LMFDB - Embedded newform 840.2.cf.a.101.19

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			101.19
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.19

$q$-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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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	−0.960362	−	0.278757i	$-0.910078\pi$
$11$	−0.791910	+	1.37163i	−0.238770	+	0.413562i	0.721592	+	0.692319i	$0.243411\pi$
$12$	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	−0.865947	−	0.500137i	$-0.833283\pi$
$17$	0.000650046	−	0.00112591i	0.000157659	−	0.000273074i	0.866104	+	0.499863i	$0.166616\pi$
$18$	−2.26998	−	3.58430i	−0.535039	−	0.844827i
$19$	0.482815	+	0.836259i	0.110765	+	0.191851i	0.916079	−	0.400998i	$-0.131336\pi$
$19$	0.482815	+	0.836259i	0.110765	+	0.191851i	−0.805314	+	0.592849i	$0.798003\pi$
$20$	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	−0.761969	−	0.647613i	$-0.775767\pi$
$23$	−2.79167	+	1.61177i	−0.582104	+	0.336078i	0.179865	+	0.983691i	$0.442434\pi$
$24$	−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	0.303985	−	0.952677i	$-0.401683\pi$
$31$	−2.05487	−	1.18638i	−0.369065	−	0.213080i	−0.673050	+	0.739597i	$0.735016\pi$
$32$	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	0.476156	−	0.879361i	$-0.342030\pi$
$37$	8.97684	−	5.18278i	1.47578	−	0.852044i	0.999627	+	0.0273169i	$0.00869632\pi$
$38$	−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	$-0.859180\pi$
$43$		−	5.61460i		−	0.856219i	0.903727	−	0.428109i	$-0.140820\pi$
$44$	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	0.885807	+	0.464053i	$0.153605\pi$
$47$	5.79156	+	10.0313i	0.844785	+	1.46321i	−0.0410220	+	0.999158i	$0.513061\pi$
$48$	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	−0.357465	−	0.933926i	$-0.616359\pi$
$53$	4.58699	−	7.94490i	0.630071	−	1.09132i	0.987537	−	0.157389i	$-0.0503077\pi$
$54$	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	0.269827	−	0.962909i	$-0.413033\pi$
$59$	−3.29646	−	1.90321i	−0.429163	−	0.247777i	−0.698990	+	0.715132i	$0.746367\pi$
$60$	2.67414	−	2.20204i	0.345230	−	0.284282i
$61$	4.28404	+	7.42017i	0.548515	+	0.950055i	0.998377	+	0.0569573i	$0.0181399\pi$
$61$	4.28404	+	7.42017i	0.548515	+	0.950055i	−0.449862	+	0.893098i	$0.648527\pi$
$62$	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	0.00885142	−	0.999961i	$-0.497182\pi$
$67$	−6.97977	−	4.02977i	−0.852714	−	0.492315i	−0.861566	+	0.507646i	$0.830516\pi$
$68$	−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	$0.189542\pi$
$71$			9.45233i			1.12178i	−0.827889	+	0.560892i	$0.810458\pi$
$72$	−8.42920	−	0.973976i	−0.993390	−	0.114784i
$73$	−7.92146	−	4.57346i	−0.927137	−	0.535283i	−0.0412319	−	0.999150i	$-0.513128\pi$
$73$	−7.92146	−	4.57346i	−0.927137	−	0.535283i	−0.885905	+	0.463867i	$0.846462\pi$
$74$	−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	0.915400	+	0.402546i	$0.131875\pi$
$79$	7.16669	+	12.4131i	0.806315	+	1.39658i	−0.109085	+	0.994032i	$0.534792\pi$
$80$	−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	$-0.816224\pi$
$83$		−	9.94503i		−	1.09161i	0.837912	−	0.545805i	$-0.183776\pi$
$84$	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	−0.900205	−	0.435467i	$-0.856583\pi$
$89$	−7.80405	−	13.5170i	−0.827228	−	1.43280i	0.0729765	−	0.997334i	$-0.476750\pi$
$90$	−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	$0.171912\pi$
$97$			10.1286i			1.02841i	−0.857669	+	0.514203i	$0.828088\pi$
$98$	−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	0.660916	−	0.750460i	$-0.270168\pi$
$101$	3.43160	+	1.98123i	0.341457	+	0.197140i	−0.319459	+	0.947600i	$0.603501\pi$
$102$	−0.00229314	+	0.00220974i	−0.000227055	+	0.000218797i
$103$	−2.98937	+	1.72591i	−0.294551	+	0.170059i	−0.639992	−	0.768381i	$-0.721063\pi$
$103$	−2.98937	+	1.72591i	−0.294551	+	0.170059i	0.345441	+	0.938440i	$0.387729\pi$
$104$	−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	0.923228	−	0.384252i	$-0.125541\pi$
$107$	1.33275	+	2.30839i	0.128842	+	0.223161i	−0.794386	+	0.607413i	$0.792207\pi$
$108$	2.91423	+	9.97533i	0.280422	+	0.959877i
$109$	−5.84319	−	3.37357i	−0.559676	−	0.323129i	0.193339	−	0.981132i	$-0.438068\pi$
$109$	−5.84319	−	3.37357i	−0.559676	−	0.323129i	−0.753015	+	0.658003i	$0.771401\pi$
$110$	−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	$-0.922974\pi$
$113$		−	5.09463i		−	0.479262i	0.970864	−	0.239631i	$-0.0770265\pi$
$114$	−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	−0.455692	−	0.890137i	$-0.650608\pi$
$131$	0.999689	−	0.577170i	0.0873432	−	0.0504276i	0.543035	+	0.839710i	$0.317275\pi$
$132$	−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	0.149559	−	0.988753i	$-0.452215\pi$
$137$	−7.39675	−	4.27052i	−0.631947	−	0.364855i	−0.781506	+	0.623898i	$0.785548\pi$
$138$	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	−0.967777	−	0.251808i	$-0.918975\pi$
$149$	−8.56852	−	14.8411i	−0.701961	−	1.21583i	0.265816	−	0.964024i	$-0.414359\pi$
$150$	−1.76383	+	1.69968i	−0.144016	+	0.138778i
$151$	3.66635	−	6.35031i	0.298364	−	0.516781i	−0.677398	−	0.735617i	$-0.736893\pi$
$151$	3.66635	−	6.35031i	0.298364	−	0.516781i	0.975762	+	0.218836i	$0.0702259\pi$
$152$	−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	0.104022	−	0.994575i	$-0.466829\pi$
$157$	11.4441	−	19.8218i	0.913338	−	1.58195i	0.809316	−	0.587374i	$-0.199838\pi$
$158$	−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	−0.823971	−	0.566632i	$-0.808246\pi$
$163$	−9.51457	+	5.49324i	−0.745238	+	0.430264i	0.0787325	+	0.996896i	$0.474913\pi$
$164$	−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	−0.660280	−	0.751020i	$-0.729562\pi$
$173$	−4.47223	+	2.58204i	−0.340017	+	0.196309i	0.320262	+	0.947329i	$0.396229\pi$
$174$	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	−0.322697	−	0.946502i	$-0.604589\pi$
$179$	8.80808	−	15.2560i	0.658347	−	1.14029i	0.981044	−	0.193787i	$-0.0620772\pi$
$180$	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	0.0477601	−	0.998859i	$-0.484792\pi$
$191$	12.9451	−	7.47388i	0.936677	−	0.540791i	0.888917	+	0.458068i	$0.151458\pi$
$192$	−5.09966	−	12.8838i	−0.368036	−	0.929812i
$193$	1.89906	−	3.28927i	0.136697	−	0.236767i	−0.789547	−	0.613690i	$-0.789685\pi$
$193$	1.89906	−	3.28927i	0.136697	−	0.236767i	0.926245	+	0.376923i	$0.123018\pi$
$194$	−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	0.0112559	−	0.999937i	$-0.496417\pi$
$199$	−11.9778	−	6.91541i	−0.849087	−	0.490220i	−0.860343	+	0.509716i	$0.829750\pi$
$200$	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	$0.102676\pi$
$211$			9.20943i			0.634003i	−0.948425	+	0.317002i	$0.897324\pi$
$212$	−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	$-0.806259\pi$
$223$		−	17.0765i		−	1.14353i	0.820418	−	0.571764i	$-0.193741\pi$
$224$	−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	0.999970	−	0.00778359i	$-0.00247762\pi$
$227$	22.4975	+	12.9890i	1.49321	+	0.862107i	0.493244	+	0.869891i	$0.335811\pi$
$228$	2.12635	+	2.58223i	0.140821	+	0.171012i
$229$	−10.8195	−	18.7399i	−0.714971	−	1.23837i	−0.962971	−	0.269606i	$-0.913106\pi$
$229$	−10.8195	−	18.7399i	−0.714971	−	1.23837i	0.247999	−	0.968760i	$-0.420227\pi$
$230$	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	0.0578466	−	0.998325i	$-0.481577\pi$
$233$	14.5217	−	8.38408i	0.951345	−	0.549259i	0.893499	+	0.449066i	$0.148243\pi$
$234$	−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	$0.0783915\pi$
$239$			7.53787i			0.487584i	−0.969827	+	0.243792i	$0.921609\pi$
$240$	−0.0643604	−	6.92790i	−0.00415444	−	0.447194i
$241$	−12.8323	−	7.40873i	−0.826601	−	0.477238i	0.0260867	−	0.999660i	$-0.491695\pi$
$241$	−12.8323	−	7.40873i	−0.826601	−	0.477238i	−0.852687	+	0.522422i	$0.825029\pi$
$242$	−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	$-0.868092\pi$
$251$		−	12.7580i		−	0.805281i	0.915358	−	0.402640i	$-0.131908\pi$
$252$	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	−0.880651	−	0.473765i	$-0.842895\pi$
$257$	−13.6364	−	23.6190i	−0.850618	−	1.47331i	0.0300331	−	0.999549i	$-0.490439\pi$
$258$	−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	−0.0166797	−	0.999861i	$-0.505310\pi$
$263$	−14.4484	−	8.34177i	−0.890925	−	0.514376i	−0.874245	+	0.485485i	$0.838643\pi$
$264$	−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	0.581695	−	0.813407i	$-0.302390\pi$
$269$	2.75722	+	1.59188i	0.168111	+	0.0970589i	−0.413584	+	0.910466i	$0.635723\pi$
$270$	−2.60401	−	6.87162i	−0.158475	−	0.418193i
$271$	20.3491	−	11.7486i	1.23612	−	0.713674i	0.267821	−	0.963469i	$-0.413696\pi$
$271$	20.3491	−	11.7486i	1.23612	−	0.713674i	0.968299	+	0.249794i	$0.0803629\pi$
$272$	−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	−0.289133	−	0.957289i	$-0.593367\pi$
$277$	−21.0161	−	12.1337i	−1.26274	−	0.729041i	−0.973603	+	0.228248i	$0.926700\pi$
$278$	−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	$0.0778350\pi$
$281$			8.11655i			0.484193i	−0.970252	+	0.242096i	$0.922165\pi$
$282$	−6.83459	−	27.5372i	−0.406994	−	1.63982i
$283$	−4.25172	+	7.36420i	−0.252739	+	0.437756i	−0.964279	−	0.264889i	$-0.914665\pi$
$283$	−4.25172	+	7.36420i	−0.252739	+	0.437756i	0.711540	+	0.702645i	$0.247998\pi$
$284$	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	$-0.907669\pi$
$293$		−	9.79161i		−	0.572032i	0.958225	−	0.286016i	$-0.0923311\pi$
$294$	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	0.464050	+	0.885809i	$0.346396\pi$
$311$	−9.43673	+	16.3449i	−0.535108	+	0.926834i	−0.999158	+	0.0410252i	$0.986938\pi$
$312$	−10.2483	+	7.17625i	−0.580197	+	0.406275i
$313$	13.8607	−	8.00248i	0.783454	−	0.452327i	−0.0541993	−	0.998530i	$-0.517261\pi$
$313$	13.8607	−	8.00248i	0.783454	−	0.452327i	0.837653	+	0.546203i	$0.183927\pi$
$314$	−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	0.979496	+	0.201463i	$0.0645695\pi$
$317$	11.8261	+	20.4834i	0.664220	+	1.15046i	−0.315276	+	0.949000i	$0.602097\pi$
$318$	−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	−0.605424	+	0.795903i	$0.706996\pi$
$331$	−29.0623	+	16.7791i	−1.59741	+	0.922264i	−0.991984	+	0.126361i	$0.959670\pi$
$332$	−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	−0.730148	−	0.683289i	$-0.760549\pi$
$347$	4.22243	−	7.31347i	0.226672	−	0.392608i	0.956820	+	0.290682i	$0.0938821\pi$
$348$	−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	−0.608661	−	0.793430i	$-0.708293\pi$
$353$	7.19217	−	12.4572i	0.382800	−	0.663030i	0.991461	+	0.130401i	$0.0416264\pi$
$354$	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	−0.289551	−	0.957163i	$-0.593506\pi$
$359$	7.47661	−	4.31662i	0.394600	−	0.227823i	0.684151	+	0.729340i	$0.260173\pi$
$360$	−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	0.425269	−	0.905067i	$-0.360180\pi$
$367$	−2.79520	−	1.61381i	−0.145908	−	0.0842402i	−0.571177	+	0.820827i	$0.693513\pi$
$368$	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	−0.00211985	−	0.999998i	$-0.500675\pi$
$373$	16.6643	−	9.62113i	0.862844	−	0.498163i	0.864964	+	0.501835i	$0.167341\pi$
$374$	−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	$0.258224\pi$
$379$			28.2338i			1.45027i	−0.688604	+	0.725137i	$0.741776\pi$
$380$	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	0.810726	−	0.585426i	$-0.199073\pi$
$383$	−1.98896	−	3.44499i	−0.101631	−	0.176031i	−0.912357	+	0.409396i	$0.865740\pi$
$384$	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	−0.171837	−	0.985125i	$-0.554970\pi$
$389$	15.1320	−	26.2095i	0.767225	−	1.32887i	0.939062	−	0.343748i	$-0.111696\pi$
$390$	−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	0.999408	−	0.0344178i	$-0.0109577\pi$
$397$	9.36263	+	16.2166i	0.469897	+	0.813886i	−0.529510	+	0.848303i	$0.677624\pi$
$398$	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	−0.949146	−	0.314837i	$-0.898050\pi$
$401$	−23.0500	+	13.3079i	−1.15106	+	0.664566i	−0.201916	+	0.979403i	$0.564717\pi$
$402$	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	−0.250488	−	0.968120i	$-0.580591\pi$
$409$	−24.5546	−	14.1766i	−1.21415	−	0.700988i	−0.963660	+	0.267131i	$0.913924\pi$
$410$	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	$-0.741688\pi$
$419$		−	29.6942i		−	1.45066i	0.688403	−	0.725329i	$-0.258312\pi$
$420$	9.16508	−	0.0351185i	0.447210	−	0.00171361i
$421$			13.9615i			0.680442i	0.940346	+	0.340221i	$0.110502\pi$
$421$			13.9615i			0.680442i	−0.940346	+	0.340221i	$0.889498\pi$
$422$	−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	−0.135102	−	0.990832i	$-0.543136\pi$
$431$	−22.0215	−	12.7141i	−1.06074	−	0.612417i	−0.925636	+	0.378414i	$0.876469\pi$
$432$	19.1813	+	8.00495i	0.922859	+	0.385138i
$433$		−	32.4681i		−	1.56032i	−0.625581	−	0.780159i	$-0.715138\pi$
$433$		−	32.4681i		−	1.56032i	0.625581	−	0.780159i	$-0.284862\pi$
$434$	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	−0.654614	−	0.755964i	$-0.727169\pi$
$439$	−6.85637	+	3.95853i	−0.327237	+	0.188930i	0.327377	+	0.944894i	$0.393835\pi$
$440$	−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	0.986160	−	0.165796i	$-0.0530194\pi$
$443$	7.35604	+	12.7410i	0.349496	+	0.605345i	−0.636664	+	0.771141i	$0.719686\pi$
$444$	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	$0.177887\pi$
$449$			22.4699i			1.06042i	−0.847866	+	0.530211i	$0.822113\pi$
$450$	−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	0.995647	−	0.0932018i	$-0.0297102\pi$
$457$	8.91676	+	15.4443i	0.417109	+	0.722453i	−0.578539	+	0.815655i	$0.696377\pi$
$458$	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	$-0.809383\pi$
$461$		−	24.2057i		−	1.12737i	0.825989	−	0.563686i	$-0.190617\pi$
$462$	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	−0.834219	−	0.551433i	$-0.814081\pi$
$467$	−16.7214	+	9.65411i	−0.773775	+	0.446739i	0.0604449	+	0.998172i	$0.480748\pi$
$468$	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	−0.878459	−	0.477818i	$-0.841428\pi$
$479$	−0.556505	+	0.963894i	−0.0254273	+	0.0440415i	0.853032	+	0.521859i	$0.174761\pi$
$480$	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	−0.991156	−	0.132700i	$-0.957635\pi$
$487$	−8.40036	+	14.5499i	−0.380657	+	0.659317i	0.610499	+	0.792017i	$0.290969\pi$
$488$	−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	−0.977200	−	0.212323i	$-0.931897\pi$
$499$	−28.6360	+	16.5330i	−1.28192	+	0.740118i	−0.304723	+	0.952441i	$0.598564\pi$
$500$	−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	−0.990039	−	0.140794i	$-0.955035\pi$
$509$	−30.7536	+	17.7556i	−1.36313	+	0.787002i	−0.373088	+	0.927796i	$0.621701\pi$
$510$	−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	−0.697916	−	0.716180i	$-0.745889\pi$
$521$	6.19190	−	10.7247i	0.271272	−	0.469857i	0.969188	+	0.246323i	$0.0792223\pi$
$522$	6.46495	+	10.2082i	0.282963	+	0.446799i
$523$	−10.2725	−	17.7925i	−0.449185	−	0.778012i	0.549148	−	0.835725i	$-0.314952\pi$
$523$	−10.2725	−	17.7925i	−0.449185	−	0.778012i	−0.998333	+	0.0577132i	$0.981619\pi$
$524$	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	−0.106265	−	0.994338i	$-0.533889\pi$
$541$	16.3217	−	9.42333i	0.701724	−	0.405140i	0.807989	+	0.589197i	$0.200556\pi$
$542$	−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	$-0.907081\pi$
$547$		−	13.4614i		−	0.575569i	0.957695	−	0.287785i	$-0.0929188\pi$
$548$	−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	0.411243	+	0.911526i	$0.365095\pi$
$557$	−13.7778	+	23.8638i	−0.583783	+	1.01114i	−0.995026	+	0.0996161i	$0.968239\pi$
$558$	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	−0.269791	−	0.962919i	$-0.586955\pi$
$563$	−29.3890	−	16.9677i	−1.23860	−	0.715105i	−0.968808	+	0.247814i	$0.920288\pi$
$564$	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	−0.439818	−	0.898087i	$-0.644957\pi$
$569$	2.81569	−	1.62564i	0.118040	−	0.0681503i	0.557857	+	0.829937i	$0.311624\pi$
$570$	−1.64126	−	1.70321i	−0.0687447	−	0.0713395i
$571$	−20.8343	−	12.0287i	−0.871890	−	0.503386i	−0.00391387	−	0.999992i	$-0.501246\pi$
$571$	−20.8343	−	12.0287i	−0.871890	−	0.503386i	−0.867976	+	0.496607i	$0.834579\pi$
$572$	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	0.709725	−	0.704479i	$-0.248819\pi$
$577$	10.9172	+	6.30307i	0.454490	+	0.262400i	−0.255234	+	0.966879i	$0.582153\pi$
$578$	−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	$0.0559682\pi$
$587$			8.47618i			0.349850i	−0.984582	+	0.174925i	$0.944032\pi$
$588$	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	0.991442	−	0.130545i	$-0.0416726\pi$
$593$	9.31853	+	16.1402i	0.382666	+	0.662797i	−0.608776	+	0.793342i	$0.708339\pi$
$594$	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	−0.207557	−	0.978223i	$-0.566551\pi$
$599$	−28.3537	−	16.3700i	−1.15850	−	0.668861i	−0.950944	+	0.309362i	$0.899885\pi$
$600$	0.427070	+	4.88033i	0.0174351	+	0.199239i
$601$		−	6.71478i		−	0.273902i	−0.990578	−	0.136951i	$-0.956270\pi$
$601$		−	6.71478i		−	0.273902i	0.990578	−	0.136951i	$-0.0437302\pi$
$602$	−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	0.151425	−	0.988469i	$-0.451614\pi$
$607$	26.6866	−	15.4075i	1.08318	−	0.625372i	0.931751	+	0.363097i	$0.118281\pi$
$608$	−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	0.924421	−	0.381375i	$-0.124549\pi$
$613$	26.1540	+	15.1000i	1.05635	+	0.609884i	0.131930	+	0.991259i	$0.457883\pi$
$614$	−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	$0.0572112\pi$
$617$			8.88102i			0.357536i	−0.983891	+	0.178768i	$0.942789\pi$
$618$	8.20623	−	2.03674i	0.330103	−	0.0819297i
$619$	−2.72170	+	4.71412i	−0.109394	+	0.189477i	−0.915525	−	0.402261i	$-0.868224\pi$
$619$	−2.72170	+	4.71412i	−0.109394	+	0.189477i	0.806131	+	0.591738i	$0.201558\pi$
$620$	−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	0.989325	−	0.145729i	$-0.0465526\pi$
$641$	34.3763	+	19.8472i	1.35778	+	0.783916i	0.368458	+	0.929645i	$0.379886\pi$
$642$	−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	−0.945840	−	0.324634i	$-0.894759\pi$
$647$	−4.87813	+	8.44917i	−0.191779	+	0.332171i	0.754061	+	0.656805i	$0.228092\pi$
$648$	−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	0.843753	−	0.536731i	$-0.180341\pi$
$653$	−1.09745	−	1.90084i	−0.0429465	−	0.0743855i	−0.886700	+	0.462346i	$0.847008\pi$
$654$	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	−0.574939	−	0.818196i	$-0.694974\pi$
$661$	10.8267	−	18.7524i	0.421109	−	0.729382i	0.996048	+	0.0888140i	$0.0283077\pi$
$662$	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	−0.109759	−	0.993958i	$-0.535008\pi$
$677$	18.1134	−	10.4578i	0.696154	−	0.401925i	0.805913	+	0.592034i	$0.201675\pi$
$678$	−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	0.195301	+	0.980743i	$0.437432\pi$
$683$	−19.6451	+	34.0263i	−0.751698	+	1.30198i	−0.946999	+	0.321236i	$0.895902\pi$
$684$	−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	−0.998631	−	0.0523123i	$-0.983341\pi$
$691$	−14.3163	−	24.7966i	−0.544619	−	0.943308i	0.454012	−	0.890996i	$-0.349992\pi$
$692$	−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	−0.829886	−	0.557933i	$-0.811594\pi$
$709$	−20.2803	+	11.7089i	−0.761644	+	0.439735i	0.0682416	+	0.997669i	$0.478261\pi$
$710$	−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	0.609793	−	0.792561i	$-0.291253\pi$
$719$	−10.2291	−	17.7174i	−0.381482	−	0.660746i	−0.991274	+	0.131815i	$0.957919\pi$
$720$	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	$0.164976\pi$
$727$			26.7145i			0.990787i	−0.868669	+	0.495393i	$0.835024\pi$
$728$	−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	0.986441	−	0.164117i	$-0.0524775\pi$
$733$	9.50542	+	16.4639i	0.351091	+	0.608107i	−0.635350	+	0.772224i	$0.719144\pi$
$734$	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	0.999710	−	0.0240645i	$-0.00766072\pi$
$739$	40.1985	+	23.2086i	1.47873	+	0.853742i	0.479015	+	0.877807i	$0.340994\pi$
$740$	−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	$-0.708342\pi$
$743$		−	43.2496i		−	1.58668i	0.608782	−	0.793338i	$-0.291658\pi$
$744$	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	0.945603	−	0.325322i	$-0.105473\pi$
$751$	5.23601	+	9.06903i	0.191065	+	0.330934i	−0.754539	+	0.656256i	$0.772139\pi$
$752$	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	$0.0957716\pi$
$757$			16.3077i			0.592713i	−0.955077	+	0.296356i	$0.904228\pi$
$758$	−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	0.981053	+	0.193740i	$0.0620619\pi$
$761$	18.1603	+	31.4546i	0.658310	+	1.14023i	−0.322742	+	0.946487i	$0.604605\pi$
$762$	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	$0.112621\pi$
$769$			19.2160i			0.692948i	−0.938060	+	0.346474i	$0.887379\pi$
$770$	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	0.124471	−	0.992223i	$-0.460277\pi$
$773$	−18.6998	−	10.7963i	−0.672584	−	0.388316i	−0.797055	+	0.603907i	$0.793610\pi$
$774$	−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	−0.997422	−	0.0717612i	$-0.977138\pi$
$787$	−12.2472	+	21.2127i	−0.436564	+	0.756151i	0.560858	+	0.827912i	$0.310471\pi$
$788$	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	$0.113024\pi$
$797$			19.6298i			0.695322i	−0.937620	+	0.347661i	$0.886976\pi$
$798$	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	0.956135	+	0.292926i	$0.0946290\pi$
$809$	48.0084	+	27.7176i	1.68788	+	0.974500i	0.731749	+	0.681574i	$0.238704\pi$
$810$	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	0.899802	+	0.436298i	$0.143711\pi$
$821$	23.7175	+	41.0799i	0.827746	+	1.43370i	−0.0720557	+	0.997401i	$0.522956\pi$
$822$	14.5170	+	15.0649i	0.506338	+	0.525450i
$823$	−24.3773	+	42.2227i	−0.849739	+	1.47179i	0.0317025	+	0.999497i	$0.489907\pi$
$823$	−24.3773	+	42.2227i	−0.849739	+	1.47179i	−0.881441	+	0.472294i	$0.843426\pi$
$824$	−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	−0.833892	−	0.551928i	$-0.813892\pi$
$829$	1.75742	−	3.04395i	0.0610379	−	0.105721i	0.894930	+	0.446207i	$0.147226\pi$
$830$	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	−0.730447	−	0.682969i	$-0.760688\pi$
$857$	6.62323	−	11.4718i	0.226245	−	0.391868i	0.956692	+	0.291101i	$0.0940216\pi$
$858$	7.13430	−	6.87481i	0.243561	−	0.234702i
$859$	12.3708	+	21.4269i	0.422088	+	0.731077i	0.996144	−	0.0877388i	$-0.0279641\pi$
$859$	12.3708	+	21.4269i	0.422088	+	0.731077i	−0.574056	+	0.818816i	$0.694631\pi$
$860$	−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	−0.336031	−	0.941851i	$-0.609085\pi$
$863$	9.15443	−	5.28531i	0.311620	−	0.179914i	0.647651	+	0.761937i	$0.275751\pi$
$864$	−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	0.263449	−	0.964673i	$-0.415140\pi$
$877$	36.4434	−	21.0406i	1.23061	−	0.710490i	0.967156	+	0.254183i	$0.0818065\pi$
$878$	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	$0.314571\pi$
$883$			49.6285i			1.67013i	−0.550150	+	0.835066i	$0.685429\pi$
$884$	−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	0.987008	+	0.160671i	$0.0513657\pi$
$887$	18.8419	+	32.6351i	0.632649	+	1.09578i	−0.354359	+	0.935109i	$0.615301\pi$
$888$	−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	0.441034	−	0.897490i	$-0.354612\pi$
$907$	−3.48443	−	2.01173i	−0.115698	−	0.0667985i	−0.556732	+	0.830692i	$0.687945\pi$
$908$	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	$-0.951094\pi$
$911$		−	9.23822i		−	0.306076i	0.988220	−	0.153038i	$-0.0489057\pi$
$912$	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	0.991906	−	0.126974i	$-0.0405266\pi$
$919$	11.7013	+	20.2672i	0.385990	+	0.668554i	−0.605916	+	0.795529i	$0.707193\pi$
$920$	−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	0.923610	−	0.383333i	$-0.125224\pi$
$929$	3.95711	+	6.85391i	0.129828	+	0.224870i	−0.793782	+	0.608203i	$0.791891\pi$
$930$	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	$0.309342\pi$
$937$			50.5634i			1.65184i	−0.563791	+	0.825918i	$0.690658\pi$
$938$	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	0.0491464	−	0.998792i	$-0.484350\pi$
$941$	−24.2724	−	14.0137i	−0.791259	−	0.456834i	−0.840406	+	0.541958i	$0.817683\pi$
$942$	−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	0.889661	−	0.456621i	$-0.150940\pi$
$947$	1.51976	+	2.63230i	0.0493855	+	0.0855381i	−0.840276	+	0.542159i	$0.817607\pi$
$948$	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	$-0.987301\pi$
$953$		−	2.46246i		−	0.0797670i	0.999204	−	0.0398835i	$-0.0126987\pi$
$954$	−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	−0.682027	−	0.731327i	$-0.738901\pi$
$971$	−12.1432	+	7.01086i	−0.389693	+	0.224989i	0.292334	+	0.956316i	$0.405568\pi$
$972$	−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	0.797973	−	0.602693i	$-0.205906\pi$
$977$	21.0989	+	12.1814i	0.675013	+	0.389719i	−0.122961	+	0.992412i	$0.539239\pi$
$978$	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	−0.942956	−	0.332918i	$-0.891967\pi$
$983$	−5.74265	+	9.94656i	−0.183162	+	0.317246i	0.759794	+	0.650164i	$0.225300\pi$
$984$	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	−0.517459	−	0.855708i	$-0.673122\pi$
$991$	15.1840	−	26.2995i	0.482336	−	0.835430i	0.999794	+	0.0202784i	$0.00645526\pi$
$992$	−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	−0.705901	−	0.708310i	$-0.749458\pi$
$997$	8.22424	−	14.2448i	0.260464	−	0.451137i	0.966365	+	0.257173i	$0.0827911\pi$
$998$	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.101.19	✓	256
3.2	odd	2	inner	840.2.cf.a.101.110	yes	256
7.5	odd	6	inner	840.2.cf.a.341.105	yes	256
8.5	even	2	inner	840.2.cf.a.101.24	yes	256
21.5	even	6	inner	840.2.cf.a.341.24	yes	256
24.5	odd	2	inner	840.2.cf.a.101.105	yes	256
56.5	odd	6	inner	840.2.cf.a.341.110	yes	256
168.5	even	6	inner	840.2.cf.a.341.19	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.19	✓	256	1.1	even	1	trivial
840.2.cf.a.101.24	yes	256	8.5	even	2	inner
840.2.cf.a.101.105	yes	256	24.5	odd	2	inner
840.2.cf.a.101.110	yes	256	3.2	odd	2	inner
840.2.cf.a.341.19	yes	256	168.5	even	6	inner
840.2.cf.a.341.24	yes	256	21.5	even	6	inner
840.2.cf.a.341.105	yes	256	7.5	odd	6	inner
840.2.cf.a.341.110	yes	256	56.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

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