LMFDB - Embedded newform 840.2.cf.a.341.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(101,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cf (of order $6$, degree $2$, 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$128$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.19
Character	$\chi$	$=$	840.341
Dual form			840.2.cf.a.101.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27612 - 0.609528i) q^{2} +(1.29538 - 1.14978i) q^{3} +(1.25695 + 1.55566i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.35388 + 0.677684i) q^{6} +(2.04884 - 1.67400i) q^{7} +(-0.655798 - 2.75135i) q^{8} +(0.356013 - 2.97880i) q^{9} +(-0.800386 - 1.16593i) q^{10} +(-0.791910 - 1.37163i) q^{11} +(3.41689 + 0.569952i) q^{12} +2.55381 q^{13} +(-3.63491 + 0.887392i) q^{14} +(1.69672 - 0.348049i) q^{15} +(-0.840151 + 3.91077i) q^{16} +(0.000650046 + 0.00112591i) q^{17} +(-2.26998 + 3.58430i) q^{18} +(0.482815 - 0.836259i) q^{19} +(0.310721 + 1.97572i) q^{20} +(0.729293 - 4.52417i) q^{21} +(0.174524 + 2.23305i) q^{22} +(-2.79167 - 1.61177i) q^{23} +(-4.01295 - 2.81002i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.25896 - 1.55662i) q^{26} +(-2.96379 - 4.26801i) q^{27} +(5.17946 + 1.08316i) q^{28} -2.84802 q^{29} +(-2.37736 - 0.590048i) q^{30} +(-2.05487 + 1.18638i) q^{31} +(3.45586 - 4.47851i) q^{32} +(-2.60289 - 0.866256i) q^{33} +(-0.000143259 - 0.00183302i) q^{34} +(2.61134 - 0.425305i) q^{35} +(5.08149 - 3.19037i) q^{36} +(8.97684 + 5.18278i) q^{37} +(-1.12585 + 0.772876i) q^{38} +(3.30815 - 2.93632i) q^{39} +(0.807738 - 2.71064i) q^{40} -1.33074 q^{41} +(-3.68827 + 5.32885i) q^{42} +5.61460i q^{43} +(1.13839 - 2.95601i) q^{44} +(1.79772 - 2.40171i) q^{45} +(2.58008 + 3.75841i) q^{46} +(5.79156 - 10.0313i) q^{47} +(3.40821 + 6.03192i) q^{48} +(1.39547 - 6.85949i) q^{49} +(-0.110192 - 1.40991i) q^{50} +(0.00213661 + 0.000711074i) q^{51} +(3.21001 + 3.97285i) q^{52} +(4.58699 + 7.94490i) q^{53} +(1.18067 + 7.25300i) q^{54} -1.58382i q^{55} +(-5.94937 - 4.53927i) q^{56} +(-0.336086 - 1.63840i) q^{57} +(3.63441 + 1.73595i) q^{58} +(-3.29646 + 1.90321i) q^{59} +(2.67414 + 2.20204i) q^{60} +(4.28404 - 7.42017i) q^{61} +(3.34538 - 0.261458i) q^{62} +(-4.25709 - 6.69904i) q^{63} +(-7.13986 + 3.60866i) q^{64} +(2.21166 + 1.27690i) q^{65} +(2.79359 + 2.69198i) q^{66} +(-6.97977 + 4.02977i) q^{67} +(-0.000934461 + 0.00242647i) q^{68} +(-5.46946 + 1.12195i) q^{69} +(-3.59162 - 1.04895i) q^{70} -9.45233i q^{71} +(-8.42920 + 0.973976i) q^{72} +(-7.92146 + 4.57346i) q^{73} +(-8.29645 - 12.0855i) q^{74} +(1.64343 + 0.546941i) q^{75} +(1.90781 - 0.300042i) q^{76} +(-3.91860 - 1.48459i) q^{77} +(-6.01135 + 1.73067i) q^{78} +(7.16669 - 12.4131i) q^{79} +(-2.68298 + 2.96675i) q^{80} +(-8.74651 - 2.12098i) q^{81} +(1.69818 + 0.811122i) q^{82} +9.94503i q^{83} +(7.95475 - 4.55213i) q^{84} +0.00130009i q^{85} +(3.42226 - 7.16489i) q^{86} +(-3.68927 + 3.27460i) q^{87} +(-3.25450 + 3.07833i) q^{88} +(-7.80405 + 13.5170i) q^{89} +(-3.75801 + 1.96911i) q^{90} +(5.23234 - 4.27507i) q^{91} +(-1.00162 - 6.36881i) q^{92} +(-1.29776 + 3.89946i) q^{93} +(-13.5050 + 9.27096i) q^{94} +(0.836259 - 0.482815i) q^{95} +(-0.672655 - 9.77484i) q^{96} -10.1286i q^{97} +(-5.96184 + 7.90294i) q^{98} +(-4.36774 + 1.87063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) $ 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−1.27612	−	0.609528i	−0.902351	−	0.431002i
$2$	−1.27612	−	0.609528i	−0.902351	−	0.431002i
$3$	1.29538	−	1.14978i	0.747887	−	0.663826i
$3$	1.29538	−	1.14978i	0.747887	−	0.663826i
$4$	1.25695	+	1.55566i	0.628475	+	0.777830i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−2.35388	+	0.677684i	−0.960967	+	0.276663i
$7$	2.04884	−	1.67400i	0.774388	−	0.632711i
$7$	2.04884	−	1.67400i	0.774388	−	0.632711i
$8$	−0.655798	−	2.75135i	−0.231860	−	0.972749i
$9$	0.356013	−	2.97880i	0.118671	−	0.992934i
$10$	−0.800386	−	1.16593i	−0.253104	−	0.368698i
$11$	−0.791910	−	1.37163i	−0.238770	−	0.413562i	0.721592	−	0.692319i	$-0.243411\pi$
$11$	−0.791910	−	1.37163i	−0.238770	−	0.413562i	−0.960362	+	0.278757i	$0.910078\pi$
$12$	3.41689	+	0.569952i	0.986372	+	0.164531i
$13$	2.55381			0.708299			0.354149	−	0.935189i	$-0.384770\pi$
$13$	2.55381			0.708299			0.354149	+	0.935189i	$0.384770\pi$
$14$	−3.63491	+	0.887392i	−0.971469	+	0.237165i
$15$	1.69672	−	0.348049i	0.438091	−	0.0898659i
$16$	−0.840151	+	3.91077i	−0.210038	+	0.977693i
$17$	0.000650046		0.00112591i	0.000157659		0.000273074i	0.866104	−	0.499863i	$-0.166616\pi$
$17$	0.000650046		0.00112591i	0.000157659		0.000273074i	−0.865947	+	0.500137i	$0.833283\pi$
$18$	−2.26998	+	3.58430i	−0.535039	+	0.844827i
$19$	0.482815	−	0.836259i	0.110765	−	0.191851i	−0.805314	−	0.592849i	$-0.798003\pi$
$19$	0.482815	−	0.836259i	0.110765	−	0.191851i	0.916079	+	0.400998i	$0.131336\pi$
$20$	0.310721	+	1.97572i	0.0694794	+	0.441783i
$21$	0.729293	−	4.52417i	0.159145	−	0.987255i
$22$	0.174524	+	2.23305i	0.0372086	+	0.476088i
$23$	−2.79167	−	1.61177i	−0.582104	−	0.336078i	0.179865	−	0.983691i	$-0.442434\pi$
$23$	−2.79167	−	1.61177i	−0.582104	−	0.336078i	−0.761969	+	0.647613i	$0.775767\pi$
$24$	−4.01295	−	2.81002i	−0.819141	−	0.573592i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−3.25896	−	1.55662i	−0.639134	−	0.305278i
$27$	−2.96379	−	4.26801i	−0.570382	−	0.821379i
$28$	5.17946	+	1.08316i	0.978825	+	0.204698i
$29$	−2.84802			−0.528864			−0.264432	−	0.964404i	$-0.585185\pi$
$29$	−2.84802			−0.528864			−0.264432	+	0.964404i	$0.585185\pi$
$30$	−2.37736	−	0.590048i	−0.434045	−	0.107728i
$31$	−2.05487	+	1.18638i	−0.369065	+	0.213080i	−0.673050	−	0.739597i	$-0.735016\pi$
$31$	−2.05487	+	1.18638i	−0.369065	+	0.213080i	0.303985	+	0.952677i	$0.401683\pi$
$32$	3.45586	−	4.47851i	0.610915	−	0.791696i
$33$	−2.60289	−	0.866256i	−0.453106	−	0.150796i
$34$	−0.000143259	−	0.00183302i	−2.45688e−5	−	0.000314360i
$35$	2.61134	−	0.425305i	0.441398	−	0.0718896i
$36$	5.08149	−	3.19037i	0.846915	−	0.531728i
$37$	8.97684	+	5.18278i	1.47578	+	0.852044i	0.999627	−	0.0273169i	$-0.00869632\pi$
$37$	8.97684	+	5.18278i	1.47578	+	0.852044i	0.476156	+	0.879361i	$0.342030\pi$
$38$	−1.12585	+	0.772876i	−0.182637	+	0.125377i
$39$	3.30815	−	2.93632i	0.529728	−	0.470187i
$40$	0.807738	−	2.71064i	0.127715	−	0.428590i
$41$	−1.33074			−0.207826			−0.103913	−	0.994586i	$-0.533136\pi$
$41$	−1.33074			−0.207826			−0.103913	+	0.994586i	$0.533136\pi$
$42$	−3.68827	+	5.32885i	−0.569113	+	0.822259i
$43$			5.61460i			0.856219i	0.903727	+	0.428109i	$0.140820\pi$
$43$			5.61460i			0.856219i	−0.903727	+	0.428109i	$0.859180\pi$
$44$	1.13839	−	2.95601i	0.171619	−	0.445636i
$45$	1.79772	−	2.40171i	0.267988	−	0.358026i
$46$	2.58008	+	3.75841i	0.380412	+	0.554148i
$47$	5.79156	−	10.0313i	0.844785	−	1.46321i	−0.0410220	−	0.999158i	$-0.513061\pi$
$47$	5.79156	−	10.0313i	0.844785	−	1.46321i	0.885807	−	0.464053i	$-0.153605\pi$
$48$	3.40821	+	6.03192i	0.491933	+	0.870633i
$49$	1.39547	−	6.85949i	0.199353	−	0.979928i
$50$	−0.110192	−	1.40991i	−0.0155835	−	0.199392i
$51$	0.00213661		0.000711074i	0.000299185		9.95703e-5i
$52$	3.21001	+	3.97285i	0.445148	+	0.550936i
$53$	4.58699	+	7.94490i	0.630071	+	1.09132i	0.987537	+	0.157389i	$0.0503077\pi$
$53$	4.58699	+	7.94490i	0.630071	+	1.09132i	−0.357465	+	0.933926i	$0.616359\pi$
$54$	1.18067	+	7.25300i	0.160669	+	0.987008i
$55$		−	1.58382i		−	0.213562i
$56$	−5.94937	−	4.53927i	−0.795019	−	0.606585i
$57$	−0.336086	−	1.63840i	−0.0445157	−	0.217012i
$58$	3.63441	+	1.73595i	0.477221	+	0.227941i
$59$	−3.29646	+	1.90321i	−0.429163	+	0.247777i	−0.698990	−	0.715132i	$-0.746367\pi$
$59$	−3.29646	+	1.90321i	−0.429163	+	0.247777i	0.269827	+	0.962909i	$0.413033\pi$
$60$	2.67414	+	2.20204i	0.345230	+	0.284282i
$61$	4.28404	−	7.42017i	0.548515	−	0.950055i	−0.449862	−	0.893098i	$-0.648527\pi$
$61$	4.28404	−	7.42017i	0.548515	−	0.950055i	0.998377	−	0.0569573i	$-0.0181399\pi$
$62$	3.34538	−	0.261458i	0.424864	−	0.0332052i
$63$	−4.25709	−	6.69904i	−0.536343	−	0.844000i
$64$	−7.13986	+	3.60866i	−0.892482	+	0.451082i
$65$	2.21166	+	1.27690i	0.274323	+	0.158380i
$66$	2.79359	+	2.69198i	0.343867	+	0.331360i
$67$	−6.97977	+	4.02977i	−0.852714	+	0.492315i	−0.861566	−	0.507646i	$-0.830516\pi$
$67$	−6.97977	+	4.02977i	−0.852714	+	0.492315i	0.00885142	+	0.999961i	$0.497182\pi$
$68$	−0.000934461		0.00242647i	−0.000113320		0.000294252i
$69$	−5.46946	+	1.12195i	−0.658445	+	0.135067i
$70$	−3.59162	−	1.04895i	−0.429280	−	0.125373i
$71$		−	9.45233i		−	1.12178i	−0.827889	−	0.560892i	$-0.810458\pi$
$71$		−	9.45233i		−	1.12178i	0.827889	−	0.560892i	$-0.189542\pi$
$72$	−8.42920	+	0.973976i	−0.993390	+	0.114784i
$73$	−7.92146	+	4.57346i	−0.927137	+	0.535283i	−0.885905	−	0.463867i	$-0.846462\pi$
$73$	−7.92146	+	4.57346i	−0.927137	+	0.535283i	−0.0412319	+	0.999150i	$0.513128\pi$
$74$	−8.29645	−	12.0855i	−0.964442	−	1.40491i
$75$	1.64343	+	0.546941i	0.189767	+	0.0631553i
$76$	1.90781	−	0.300042i	0.218841	−	0.0344172i
$77$	−3.91860	−	1.48459i	−0.446566	−	0.169185i
$78$	−6.01135	+	1.73067i	−0.680652	+	0.195960i
$79$	7.16669	−	12.4131i	0.806315	−	1.39658i	−0.109085	−	0.994032i	$-0.534792\pi$
$79$	7.16669	−	12.4131i	0.806315	−	1.39658i	0.915400	−	0.402546i	$-0.131875\pi$
$80$	−2.68298	+	2.96675i	−0.299966	+	0.331693i
$81$	−8.74651	−	2.12098i	−0.971834	−	0.235665i
$82$	1.69818	+	0.811122i	0.187532	+	0.0895734i
$83$			9.94503i			1.09161i	0.837912	+	0.545805i	$0.183776\pi$
$83$			9.94503i			1.09161i	−0.837912	+	0.545805i	$0.816224\pi$
$84$	7.95475	−	4.55213i	0.867935	−	0.496678i
$85$			0.00130009i			0.000141015i
$86$	3.42226	−	7.16489i	0.369032	−	0.772610i
$87$	−3.68927	+	3.27460i	−0.395531	+	0.351074i
$88$	−3.25450	+	3.07833i	−0.346931	+	0.328151i
$89$	−7.80405	+	13.5170i	−0.827228	+	1.43280i	0.0729765	+	0.997334i	$0.476750\pi$
$89$	−7.80405	+	13.5170i	−0.827228	+	1.43280i	−0.900205	+	0.435467i	$0.856583\pi$
$90$	−3.75801	+	1.96911i	−0.396129	+	0.207562i
$91$	5.23234	−	4.27507i	0.548498	−	0.448149i
$92$	−1.00162	−	6.36881i	−0.104427	−	0.663994i
$93$	−1.29776	+	3.89946i	−0.134571	+	0.404355i
$94$	−13.5050	+	9.27096i	−1.39294	+	0.956227i
$95$	0.836259	−	0.482815i	0.0857984	−	0.0495357i
$96$	−0.672655	−	9.77484i	−0.0686525	−	0.997641i
$97$		−	10.1286i		−	1.02841i	−0.857669	−	0.514203i	$-0.828088\pi$
$97$		−	10.1286i		−	1.02841i	0.857669	−	0.514203i	$-0.171912\pi$
$98$	−5.96184	+	7.90294i	−0.602237	+	0.798318i
$99$	−4.36774	+	1.87063i	−0.438974	+	0.188005i
$100$	−0.718765	+	1.86638i	−0.0718765	+	0.186638i
$101$	3.43160	−	1.98123i	0.341457	−	0.197140i	−0.319459	−	0.947600i	$-0.603501\pi$
$101$	3.43160	−	1.98123i	0.341457	−	0.197140i	0.660916	+	0.750460i	$0.270168\pi$
$102$	−0.00229314	−	0.00220974i	−0.000227055	−	0.000218797i
$103$	−2.98937	−	1.72591i	−0.294551	−	0.170059i	0.345441	−	0.938440i	$-0.387729\pi$
$103$	−2.98937	−	1.72591i	−0.294551	−	0.170059i	−0.639992	+	0.768381i	$0.721063\pi$
$104$	−1.67478	−	7.02642i	−0.164226	−	0.688997i
$105$	2.89367	−	3.55340i	0.282394	−	0.346776i
$106$	−1.01090	−	12.9345i	−0.0981869	−	1.25631i
$107$	1.33275	−	2.30839i	0.128842	−	0.223161i	−0.794386	−	0.607413i	$-0.792207\pi$
$107$	1.33275	−	2.30839i	0.128842	−	0.223161i	0.923228	+	0.384252i	$0.125541\pi$
$108$	2.91423	−	9.97533i	0.280422	−	0.959877i
$109$	−5.84319	+	3.37357i	−0.559676	+	0.323129i	−0.753015	−	0.658003i	$-0.771401\pi$
$109$	−5.84319	+	3.37357i	−0.559676	+	0.323129i	0.193339	+	0.981132i	$0.438068\pi$
$110$	−0.965383	+	2.02114i	−0.0920457	+	0.192708i
$111$	17.5875	−	3.60772i	1.66933	−	0.342430i
$112$	4.82529	+	9.41895i	0.455947	+	0.890007i
$113$			5.09463i			0.479262i	0.970864	+	0.239631i	$0.0770265\pi$
$113$			5.09463i			0.479262i	−0.970864	+	0.239631i	$0.922974\pi$
$114$	−0.569768	+	2.29565i	−0.0533636	+	0.215007i
$115$	−1.61177	−	2.79167i	−0.150299	−	0.260325i
$116$	−3.57982	−	4.43055i	−0.332378	−	0.411366i
$117$	0.909188	−	7.60729i	0.0840545	−	0.703294i
$118$	5.36673	−	0.419436i	0.494048	−	0.0386122i
$119$	0.00321661	+	0.00121864i	0.000294866	+	0.000111712i
$120$	−2.07031	−	4.44002i	−0.188993	−	0.405317i
$121$	4.24576	−	7.35387i	0.385978	−	0.668533i
$122$	−9.98974	+	6.85777i	−0.904428	+	0.620873i
$123$	−1.72381	+	1.53005i	−0.155431	+	0.137960i
$124$	−4.42847	−	1.70545i	−0.397688	−	0.153154i
$125$			1.00000i			0.0894427i
$126$	1.34929	+	11.1436i	0.120204	+	0.992749i
$127$	−2.78021			−0.246704			−0.123352	−	0.992363i	$-0.539364\pi$
$127$	−2.78021			−0.246704			−0.123352	+	0.992363i	$0.539364\pi$
$128$	11.3109	−	0.253128i	0.999750	−	0.0223735i
$129$	6.45555	+	7.27303i	0.568380	+	0.640355i
$130$	−2.04403	−	2.97755i	−0.179273	−	0.261148i
$131$	0.999689	+	0.577170i	0.0873432	+	0.0504276i	0.543035	−	0.839710i	$-0.317275\pi$
$131$	0.999689	+	0.577170i	0.0873432	+	0.0504276i	−0.455692	+	0.890137i	$0.650608\pi$
$132$	−1.92411	−	5.13806i	−0.167472	−	0.447211i
$133$	−0.410687	−	2.52159i	−0.0356111	−	0.218650i
$134$	11.3633	−	0.888094i	0.981636	−	0.0767196i
$135$	−0.432715	−	5.17810i	−0.0372422	−	0.445660i
$136$	0.00267148	−	0.00252688i	0.000229078	−	0.000216678i
$137$	−7.39675	+	4.27052i	−0.631947	+	0.364855i	−0.781506	−	0.623898i	$-0.785548\pi$
$137$	−7.39675	+	4.27052i	−0.631947	+	0.364855i	0.149559	+	0.988753i	$0.452215\pi$
$138$	7.66353	+	1.90205i	0.652363	+	0.161913i
$139$	13.1724			1.11727			0.558633	−	0.829415i	$-0.311326\pi$
$139$	13.1724			1.11727			0.558633	+	0.829415i	$0.311326\pi$
$140$	3.94396	+	3.52777i	0.333325	+	0.298151i
$141$	−4.03149	−	19.6533i	−0.339513	−	1.65511i
$142$	−5.76146	+	12.0623i	−0.483491	+	1.01224i
$143$	−2.02239	−	3.50288i	−0.169120	−	0.292925i
$144$	11.3503	+	3.89493i	0.945859	+	0.324577i
$145$	−2.46646	−	1.42401i	−0.204828	−	0.118258i
$146$	12.8964	−	1.00791i	1.06731	−	0.0834155i
$147$	−6.07925	−	10.4901i	−0.501408	−	0.865211i
$148$	3.22080	+	20.4794i	0.264748	+	1.68340i
$149$	−8.56852	+	14.8411i	−0.701961	+	1.21583i	0.265816	+	0.964024i	$0.414359\pi$
$149$	−8.56852	+	14.8411i	−0.701961	+	1.21583i	−0.967777	+	0.251808i	$0.918975\pi$
$150$	−1.76383	−	1.69968i	−0.144016	−	0.138778i
$151$	3.66635	+	6.35031i	0.298364	+	0.516781i	0.975762	−	0.218836i	$-0.0702259\pi$
$151$	3.66635	+	6.35031i	0.298364	+	0.516781i	−0.677398	+	0.735617i	$0.736893\pi$
$152$	−2.61747	−	0.779975i	−0.212305	−	0.0632643i
$153$	0.00358530	−	0.00153552i	0.000289854	−	0.000124139i
$154$	4.09569	+	4.28301i	0.330040	+	0.345134i
$155$	−2.37276			−0.190584
$156$	8.72609	+	1.45555i	0.698646	+	0.116537i
$157$	11.4441	+	19.8218i	0.913338	+	1.58195i	0.809316	+	0.587374i	$0.199838\pi$
$157$	11.4441	+	19.8218i	0.913338	+	1.58195i	0.104022	+	0.994575i	$0.466829\pi$
$158$	−16.7116	+	11.4722i	−1.32951	+	0.912681i
$159$	15.0768	+	5.01762i	1.19567	+	0.397924i
$160$	5.23212	−	2.15057i	0.413635	−	0.170018i
$161$	−8.41778	+	1.37099i	−0.663414	+	0.108049i
$162$	9.86877	+	8.03787i	0.775364	+	0.631514i
$163$	−9.51457	−	5.49324i	−0.745238	−	0.430264i	0.0787325	−	0.996896i	$-0.474913\pi$
$163$	−9.51457	−	5.49324i	−0.745238	−	0.430264i	−0.823971	+	0.566632i	$0.808246\pi$
$164$	−1.67267	−	2.07017i	−0.130614	−	0.161653i
$165$	−1.82104	−	2.05165i	−0.141768	−	0.159721i
$166$	6.06178	−	12.6910i	0.470485	−	0.985015i
$167$	22.2823			1.72426			0.862128	−	0.506690i	$-0.169131\pi$
$167$	22.2823			1.72426			0.862128	+	0.506690i	$0.169131\pi$
$168$	−12.9259	+	0.960401i	−0.997251	+	0.0740966i
$169$	−6.47806			−0.498313
$170$	0.000792443	−	0.00165907i	6.07776e−5	−	0.000127245i
$171$	−2.31916	−	1.73593i	−0.177351	−	0.132750i
$172$	−8.73440	+	7.05727i	−0.665992	+	0.538112i
$173$	−4.47223	−	2.58204i	−0.340017	−	0.196309i	0.320262	−	0.947329i	$-0.396229\pi$
$173$	−4.47223	−	2.58204i	−0.340017	−	0.196309i	−0.660280	+	0.751020i	$0.729562\pi$
$174$	6.70390	−	1.93006i	0.508221	−	0.146317i
$175$	2.47414	+	0.937347i	0.187028	+	0.0708568i
$176$	6.02945	−	1.94461i	0.454487	−	0.146580i
$177$	−2.08189	+	6.25559i	−0.156484	+	0.470199i
$178$	18.1979	−	12.4925i	1.36399	−	0.936353i
$179$	8.80808	+	15.2560i	0.658347	+	1.14029i	0.981044	+	0.193787i	$0.0620772\pi$
$179$	8.80808	+	15.2560i	0.658347	+	1.14029i	−0.322697	+	0.946502i	$0.604589\pi$
$180$	5.99588	−	0.222198i	0.446907	−	0.0165616i
$181$	−7.54524			−0.560833			−0.280417	−	0.959878i	$-0.590473\pi$
$181$	−7.54524			−0.560833			−0.280417	+	0.959878i	$0.590473\pi$
$182$	−9.28285	+	2.26623i	−0.688091	+	0.167984i
$183$	−2.98211	−	14.5376i	−0.220444	−	1.07465i
$184$	−2.60378	+	8.73786i	−0.191953	+	0.644164i
$185$	5.18278	+	8.97684i	0.381046	+	0.659990i
$186$	4.03292	−	4.18514i	0.295708	−	0.306869i
$187$	0.00102956	−	0.00178324i	7.52886e−5	−	0.000130404i
$188$	22.8849	−	3.59912i	1.66906	−	0.262493i
$189$	−13.2170	−	3.78308i	−0.961393	−	0.275179i
$190$	−1.36145	+	0.106404i	−0.0987703	+	0.00771938i
$191$	12.9451	+	7.47388i	0.936677	+	0.540791i	0.888917	−	0.458068i	$-0.151458\pi$
$191$	12.9451	+	7.47388i	0.936677	+	0.540791i	0.0477601	+	0.998859i	$0.484792\pi$
$192$	−5.09966	+	12.8838i	−0.368036	+	0.929812i
$193$	1.89906	+	3.28927i	0.136697	+	0.236767i	0.926245	−	0.376923i	$-0.123018\pi$
$193$	1.89906	+	3.28927i	0.136697	+	0.236767i	−0.789547	+	0.613690i	$0.789685\pi$
$194$	−6.17368	+	12.9253i	−0.443245	+	0.927983i
$195$	4.33310	−	0.888851i	0.310300	−	0.0636519i
$196$	12.4251	−	6.45117i	0.887505	−	0.460798i
$197$	18.1418			1.29255			0.646276	−	0.763104i	$-0.276326\pi$
$197$	18.1418			1.29255			0.646276	+	0.763104i	$0.276326\pi$
$198$	6.71395	+	0.275123i	0.477139	+	0.0195521i
$199$	−11.9778	+	6.91541i	−0.849087	+	0.490220i	−0.860343	−	0.509716i	$-0.829750\pi$
$199$	−11.9778	+	6.91541i	−0.849087	+	0.490220i	0.0112559	+	0.999937i	$0.496417\pi$
$200$	2.05484	−	1.94361i	0.145299	−	0.137434i
$201$	−4.40809	+	13.2453i	−0.310923	+	0.934250i
$202$	−5.58674	+	0.436631i	−0.393082	+	0.0307212i
$203$	−5.83513	+	4.76758i	−0.409546	+	0.334618i
$204$	0.00157942	+	0.00421762i	0.000110582	+	0.000295292i
$205$	−1.15245	−	0.665368i	−0.0804907	−	0.0464713i
$206$	2.76279	+	4.02457i	0.192493	+	0.280405i
$207$	−5.79502	+	7.74202i	−0.402782	+	0.538108i
$208$	−2.14558	+	9.98736i	−0.148769	+	0.692499i
$209$	−1.52938			−0.105790
$210$	−5.85856	+	2.77078i	−0.404279	+	0.191202i
$211$		−	9.20943i		−	0.634003i	−0.948425	−	0.317002i	$-0.897324\pi$
$211$		−	9.20943i		−	0.634003i	0.948425	−	0.317002i	$-0.102676\pi$
$212$	−6.59393	+	17.1221i	−0.452873	+	1.17595i
$213$	−10.8681	−	12.2443i	−0.744670	−	0.838969i
$214$	−3.10778	+	2.13343i	−0.212443	+	0.145838i
$215$	−2.80730	+	4.86239i	−0.191456	+	0.331612i
$216$	−9.79915	+	10.9534i	−0.666747	+	0.745284i
$217$	−2.22410	+	5.87054i	−0.150982	+	0.398518i
$218$	9.51288	−	0.743478i	0.644294	−	0.0503547i
$219$	−5.00282	+	15.0323i	−0.338059	+	1.01579i
$220$	2.46388	−	1.99078i	0.166115	−	0.134219i
$221$	0.00166009	+	0.00287537i	0.000111670	+	0.000193418i
$222$	−24.6427	−	6.11618i	−1.65391	−	0.410491i
$223$			17.0765i			1.14353i	0.820418	+	0.571764i	$0.193741\pi$
$223$			17.0765i			1.14353i	−0.820418	+	0.571764i	$0.806259\pi$
$224$	−0.416518	−	14.9608i	−0.0278298	−	0.999613i
$225$	2.75772	−	1.18108i	0.183848	−	0.0787390i
$226$	3.10532	−	6.50134i	0.206563	−	0.432463i
$227$	22.4975	−	12.9890i	1.49321	−	0.862107i	0.493244	−	0.869891i	$-0.335811\pi$
$227$	22.4975	−	12.9890i	1.49321	−	0.862107i	0.999970	+	0.00778359i	$0.00247762\pi$
$228$	2.12635	−	2.58223i	0.140821	−	0.171012i
$229$	−10.8195	+	18.7399i	−0.714971	+	1.23837i	0.247999	+	0.968760i	$0.420227\pi$
$229$	−10.8195	+	18.7399i	−0.714971	+	1.23837i	−0.962971	+	0.269606i	$0.913106\pi$
$230$	0.355208	+	4.54492i	0.0234217	+	0.299683i
$231$	−6.78302	+	2.58242i	−0.446290	+	0.169911i
$232$	1.86773	+	7.83591i	0.122622	+	0.514452i
$233$	14.5217	+	8.38408i	0.951345	+	0.549259i	0.893499	−	0.449066i	$-0.148243\pi$
$233$	14.5217	+	8.38408i	0.951345	+	0.549259i	0.0578466	+	0.998325i	$0.481577\pi$
$234$	−5.79709	+	9.15361i	−0.378967	+	0.598390i
$235$	10.0313	−	5.79156i	0.654368	−	0.377800i
$236$	−7.10424	−	2.73593i	−0.462446	−	0.178094i
$237$	−4.98872	−	24.3197i	−0.324052	−	1.57974i
$238$	−0.00336198	−	0.00351574i	−0.000217925	−	0.000227892i
$239$		−	7.53787i		−	0.487584i	−0.969827	−	0.243792i	$-0.921609\pi$
$239$		−	7.53787i		−	0.487584i	0.969827	−	0.243792i	$-0.0783915\pi$
$240$	−0.0643604	+	6.92790i	−0.00415444	+	0.447194i
$241$	−12.8323	+	7.40873i	−0.826601	+	0.477238i	−0.852687	−	0.522422i	$-0.825029\pi$
$241$	−12.8323	+	7.40873i	−0.826601	+	0.477238i	0.0260867	+	0.999660i	$0.491695\pi$
$242$	−9.90047	+	6.79649i	−0.636426	+	0.436895i
$243$	−13.7687	+	7.30909i	−0.883263	+	0.468878i
$244$	16.9281	−	2.66228i	1.08371	−	0.170435i
$245$	4.63826	−	5.24276i	0.296328	−	0.334948i
$246$	3.13239	−	0.901819i	0.199714	−	0.0574979i
$247$	1.23302	−	2.13565i	0.0784549	−	0.135888i
$248$	4.61172	+	4.87564i	0.292845	+	0.309603i
$249$	11.4346	+	12.8826i	0.724638	+	0.816401i
$250$	0.609528	−	1.27612i	0.0385500	−	0.0807087i
$251$			12.7580i			0.805281i	0.915358	+	0.402640i	$0.131908\pi$
$251$			12.7580i			0.805281i	−0.915358	+	0.402640i	$0.868092\pi$
$252$	5.07048	−	15.0429i	0.319410	−	0.947617i
$253$			5.10552i			0.320981i
$254$	3.54788	+	1.69462i	0.222614	+	0.106330i
$255$	0.00149482	+	0.00168411i	9.36093e−5	+	0.000105463i
$256$	−14.5883	−	6.57128i	−0.911768	−	0.410705i
$257$	−13.6364	+	23.6190i	−0.850618	+	1.47331i	0.0300331	+	0.999549i	$0.490439\pi$
$257$	−13.6364	+	23.6190i	−0.850618	+	1.47331i	−0.880651	+	0.473765i	$0.842895\pi$
$258$	−3.80492	−	13.2161i	−0.236884	−	0.822798i
$259$	27.0680	−	4.40852i	1.68193	−	0.273932i
$260$	0.793523	+	5.04560i	0.0492122	+	0.312915i
$261$	−1.01393	+	8.48369i	−0.0627608	+	0.525127i
$262$	−0.923918	−	1.34588i	−0.0570798	−	0.0831485i
$263$	−14.4484	+	8.34177i	−0.890925	+	0.514376i	−0.874245	−	0.485485i	$-0.838643\pi$
$263$	−14.4484	+	8.34177i	−0.890925	+	0.514376i	−0.0166797	+	0.999861i	$0.505310\pi$
$264$	−0.676402	+	7.72956i	−0.0416297	+	0.475722i
$265$			9.17398i			0.563553i
$266$	−1.01290	+	3.46817i	−0.0621046	+	0.212647i
$267$	5.43239	+	26.4826i	0.332457	+	1.62071i
$268$	−15.0422	−	5.79292i	−0.918847	−	0.353859i
$269$	2.75722	−	1.59188i	0.168111	−	0.0970589i	−0.413584	−	0.910466i	$-0.635723\pi$
$269$	2.75722	−	1.59188i	0.168111	−	0.0970589i	0.581695	+	0.813407i	$0.302390\pi$
$270$	−2.60401	+	6.87162i	−0.158475	+	0.418193i
$271$	20.3491	+	11.7486i	1.23612	+	0.713674i	0.968299	−	0.249794i	$-0.0803629\pi$
$271$	20.3491	+	11.7486i	1.23612	+	0.713674i	0.267821	+	0.963469i	$0.413696\pi$
$272$	−0.00494933	+	0.00159625i	−0.000300097	+	9.67867e-5i
$273$	1.86247	−	11.5539i	0.112722	−	0.699272i
$274$	12.0421	−	0.941150i	0.727491	−	0.0568570i
$275$	0.791910	−	1.37163i	0.0477540	−	0.0827123i
$276$	−8.62021	−	7.09837i	−0.518876	−	0.427272i
$277$	−21.0161	+	12.1337i	−1.26274	+	0.729041i	−0.973603	−	0.228248i	$-0.926700\pi$
$277$	−21.0161	+	12.1337i	−1.26274	+	0.729041i	−0.289133	+	0.957289i	$0.593367\pi$
$278$	−16.8095	−	8.02893i	−1.00817	−	0.481543i
$279$	2.80243	+	6.54341i	0.167777	+	0.391744i
$280$	−2.88268	−	6.90581i	−0.172273	−	0.412701i
$281$		−	8.11655i		−	0.484193i	−0.970252	−	0.242096i	$-0.922165\pi$
$281$		−	8.11655i		−	0.484193i	0.970252	−	0.242096i	$-0.0778350\pi$
$282$	−6.83459	+	27.5372i	−0.406994	+	1.63982i
$283$	−4.25172	−	7.36420i	−0.252739	−	0.437756i	0.711540	−	0.702645i	$-0.247998\pi$
$283$	−4.25172	−	7.36420i	−0.252739	−	0.437756i	−0.964279	+	0.264889i	$0.914665\pi$
$284$	14.7046	−	11.8811i	0.872557	−	0.705014i
$285$	0.528142	−	1.58694i	0.0312844	−	0.0940023i
$286$	0.445700	+	5.70278i	0.0263548	+	0.337213i
$287$	−2.72646	+	2.22765i	−0.160938	+	0.131494i
$288$	−12.1103	−	11.8887i	−0.713604	−	0.700549i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	2.27952	+	3.32058i	0.133858	+	0.194991i
$291$	−11.6457	−	13.1204i	−0.682682	−	0.769132i
$292$	−17.0716	−	6.57448i	−0.999041	−	0.384743i
$293$			9.79161i			0.572032i	0.958225	+	0.286016i	$0.0923311\pi$
$293$			9.79161i			0.572032i	−0.958225	+	0.286016i	$0.907669\pi$
$294$	1.36380	+	17.0921i	0.0795384	+	0.996832i
$295$	−3.80642			−0.221619
$296$	8.37265	−	28.0973i	0.486650	−	1.63312i
$297$	−3.50707	+	7.44511i	−0.203501	+	0.432009i
$298$	19.9805	−	13.7162i	1.15744	−	0.794561i
$299$	−7.12939	−	4.11616i	−0.412303	−	0.238044i
$300$	1.21485	+	3.24409i	0.0701396	+	0.187298i
$301$	9.39882	+	11.5034i	0.541739	+	0.663045i
$302$	−0.808003	−	10.3385i	−0.0464953	−	0.594913i
$303$	2.16724	−	6.51203i	0.124504	−	0.374106i
$304$	2.86478	+	2.59076i	0.164307	+	0.148590i
$305$	7.42017	−	4.28404i	0.424878	−	0.245303i
$306$	−0.00551120		0.000225837i	−0.000315054		1.29102e-5i
$307$	20.0331			1.14335			0.571676	−	0.820479i	$-0.306293\pi$
$307$	20.0331			1.14335			0.571676	+	0.820479i	$0.306293\pi$
$308$	−2.61597	−	7.96206i	−0.149059	−	0.453680i
$309$	−5.85678	+	1.20140i	−0.333181	+	0.0683455i
$310$	3.02792	+	1.44626i	0.171974	+	0.0821422i
$311$	−9.43673	−	16.3449i	−0.535108	−	0.926834i	−0.999158	−	0.0410252i	$-0.986938\pi$
$311$	−9.43673	−	16.3449i	−0.535108	−	0.926834i	0.464050	−	0.885809i	$-0.346396\pi$
$312$	−10.2483	−	7.17625i	−0.580197	−	0.406275i
$313$	13.8607	+	8.00248i	0.783454	+	0.452327i	0.837653	−	0.546203i	$-0.183927\pi$
$313$	13.8607	+	8.00248i	0.783454	+	0.452327i	−0.0541993	+	0.998530i	$0.517261\pi$
$314$	−2.52209	−	32.2704i	−0.142330	−	1.82112i
$315$	−0.337227	−	7.93009i	−0.0190006	−	0.446810i
$316$	28.3187	−	4.45369i	1.59305	−	0.250539i
$317$	11.8261	−	20.4834i	0.664220	−	1.15046i	−0.315276	−	0.949000i	$-0.602097\pi$
$317$	11.8261	−	20.4834i	0.664220	−	1.15046i	0.979496	−	0.201463i	$-0.0645695\pi$
$318$	−16.1813	−	15.5928i	−0.907405	−	0.874401i
$319$	2.25538	+	3.90643i	0.126277	+	0.218718i
$320$	−7.98763	−	0.444738i	−0.446522	−	0.0248616i
$321$	−0.927725	−	4.52261i	−0.0517806	−	0.252428i
$322$	11.5777	+	3.38133i	0.645202	+	0.188434i
$323$	0.00125541			6.98527e−5
$324$	−7.69441	−	16.2726i	−0.427467	−	0.904031i
$325$	1.27690	+	2.21166i	0.0708299	+	0.122681i
$326$	8.79342	+	12.8094i	0.487022	+	0.709448i
$327$	−3.69028	+	11.0884i	−0.204073	+	0.613192i
$328$	0.872694	+	3.66132i	0.0481865	+	0.202163i
$329$	−4.92635	−	30.2475i	−0.271599	−	1.66760i
$330$	1.07333	+	3.72812i	0.0590848	+	0.205226i
$331$	−29.0623	−	16.7791i	−1.59741	−	0.922264i	−0.991984	−	0.126361i	$-0.959670\pi$
$331$	−29.0623	−	16.7791i	−1.59741	−	0.922264i	−0.605424	−	0.795903i	$-0.706996\pi$
$332$	−15.4711	+	12.5004i	−0.849086	+	0.686049i
$333$	18.6343	−	24.8951i	1.02116	−	1.36424i
$334$	−28.4348	−	13.5817i	−1.55588	−	0.743157i
$335$	−8.05954			−0.440340
$336$	17.0803	+	6.65309i	0.931806	+	0.362956i
$337$	−11.9306			−0.649902			−0.324951	−	0.945731i	$-0.605348\pi$
$337$	−11.9306			−0.649902			−0.324951	+	0.945731i	$0.605348\pi$
$338$	8.26677	+	3.94856i	0.449653	+	0.214774i
$339$	5.85770	+	6.59947i	0.318146	+	0.358434i
$340$	−0.00202250	+	0.00163415i	−0.000109685	+	8.86243e-5i
$341$	3.25454	+	1.87901i	0.176243	+	0.101754i
$342$	1.90143	+	3.62884i	0.102817	+	0.196225i
$343$	−8.62368	−	16.3900i	−0.465635	−	0.884977i
$344$	15.4477	−	3.68204i	0.832886	−	0.198522i
$345$	−5.29766	−	1.76309i	−0.285217	−	0.0949215i
$346$	4.13326	+	6.02094i	0.222205	+	0.323688i
$347$	4.22243	+	7.31347i	0.226672	+	0.392608i	0.956820	−	0.290682i	$-0.0938821\pi$
$347$	4.22243	+	7.31347i	0.226672	+	0.392608i	−0.730148	+	0.683289i	$0.760549\pi$
$348$	−9.73139	−	1.62323i	−0.521657	−	0.0870145i
$349$	−22.2036			−1.18853			−0.594266	−	0.804268i	$-0.702557\pi$
$349$	−22.2036			−1.18853			−0.594266	+	0.804268i	$0.702557\pi$
$350$	−2.58596	−	2.70422i	−0.138225	−	0.144547i
$351$	−7.56896	−	10.8997i	−0.404001	−	0.581782i
$352$	−8.87958	−	1.19358i	−0.473283	−	0.0636178i
$353$	7.19217	+	12.4572i	0.382800	+	0.663030i	0.991461	−	0.130401i	$-0.0416264\pi$
$353$	7.19217	+	12.4572i	0.382800	+	0.663030i	−0.608661	+	0.793430i	$0.708293\pi$
$354$	6.46969	−	6.71389i	0.343860	−	0.356839i
$355$	4.72616	−	8.18595i	0.250839	−	0.434465i
$356$	−30.8372	+	4.84977i	−1.63437	+	0.257038i
$357$	0.00556790	−	0.00211980i	0.000294684	−	0.000112192i
$358$	−1.94115	−	24.8373i	−0.102593	−	1.31269i
$359$	7.47661	+	4.31662i	0.394600	+	0.227823i	0.684151	−	0.729340i	$-0.260173\pi$
$359$	7.47661	+	4.31662i	0.394600	+	0.227823i	−0.289551	+	0.957163i	$0.593506\pi$
$360$	−7.78689	−	3.37111i	−0.410405	−	0.177673i
$361$	9.03378	+	15.6470i	0.475462	+	0.823525i
$362$	9.62861	+	4.59904i	0.506069	+	0.241720i
$363$	−2.95546	−	14.4077i	−0.155122	−	0.756210i
$364$	13.2273	+	2.76619i	0.693301	+	0.144988i
$365$	−9.14691			−0.478771
$366$	−5.05557	+	20.3694i	−0.264259	+	1.06473i
$367$	−2.79520	+	1.61381i	−0.145908	+	0.0842402i	−0.571177	−	0.820827i	$-0.693513\pi$
$367$	−2.79520	+	1.61381i	−0.145908	+	0.0842402i	0.425269	+	0.905067i	$0.360180\pi$
$368$	8.64870	−	9.56346i	0.450845	−	0.498530i
$369$	−0.473759	+	3.96400i	−0.0246629	+	0.206358i
$370$	−1.14220	−	14.6145i	−0.0593800	−	0.759774i
$371$	22.6977	+	8.59920i	1.17841	+	0.446448i
$372$	−7.69744	+	2.88255i	−0.399094	+	0.149453i
$373$	16.6643	+	9.62113i	0.862844	+	0.498163i	0.864964	−	0.501835i	$-0.167341\pi$
$373$	16.6643	+	9.62113i	0.862844	+	0.498163i	−0.00211985	+	0.999998i	$0.500675\pi$
$374$	−0.00240077	+	0.00164808i	−0.000124141	+	8.52204e-5i
$375$	1.14978	+	1.29538i	0.0593744	+	0.0668931i
$376$	−31.3976	−	9.35612i	−1.61921	−	0.482505i
$377$	−7.27330			−0.374594
$378$	14.5605	+	12.8838i	0.748912	+	0.662670i
$379$		−	28.2338i		−	1.45027i	−0.688604	−	0.725137i	$-0.741776\pi$
$379$		−	28.2338i		−	1.45027i	0.688604	−	0.725137i	$-0.258224\pi$
$380$	1.80223	+	0.694061i	0.0924525	+	0.0356046i
$381$	−3.60143	+	3.19663i	−0.184507	+	0.163768i
$382$	−11.9640	−	17.4280i	−0.612130	−	0.891693i
$383$	−1.98896	+	3.44499i	−0.101631	+	0.176031i	−0.912357	−	0.409396i	$-0.865740\pi$
$383$	−1.98896	+	3.44499i	−0.101631	+	0.176031i	0.810726	+	0.585426i	$0.199073\pi$
$384$	14.3608	−	13.3329i	0.732848	−	0.680392i
$385$	−2.65131	−	3.24499i	−0.135123	−	0.165380i
$386$	−0.418521	−	5.35502i	−0.0213021	−	0.272563i
$387$	16.7248	+	1.99887i	0.850168	+	0.101608i
$388$	15.7567	−	12.7312i	0.799924	−	0.646328i
$389$	15.1320	+	26.2095i	0.767225	+	1.32887i	0.939062	+	0.343748i	$0.111696\pi$
$389$	15.1320	+	26.2095i	0.767225	+	1.32887i	−0.171837	+	0.985125i	$0.554970\pi$
$390$	−6.07132	−	1.50687i	−0.307433	−	0.0763033i
$391$		−	0.00419091i		−	0.000211943i
$392$	−19.7880	+	0.659014i	−0.999446	+	0.0332852i
$393$	1.95859	−	0.401767i	0.0987980	−	0.0202665i
$394$	−23.1511	−	11.0580i	−1.16634	−	0.557092i
$395$	12.4131	−	7.16669i	0.624569	−	0.360595i
$396$	−8.40009	−	4.44343i	−0.422120	−	0.223291i
$397$	9.36263	−	16.2166i	0.469897	−	0.813886i	−0.529510	−	0.848303i	$-0.677624\pi$
$397$	9.36263	−	16.2166i	0.469897	−	0.813886i	0.999408	+	0.0344178i	$0.0109577\pi$
$398$	19.5003	−	1.52404i	0.977460	−	0.0763933i
$399$	−3.43127	−	2.79421i	−0.171778	−	0.139886i
$400$	−3.80690	+	1.22779i	−0.190345	+	0.0613897i
$401$	−23.0500	−	13.3079i	−1.15106	−	0.664566i	−0.201916	−	0.979403i	$-0.564717\pi$
$401$	−23.0500	−	13.3079i	−1.15106	−	0.664566i	−0.949146	+	0.314837i	$0.898050\pi$
$402$	13.6986	−	14.2157i	0.683225	−	0.709013i
$403$	−5.24774	+	3.02978i	−0.261408	+	0.150924i
$404$	7.39547	+	2.84808i	0.367939	+	0.141697i
$405$	−6.51421	−	6.21008i	−0.323694	−	0.308581i
$406$	10.3523	−	2.52731i	0.513776	−	0.125428i
$407$		−	16.4172i		−	0.813770i
$408$	0.000555230	−	0.00634488i	2.74880e−5	−	0.000314118i
$409$	−24.5546	+	14.1766i	−1.21415	+	0.700988i	−0.963660	−	0.267131i	$-0.913924\pi$
$409$	−24.5546	+	14.1766i	−1.21415	+	0.700988i	−0.250488	+	0.968120i	$0.580591\pi$
$410$	1.06510	+	1.55154i	0.0526017	+	0.0766251i
$411$	−4.67144	+	14.0366i	−0.230425	+	0.692373i
$412$	−1.07256	−	6.81982i	−0.0528410	−	0.335988i
$413$	−3.56794	+	9.41764i	−0.175567	+	0.463412i
$414$	12.1141	−	6.34750i	0.595376	−	0.311963i
$415$	−4.97252	+	8.61265i	−0.244091	+	0.422778i
$416$	8.82560	−	11.4373i	0.432711	−	0.560757i
$417$	17.0632	−	15.1453i	0.835589	−	0.741670i
$418$	1.95167	+	0.932202i	0.0954594	+	0.0455955i
$419$			29.6942i			1.45066i	0.688403	+	0.725329i	$0.258312\pi$
$419$			29.6942i			1.45066i	−0.688403	+	0.725329i	$0.741688\pi$
$420$	9.16508	+	0.0351185i	0.447210	+	0.00171361i
$421$		−	13.9615i		−	0.680442i	−0.940346	−	0.340221i	$-0.889498\pi$
$421$		−	13.9615i		−	0.680442i	0.940346	−	0.340221i	$-0.110502\pi$
$422$	−5.61341	+	11.7523i	−0.273256	+	0.572094i
$423$	−27.8193	−	20.8232i	−1.35262	−	1.01246i
$424$	18.8511	−	17.8307i	0.915488	−	0.865933i
$425$	−0.000650046		0.00112591i	−3.15319e−5		5.46148e-5i
$426$	6.40569	+	22.2496i	0.310357	+	1.07800i
$427$	−3.64404	−	22.3742i	−0.176348	−	1.08276i
$428$	5.26627	−	0.828228i	0.254555	−	0.0400339i
$429$	−6.64729	−	2.21225i	−0.320934	−	0.106809i
$430$	6.54621	−	4.49385i	0.315686	−	0.216713i
$431$	−22.0215	+	12.7141i	−1.06074	+	0.612417i	−0.925636	−	0.378414i	$-0.876469\pi$
$431$	−22.0215	+	12.7141i	−1.06074	+	0.612417i	−0.135102	+	0.990832i	$0.543136\pi$
$432$	19.1813	−	8.00495i	0.922859	−	0.385138i
$433$			32.4681i			1.56032i	0.625581	+	0.780159i	$0.284862\pi$
$433$			32.4681i			1.56032i	−0.625581	+	0.780159i	$0.715138\pi$
$434$	6.41647	−	6.13585i	0.308000	−	0.294530i
$435$	−4.83230	+	0.991252i	−0.231691	+	0.0475269i
$436$	−12.5927	−	4.84960i	−0.603082	−	0.232254i
$437$	−2.69572	+	1.55637i	−0.128954	+	0.0744515i
$438$	15.5468	−	16.1336i	0.742855	−	0.770894i
$439$	−6.85637	−	3.95853i	−0.327237	−	0.188930i	0.327377	−	0.944894i	$-0.393835\pi$
$439$	−6.85637	−	3.95853i	−0.327237	−	0.188930i	−0.654614	+	0.755964i	$0.727169\pi$
$440$	−4.35764	+	1.03867i	−0.207743	+	0.0495165i
$441$	−19.9363	−	6.59890i	−0.949346	−	0.314233i
$442$	−0.000365857	−	0.00468118i	−1.74020e−5	−	0.000222661i
$443$	7.35604	−	12.7410i	0.349496	−	0.605345i	−0.636664	−	0.771141i	$-0.719686\pi$
$443$	7.35604	−	12.7410i	0.349496	−	0.605345i	0.986160	+	0.165796i	$0.0530194\pi$
$444$	27.7190	+	22.8254i	1.31548	+	1.08324i
$445$	−13.5170	+	7.80405i	−0.640768	+	0.369948i
$446$	10.4086	−	21.7916i	0.492862	−	1.03186i
$447$	5.96453	+	29.0768i	0.282113	+	1.37528i
$448$	−8.58752	+	19.3457i	−0.405722	+	0.913996i
$449$		−	22.4699i		−	1.06042i	−0.847866	−	0.530211i	$-0.822113\pi$
$449$		−	22.4699i		−	1.06042i	0.847866	−	0.530211i	$-0.177887\pi$
$450$	−4.23908	−	0.173708i	−0.199832	−	0.00818869i
$451$	1.05382	+	1.82528i	0.0496226	+	0.0859489i
$452$	−7.92550	+	6.40369i	−0.372784	+	0.301204i
$453$	12.0508	+	4.01056i	0.566195	+	0.188432i
$454$	−36.6266	+	2.86255i	−1.71897	+	0.134346i
$455$	6.66887	−	1.08615i	0.312641	−	0.0509194i
$456$	−4.28742	+	1.99915i	−0.200777	+	0.0936189i
$457$	8.91676	−	15.4443i	0.417109	−	0.722453i	−0.578539	−	0.815655i	$-0.696377\pi$
$457$	8.91676	−	15.4443i	0.417109	−	0.722453i	0.995647	+	0.0932018i	$0.0297102\pi$
$458$	25.2294	−	17.3195i	1.17889	−	0.809288i
$459$	0.00287881	−	0.00611138i	0.000134371	−	0.000285255i
$460$	2.31697	−	6.01636i	0.108029	−	0.280514i
$461$			24.2057i			1.12737i	0.825989	+	0.563686i	$0.190617\pi$
$461$			24.2057i			1.12737i	−0.825989	+	0.563686i	$0.809383\pi$
$462$	10.2300	+	0.838973i	0.475942	+	0.0390326i
$463$	32.9835			1.53287			0.766436	−	0.642321i	$-0.222028\pi$
$463$	32.9835			1.53287			0.766436	+	0.642321i	$0.222028\pi$
$464$	2.39277	−	11.1380i	0.111081	−	0.517067i
$465$	−3.07362	+	2.72815i	−0.142536	+	0.126515i
$466$	−13.4210	−	19.5504i	−0.621716	−	0.905656i
$467$	−16.7214	−	9.65411i	−0.773775	−	0.446739i	0.0604449	−	0.998172i	$-0.480748\pi$
$467$	−16.7214	−	9.65411i	−0.773775	−	0.446739i	−0.834219	+	0.551433i	$0.814081\pi$
$468$	12.9771	−	8.14760i	0.599869	−	0.376623i
$469$	−7.55459	+	19.9405i	−0.348838	+	0.920765i
$470$	−16.3312	+	1.27636i	−0.753302	+	0.0588742i
$471$	37.6151	+	12.5185i	1.73321	+	0.576822i
$472$	7.39822	+	7.82160i	0.340531	+	0.360018i
$473$	7.70115	−	4.44626i	0.354099	−	0.204439i
$474$	−8.45738	+	34.0756i	−0.388460	+	1.56514i
$475$	0.965629			0.0443061
$476$	0.00214734	+	0.00653572i	9.84231e−5	+	0.000299564i
$477$	25.2993	−	10.8352i	1.15838	−	0.496112i
$478$	−4.59455	+	9.61921i	−0.210150	+	0.439972i
$479$	−0.556505	−	0.963894i	−0.0254273	−	0.0440415i	0.853032	−	0.521859i	$-0.174761\pi$
$479$	−0.556505	−	0.963894i	−0.0254273	−	0.0440415i	−0.878459	+	0.477818i	$0.841428\pi$
$480$	4.30489	−	8.80159i	0.196490	−	0.401736i
$481$	22.9251	+	13.2358i	1.04530	+	0.603502i
$482$	20.8913	−	1.63276i	0.951574	−	0.0743702i
$483$	−9.32788	+	11.4545i	−0.424433	+	0.521200i
$484$	16.7768	−	2.63850i	0.762583	−	0.119932i
$485$	5.06431	−	8.77164i	0.229959	−	0.398300i
$486$	22.0256	−	0.934835i	0.999101	−	0.0424050i
$487$	−8.40036	−	14.5499i	−0.380657	−	0.659317i	0.610499	−	0.792017i	$-0.290969\pi$
$487$	−8.40036	−	14.5499i	−0.380657	−	0.659317i	−0.991156	+	0.132700i	$0.957635\pi$
$488$	−23.2250	−	6.92076i	−1.05134	−	0.313288i
$489$	−18.6410	+	3.82383i	−0.842974	+	0.172920i
$490$	−9.11457	+	3.86323i	−0.411755	+	0.174523i
$491$	−24.9428			−1.12565			−0.562826	−	0.826575i	$-0.690286\pi$
$491$	−24.9428			−1.12565			−0.562826	+	0.826575i	$0.690286\pi$
$492$	−4.54698	−	0.758455i	−0.204994	−	0.0341938i
$493$	−0.00185135	−	0.00320663i	−8.33804e−5	−	0.000144419i
$494$	−2.87521	+	1.97378i	−0.129362	+	0.0888044i
$495$	−4.71789	−	0.563860i	−0.212053	−	0.0253436i
$496$	−2.91326	−	9.03286i	−0.130809	−	0.405587i
$497$	−15.8232	−	19.3663i	−0.709766	−	0.868696i
$498$	−6.73959	−	23.4094i	−0.302008	−	1.04900i
$499$	−28.6360	−	16.5330i	−1.28192	−	0.740118i	−0.304723	−	0.952441i	$-0.598564\pi$
$499$	−28.6360	−	16.5330i	−1.28192	−	0.740118i	−0.977200	+	0.212323i	$0.931897\pi$
$500$	−1.55566	+	1.25695i	−0.0695712	+	0.0562125i
$501$	28.8640	−	25.6197i	1.28955	−	1.14461i
$502$	7.77639	−	16.2808i	0.347077	−	0.726646i
$503$	14.4817			0.645709			0.322854	−	0.946449i	$-0.395358\pi$
$503$	14.4817			0.645709			0.322854	+	0.946449i	$0.395358\pi$
$504$	−15.6396	+	16.1060i	−0.696644	+	0.717417i
$505$	3.96247			0.176328
$506$	3.11196	−	6.51524i	0.138343	−	0.289638i
$507$	−8.39155	+	7.44835i	−0.372682	+	0.330793i
$508$	−3.49459	−	4.32506i	−0.155047	−	0.191894i
$509$	−30.7536	−	17.7556i	−1.36313	−	0.787002i	−0.373088	−	0.927796i	$-0.621701\pi$
$509$	−30.7536	−	17.7556i	−1.36313	−	0.787002i	−0.990039	+	0.140794i	$0.955035\pi$
$510$	−0.000881052	−	0.00306026i	−3.90136e−5	−	0.000135511i
$511$	−8.57383	+	22.6308i	−0.379284	+	1.00113i
$512$	14.6110	+	17.2777i	0.645721	+	0.763574i
$513$	−5.00013	+	0.417842i	−0.220761	+	0.0184482i
$514$	31.7982	−	21.8288i	1.40256	−	0.962829i
$515$	−1.72591	−	2.98937i	−0.0760527	−	0.131727i
$516$	−3.20005	+	19.1845i	−0.140874	+	0.844550i
$517$	−18.3456			−0.806837
$518$	−37.2291	−	10.8729i	−1.63575	−	0.477730i
$519$	−8.76201	+	1.79736i	−0.384610	+	0.0788951i
$520$	2.06281	−	6.92245i	0.0904601	−	0.303570i
$521$	6.19190	+	10.7247i	0.271272	+	0.469857i	0.969188	−	0.246323i	$-0.0792223\pi$
$521$	6.19190	+	10.7247i	0.271272	+	0.469857i	−0.697916	+	0.716180i	$0.745889\pi$
$522$	6.46495	−	10.2082i	0.282963	−	0.446799i
$523$	−10.2725	+	17.7925i	−0.449185	+	0.778012i	−0.998333	−	0.0577132i	$-0.981619\pi$
$523$	−10.2725	+	17.7925i	−0.449185	+	0.778012i	0.549148	+	0.835725i	$0.314952\pi$
$524$	0.358679	+	2.28065i	0.0156689	+	0.0996306i
$525$	4.28269	−	1.63050i	0.186912	−	0.0711608i
$526$	23.5224	−	1.83839i	1.02562	−	0.0801575i
$527$	−0.00267152	−	0.00154240i	−0.000116373	−	6.71881e-5i
$528$	5.57456	−	9.45154i	0.242601	−	0.411326i
$529$	−6.30438	−	10.9195i	−0.274103	−	0.474761i
$530$	5.59180	−	11.7071i	0.242892	−	0.508523i
$531$	4.49571	+	10.4971i	0.195097	+	0.455534i
$532$	3.40652	−	3.80840i	0.147691	−	0.165115i
$533$	−3.39845			−0.147203
$534$	9.20953	−	37.1061i	0.398535	−	1.60574i
$535$	2.30839	−	1.33275i	0.0998005	−	0.0576198i
$536$	15.6646	+	16.5611i	0.676609	+	0.715329i
$537$	28.9509	+	9.63500i	1.24932	+	0.415781i
$538$	−4.48884	+	0.350825i	−0.193528	+	0.0151251i
$539$	−10.5138	+	3.51804i	−0.452860	+	0.151533i
$540$	7.51146	−	7.18178i	0.323242	−	0.309054i
$541$	16.3217	+	9.42333i	0.701724	+	0.405140i	0.807989	−	0.589197i	$-0.200556\pi$
$541$	16.3217	+	9.42333i	0.701724	+	0.405140i	−0.106265	+	0.994338i	$0.533889\pi$
$542$	−18.8068	−	27.3959i	−0.807820	−	1.17675i
$543$	−9.77395	+	8.67537i	−0.419440	+	0.372296i
$544$	0.00728888		0.000979758i	0.000312508		4.20068e-5i
$545$	−6.74713			−0.289015
$546$	−9.41915	+	13.6089i	−0.403102	+	0.582405i
$547$			13.4614i			0.575569i	0.957695	+	0.287785i	$0.0929188\pi$
$547$			13.4614i			0.575569i	−0.957695	+	0.287785i	$0.907081\pi$
$548$	−15.9408	−	6.13900i	−0.680958	−	0.262245i
$549$	−20.5780	−	15.4030i	−0.878249	−	0.657383i
$550$	−1.84662	+	1.26767i	−0.0787400	+	0.0540535i
$551$	−1.37507	+	2.38169i	−0.0585798	+	0.101463i
$552$	6.67374	+	14.3126i	0.284053	+	0.609185i
$553$	−6.09605	−	37.4294i	−0.259231	−	1.59166i
$554$	34.2148	−	2.67406i	1.45365	−	0.113610i
$555$	17.0351	+	5.66935i	0.723098	+	0.240651i
$556$	16.5570	+	20.4917i	0.702174	+	0.869042i
$557$	−13.7778	−	23.8638i	−0.583783	−	1.01114i	−0.995026	−	0.0996161i	$-0.968239\pi$
$557$	−13.7778	−	23.8638i	−0.583783	−	1.01114i	0.411243	−	0.911526i	$-0.365095\pi$
$558$	0.412168	−	10.0583i	0.0174484	−	0.425802i
$559$			14.3386i			0.606459i
$560$	−0.530652	+	10.5697i	−0.0224241	+	0.446651i
$561$	−0.000716672	−	0.00349374i	−3.02579e−5	−	0.000147506i
$562$	−4.94726	+	10.3577i	−0.208688	+	0.436912i
$563$	−29.3890	+	16.9677i	−1.23860	+	0.715105i	−0.968808	−	0.247814i	$-0.920288\pi$
$563$	−29.3890	+	16.9677i	−1.23860	+	0.715105i	−0.269791	+	0.962919i	$0.586955\pi$
$564$	25.5065	−	30.9749i	1.07402	−	1.30428i
$565$	−2.54731	+	4.41208i	−0.107166	+	0.185617i
$566$	0.937009	+	11.9891i	0.0393854	+	0.503941i
$567$	−21.4707	+	10.2961i	−0.901684	+	0.432395i
$568$	−26.0067	+	6.19882i	−1.09122	+	0.260097i
$569$	2.81569	+	1.62564i	0.118040	+	0.0681503i	0.557857	−	0.829937i	$-0.311624\pi$
$569$	2.81569	+	1.62564i	0.118040	+	0.0681503i	−0.439818	+	0.898087i	$0.644957\pi$
$570$	−1.64126	+	1.70321i	−0.0687447	+	0.0713395i
$571$	−20.8343	+	12.0287i	−0.871890	+	0.503386i	−0.867976	−	0.496607i	$-0.834579\pi$
$571$	−20.8343	+	12.0287i	−0.871890	+	0.503386i	−0.00391387	+	0.999992i	$0.501246\pi$
$572$	2.90724	−	7.54909i	0.121558	−	0.315643i
$573$	25.3622	−	5.20255i	1.05952	−	0.217340i
$574$	4.83710	−	1.18088i	0.201897	−	0.0492892i
$575$		−	3.22354i		−	0.134431i
$576$	8.20760	+	22.5529i	0.341983	+	0.939706i
$577$	10.9172	−	6.30307i	0.454490	−	0.262400i	−0.255234	−	0.966879i	$-0.582153\pi$
$577$	10.9172	−	6.30307i	0.454490	−	0.262400i	0.709725	+	0.704479i	$0.248819\pi$
$578$	−19.8207	+	13.6066i	−0.824434	+	0.565958i
$579$	6.24193	+	2.07735i	0.259406	+	0.0863316i
$580$	−0.884942	−	5.62688i	−0.0367452	−	0.233644i
$581$	16.6480	+	20.3758i	0.690674	+	0.845329i
$582$	6.86400	+	23.8415i	0.284522	+	0.988264i
$583$	7.26497	−	12.5833i	0.300884	−	0.521147i
$584$	17.7781	+	18.7954i	0.735661	+	0.777761i
$585$	4.59102	−	6.13351i	0.189815	−	0.253589i
$586$	5.96827	−	12.4952i	0.246547	−	0.516174i
$587$		−	8.47618i		−	0.349850i	−0.984582	−	0.174925i	$-0.944032\pi$
$587$		−	8.47618i		−	0.349850i	0.984582	−	0.174925i	$-0.0559682\pi$
$588$	8.67775	−	22.6428i	0.357864	−	0.933774i
$589$			2.29120i			0.0944074i
$590$	4.85744	+	2.32012i	0.199978	+	0.0955180i
$591$	23.5005	−	20.8591i	0.966683	−	0.858029i
$592$	−27.8106	+	30.7521i	−1.14301	+	1.26390i
$593$	9.31853	−	16.1402i	0.382666	−	0.662797i	−0.608776	−	0.793342i	$-0.708339\pi$
$593$	9.31853	−	16.1402i	0.382666	−	0.662797i	0.991442	+	0.130545i	$0.0416726\pi$
$594$	9.01343	−	7.36317i	0.369826	−	0.302115i
$595$	0.00217635	+	0.00266368i	8.92217e−5	+	0.000109200i
$596$	−33.8579	+	5.32485i	−1.38687	+	0.218114i
$597$	−7.56464	+	22.7300i	−0.309600	+	0.930275i
$598$	6.58903	+	9.59827i	0.269445	+	0.392502i
$599$	−28.3537	+	16.3700i	−1.15850	+	0.668861i	−0.950944	−	0.309362i	$-0.899885\pi$
$599$	−28.3537	+	16.3700i	−1.15850	+	0.668861i	−0.207557	+	0.978223i	$0.566551\pi$
$600$	0.427070	−	4.88033i	0.0174351	−	0.199239i
$601$			6.71478i			0.273902i	0.990578	+	0.136951i	$0.0437302\pi$
$601$			6.71478i			0.273902i	−0.990578	+	0.136951i	$0.956270\pi$
$602$	−4.98235	−	20.4085i	−0.203065	−	0.831790i
$603$	9.51900	+	22.2260i	0.387644	+	0.905112i
$604$	−5.27049	+	13.6856i	−0.214453	+	0.556860i
$605$	7.35387	−	4.24576i	0.298977	−	0.172615i
$606$	−6.73492	+	6.98912i	−0.273587	+	0.283914i
$607$	26.6866	+	15.4075i	1.08318	+	0.625372i	0.931751	−	0.363097i	$-0.118281\pi$
$607$	26.6866	+	15.4075i	1.08318	+	0.625372i	0.151425	+	0.988469i	$0.451614\pi$
$608$	−2.07666	−	5.05228i	−0.0842196	−	0.204897i
$609$	−2.07704	+	12.8849i	−0.0841660	+	0.522124i
$610$	−12.0802	+	0.944130i	−0.489115	+	0.0382267i
$611$	14.7905	−	25.6179i	0.598361	−	1.03639i
$612$	0.00689528	+	0.00364743i	0.000278725	+	0.000147438i
$613$	26.1540	−	15.1000i	1.05635	−	0.609884i	0.131930	−	0.991259i	$-0.457883\pi$
$613$	26.1540	−	15.1000i	1.05635	−	0.609884i	0.924421	+	0.381375i	$0.124549\pi$
$614$	−25.5646	−	12.2108i	−1.03170	−	0.492787i
$615$	−2.25789	+	0.463162i	−0.0910468	+	0.0186765i
$616$	−1.51482	+	11.7550i	−0.0610337	+	0.473623i
$617$		−	8.88102i		−	0.357536i	−0.983891	−	0.178768i	$-0.942789\pi$
$617$		−	8.88102i		−	0.357536i	0.983891	−	0.178768i	$-0.0572112\pi$
$618$	8.20623	+	2.03674i	0.330103	+	0.0819297i
$619$	−2.72170	−	4.71412i	−0.109394	−	0.189477i	0.806131	−	0.591738i	$-0.201558\pi$
$619$	−2.72170	−	4.71412i	−0.109394	−	0.189477i	−0.915525	+	0.402261i	$0.868224\pi$
$620$	−2.98244	−	3.69120i	−0.119778	−	0.148242i
$621$	1.39488	+	16.6918i	0.0559744	+	0.669821i
$622$	2.07970	+	26.6100i	0.0833883	+	1.06696i
$623$	6.63820	+	40.7581i	0.265954	+	1.63294i
$624$	8.70393	+	15.4044i	0.348436	+	0.616668i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−12.8101	−	18.6606i	−0.511996	−	0.745828i
$627$	−1.98113	+	1.75845i	−0.0791187	+	0.0702259i
$628$	−16.4512	+	42.7181i	−0.656476	+	1.70464i
$629$			0.0134762i			0.000537331i
$630$	−4.40327	+	10.3253i	−0.175431	+	0.411369i
$631$	−27.6620			−1.10121			−0.550603	−	0.834767i	$-0.685602\pi$
$631$	−27.6620			−1.10121			−0.550603	+	0.834767i	$0.685602\pi$
$632$	−38.8526	−	11.5776i	−1.54547	−	0.460532i
$633$	−10.5888	−	11.9297i	−0.420868	−	0.474163i
$634$	−27.5767	+	18.9309i	−1.09521	+	0.751842i
$635$	−2.40773	−	1.39011i	−0.0955480	−	0.0551647i
$636$	11.1450	+	29.7612i	0.441930	+	1.18011i
$637$	3.56376	−	17.5178i	0.141201	−	0.694082i
$638$	−0.497048	−	6.35978i	−0.0196783	−	0.251786i
$639$	−28.1566	−	3.36515i	−1.11386	−	0.133123i
$640$	9.92207	+	5.43622i	0.392204	+	0.214886i
$641$	34.3763	−	19.8472i	1.35778	−	0.783916i	0.368458	−	0.929645i	$-0.379886\pi$
$641$	34.3763	−	19.8472i	1.35778	−	0.783916i	0.989325	+	0.145729i	$0.0465526\pi$
$642$	−1.57277	+	6.33686i	−0.0620724	+	0.250096i
$643$	−49.5521			−1.95415			−0.977073	−	0.212905i	$-0.931708\pi$
$643$	−49.5521			−1.95415			−0.977073	+	0.212905i	$0.931708\pi$
$644$	−12.7135	−	11.3719i	−0.500983	−	0.448117i
$645$	1.95416	+	9.52641i	0.0769448	+	0.375102i
$646$	−0.00160205		0.000765206i	−6.30317e−5		3.01066e-5i
$647$	−4.87813	−	8.44917i	−0.191779	−	0.332171i	0.754061	−	0.656805i	$-0.228092\pi$
$647$	−4.87813	−	8.44917i	−0.191779	−	0.332171i	−0.945840	+	0.324634i	$0.894759\pi$
$648$	−0.0996207	+	25.4556i	−0.00391347	+	0.999992i
$649$	5.22100	+	3.01435i	0.204942	+	0.118323i
$650$	−0.281408	−	3.60065i	−0.0110377	−	0.141229i
$651$	3.86878	+	10.1618i	0.151629	+	0.398272i
$652$	−3.41373	−	21.7061i	−0.133692	−	0.850078i
$653$	−1.09745	+	1.90084i	−0.0429465	+	0.0743855i	−0.886700	−	0.462346i	$-0.847008\pi$
$653$	−1.09745	+	1.90084i	−0.0429465	+	0.0743855i	0.843753	+	0.536731i	$0.180341\pi$
$654$	11.4679	−	11.9008i	0.448432	−	0.465358i
$655$	0.577170	+	0.999689i	0.0225519	+	0.0390611i
$656$	1.11802	−	5.20421i	0.0436513	−	0.203190i
$657$	10.8033	+	25.2247i	0.421476	+	0.984108i
$658$	−12.1501	+	41.6021i	−0.473660	+	1.62182i
$659$	−10.0050			−0.389739			−0.194869	−	0.980829i	$-0.562428\pi$
$659$	−10.0050			−0.389739			−0.194869	+	0.980829i	$0.562428\pi$
$660$	0.902701	−	5.41174i	0.0351376	−	0.210652i
$661$	10.8267	+	18.7524i	0.421109	+	0.729382i	0.996048	−	0.0888140i	$-0.0283077\pi$
$661$	10.8267	+	18.7524i	0.421109	+	0.729382i	−0.574939	+	0.818196i	$0.694974\pi$
$662$	26.8595	+	39.1264i	1.04393	+	1.52069i
$663$	0.00545649	+	0.00181595i	0.000211912	+	7.05255e-5i
$664$	27.3623	−	6.52193i	1.06186	−	0.253100i
$665$	0.905130	−	2.38910i	0.0350994	−	0.0926455i
$666$	−38.9539	+	20.4109i	−1.50943	+	0.790906i
$667$	7.95074	+	4.59036i	0.307854	+	0.177740i
$668$	28.0077	+	34.6637i	1.08365	+	1.34118i
$669$	19.6342	+	22.1206i	0.759103	+	0.855230i
$670$	10.2849	+	4.91252i	0.397341	+	0.189787i
$671$	−13.5703			−0.523875
$672$	−17.7412	−	18.9010i	−0.684382	−	0.729124i
$673$	22.8109			0.879296			0.439648	−	0.898170i	$-0.355103\pi$
$673$	22.8109			0.879296			0.439648	+	0.898170i	$0.355103\pi$
$674$	15.2249	+	7.27205i	0.586440	+	0.280109i
$675$	2.21431	−	4.70073i	0.0852288	−	0.180931i
$676$	−8.14261	−	10.0777i	−0.313177	−	0.387602i
$677$	18.1134	+	10.4578i	0.696154	+	0.401925i	0.805913	−	0.592034i	$-0.201675\pi$
$677$	18.1134	+	10.4578i	0.696154	+	0.401925i	−0.109759	+	0.993958i	$0.535008\pi$
$678$	−3.45255	−	11.9921i	−0.132594	−	0.460555i
$679$	−16.9553	−	20.7519i	−0.650684	−	0.796385i
$680$	0.00357701		0.000852598i	0.000137172		3.26956e-5i
$681$	14.2084	−	42.6928i	0.544467	−	1.63599i
$682$	−3.00787	−	4.38157i	−0.115177	−	0.167779i
$683$	−19.6451	−	34.0263i	−0.751698	−	1.30198i	−0.946999	−	0.321236i	$-0.895902\pi$
$683$	−19.6451	−	34.0263i	−0.751698	−	1.30198i	0.195301	−	0.980743i	$-0.437432\pi$
$684$	−0.214561	−	5.78980i	−0.00820393	−	0.221379i
$685$	−8.54103			−0.326336
$686$	1.01465	+	26.1719i	0.0387397	+	0.999249i
$687$	7.53142	+	36.7153i	0.287342	+	1.40077i
$688$	−21.9574	−	4.71711i	−0.837119	−	0.179838i
$689$	11.7143	+	20.2897i	0.446279	+	0.772978i
$690$	5.68579	+	5.47898i	0.216454	+	0.208581i
$691$	−14.3163	+	24.7966i	−0.544619	+	0.943308i	0.454012	+	0.890996i	$0.349992\pi$
$691$	−14.3163	+	24.7966i	−0.544619	+	0.943308i	−0.998631	+	0.0523123i	$0.983341\pi$
$692$	−1.60459	−	10.2028i	−0.0609974	−	0.387851i
$693$	−5.81737	+	11.1442i	−0.220983	+	0.423333i
$694$	−0.930554	−	11.9065i	−0.0353233	−	0.451966i
$695$	11.4076	+	6.58618i	0.432715	+	0.249828i
$696$	11.4290	+	8.00299i	0.433214	+	0.303353i
$697$	−0.000865040	−	0.00149829i	−3.27657e−5	−	5.67519e-5i
$698$	28.3344	+	13.5337i	1.07247	+	0.512259i
$699$	28.4509	−	5.83614i	1.07611	−	0.220743i
$700$	1.65168	+	5.02712i	0.0624277	+	0.190007i
$701$	−12.4837			−0.471503			−0.235752	−	0.971813i	$-0.575755\pi$
$701$	−12.4837			−0.471503			−0.235752	+	0.971813i	$0.575755\pi$
$702$	3.01522	+	18.5228i	0.113802	+	0.699097i
$703$	8.66830	−	5.00464i	0.326931	−	0.188754i
$704$	10.6039	+	6.93550i	0.399648	+	0.261391i
$705$	6.33528	−	19.0360i	0.238600	−	0.716938i
$706$	−1.58503	−	20.2807i	−0.0596535	−	0.763273i
$707$	3.71421	−	9.80371i	0.139687	−	0.368707i
$708$	−12.3484	+	4.62425i	−0.464081	+	0.173790i
$709$	−20.2803	−	11.7089i	−0.761644	−	0.439735i	0.0682416	−	0.997669i	$-0.478261\pi$
$709$	−20.2803	−	11.7089i	−0.761644	−	0.439735i	−0.829886	+	0.557933i	$0.811594\pi$
$710$	−11.0207	+	7.56551i	−0.413600	+	0.283928i
$711$	−34.4246	−	25.7673i	−1.29102	−	0.966351i
$712$	42.3079	+	12.6073i	1.58556	+	0.472477i
$713$	7.64869			0.286446
$714$	−0.00839737		0.000688678i	−0.000314264		2.57731e-5i
$715$		−	4.04477i		−	0.151266i
$716$	−12.6619	+	32.8784i	−0.473197	+	1.22873i
$717$	−8.66689	−	9.76440i	−0.323671	−	0.364658i
$718$	−6.90993	−	10.0657i	−0.257876	−	0.375649i
$719$	−10.2291	+	17.7174i	−0.381482	+	0.660746i	−0.991274	−	0.131815i	$-0.957919\pi$
$719$	−10.2291	+	17.7174i	−0.381482	+	0.660746i	0.609793	+	0.792561i	$0.291253\pi$
$720$	7.88219	+	9.04826i	0.293752	+	0.337209i
$721$	−9.01389	+	1.46808i	−0.335695	+	0.0546740i
$722$	−1.99089	−	25.4737i	−0.0740934	−	0.948033i
$723$	−8.10427	+	24.3514i	−0.301401	+	0.905639i
$724$	−9.48400	−	11.7378i	−0.352470	−	0.436233i
$725$	−1.42401	−	2.46646i	−0.0528864	−	0.0916020i
$726$	−5.01040	+	20.1874i	−0.185953	+	0.749224i
$727$		−	26.7145i		−	0.990787i	−0.868669	−	0.495393i	$-0.835024\pi$
$727$		−	26.7145i		−	0.990787i	0.868669	−	0.495393i	$-0.164976\pi$
$728$	−15.1936	−	11.5924i	−0.563111	−	0.429643i
$729$	−9.43185	+	25.2990i	−0.349328	+	0.937001i
$730$	11.6725	+	5.57530i	0.432020	+	0.206351i
$731$	−0.00632155	+	0.00364975i	−0.000233811	+	0.000134991i
$732$	18.8672	−	22.9122i	0.697353	−	0.846860i
$733$	9.50542	−	16.4639i	0.351091	−	0.608107i	−0.635350	−	0.772224i	$-0.719144\pi$
$733$	9.50542	−	16.4639i	0.351091	−	0.608107i	0.986441	+	0.164117i	$0.0524775\pi$
$734$	4.55067	−	0.355657i	0.167968	−	0.0131275i
$735$	−0.0197171	−	12.1243i	−0.000727276	−	0.447213i
$736$	−16.8660	+	6.93247i	−0.621687	+	0.255534i
$737$	11.0547	+	6.38243i	0.407205	+	0.235100i
$738$	3.02074	−	4.76976i	0.111195	−	0.175577i
$739$	40.1985	−	23.2086i	1.47873	−	0.853742i	0.479015	−	0.877807i	$-0.340994\pi$
$739$	40.1985	−	23.2086i	1.47873	−	0.853742i	0.999710	+	0.0240645i	$0.00766072\pi$
$740$	−7.45040	+	19.3461i	−0.273882	+	0.711176i
$741$	−0.858300	−	4.18417i	−0.0315304	−	0.153709i
$742$	−23.7235	−	24.8085i	−0.870917	−	0.910748i
$743$			43.2496i			1.58668i	0.608782	+	0.793338i	$0.291658\pi$
$743$			43.2496i			1.58668i	−0.608782	+	0.793338i	$0.708342\pi$
$744$	11.5798	+	1.01333i	0.424537	+	0.0371506i
$745$	−14.8411	+	8.56852i	−0.543737	+	0.313926i
$746$	−15.4012	−	22.4350i	−0.563879	−	0.821405i
$747$	29.6243	+	3.54056i	1.08390	+	0.129542i
$748$	0.00406822		0.000639811i	0.000148749		2.33938e-5i
$749$	−1.13365	−	6.96054i	−0.0414227	−	0.254333i
$750$	−0.677684	−	2.35388i	−0.0247455	−	0.0859515i
$751$	5.23601	−	9.06903i	0.191065	−	0.330934i	−0.754539	−	0.656256i	$-0.772139\pi$
$751$	5.23601	−	9.06903i	0.191065	−	0.330934i	0.945603	+	0.325322i	$0.105473\pi$
$752$	34.3642	+	31.0772i	1.25314	+	1.13327i
$753$	14.6689	+	16.5265i	0.534566	+	0.602259i
$754$	9.28159	+	4.43328i	0.338015	+	0.161451i
$755$			7.33270i			0.266864i
$756$	−10.7279	−	25.3162i	−0.390170	−	0.920743i
$757$		−	16.3077i		−	0.592713i	−0.955077	−	0.296356i	$-0.904228\pi$
$757$		−	16.3077i		−	0.592713i	0.955077	−	0.296356i	$-0.0957716\pi$
$758$	−17.2093	+	36.0297i	−0.625071	+	1.30866i
$759$	5.87022	+	6.61358i	0.213075	+	0.240058i
$760$	−1.87681	−	1.98421i	−0.0680790	−	0.0719750i
$761$	18.1603	−	31.4546i	0.658310	−	1.14023i	−0.322742	−	0.946487i	$-0.604605\pi$
$761$	18.1603	−	31.4546i	0.658310	−	1.14023i	0.981053	−	0.193740i	$-0.0620619\pi$
$762$	6.54428	−	1.88410i	0.237074	−	0.0682539i
$763$	−6.32441	+	16.6934i	−0.228959	+	0.604341i
$764$	4.64459	+	29.5325i	0.168035	+	1.06845i
$765$	0.00387272		0.000462849i	0.000140018		1.67344e-5i
$766$	4.63797	−	3.18388i	0.167577	−	0.115038i
$767$	−8.41853	+	4.86044i	−0.303975	+	0.175500i
$768$	−26.4529	+	8.26103i	−0.954536	+	0.298094i
$769$		−	19.2160i		−	0.692948i	−0.938060	−	0.346474i	$-0.887379\pi$
$769$		−	19.2160i		−	0.692948i	0.938060	−	0.346474i	$-0.112621\pi$
$770$	1.40547	+	5.75704i	0.0506496	+	0.207469i
$771$	9.49231	+	46.2745i	0.341857	+	1.66654i
$772$	−2.72995	+	7.08873i	−0.0982532	+	0.255129i
$773$	−18.6998	+	10.7963i	−0.672584	+	0.388316i	−0.797055	−	0.603907i	$-0.793610\pi$
$773$	−18.6998	+	10.7963i	−0.672584	+	0.388316i	0.124471	+	0.992223i	$0.460277\pi$
$774$	−20.1244	−	12.7450i	−0.723357	−	0.458110i
$775$	−2.05487	−	1.18638i	−0.0738130	−	0.0426160i
$776$	−27.8674	+	6.64233i	−1.00038	+	0.238446i
$777$	29.9945	−	36.8330i	1.07605	−	1.32138i
$778$	−3.33485	−	42.6698i	−0.119560	−	1.52979i
$779$	−0.642499	+	1.11284i	−0.0230199	+	0.0398717i
$780$	6.82924	+	5.62358i	0.244526	+	0.201357i
$781$	−12.9651	+	7.48539i	−0.463927	+	0.267848i
$782$	−0.00255448	+	0.00534809i	−9.13479e−5	+	0.000191247i
$783$	8.44095	+	12.1554i	0.301655	+	0.434398i
$784$	25.6535	+	11.2204i	0.916197	+	0.400728i
$785$			22.8882i			0.816915i
$786$	−2.74428	−	0.681116i	−0.0978854	−	0.0242946i
$787$	−12.2472	−	21.2127i	−0.436564	−	0.756151i	0.560858	−	0.827912i	$-0.310471\pi$
$787$	−12.2472	−	21.2127i	−0.436564	−	0.756151i	−0.997422	+	0.0717612i	$0.977138\pi$
$788$	22.8034	+	28.2225i	0.812336	+	1.00538i
$789$	−9.12491	+	27.4182i	−0.324855	+	0.976114i
$790$	−20.2088	+	1.57942i	−0.718998	+	0.0561932i
$791$	8.52839	+	10.4381i	0.303235	+	0.371135i
$792$	8.01110	+	10.7904i	0.284662	+	0.383421i
$793$	10.9406	−	18.9497i	0.388512	−	0.672923i
$794$	−21.8323	+	14.9874i	−0.774798	+	0.531884i
$795$	10.5481	+	11.8838i	0.374101	+	0.421474i
$796$	−25.8136	−	9.94111i	−0.914938	−	0.352353i
$797$		−	19.6298i		−	0.695322i	−0.937620	−	0.347661i	$-0.886976\pi$
$797$		−	19.6298i		−	0.695322i	0.937620	−	0.347661i	$-0.113024\pi$
$798$	2.67555	+	5.65720i	0.0947134	+	0.200263i
$799$	0.0150591			0.000532753
$800$	5.60643	+	0.753606i	0.198217	+	0.0266440i
$801$	37.4862	+	28.0590i	1.32451	+	0.991414i
$802$	21.3029	+	31.0321i	0.752233	+	1.09578i
$803$	12.5462	+	7.24353i	0.442745	+	0.255619i
$804$	−26.1459	+	9.79116i	−0.922094	+	0.345308i
$805$	−7.97551	−	3.02158i	−0.281100	−	0.106497i
$806$	8.54347	−	0.667713i	0.300931	−	0.0235192i
$807$	1.74133	−	5.23229i	0.0612978	−	0.184185i
$808$	−7.70150	−	8.14224i	−0.270938	−	0.286443i
$809$	48.0084	−	27.7176i	1.68788	−	0.974500i	0.731749	−	0.681574i	$-0.238704\pi$
$809$	48.0084	−	27.7176i	1.68788	−	0.974500i	0.956135	−	0.292926i	$-0.0946290\pi$
$810$	4.52768	+	11.8954i	0.159086	+	0.417961i
$811$	19.9803			0.701602			0.350801	−	0.936450i	$-0.385909\pi$
$811$	19.9803			0.701602			0.350801	+	0.936450i	$0.385909\pi$
$812$	−14.7512	−	3.08487i	−0.517666	−	0.108258i
$813$	39.8681	−	8.17816i	1.39823	−	0.286820i
$814$	−10.0067	+	20.9503i	−0.350736	+	0.734306i
$815$	−5.49324	−	9.51457i	−0.192420	−	0.333281i
$816$	−0.00457592	+	0.00775838i	−0.000160189	+	0.000271598i
$817$	4.69526	+	2.71081i	0.164266	+	0.0948393i
$818$	39.9756	−	3.12429i	1.39771	−	0.109238i
$819$	−10.8718	−	17.1081i	−0.379891	−	0.597804i
$820$	−0.413488	−	2.62916i	−0.0144396	−	0.0918141i
$821$	23.7175	−	41.0799i	0.827746	−	1.43370i	−0.0720557	−	0.997401i	$-0.522956\pi$
$821$	23.7175	−	41.0799i	0.827746	−	1.43370i	0.899802	−	0.436298i	$-0.143711\pi$
$822$	14.5170	−	15.0649i	0.506338	−	0.525450i
$823$	−24.3773	−	42.2227i	−0.849739	−	1.47179i	−0.881441	−	0.472294i	$-0.843426\pi$
$823$	−24.3773	−	42.2227i	−0.849739	−	1.47179i	0.0317025	−	0.999497i	$-0.489907\pi$
$824$	−2.78817	+	9.35664i	−0.0971304	+	0.325954i
$825$	−0.551247	−	2.68730i	−0.0191920	−	0.0935598i
$826$	10.2934	−	9.84325i	0.358154	−	0.342490i
$827$	21.8780			0.760771			0.380386	−	0.924828i	$-0.375791\pi$
$827$	21.8780			0.760771			0.380386	+	0.924828i	$0.375791\pi$
$828$	−19.3280	+	0.716264i	−0.671694	+	0.0248919i
$829$	1.75742	+	3.04395i	0.0610379	+	0.105721i	0.894930	−	0.446207i	$-0.147226\pi$
$829$	1.75742	+	3.04395i	0.0610379	+	0.105721i	−0.833892	+	0.551928i	$0.813892\pi$
$830$	11.5952	−	7.95986i	0.402474	−	0.276291i
$831$	−13.2728	+	39.8816i	−0.460428	+	1.38348i
$832$	−18.2338	+	9.21582i	−0.632144	+	0.319501i
$833$	0.00863031	−	0.00288781i	0.000299023	−	0.000100057i
$834$	−31.0062	+	8.92670i	−1.07366	+	0.309106i
$835$	19.2970	+	11.1412i	0.667802	+	0.385555i
$836$	−1.92236	−	2.37920i	−0.0664862	−	0.0822863i
$837$	11.1537	+	5.25402i	0.385528	+	0.181605i
$838$	18.0995	−	37.8933i	0.625236	−	1.30900i
$839$	−0.0334897			−0.00115619			−0.000578097	−	1.00000i	$-0.500184\pi$
$839$	−0.0334897			−0.00115619			−0.000578097		1.00000i	$0.500184\pi$
$840$	−11.6743	−	5.63119i	−0.402802	−	0.194295i
$841$	−20.8888			−0.720302
$842$	−8.50993	+	17.8165i	−0.293272	+	0.613997i
$843$	−9.33224	−	10.5140i	−0.321419	−	0.362121i
$844$	14.3267	−	11.5758i	0.493147	−	0.398455i
$845$	−5.61017	−	3.23903i	−0.192996	−	0.111426i
$846$	22.8084	+	43.5294i	0.784168	+	1.49657i
$847$	−3.61148	−	22.1743i	−0.124092	−	0.761917i
$848$	−34.9245	+	11.2638i	−1.19931	+	0.386799i
$849$	−13.9748	−	4.65088i	−0.479614	−	0.159618i
$850$	0.00151581	−	0.00104058i	5.19919e−5	−	3.56914e-5i
$851$	−16.7069	−	28.9372i	−0.572706	−	0.991956i
$852$	5.38737	−	32.2976i	0.184568	−	1.10650i
$853$	22.8091			0.780969			0.390484	−	0.920610i	$-0.372308\pi$
$853$	22.8091			0.780969			0.390484	+	0.920610i	$0.372308\pi$
$854$	−8.98747	+	30.7732i	−0.307545	+	1.05304i
$855$	−1.14049	−	2.66294i	−0.0390039	−	0.0910706i
$856$	−7.22521	−	2.15303i	−0.246953	−	0.0735889i
$857$	6.62323	+	11.4718i	0.226245	+	0.391868i	0.956692	−	0.291101i	$-0.0940216\pi$
$857$	6.62323	+	11.4718i	0.226245	+	0.391868i	−0.730447	+	0.682969i	$0.760688\pi$
$858$	7.13430	+	6.87481i	0.243561	+	0.234702i
$859$	12.3708	−	21.4269i	0.422088	−	0.731077i	−0.574056	−	0.818816i	$-0.694631\pi$
$859$	12.3708	−	21.4269i	0.422088	−	0.731077i	0.996144	+	0.0877388i	$0.0279641\pi$
$860$	−11.0929	+	1.74458i	−0.378263	+	0.0594896i
$861$	−0.970497	+	6.02048i	−0.0330745	+	0.205177i
$862$	35.8516	−	2.80198i	1.22111	−	0.0954358i
$863$	9.15443	+	5.28531i	0.311620	+	0.179914i	0.647651	−	0.761937i	$-0.275751\pi$
$863$	9.15443	+	5.28531i	0.311620	+	0.179914i	−0.336031	+	0.941851i	$0.609085\pi$
$864$	−29.3568	−	1.47626i	−0.998738	−	0.0502235i
$865$	−2.58204	−	4.47223i	−0.0877921	−	0.152060i
$866$	19.7902	−	41.4331i	0.672500	−	1.40795i
$867$	−5.91683	−	28.8443i	−0.200946	−	0.979602i
$868$	−11.9281	+	3.91904i	−0.404867	+	0.133021i
$869$	−22.7015			−0.770095
$870$	6.77078	+	1.68047i	0.229551	+	0.0569733i
$871$	−17.8250	+	10.2913i	−0.603977	+	0.348706i
$872$	13.1138	+	13.8643i	0.444090	+	0.469504i
$873$	−30.1711	−	3.60592i	−1.02114	−	0.122042i
$874$	4.38871	−	0.342999i	0.148450	−	0.0116021i
$875$	1.67400	+	2.04884i	0.0565914	+	0.0692634i
$876$	−29.6734	+	11.1122i	−1.00257	+	0.375445i
$877$	36.4434	+	21.0406i	1.23061	+	0.710490i	0.967156	−	0.254183i	$-0.0818065\pi$
$877$	36.4434	+	21.0406i	1.23061	+	0.710490i	0.263449	+	0.964673i	$0.415140\pi$
$878$	6.33670	+	9.23070i	0.213853	+	0.311521i
$879$	11.2582	+	12.6838i	0.379730	+	0.427816i
$880$	6.19396	+	1.33065i	0.208798	+	0.0448561i
$881$	−3.56867			−0.120232			−0.0601158	−	0.998191i	$-0.519147\pi$
$881$	−3.56867			−0.120232			−0.0601158	+	0.998191i	$0.519147\pi$
$882$	21.4188	+	20.5727i	0.721208	+	0.692718i
$883$		−	49.6285i		−	1.67013i	−0.550150	−	0.835066i	$-0.685429\pi$
$883$		−	49.6285i		−	1.67013i	0.550150	−	0.835066i	$-0.314571\pi$
$884$	−0.00238643	+	0.00619673i	−8.02645e−5	+	0.000208419i
$885$	−4.93076	+	4.37655i	−0.165746	+	0.147116i
$886$	−17.1532	+	11.7753i	−0.576273	+	0.395600i
$887$	18.8419	−	32.6351i	0.632649	−	1.09578i	−0.354359	−	0.935109i	$-0.615301\pi$
$887$	18.8419	−	32.6351i	0.632649	−	1.09578i	0.987008	−	0.160671i	$-0.0513657\pi$
$888$	−21.4599	−	46.0233i	−0.720148	−	1.54444i
$889$	−5.69620	+	4.65407i	−0.191045	+	0.156092i
$890$	22.0061	−	1.71988i	0.737646	−	0.0576506i
$891$	4.01725	+	13.6766i	0.134583	+	0.458183i
$892$	−26.5652	+	21.4643i	−0.889470	+	0.718679i
$893$	−5.59250	−	9.68649i	−0.187146	−	0.324146i
$894$	10.1117	−	40.7409i	0.338185	−	1.36258i
$895$			17.6162i			0.588843i
$896$	22.7504	−	19.4530i	0.760038	−	0.649879i
$897$	−13.9679	+	2.86525i	−0.466376	+	0.0956679i
$898$	−13.6961	+	28.6743i	−0.457043	+	0.956873i
$899$	5.85231	−	3.37883i	0.195185	−	0.112690i
$900$	5.30369	+	2.80551i	0.176790	+	0.0935171i
$901$	−0.00596351	+	0.0103291i	−0.000198673	+	0.000344112i
$902$	−0.232245	−	2.97160i	−0.00773292	−	0.0989435i
$903$	25.4014	+	4.09469i	0.845306	+	0.136263i
$904$	14.0171	−	3.34105i	0.466202	−	0.111122i
$905$	−6.53437	−	3.77262i	−0.217210	−	0.125406i
$906$	−12.9337	−	12.4632i	−0.429692	−	0.414063i
$907$	−3.48443	+	2.01173i	−0.115698	+	0.0667985i	−0.556732	−	0.830692i	$-0.687945\pi$
$907$	−3.48443	+	2.01173i	−0.115698	+	0.0667985i	0.441034	+	0.897490i	$0.354612\pi$
$908$	48.4847	+	18.6720i	1.60902	+	0.619653i
$909$	−4.68001	−	10.9274i	−0.155226	−	0.362439i
$910$	−9.17230	−	2.67881i	−0.304059	−	0.0888018i
$911$			9.23822i			0.306076i	0.988220	+	0.153038i	$0.0489057\pi$
$911$			9.23822i			0.306076i	−0.988220	+	0.153038i	$0.951094\pi$
$912$	6.68979	+	0.0621483i	0.221521	+	0.00205793i
$913$	13.6409	−	7.87557i	0.451448	−	0.260643i
$914$	−20.7926	+	14.2737i	−0.687757	+	0.472132i
$915$	4.68623	−	14.0810i	0.154922	−	0.465504i
$916$	−42.7524	+	6.72369i	−1.41258	+	0.222157i
$917$	3.01438	−	0.490947i	0.0995436	−	0.0162125i
$918$	−0.00739875	+	0.00604412i	−0.000244195	+	0.000199486i
$919$	11.7013	−	20.2672i	0.385990	−	0.668554i	−0.605916	−	0.795529i	$-0.707193\pi$
$919$	11.7013	−	20.2672i	0.385990	−	0.668554i	0.991906	+	0.126974i	$0.0405266\pi$
$920$	−6.62387	+	6.26532i	−0.218383	+	0.206562i
$921$	25.9505	−	23.0337i	0.855098	−	0.758986i
$922$	14.7541	−	30.8893i	0.485899	−	1.01729i
$923$		−	24.1394i		−	0.794559i
$924$	−12.5433	−	7.30609i	−0.412644	−	0.240353i
$925$			10.3656i			0.340818i
$926$	−42.0908	−	20.1044i	−1.38319	−	0.660670i
$927$	−6.20540	+	8.29028i	−0.203812	+	0.272289i
$928$	−9.84236	+	12.7549i	−0.323091	+	0.418700i
$929$	3.95711	−	6.85391i	0.129828	−	0.224870i	−0.793782	−	0.608203i	$-0.791891\pi$
$929$	3.95711	−	6.85391i	0.129828	−	0.224870i	0.923610	+	0.383333i	$0.125224\pi$
$930$	5.58518	−	1.60798i	0.183145	−	0.0527277i
$931$	−5.06256	−	4.47884i	−0.165919	−	0.146788i
$932$	5.21023	+	33.1291i	0.170667	+	1.08518i
$933$	−31.0172	−	10.3227i	−1.01546	−	0.337949i
$934$	15.4540	+	22.5120i	0.505671	+	0.736614i
$935$	0.00178324	−	0.00102956i	5.83183e−5	−	3.36701e-5i
$936$	−21.5266	+	2.48735i	−0.703617	+	0.0813015i
$937$		−	50.5634i		−	1.65184i	−0.563791	−	0.825918i	$-0.690658\pi$
$937$		−	50.5634i		−	1.65184i	0.563791	−	0.825918i	$-0.309342\pi$
$938$	21.7948	−	20.8416i	0.711626	−	0.680503i
$939$	27.1560	−	5.57051i	0.886201	−	0.181787i
$940$	21.6185	+	8.32554i	0.705118	+	0.271549i
$941$	−24.2724	+	14.0137i	−0.791259	+	0.456834i	−0.840406	−	0.541958i	$-0.817683\pi$
$941$	−24.2724	+	14.0137i	−0.791259	+	0.456834i	0.0491464	+	0.998792i	$0.484350\pi$
$942$	−40.3709	−	38.9025i	−1.31536	−	1.26751i
$943$	3.71498	+	2.14484i	0.120976	+	0.0698457i
$944$	−4.67351	−	14.4907i	−0.152110	−	0.471632i
$945$	−9.55469	−	9.88473i	−0.310814	−	0.321550i
$946$	−12.5377	+	0.979881i	−0.407635	+	0.0318587i
$947$	1.51976	−	2.63230i	0.0493855	−	0.0855381i	−0.840276	−	0.542159i	$-0.817607\pi$
$947$	1.51976	−	2.63230i	0.0493855	−	0.0855381i	0.889661	+	0.456621i	$0.150940\pi$
$948$	31.5626	−	38.3294i	1.02511	−	1.24488i
$949$	−20.2299	+	11.6797i	−0.656690	+	0.379140i
$950$	−1.23226	−	0.588578i	−0.0399797	−	0.0190960i
$951$	−8.23213	−	40.1312i	−0.266945	−	1.30134i
$952$	0.00124345	−	0.00964921i	4.03005e−5	−	0.000312733i
$953$			2.46246i			0.0797670i	0.999204	+	0.0398835i	$0.0126987\pi$
$953$			2.46246i			0.0797670i	−0.999204	+	0.0398835i	$0.987301\pi$
$954$	−38.8893	−	1.59360i	−1.25909	−	0.0515946i
$955$	7.47388	+	12.9451i	0.241849	+	0.418895i
$956$	11.7264	−	9.47473i	0.379258	−	0.306435i
$957$	7.41310	+	2.46712i	0.239632	+	0.0797506i
$958$	0.122644	+	1.56925i	0.00396246	+	0.0507001i
$959$	−8.00591	+	21.1317i	−0.258524	+	0.682379i
$960$	−10.8584	+	8.60791i	−0.350452	+	0.277819i
$961$	−12.6850	+	21.9711i	−0.409194	+	0.708745i
$962$	−21.1875	−	30.8640i	−0.683114	−	0.995095i
$963$	−6.40176	−	4.79181i	−0.206294	−	0.154414i
$964$	−27.6550	−	10.6503i	−0.890708	−	0.343022i
$965$			3.79812i			0.122266i
$966$	18.8853	−	8.93174i	0.607626	−	0.287374i
$967$	−31.6944			−1.01922			−0.509611	−	0.860405i	$-0.670211\pi$
$967$	−31.6944			−1.01922			−0.509611	+	0.860405i	$0.670211\pi$
$968$	−23.0174	−	6.85891i	−0.739808	−	0.220454i
$969$	0.00162623	−	0.00144344i	5.22420e−5	−	4.63700e-5i
$970$	−11.8092	+	8.10681i	−0.379171	+	0.260294i
$971$	−12.1432	−	7.01086i	−0.389693	−	0.224989i	0.292334	−	0.956316i	$-0.405568\pi$
$971$	−12.1432	−	7.01086i	−0.389693	−	0.224989i	−0.682027	+	0.731327i	$0.738901\pi$
$972$	−28.6770	−	12.2323i	−0.919816	−	0.392350i
$973$	26.9880	−	22.0505i	0.865197	−	0.706906i
$974$	1.85130	+	23.6876i	0.0593195	+	0.758999i
$975$	4.19700	+	1.39678i	0.134412	+	0.0447328i
$976$	25.4194	+	22.9880i	0.813654	+	0.735827i
$977$	21.0989	−	12.1814i	0.675013	−	0.389719i	−0.122961	−	0.992412i	$-0.539239\pi$
$977$	21.0989	−	12.1814i	0.675013	−	0.389719i	0.797973	+	0.602693i	$0.205906\pi$
$978$	26.1188	+	6.48255i	0.835187	+	0.207289i
$979$	24.7204			0.790069
$980$	13.9860	+	0.625661i	0.446767	+	0.0199860i
$981$	7.96894	+	18.6067i	0.254429	+	0.594067i
$982$	31.8299	+	15.2033i	1.01573	+	0.485158i
$983$	−5.74265	−	9.94656i	−0.183162	−	0.317246i	0.759794	−	0.650164i	$-0.225300\pi$
$983$	−5.74265	−	9.94656i	−0.183162	−	0.317246i	−0.942956	+	0.332918i	$0.891967\pi$
$984$	5.34018	+	3.73939i	0.170239	+	0.119207i
$985$	15.7113	+	9.07091i	0.500603	+	0.289023i
$986$	0.000408006		0.00522048i	1.29935e−5		0.000166254i
$987$	−41.1595	−	33.5177i	−1.31012	−	1.06688i
$988$	4.87218	−	0.766249i	0.155005	−	0.0243776i
$989$	9.04946	−	15.6741i	0.287756	−	0.498408i
$990$	5.67689	+	3.59524i	0.180423	+	0.114264i
$991$	15.1840	+	26.2995i	0.482336	+	0.835430i	0.999794	−	0.0202784i	$-0.00645526\pi$
$991$	15.1840	+	26.2995i	0.482336	+	0.835430i	−0.517459	+	0.855708i	$0.673122\pi$
$992$	−1.78812	+	13.3027i	−0.0567730	+	0.422361i
$993$	−56.9390	+	11.6799i	−1.80690	+	0.370651i
$994$	8.38791	+	34.3583i	0.266048	+	1.08978i
$995$	−13.8308			−0.438466
$996$	−5.66819	+	33.9811i	−0.179603	+	1.07673i
$997$	8.22424	+	14.2448i	0.260464	+	0.451137i	0.966365	−	0.257173i	$-0.0827911\pi$
$997$	8.22424	+	14.2448i	0.260464	+	0.451137i	−0.705901	+	0.708310i	$0.749458\pi$
$998$	26.4655	+	38.5525i	0.837752	+	1.22036i
$999$	−4.48533	−	53.6739i	−0.141910	−	1.69817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cf.a.341.19	yes	256
3.2	odd	2	inner	840.2.cf.a.341.110	yes	256
7.3	odd	6	inner	840.2.cf.a.101.105	yes	256
8.5	even	2	inner	840.2.cf.a.341.24	yes	256
21.17	even	6	inner	840.2.cf.a.101.24	yes	256
24.5	odd	2	inner	840.2.cf.a.341.105	yes	256
56.45	odd	6	inner	840.2.cf.a.101.110	yes	256
168.101	even	6	inner	840.2.cf.a.101.19	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.19	✓	256	168.101	even	6	inner
840.2.cf.a.101.24	yes	256	21.17	even	6	inner
840.2.cf.a.101.105	yes	256	7.3	odd	6	inner
840.2.cf.a.101.110	yes	256	56.45	odd	6	inner
840.2.cf.a.341.19	yes	256	1.1	even	1	trivial
840.2.cf.a.341.24	yes	256	8.5	even	2	inner
840.2.cf.a.341.105	yes	256	24.5	odd	2	inner
840.2.cf.a.341.110	yes	256	3.2	odd	2	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27612 - 0.609528i) q^{2} +(1.29538 - 1.14978i) q^{3} +(1.25695 + 1.55566i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.35388 + 0.677684i) q^{6} +(2.04884 - 1.67400i) q^{7} +(-0.655798 - 2.75135i) q^{8} +(0.356013 - 2.97880i) q^{9} +(-0.800386 - 1.16593i) q^{10} +(-0.791910 - 1.37163i) q^{11} +(3.41689 + 0.569952i) q^{12} +2.55381 q^{13} +(-3.63491 + 0.887392i) q^{14} +(1.69672 - 0.348049i) q^{15} +(-0.840151 + 3.91077i) q^{16} +(0.000650046 + 0.00112591i) q^{17} +(-2.26998 + 3.58430i) q^{18} +(0.482815 - 0.836259i) q^{19} +(0.310721 + 1.97572i) q^{20} +(0.729293 - 4.52417i) q^{21} +(0.174524 + 2.23305i) q^{22} +(-2.79167 - 1.61177i) q^{23} +(-4.01295 - 2.81002i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.25896 - 1.55662i) q^{26} +(-2.96379 - 4.26801i) q^{27} +(5.17946 + 1.08316i) q^{28} -2.84802 q^{29} +(-2.37736 - 0.590048i) q^{30} +(-2.05487 + 1.18638i) q^{31} +(3.45586 - 4.47851i) q^{32} +(-2.60289 - 0.866256i) q^{33} +(-0.000143259 - 0.00183302i) q^{34} +(2.61134 - 0.425305i) q^{35} +(5.08149 - 3.19037i) q^{36} +(8.97684 + 5.18278i) q^{37} +(-1.12585 + 0.772876i) q^{38} +(3.30815 - 2.93632i) q^{39} +(0.807738 - 2.71064i) q^{40} -1.33074 q^{41} +(-3.68827 + 5.32885i) q^{42} +5.61460i q^{43} +(1.13839 - 2.95601i) q^{44} +(1.79772 - 2.40171i) q^{45} +(2.58008 + 3.75841i) q^{46} +(5.79156 - 10.0313i) q^{47} +(3.40821 + 6.03192i) q^{48} +(1.39547 - 6.85949i) q^{49} +(-0.110192 - 1.40991i) q^{50} +(0.00213661 + 0.000711074i) q^{51} +(3.21001 + 3.97285i) q^{52} +(4.58699 + 7.94490i) q^{53} +(1.18067 + 7.25300i) q^{54} -1.58382i q^{55} +(-5.94937 - 4.53927i) q^{56} +(-0.336086 - 1.63840i) q^{57} +(3.63441 + 1.73595i) q^{58} +(-3.29646 + 1.90321i) q^{59} +(2.67414 + 2.20204i) q^{60} +(4.28404 - 7.42017i) q^{61} +(3.34538 - 0.261458i) q^{62} +(-4.25709 - 6.69904i) q^{63} +(-7.13986 + 3.60866i) q^{64} +(2.21166 + 1.27690i) q^{65} +(2.79359 + 2.69198i) q^{66} +(-6.97977 + 4.02977i) q^{67} +(-0.000934461 + 0.00242647i) q^{68} +(-5.46946 + 1.12195i) q^{69} +(-3.59162 - 1.04895i) q^{70} -9.45233i q^{71} +(-8.42920 + 0.973976i) q^{72} +(-7.92146 + 4.57346i) q^{73} +(-8.29645 - 12.0855i) q^{74} +(1.64343 + 0.546941i) q^{75} +(1.90781 - 0.300042i) q^{76} +(-3.91860 - 1.48459i) q^{77} +(-6.01135 + 1.73067i) q^{78} +(7.16669 - 12.4131i) q^{79} +(-2.68298 + 2.96675i) q^{80} +(-8.74651 - 2.12098i) q^{81} +(1.69818 + 0.811122i) q^{82} +9.94503i q^{83} +(7.95475 - 4.55213i) q^{84} +0.00130009i q^{85} +(3.42226 - 7.16489i) q^{86} +(-3.68927 + 3.27460i) q^{87} +(-3.25450 + 3.07833i) q^{88} +(-7.80405 + 13.5170i) q^{89} +(-3.75801 + 1.96911i) q^{90} +(5.23234 - 4.27507i) q^{91} +(-1.00162 - 6.36881i) q^{92} +(-1.29776 + 3.89946i) q^{93} +(-13.5050 + 9.27096i) q^{94} +(0.836259 - 0.482815i) q^{95} +(-0.672655 - 9.77484i) q^{96} -10.1286i q^{97} +(-5.96184 + 7.90294i) q^{98} +(-4.36774 + 1.87063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) \) 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

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