+	0.702887i	$0.248106\pi$
$888$	38.1592	−	13.7300i	1.28054	−	0.460748i
$889$	−7.15345	+	4.77978i	−0.239919	+	0.160309i
$890$	16.5870	+	0.805034i	0.555997	+	0.0269848i
$891$	4.17053	+	5.08180i	0.139718	+	0.170247i
$892$	15.9980	+	4.83229i	0.535653	+	0.161797i
$893$	−54.8265	+	29.3054i	−1.83470	+	0.980668i
$894$	−0.399517	−	0.239141i	−0.0133619	−	0.00799806i
$895$	−14.5234			−0.485465
$896$	−0.300445	+	6.67979i	−0.0100372	+	0.223156i
$897$	−22.4241			−0.748719
$898$	9.77811	+	5.85292i	0.326300	+	0.195314i
$899$	−3.58333	+	1.91533i	−0.119511	+	0.0638798i
$900$	−0.591816	+	1.95930i	−0.0197272	+	0.0653099i
$901$	26.5492	+	32.3503i	0.884481	+	1.07774i
$902$	20.5218	+	0.996007i	0.683302	+	0.0331634i
$903$	1.82307	−	1.21813i	0.0606679	−	0.0405370i
$904$	−16.3449	−	7.69510i	−0.543623	−	0.255935i
$905$	−10.7392	+	16.0723i	−0.356982	+	0.534262i
$906$	−4.54974	−	30.5474i	−0.151155	−	1.01487i
$907$	8.50015	−	2.57849i	0.282243	−	0.0856175i	−0.145989	−	0.989286i	$-0.546637\pi$
$907$	8.50015	−	2.57849i	0.282243	−	0.0856175i	0.428232	+	0.903669i	$0.359137\pi$
$908$	−48.3799	+	9.68286i	−1.60554	+	0.321337i
$909$	−1.38453	−	1.13626i	−0.0459221	−	0.0376873i
$910$	4.04514	−	0.201123i	0.134095	−	0.00666716i
$911$	−35.8728	−	14.8590i	−1.18852	−	0.492301i	−0.301247	−	0.953546i	$-0.597403\pi$
$911$	−35.8728	−	14.8590i	−1.18852	−	0.492301i	−0.887273	+	0.461245i	$0.847403\pi$
$912$	42.9427	−	0.101578i	1.42197	−	0.00336359i
$913$	−7.15687	+	2.96447i	−0.236858	+	0.0981097i
$914$	−16.4482	+	7.79132i	−0.544057	+	0.257714i
$915$	1.02514	+	10.4084i	0.0338901	+	0.344092i
$916$	−27.5830	+	11.4635i	−0.911367	+	0.378764i
$917$	3.20242	−	5.99131i	0.105753	−	0.197850i
$918$	−38.3597	−	9.58449i	−1.26606	−	0.316335i
$919$	−50.7807	+	10.1009i	−1.67510	+	0.333198i	−0.939063	−	0.343744i	$-0.888305\pi$
$919$	−50.7807	+	10.1009i	−1.67510	+	0.333198i	−0.736036	+	0.676942i	$0.763305\pi$
$920$	−6.90916	−	6.23980i	−0.227788	−	0.205720i
$921$	6.74270	−	33.8978i	0.222179	−	1.11697i
$922$	−1.32144	−	3.68630i	−0.0435192	−	0.121402i
$923$	−0.201706	+	2.04795i	−0.00663922	+	0.0674092i
$924$	2.14041	−	0.652051i	0.0704142	−	0.0214509i
$925$	2.96040	−	9.75913i	0.0973373	−	0.320878i
$926$	11.8294	+	15.9304i	0.388737	+	0.523504i
$927$	4.52496	+	4.52496i	0.148619	+	0.148619i
$928$	−26.6415	+	4.03243i	−0.874550	+	0.132371i
$929$	16.1691	−	16.1691i	0.530490	−	0.530490i	−0.390228	−	0.920718i	$-0.627604\pi$
$929$	16.1691	−	16.1691i	0.530490	−	0.530490i	0.920718	+	0.390228i	$0.127604\pi$
$930$	−1.67782	−	0.247867i	−0.0550178	−	0.00812787i
$931$	−48.5981	−	14.7421i	−1.59274	−	0.483152i
$932$	−18.1574	−	22.0715i	−0.594764	−	0.722977i
$933$	3.46556	+	0.341328i	0.113457	+	0.0111746i
$934$	−20.6283	+	43.6816i	−0.674977	+	1.42931i
$935$	−6.52693	−	1.29829i	−0.213453	−	0.0424585i
$936$	13.5996	−	3.43216i	0.444515	−	0.112184i
$937$	2.02833	+	10.1971i	0.0662625	+	0.333124i	0.999670	−	0.0256943i	$-0.00817965\pi$
$937$	2.02833	+	10.1971i	0.0662625	+	0.333124i	−0.933407	+	0.358819i	$0.883180\pi$
$938$	4.50190	−	2.70196i	0.146992	−	0.0882221i
$939$	6.76721	+	3.61715i	0.220839	+	0.118041i
$940$	16.2826	−	0.0192577i	0.531080	−	0.000628117i
$941$	21.0316	−	2.07143i	0.685611	−	0.0675268i	0.250787	−	0.968042i	$-0.419311\pi$
$941$	21.0316	−	2.07143i	0.685611	−	0.0675268i	0.434824	+	0.900516i	$0.356811\pi$
$942$	−38.8645	−	13.8800i	−1.26627	−	0.452236i
$943$	13.5915	+	32.8128i	0.442600	+	1.06853i
$944$	1.68313	+	16.6844i	0.0547812	+	0.543031i
$945$	1.27935	−	3.08862i	0.0416172	−	0.100473i
$946$	3.37201	−	3.72487i	0.109634	−	0.121106i
$947$	−7.19392	+	8.76582i	−0.233771	+	0.284851i	−0.876662	−	0.481107i	$-0.840235\pi$
$947$	−7.19392	+	8.76582i	−0.233771	+	0.284851i	0.642891	+	0.765958i	$0.277735\pi$
$948$	−30.7468	+	20.5970i	−0.998610	+	0.668960i
$949$	−9.07450	−	29.9146i	−0.294571	−	0.971069i
$950$	6.42780	−	8.67761i	0.208545	−	0.281539i
$951$	−5.01157	−	3.34863i	−0.162511	−	0.108587i
$952$	−4.91004	+	6.64503i	−0.159135	+	0.215367i
$953$	−7.82782	−	11.7152i	−0.253568	−	0.379491i	0.682746	−	0.730656i	$-0.260786\pi$
$953$	−7.82782	−	11.7152i	−0.253568	−	0.379491i	−0.936314	+	0.351165i	$0.885786\pi$
$954$	−9.07479	+	8.23469i	−0.293807	+	0.266608i
$955$	4.73608	−	3.88680i	0.153256	−	0.125774i
$956$	−21.7866	−	17.8367i	−0.704630	−	0.576881i
$957$	4.25040	+	7.95194i	0.137396	+	0.257050i
$958$	−5.16431	−	20.5655i	−0.166851	−	0.664441i
$959$			11.6888i			0.377451i
$960$	−9.93810	−	5.26678i	−0.320751	−	0.169984i
$961$		−	30.2724i		−	0.976528i
$962$	−67.7829	+	17.0214i	−2.18541	+	0.548790i
$963$	−6.38551	−	11.9464i	−0.205770	−	0.384969i
$964$	−1.31677	−	13.2092i	−0.0424102	−	0.425439i
$965$	−17.8875	+	14.6799i	−0.575820	+	0.472563i
$966$	2.59918	+	2.86434i	0.0836271	+	0.0921587i
$967$	−21.9815	−	32.8976i	−0.706877	−	1.05792i	−0.994956	−	0.100309i	$-0.968017\pi$
$967$	−21.9815	−	32.8976i	−0.706877	−	1.05792i	0.288080	−	0.957606i	$-0.406983\pi$
$968$	−22.2646	+	13.3986i	−0.715610	+	0.430648i
$969$	44.1198	+	29.4799i	1.41733	+	0.947032i
$970$	−18.3434	−	13.5876i	−0.588971	−	0.436271i
$971$	−17.2120	−	56.7404i	−0.552360	−	1.82089i	−0.570846	−	0.821057i	$-0.693385\pi$
$971$	−17.2120	−	56.7404i	−0.552360	−	1.82089i	0.0184867	−	0.999829i	$-0.494115\pi$
$972$	3.91935	−	19.8264i	0.125713	−	0.635932i
$973$	0.235874	−	0.287413i	0.00756177	−	0.00921405i
$974$	26.7763	+	24.2398i	0.857967	+	0.776693i
$975$	−2.60712	+	6.29415i	−0.0834947	+	0.201574i
$976$	29.6198	+	2.84657i	0.948106	+	0.0911163i
$977$	−3.14089	−	7.58279i	−0.100486	−	0.242595i	0.865639	−	0.500668i	$-0.166912\pi$
$977$	−3.14089	−	7.58279i	−0.100486	−	0.242595i	−0.966125	+	0.258073i	$0.916912\pi$
$978$	4.53413	−	12.6957i	0.144985	−	0.405964i
$979$	−15.7342	+	1.54968i	−0.502867	+	0.0495281i
$980$	9.41663	+	9.39439i	0.300803	+	0.300093i
$981$	−4.96175	−	2.65211i	−0.158416	−	0.0846753i
$982$	−27.6435	−	46.0586i	−0.882140	−	1.46979i
$983$	−6.97898	−	35.0857i	−0.222595	−	1.11906i	−0.916819	−	0.399302i	$-0.869252\pi$
$983$	−6.97898	−	35.0857i	−0.222595	−	1.11906i	0.694224	−	0.719759i	$-0.255748\pi$
$984$	25.6216	+	34.4190i	0.816787	+	1.09724i
$985$	6.32408	+	1.25794i	0.201502	+	0.0400812i
$986$	−30.1064	−	14.2175i	−0.958783	−	0.452777i
$987$	−6.73221	−	0.663065i	−0.214289	−	0.0211056i
$988$	−73.6561	−	7.16655i	−2.34331	−	0.227998i
$989$	8.31140	+	2.52124i	0.264287	+	0.0801707i
$990$	0.284779	−	1.92768i	0.00905087	−	0.0612656i
$991$	23.7162	−	23.7162i	0.753368	−	0.753368i	−0.221738	−	0.975106i	$-0.571173\pi$
$991$	23.7162	−	23.7162i	0.753368	−	0.753368i	0.975106	+	0.221738i	$0.0711729\pi$
$992$	−1.61217	+	4.54807i	−0.0511866	+	0.144401i
$993$	12.1863	+	12.1863i	0.386722	+	0.386722i
$994$	0.284975	−	0.211613i	0.00903886	−	0.00671196i
$995$	−7.26835	+	23.9605i	−0.230422	+	0.759600i
$996$	−14.2767	−	7.60935i	−0.452374	−	0.241112i
$997$	3.83770	−	38.9649i	0.121541	−	1.23403i	−0.720053	−	0.693919i	$-0.755883\pi$
$997$	3.83770	−	38.9649i	0.121541	−	1.23403i	0.841594	−	0.540110i	$-0.181617\pi$
$998$	27.6488	−	9.91135i	0.875208	−	0.313738i
$999$	−11.2542	+	56.5787i	−0.356067	+	1.79007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.20	✓	1024
128.109	even	32	inner	640.2.bm.a.621.20	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.20	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.20	yes	1024	128.109	even	32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.726334 + 1.21344i) q^{2} +(-1.23992 + 0.662750i) q^{3} +(-0.944879 - 1.76273i) q^{4} +(0.634393 + 0.773010i) q^{5} +(0.0963861 - 1.98595i) q^{6} +(0.491409 - 0.328349i) q^{7} +(2.82526 + 0.133772i) q^{8} +(-0.568550 + 0.850895i) q^{9} +(-1.39878 + 0.208335i) q^{10} +(1.28844 - 0.390843i) q^{11} +(2.33982 + 1.55942i) q^{12} +(-3.74579 - 3.07409i) q^{13} +(0.0415053 + 0.834787i) q^{14} +(-1.29891 - 0.538026i) q^{15} +(-2.21441 + 3.33113i) q^{16} +(-4.56638 + 1.89146i) q^{17} +(-0.619554 - 1.30794i) q^{18} +(0.748461 + 7.59925i) q^{19} +(0.763181 - 1.84866i) q^{20} +(-0.391694 + 0.732807i) q^{21} +(-0.461569 + 1.84732i) q^{22} +(-3.22825 + 0.642139i) q^{23} +(-3.59175 + 1.70658i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(6.45092 - 2.31248i) q^{26} +(0.554440 - 5.62933i) q^{27} +(-1.04311 - 0.555969i) q^{28} +(1.38269 - 4.55813i) q^{29} +(1.59630 - 1.18536i) q^{30} +(-0.603170 - 0.603170i) q^{31} +(-2.43373 - 5.10656i) q^{32} +(-1.33852 + 1.33852i) q^{33} +(1.02155 - 6.91487i) q^{34} +(0.565564 + 0.171562i) q^{35} +(2.03711 + 0.198205i) q^{36} +(-10.1492 - 0.999604i) q^{37} +(-9.76487 - 4.61138i) q^{38} +(6.68183 + 1.32910i) q^{39} +(1.68892 + 2.26882i) q^{40} +(-2.10509 - 10.5830i) q^{41} +(-0.604718 - 1.00756i) q^{42} +(-2.32716 - 1.24389i) q^{43} +(-1.90636 - 1.90186i) q^{44} +(-1.01844 + 0.100307i) q^{45} +(1.56559 - 4.38370i) q^{46} +(3.11554 + 7.52159i) q^{47} +(0.537981 - 5.59793i) q^{48} +(-2.54511 + 6.14445i) q^{49} +(-1.04842 - 0.949108i) q^{50} +(4.40838 - 5.37163i) q^{51} +(-1.87946 + 9.50745i) q^{52} +(-2.45787 - 8.10252i) q^{53} +(6.42815 + 4.76155i) q^{54} +(1.11950 + 0.748026i) q^{55} +(1.43228 - 0.861935i) q^{56} +(-5.96444 - 8.92641i) q^{57} +(4.52673 + 4.98854i) q^{58} +(3.24067 - 2.65955i) q^{59} +(0.278920 + 2.79799i) q^{60} +(-3.50675 - 6.56066i) q^{61} +(1.17001 - 0.293809i) q^{62} +0.604820i q^{63} +(7.96421 + 0.755884i) q^{64} -4.84572i q^{65} +(-0.652005 - 2.59644i) q^{66} +(-2.96125 - 5.54011i) q^{67} +(7.64880 + 6.26209i) q^{68} +(3.57719 - 2.93573i) q^{69} +(-0.618968 + 0.561667i) q^{70} +(-0.235938 - 0.353105i) q^{71} +(-1.72013 + 2.32795i) q^{72} +(5.36398 + 3.58409i) q^{73} +(8.58463 - 11.5894i) q^{74} +(-0.408120 - 1.34539i) q^{75} +(12.6882 - 8.49970i) q^{76} +(0.504816 - 0.615120i) q^{77} +(-6.46602 + 7.14264i) q^{78} +(-5.03667 + 12.1596i) q^{79} +(-3.97980 + 0.401484i) q^{80} +(1.86851 + 4.51097i) q^{81} +(14.3708 + 5.13238i) q^{82} +(-5.72577 + 0.563939i) q^{83} +(1.66184 - 0.00196549i) q^{84} +(-4.35900 - 2.32993i) q^{85} +(3.19968 - 1.92039i) q^{86} +(1.30648 + 6.56810i) q^{87} +(3.69245 - 0.931876i) q^{88} +(-11.5169 - 2.29086i) q^{89} +(0.618007 - 1.30867i) q^{90} +(-2.85009 - 0.280709i) q^{91} +(4.18222 + 5.08378i) q^{92} +(1.14763 + 0.348131i) q^{93} +(-11.3899 - 1.68265i) q^{94} +(-5.39948 + 5.39948i) q^{95} +(6.40200 + 4.71877i) q^{96} +(11.4138 + 11.4138i) q^{97} +(-5.60733 - 7.55127i) q^{98} +(-0.399974 + 1.31854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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