LMFDB - Embedded newform 840.2.cf.a.101.110

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			101.110
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.110

$q$-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} +(-1.64343 - 0.546941i) q^{3} +(1.25695 - 1.55566i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-2.43058 + 0.303755i) q^{6} +(2.04884 + 1.67400i) q^{7} +(0.655798 - 2.75135i) q^{8} +(2.40171 + 1.79772i) q^{9} +(-0.800386 + 1.16593i) q^{10} +(0.791910 - 1.37163i) q^{11} +(-2.91656 + 1.86914i) 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} +(4.16062 + 0.830186i) q^{18} +(0.482815 + 0.836259i) q^{19} +(-0.310721 + 1.97572i) q^{20} +(-2.45154 - 3.87169i) q^{21} +(0.174524 - 2.23305i) q^{22} +(2.79167 - 1.61177i) q^{23} +(-2.58258 + 4.16296i) 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} +(1.95307 - 1.47835i) q^{30} +(-2.05487 - 1.18638i) q^{31} +(-3.45586 - 4.47851i) q^{32} +(-2.05165 + 1.82104i) q^{33} +(-0.000143259 + 0.00183302i) q^{34} +(-2.61134 - 0.425305i) q^{35} +(5.81547 - 1.47660i) q^{36} +(8.97684 - 5.18278i) q^{37} +(1.12585 + 0.772876i) q^{38} +(-4.19700 - 1.39678i) q^{39} +(0.807738 + 2.71064i) q^{40} +1.33074 q^{41} +(-5.48835 - 3.44644i) q^{42} -5.61460i q^{43} +(-1.13839 - 2.95601i) q^{44} +(-2.97880 - 0.356013i) q^{45} +(2.58008 - 3.75841i) q^{46} +(-5.79156 - 10.0313i) q^{47} +(-0.758235 + 6.88659i) q^{48} +(1.39547 + 6.85949i) q^{49} +(0.110192 - 1.40991i) q^{50} +(0.00168411 - 0.00149482i) q^{51} +(3.21001 - 3.97285i) q^{52} +(-4.58699 + 7.94490i) q^{53} +(-6.38362 - 3.63997i) 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} +(1.59125 - 3.07700i) q^{60} +(4.28404 + 7.42017i) q^{61} +(-3.34538 - 0.261458i) q^{62} +(1.91134 + 7.70369i) q^{63} +(-7.13986 - 3.60866i) q^{64} +(-2.21166 + 1.27690i) q^{65} +(-1.50816 + 3.57440i) 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} +(6.52119 - 5.42901i) q^{72} +(-7.92146 - 4.57346i) q^{73} +(8.29645 - 12.0855i) q^{74} +(-1.29538 + 1.14978i) q^{75} +(1.90781 + 0.300042i) q^{76} +(3.91860 - 1.48459i) q^{77} +(-6.20724 + 0.775732i) q^{78} +(7.16669 + 12.4131i) q^{79} +(2.68298 + 2.96675i) q^{80} +(2.53643 + 8.63519i) q^{81} +(1.69818 - 0.811122i) q^{82} +9.94503i q^{83} +(-9.10449 - 1.05276i) q^{84} -0.00130009i q^{85} +(-3.42226 - 7.16489i) q^{86} +(-4.68052 - 1.55770i) q^{87} +(-3.25450 - 3.07833i) q^{88} +(7.80405 + 13.5170i) q^{89} +(-4.01830 + 1.36135i) q^{90} +(5.23234 + 4.27507i) q^{91} +(1.00162 - 6.36881i) q^{92} +(2.72815 + 3.07362i) q^{93} +(-13.5050 - 9.27096i) q^{94} +(-0.836259 - 0.482815i) q^{95} +(3.22997 + 9.25026i) 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
$3$	−1.64343	−	0.546941i	−0.948834	−	0.315777i
$3$	−1.64343	−	0.546941i	−0.948834	−	0.315777i
$4$	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
$6$	−2.43058	+	0.303755i	−0.992281	+	0.124007i
$7$	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
$9$	2.40171	+	1.79772i	0.800570	+	0.599239i
$10$	−0.800386	+	1.16593i	−0.253104	+	0.368698i
$11$	0.791910	−	1.37163i	0.238770	−	0.413562i	−0.721592	−	0.692319i	$-0.756589\pi$
$11$	0.791910	−	1.37163i	0.238770	−	0.413562i	0.960362	+	0.278757i	$0.0899225\pi$
$12$	−2.91656	+	1.86914i	−0.841939	+	0.539573i
$13$	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	$-0.833384\pi$
$17$	−0.000650046		0.00112591i	−0.000157659		0.000273074i	0.865947	+	0.500137i	$0.166717\pi$
$18$	4.16062	+	0.830186i	0.980668	+	0.195677i
$19$	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
$21$	−2.45154	−	3.87169i	−0.534970	−	0.844871i
$22$	0.174524	−	2.23305i	0.0372086	−	0.476088i
$23$	2.79167	−	1.61177i	0.582104	−	0.336078i	−0.179865	−	0.983691i	$-0.557566\pi$
$23$	2.79167	−	1.61177i	0.582104	−	0.336078i	0.761969	+	0.647613i	$0.224233\pi$
$24$	−2.58258	+	4.16296i	−0.527168	+	0.849761i
$25$	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	$-0.414815\pi$
$29$	2.84802			0.528864			0.264432	+	0.964404i	$0.414815\pi$
$30$	1.95307	−	1.47835i	0.356580	−	0.269909i
$31$	−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
$33$	−2.05165	+	1.82104i	−0.357146	+	0.317003i
$34$	−0.000143259		0.00183302i	−2.45688e−5		0.000314360i
$35$	−2.61134	−	0.425305i	−0.441398	−	0.0718896i
$36$	5.81547	−	1.47660i	0.969244	−	0.246101i
$37$	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
$39$	−4.19700	−	1.39678i	−0.672058	−	0.223664i
$40$	0.807738	+	2.71064i	0.127715	+	0.428590i
$41$	1.33074			0.207826			0.103913	−	0.994586i	$-0.466864\pi$
$41$	1.33074			0.207826			0.103913	+	0.994586i	$0.466864\pi$
$42$	−5.48835	−	3.44644i	−0.846871	−	0.531798i
$43$		−	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
$45$	−2.97880	−	0.356013i	−0.444053	−	0.0530712i
$46$	2.58008	−	3.75841i	0.380412	−	0.554148i
$47$	−5.79156	−	10.0313i	−0.844785	−	1.46321i	−0.885807	−	0.464053i	$-0.846395\pi$
$47$	−5.79156	−	10.0313i	−0.844785	−	1.46321i	0.0410220	−	0.999158i	$-0.486939\pi$
$48$	−0.758235	+	6.88659i	−0.109442	+	0.993993i
$49$	1.39547	+	6.85949i	0.199353	+	0.979928i
$50$	0.110192	−	1.40991i	0.0155835	−	0.199392i
$51$	0.00168411	−	0.00149482i	0.000235823	−	0.000209317i
$52$	3.21001	−	3.97285i	0.445148	−	0.550936i
$53$	−4.58699	+	7.94490i	−0.630071	+	1.09132i	0.357465	+	0.933926i	$0.383641\pi$
$53$	−4.58699	+	7.94490i	−0.630071	+	1.09132i	−0.987537	+	0.157389i	$0.949692\pi$
$54$	−6.38362	−	3.63997i	−0.868701	−	0.495337i
$55$			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	$-0.253633\pi$
$59$	3.29646	+	1.90321i	0.429163	+	0.247777i	−0.269827	+	0.962909i	$0.586967\pi$
$60$	1.59125	−	3.07700i	0.205429	−	0.397239i
$61$	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
$63$	1.91134	+	7.70369i	0.240807	+	0.970573i
$64$	−7.13986	−	3.60866i	−0.892482	−	0.451082i
$65$	−2.21166	+	1.27690i	−0.274323	+	0.158380i
$66$	−1.50816	+	3.57440i	−0.185642	+	0.439979i
$67$	−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	$-0.810458\pi$
$71$		−	9.45233i		−	1.12178i	0.827889	−	0.560892i	$-0.189542\pi$
$72$	6.52119	−	5.42901i	0.768529	−	0.639815i
$73$	−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
$75$	−1.29538	+	1.14978i	−0.149577	+	0.132765i
$76$	1.90781	+	0.300042i	0.218841	+	0.0344172i
$77$	3.91860	−	1.48459i	0.446566	−	0.169185i
$78$	−6.20724	+	0.775732i	−0.702832	+	0.0878343i
$79$	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
$81$	2.53643	+	8.63519i	0.281826	+	0.959466i
$82$	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	$0.816224\pi$
$84$	−9.10449	−	1.05276i	−0.993381	−	0.114865i
$85$		−	0.00130009i		−	0.000141015i
$86$	−3.42226	−	7.16489i	−0.369032	−	0.772610i
$87$	−4.68052	−	1.55770i	−0.501804	−	0.167003i
$88$	−3.25450	−	3.07833i	−0.346931	−	0.328151i
$89$	7.80405	+	13.5170i	0.827228	+	1.43280i	0.900205	+	0.435467i	$0.143417\pi$
$89$	7.80405	+	13.5170i	0.827228	+	1.43280i	−0.0729765	+	0.997334i	$0.523250\pi$
$90$	−4.01830	+	1.36135i	−0.423566	+	0.143499i
$91$	5.23234	+	4.27507i	0.548498	+	0.448149i
$92$	1.00162	−	6.36881i	0.104427	−	0.663994i
$93$	2.72815	+	3.07362i	0.282896	+	0.318719i
$94$	−13.5050	−	9.27096i	−1.39294	−	0.956227i
$95$	−0.836259	−	0.482815i	−0.0857984	−	0.0495357i
$96$	3.22997	+	9.25026i	0.329658	+	0.944101i
$97$			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	0.319459	−	0.947600i	$-0.396499\pi$
$101$	−3.43160	−	1.98123i	−0.341457	−	0.197140i	−0.660916	+	0.750460i	$0.729832\pi$
$102$	0.00123799	−	0.00293408i	0.000122579	−	0.000290517i
$103$	−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
$105$	4.05894	+	2.12721i	0.396112	+	0.207594i
$106$	−1.01090	+	12.9345i	−0.0981869	+	1.25631i
$107$	−1.33275	−	2.30839i	−0.128842	−	0.223161i	0.794386	−	0.607413i	$-0.207793\pi$
$107$	−1.33275	−	2.30839i	−0.128842	−	0.223161i	−0.923228	+	0.384252i	$0.874459\pi$
$108$	−10.3649	−	0.754026i	−0.997364	−	0.0725562i
$109$	−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	$0.0770265\pi$
$113$			5.09463i			0.479262i	−0.970864	+	0.239631i	$0.922974\pi$
$114$	−1.42754	−	1.88594i	−0.133701	−	0.176635i
$115$	−1.61177	+	2.79167i	−0.150299	+	0.260325i
$116$	3.57982	−	4.43055i	0.332378	−	0.411366i
$117$	6.13351	+	4.59102i	0.567043	+	0.424440i
$118$	5.36673	+	0.419436i	0.494048	+	0.0386122i
$119$	−0.00321661	+	0.00121864i	−0.000294866	+	0.000111712i
$120$	0.155101	−	4.89652i	0.0141587	−	0.446989i
$121$	4.24576	+	7.35387i	0.385978	+	0.668533i
$122$	9.98974	+	6.85777i	0.904428	+	0.620873i
$123$	−2.18697	−	0.727834i	−0.197192	−	0.0656266i
$124$	−4.42847	+	1.70545i	−0.397688	+	0.153154i
$125$			1.00000i			0.0894427i
$126$	7.13471	+	8.66579i	0.635611	+	0.772010i
$127$	−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
$129$	−3.07086	+	9.22719i	−0.270374	+	0.812409i
$130$	−2.04403	+	2.97755i	−0.179273	+	0.261148i
$131$	−0.999689	+	0.577170i	−0.0873432	+	0.0504276i	−0.543035	−	0.839710i	$-0.682725\pi$
$131$	−0.999689	+	0.577170i	−0.0873432	+	0.0504276i	0.455692	+	0.890137i	$0.349392\pi$
$132$	0.254106	+	5.48063i	0.0221171	+	0.477027i
$133$	−0.410687	+	2.52159i	−0.0356111	+	0.218650i
$134$	−11.3633	−	0.888094i	−0.981636	−	0.0767196i
$135$	4.70073	+	2.21431i	0.404574	+	0.190577i
$136$	0.00267148	+	0.00252688i	0.000229078	+	0.000216678i
$137$	7.39675	+	4.27052i	0.631947	+	0.364855i	0.781506	−	0.623898i	$-0.214452\pi$
$137$	7.39675	+	4.27052i	0.631947	+	0.364855i	−0.149559	+	0.988753i	$0.547785\pi$
$138$	−6.29581	+	4.76553i	−0.535935	+	0.405669i
$139$	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
$144$	5.01266	−	10.9029i	0.417722	−	0.908575i
$145$	−2.46646	+	1.42401i	−0.204828	+	0.118258i
$146$	−12.8964	−	1.00791i	−1.06731	−	0.0834155i
$147$	1.45838	−	12.0363i	0.120285	−	0.992739i
$148$	3.22080	−	20.4794i	0.264748	−	1.68340i
$149$	8.56852	+	14.8411i	0.701961	+	1.21583i	0.967777	+	0.251808i	$0.0810252\pi$
$149$	8.56852	+	14.8411i	0.701961	+	1.21583i	−0.265816	+	0.964024i	$0.585641\pi$
$150$	−0.952232	+	2.25682i	−0.0777494	+	0.184269i
$151$	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
$156$	−7.44834	+	4.77341i	−0.596344	+	0.382179i
$157$	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
$159$	11.8838	−	10.5481i	0.942445	−	0.836515i
$160$	5.23212	+	2.15057i	0.413635	+	0.170018i
$161$	8.41778	+	1.37099i	0.663414	+	0.108049i
$162$	8.50018	+	9.47349i	0.667837	+	0.744308i
$163$	−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
$165$	0.866256	−	2.60289i	0.0674380	−	0.202635i
$166$	6.06178	+	12.6910i	0.470485	+	0.985015i
$167$	−22.2823			−1.72426			−0.862128	−	0.506690i	$-0.830869\pi$
$167$	−22.2823			−1.72426			−0.862128	+	0.506690i	$0.830869\pi$
$168$	−12.2601	+	4.20600i	−0.945886	+	0.324500i
$169$	−6.47806			−0.498313
$170$	−0.000792443	−	0.00165907i	−6.07776e−5	−	0.000127245i
$171$	−0.343776	+	2.87642i	−0.0262892	+	0.219965i
$172$	−8.73440	−	7.05727i	−0.665992	−	0.538112i
$173$	4.47223	−	2.58204i	0.340017	−	0.196309i	−0.320262	−	0.947329i	$-0.603771\pi$
$173$	4.47223	−	2.58204i	0.340017	−	0.196309i	0.660280	+	0.751020i	$0.270438\pi$
$174$	−6.92235	+	0.865101i	−0.524782	+	0.0655831i
$175$	2.47414	−	0.937347i	0.187028	−	0.0708568i
$176$	−6.02945	−	1.94461i	−0.454487	−	0.146580i
$177$	−4.37655	−	4.93076i	−0.328962	−	0.370619i
$178$	18.1979	+	12.4925i	1.36399	+	0.936353i
$179$	−8.80808	+	15.2560i	−0.658347	+	1.14029i	0.322697	+	0.946502i	$0.395411\pi$
$179$	−8.80808	+	15.2560i	−0.658347	+	1.14029i	−0.981044	+	0.193787i	$0.937923\pi$
$180$	−4.29804	+	4.18651i	−0.320357	+	0.312044i
$181$	−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
$186$	5.35489	+	2.25941i	0.392640	+	0.165668i
$187$	0.00102956	+	0.00178324i	7.52886e−5	+	0.000130404i
$188$	−22.8849	−	3.59912i	−1.66906	−	0.262493i
$189$	1.07231	−	13.7058i	0.0779987	−	0.996953i
$190$	−1.36145	−	0.106404i	−0.0987703	−	0.00771938i
$191$	−12.9451	+	7.47388i	−0.936677	+	0.540791i	−0.888917	−	0.458068i	$-0.848542\pi$
$191$	−12.9451	+	7.47388i	−0.936677	+	0.540791i	−0.0477601	+	0.998859i	$0.515208\pi$
$192$	9.76012	+	9.83565i	0.704376	+	0.709827i
$193$	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	$-0.723674\pi$
$197$	−18.1418			−1.29255			−0.646276	+	0.763104i	$0.723674\pi$
$198$	4.43355	−	5.04940i	0.315079	−	0.358845i
$199$	−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
$201$	9.26670	+	10.4402i	0.653623	+	0.736392i
$202$	−5.58674	−	0.436631i	−0.393082	−	0.0307212i
$203$	5.83513	+	4.76758i	0.409546	+	0.334618i
$204$	−0.000208585	−	0.00449882i	−1.46039e−5	−	0.000314980i
$205$	−1.15245	+	0.665368i	−0.0804907	+	0.0464713i
$206$	−2.76279	+	4.02457i	−0.192493	+	0.280405i
$207$	9.60230	+	1.14762i	0.667406	+	0.0797653i
$208$	−2.14558	−	9.98736i	−0.148769	−	0.692499i
$209$	1.52938			0.105790
$210$	6.47628	+	0.240530i	0.446905	+	0.0165982i
$211$			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
$213$	−5.16987	+	15.5342i	−0.354233	+	1.06439i
$214$	−3.10778	−	2.13343i	−0.212443	−	0.145838i
$215$	2.80730	+	4.86239i	0.191456	+	0.331612i
$216$	−13.6864	+	5.35548i	−0.931245	+	0.364394i
$217$	−2.22410	−	5.87054i	−0.150982	−	0.398518i
$218$	−9.51288	−	0.743478i	−0.644294	−	0.0503547i
$219$	10.5169	+	11.8487i	0.710669	+	0.800662i
$220$	2.46388	+	1.99078i	0.166115	+	0.134219i
$221$	−0.00166009	+	0.00287537i	−0.000111670	+	0.000193418i
$222$	−20.2447	+	15.3239i	−1.35873	+	1.02848i
$223$		−	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	−0.493244	−	0.869891i	$-0.664189\pi$
$227$	−22.4975	−	12.9890i	−1.49321	−	0.862107i	−0.999970	+	0.00778359i	$0.997522\pi$
$228$	−2.97124	−	1.53656i	−0.196775	−	0.101761i
$229$	−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
$231$	−7.25191	+	0.296574i	−0.477141	+	0.0195131i
$232$	1.86773	−	7.83591i	0.122622	−	0.514452i
$233$	−14.5217	+	8.38408i	−0.951345	+	0.549259i	−0.893499	−	0.449066i	$-0.851757\pi$
$233$	−14.5217	+	8.38408i	−0.951345	+	0.549259i	−0.0578466	+	0.998325i	$0.518423\pi$
$234$	10.6254	+	2.12014i	0.694606	+	0.138598i
$235$	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	$-0.0783915\pi$
$240$	−2.78664	−	6.34308i	−0.179877	−	0.409444i
$241$	−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
$243$	0.554499	−	15.5786i	0.0355711	−	0.999367i
$244$	16.9281	+	2.66228i	1.08371	+	0.170435i
$245$	−4.63826	−	5.24276i	−0.296328	−	0.334948i
$246$	−3.23447	+	0.404218i	−0.206222	+	0.0257720i
$247$	1.23302	+	2.13565i	0.0784549	+	0.135888i
$248$	−4.61172	+	4.87564i	−0.292845	+	0.309603i
$249$	5.43935	−	16.3439i	0.344705	−	1.03576i
$250$	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	$0.868092\pi$
$252$	14.3868	+	6.70975i	0.906282	+	0.422675i
$253$		−	5.10552i		−	0.320981i
$254$	−3.54788	+	1.69462i	−0.222614	+	0.106330i
$255$	−0.000711074		0.00213661i	−4.45292e−5		0.000133800i
$256$	−14.5883	+	6.57128i	−0.911768	+	0.410705i
$257$	13.6364	+	23.6190i	0.850618	+	1.47331i	0.880651	+	0.473765i	$0.157105\pi$
$257$	13.6364	+	23.6190i	0.850618	+	1.47331i	−0.0300331	+	0.999549i	$0.509561\pi$
$258$	1.70546	+	13.6468i	0.106177	+	0.849610i
$259$	27.0680	+	4.40852i	1.68193	+	0.273932i
$260$	−0.793523	+	5.04560i	−0.0492122	+	0.312915i
$261$	6.84013	+	5.11994i	0.423393	+	0.316916i
$262$	−0.923918	+	1.34588i	−0.0570798	+	0.0831485i
$263$	14.4484	+	8.34177i	0.890925	+	0.514376i	0.874245	−	0.485485i	$-0.161357\pi$
$263$	14.4484	+	8.34177i	0.890925	+	0.514376i	0.0166797	+	0.999861i	$0.494690\pi$
$264$	3.66487	+	6.83904i	0.225557	+	0.420914i
$265$		−	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	$-0.364277\pi$
$269$	−2.75722	−	1.59188i	−0.168111	−	0.0970589i	−0.581695	+	0.813407i	$0.697610\pi$
$270$	7.34836	−	0.0395072i	0.447207	−	0.00240433i
$271$	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
$273$	−6.26076	−	9.88754i	−0.378919	−	0.598421i
$274$	12.0421	+	0.941150i	0.727491	+	0.0568570i
$275$	−0.791910	−	1.37163i	−0.0477540	−	0.0827123i
$276$	−5.12946	+	9.91885i	−0.308757	+	0.597044i
$277$	−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	$-0.922165\pi$
$281$		−	8.11655i		−	0.484193i	0.970252	−	0.242096i	$-0.0778350\pi$
$282$	17.1239	+	22.6226i	1.01971	+	1.34716i
$283$	−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
$285$	1.11026	+	1.25086i	0.0657662	+	0.0740943i
$286$	0.445700	−	5.70278i	0.0263548	−	0.337213i
$287$	2.72646	+	2.22765i	0.160938	+	0.131494i
$288$	−0.248882	−	16.9687i	−0.0146655	−	0.999892i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−2.27952	+	3.32058i	−0.133858	+	0.194991i
$291$	5.53976	−	16.6457i	0.324746	−	0.975786i
$292$	−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	$0.907669\pi$
$294$	−5.47541	−	16.2487i	−0.319332	−	0.947643i
$295$	−3.80642			−0.221619
$296$	−8.37265	−	28.0973i	−0.486650	−	1.63312i
$297$	−8.20119	+	0.685343i	−0.475881	+	0.0397676i
$298$	19.9805	+	13.7162i	1.15744	+	0.794561i
$299$	7.12939	−	4.11616i	0.412303	−	0.238044i
$300$	0.160438	+	3.46038i	0.00926292	+	0.199785i
$301$	9.39882	−	11.5034i	0.541739	−	0.663045i
$302$	0.808003	−	10.3385i	0.0464953	−	0.594913i
$303$	4.55597	+	5.13290i	0.261733	+	0.294877i
$304$	2.86478	−	2.59076i	0.164307	−	0.148590i
$305$	−7.42017	−	4.28404i	−0.424878	−	0.245303i
$306$	−0.00363932	+	0.00414484i	−0.000208046	+	0.000236945i
$307$	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	$-0.653604\pi$
$311$	9.43673	−	16.3449i	0.535108	−	0.926834i	0.999158	−	0.0410252i	$-0.0130624\pi$
$312$	−6.59542	+	10.6314i	−0.373392	+	0.601885i
$313$	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
$315$	−5.50712	−	5.71591i	−0.310291	−	0.322055i
$316$	28.3187	+	4.45369i	1.59305	+	0.250539i
$317$	−11.8261	−	20.4834i	−0.664220	−	1.15046i	−0.979496	−	0.201463i	$-0.935430\pi$
$317$	−11.8261	−	20.4834i	−0.664220	−	1.15046i	0.315276	−	0.949000i	$-0.397903\pi$
$318$	8.73575	−	20.7041i	0.489877	−	1.16103i
$319$	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
$324$	16.6216	+	6.90819i	0.923421	+	0.383788i
$325$	1.27690	−	2.21166i	0.0708299	−	0.122681i
$326$	−8.79342	+	12.8094i	−0.487022	+	0.709448i
$327$	7.75772	+	8.74010i	0.429003	+	0.483328i
$328$	0.872694	−	3.66132i	0.0481865	−	0.202163i
$329$	4.92635	−	30.2475i	0.271599	−	1.66760i
$330$	−0.481093	−	3.84961i	−0.0264833	−	0.211914i
$331$	−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
$333$	30.8769	+	3.69027i	1.69205	+	0.202226i
$334$	−28.4348	+	13.5817i	−1.55588	+	0.743157i
$335$	8.05954			0.440340
$336$	−13.0816	+	12.8402i	−0.713661	+	0.700491i
$337$	−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
$339$	2.78646	−	8.37265i	0.151340	−	0.454740i
$340$	−0.00202250	−	0.00163415i	−0.000109685	−	8.86243e-5i
$341$	−3.25454	+	1.87901i	−0.176243	+	0.101754i
$342$	1.31456	+	3.88019i	0.0710832	+	0.209816i
$343$	−8.62368	+	16.3900i	−0.465635	+	0.884977i
$344$	−15.4477	−	3.68204i	−0.832886	−	0.198522i
$345$	4.17571	−	3.70637i	0.224813	−	0.199544i
$346$	4.13326	−	6.02094i	0.222205	−	0.323688i
$347$	−4.22243	+	7.31347i	−0.226672	+	0.392608i	−0.956820	−	0.290682i	$-0.906118\pi$
$347$	−4.22243	+	7.31347i	−0.226672	+	0.392608i	0.730148	+	0.683289i	$0.239451\pi$
$348$	−8.30643	+	5.32334i	−0.445271	+	0.285361i
$349$	−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	$-0.958374\pi$
$353$	−7.19217	+	12.4572i	−0.382800	+	0.663030i	0.608661	+	0.793430i	$0.291707\pi$
$354$	−8.59043	−	3.62460i	−0.456576	−	0.192645i
$355$	4.72616	+	8.18595i	0.250839	+	0.434465i
$356$	30.8372	+	4.84977i	1.63437	+	0.257038i
$357$	0.00595280		0.000243445i	0.000315055		1.28845e-5i
$358$	−1.94115	+	24.8373i	−0.102593	+	1.31269i
$359$	−7.47661	+	4.31662i	−0.394600	+	0.227823i	−0.684151	−	0.729340i	$-0.739827\pi$
$359$	−7.47661	+	4.31662i	−0.394600	+	0.227823i	0.289551	+	0.957163i	$0.406494\pi$
$360$	−2.93301	+	7.96225i	−0.154583	+	0.419648i
$361$	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
$366$	−12.6666	−	16.7340i	−0.662095	−	0.874702i
$367$	−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
$369$	3.19604	+	2.39229i	0.166379	+	0.124537i
$370$	−1.14220	+	14.6145i	−0.0593800	+	0.759774i
$371$	−22.6977	+	8.59920i	−1.17841	+	0.446448i
$372$	8.21065	−	0.380681i	0.425702	−	0.0197374i
$373$	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
$375$	0.546941	−	1.64343i	0.0282439	−	0.0848663i
$376$	−31.3976	+	9.35612i	−1.61921	+	0.482505i
$377$	7.27330			0.374594
$378$	−6.98571	−	18.1439i	−0.359306	−	0.933220i
$379$			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
$381$	4.56908	+	1.52061i	0.234081	+	0.0779033i
$382$	−11.9640	+	17.4280i	−0.612130	+	0.891693i
$383$	1.98896	+	3.44499i	0.101631	+	0.176031i	0.912357	−	0.409396i	$-0.134260\pi$
$383$	1.98896	+	3.44499i	0.101631	+	0.176031i	−0.810726	+	0.585426i	$0.800927\pi$
$384$	18.4502	+	6.60238i	0.941531	+	0.336926i
$385$	−2.65131	+	3.24499i	−0.135123	+	0.165380i
$386$	0.418521	−	5.35502i	0.0213021	−	0.272563i
$387$	10.0935	−	13.4846i	0.513079	−	0.685463i
$388$	15.7567	+	12.7312i	0.799924	+	0.646328i
$389$	−15.1320	+	26.2095i	−0.767225	+	1.32887i	0.171837	+	0.985125i	$0.445030\pi$
$389$	−15.1320	+	26.2095i	−0.767225	+	1.32887i	−0.939062	+	0.343748i	$0.888304\pi$
$390$	4.98776	−	3.77542i	0.252565	−	0.191176i
$391$			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
$396$	2.57998	−	9.14600i	0.129649	−	0.459604i
$397$	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
$399$	2.05410	−	3.91943i	0.102833	−	0.196217i
$400$	−3.80690	−	1.22779i	−0.190345	−	0.0613897i
$401$	23.0500	−	13.3079i	1.15106	−	0.664566i	0.201916	−	0.979403i	$-0.435283\pi$
$401$	23.0500	−	13.3079i	1.15106	−	0.664566i	0.949146	+	0.314837i	$0.101950\pi$
$402$	18.1890	+	7.67455i	0.907183	+	0.382772i
$403$	−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
$408$	−0.00300834	−	0.00561388i	−0.000148935	−	0.000277929i
$409$	−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
$411$	−9.82031	−	11.0639i	−0.484400	−	0.545741i
$412$	−1.07256	+	6.81982i	−0.0528410	+	0.335988i
$413$	3.56794	+	9.41764i	0.175567	+	0.463412i
$414$	12.9532	−	4.38837i	0.636613	−	0.215677i
$415$	−4.97252	−	8.61265i	−0.244091	−	0.422778i
$416$	−8.82560	−	11.4373i	−0.432711	−	0.560757i
$417$	−21.6478	−	7.20451i	−1.06010	−	0.352806i
$418$	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	$0.741688\pi$
$420$	8.41110	−	3.64053i	0.410420	−	0.177640i
$421$			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
$423$	4.12374	−	34.5038i	0.200503	−	1.67763i
$424$	18.8511	+	17.8307i	0.915488	+	0.865933i
$425$	0.000650046		0.00112591i	3.15319e−5		5.46148e-5i
$426$	2.87119	+	22.9747i	0.139110	+	1.11313i
$427$	−3.64404	+	22.3742i	−0.176348	+	1.08276i
$428$	−5.26627	−	0.828228i	−0.254555	−	0.0400339i
$429$	−5.23951	+	4.65060i	−0.252966	+	0.224533i
$430$	6.54621	+	4.49385i	0.315686	+	0.216713i
$431$	22.0215	+	12.7141i	1.06074	+	0.612417i	0.925636	−	0.378414i	$-0.123531\pi$
$431$	22.0215	+	12.7141i	1.06074	+	0.612417i	0.135102	+	0.990832i	$0.456864\pi$
$432$	−14.2012	+	15.1765i	−0.683255	+	0.730180i
$433$		−	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
$438$	20.6430	+	8.70998i	0.986360	+	0.416179i
$439$	−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
$441$	−8.97991	+	18.9832i	−0.427615	+	0.903961i
$442$	−0.000365857		0.00468118i	−1.74020e−5		0.000222661i
$443$	−7.35604	−	12.7410i	−0.349496	−	0.605345i	0.636664	−	0.771141i	$-0.280314\pi$
$443$	−7.35604	−	12.7410i	−0.349496	−	0.605345i	−0.986160	+	0.165796i	$0.946981\pi$
$444$	−16.4942	+	31.8948i	−0.782779	+	1.51366i
$445$	−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	$-0.177887\pi$
$450$	2.79927	−	3.18811i	0.131959	−	0.150289i
$451$	1.05382	−	1.82528i	0.0496226	−	0.0859489i
$452$	7.92550	+	6.40369i	0.372784	+	0.301204i
$453$	−9.49863	+	8.43100i	−0.446285	+	0.396123i
$454$	−36.6266	−	2.86255i	−1.71897	−	0.134346i
$455$	−6.66887	−	1.08615i	−0.312641	−	0.0509194i
$456$	−4.72823	−	0.149770i	−0.221419	−	0.00701362i
$457$	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
$459$	0.00673201		0.000562569i	0.000314223		2.62585e-5i
$460$	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	$0.809383\pi$
$462$	−9.07352	+	4.79871i	−0.422139	+	0.223256i
$463$	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
$465$	−3.89946	−	1.29776i	−0.180833	−	0.0601821i
$466$	−13.4210	+	19.5504i	−0.621716	+	0.905656i
$467$	16.7214	−	9.65411i	0.773775	−	0.446739i	−0.0604449	−	0.998172i	$-0.519252\pi$
$467$	16.7214	−	9.65411i	0.773775	−	0.446739i	0.834219	+	0.551433i	$0.185919\pi$
$468$	14.8516	−	3.77096i	0.686515	−	0.174313i
$469$	−7.55459	−	19.9405i	−0.348838	−	0.920765i
$470$	16.3312	+	1.27636i	0.753302	+	0.0588742i
$471$	−29.6489	+	26.3164i	−1.36615	+	1.21260i
$472$	7.39822	−	7.82160i	0.340531	−	0.360018i
$473$	−7.70115	−	4.44626i	−0.354099	−	0.204439i
$474$	−21.1898	−	27.9941i	−0.973278	−	1.28581i
$475$	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	$-0.825239\pi$
$479$	0.556505	−	0.963894i	0.0254273	−	0.0440415i	0.878459	+	0.477818i	$0.158572\pi$
$480$	−7.42237	−	6.39597i	−0.338783	−	0.291935i
$481$	22.9251	−	13.2358i	1.04530	−	0.603502i
$482$	−20.8913	−	1.63276i	−0.951574	−	0.0743702i
$483$	−13.0842	−	6.85715i	−0.595350	−	0.312011i
$484$	16.7768	+	2.63850i	0.762583	+	0.119932i
$485$	−5.06431	−	8.77164i	−0.229959	−	0.398300i
$486$	−8.78799	−	20.2181i	−0.398631	−	0.917111i
$487$	−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	$-0.309714\pi$
$491$	24.9428			1.12565			0.562826	+	0.826575i	$0.309714\pi$
$492$	−3.88117	+	2.48733i	−0.174977	+	0.112137i
$493$	−0.00185135	+	0.00320663i	−8.33804e−5	+	0.000144419i
$494$	2.87521	+	1.97378i	0.129362	+	0.0888044i
$495$	−2.84726	+	3.80388i	−0.127975	+	0.170972i
$496$	−2.91326	+	9.03286i	−0.130809	+	0.405587i
$497$	15.8232	−	19.3663i	0.709766	−	0.868696i
$498$	−3.02085	−	24.1722i	−0.135368	−	1.08318i
$499$	−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
$501$	36.6194	+	12.1871i	1.63603	+	0.544480i
$502$	7.77639	+	16.2808i	0.347077	+	0.726646i
$503$	−14.4817			−0.645709			−0.322854	−	0.946449i	$-0.604642\pi$
$503$	−14.4817			−0.645709			−0.322854	+	0.946449i	$0.604642\pi$
$504$	22.4490	−	0.206717i	0.999958	−	0.00920790i
$505$	3.96247			0.176328
$506$	−3.11196	−	6.51524i	−0.138343	−	0.289638i
$507$	10.6462	+	3.54312i	0.472816	+	0.157355i
$508$	−3.49459	+	4.32506i	−0.155047	+	0.191894i
$509$	30.7536	−	17.7556i	1.36313	−	0.787002i	0.373088	−	0.927796i	$-0.378299\pi$
$509$	30.7536	−	17.7556i	1.36313	−	0.787002i	0.990039	+	0.140794i	$0.0449655\pi$
$510$	0.000394909		0.00315998i	1.74869e−5		0.000139926i
$511$	−8.57383	−	22.6308i	−0.379284	−	1.00113i
$512$	−14.6110	+	17.2777i	−0.645721	+	0.763574i
$513$	2.13820	−	4.53916i	0.0944039	−	0.200409i
$514$	31.7982	+	21.8288i	1.40256	+	0.962829i
$515$	1.72591	−	2.98937i	0.0760527	−	0.131727i
$516$	10.4945	+	16.3753i	0.461992	+	0.720884i
$517$	−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	$-0.920778\pi$
$521$	−6.19190	+	10.7247i	−0.271272	+	0.469857i	0.697916	+	0.716180i	$0.254111\pi$
$522$	11.8495	+	2.36439i	0.518641	+	0.103486i
$523$	−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
$525$	−4.57875	+	0.187252i	−0.199833	+	0.00817236i
$526$	23.5224	+	1.83839i	1.02562	+	0.0801575i
$527$	0.00267152	−	0.00154240i	0.000116373	−	6.71881e-5i
$528$	8.84539	+	6.49357i	0.384946	+	0.282597i
$529$	−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
$534$	−23.0743	−	30.4837i	−0.998521	−	1.31916i
$535$	2.30839	+	1.33275i	0.0998005	+	0.0576198i
$536$	−15.6646	+	16.5611i	−0.676609	+	0.715329i
$537$	22.8196	−	20.2547i	0.984738	−	0.874055i
$538$	−4.48884	−	0.350825i	−0.193528	−	0.0151251i
$539$	10.5138	+	3.51804i	0.452860	+	0.151533i
$540$	9.35329	−	4.52945i	0.402502	−	0.194917i
$541$	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
$543$	12.4001	+	4.12680i	0.532138	+	0.177098i
$544$	0.00728888		0.000979758i	0.000312508		4.20068e-5i
$545$	6.74713			0.289015
$546$	−14.0162	−	8.80155i	−0.599838	−	0.376672i
$547$		−	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
$549$	−3.05034	+	25.5226i	−0.130185	+	1.08928i
$550$	−1.84662	−	1.26767i	−0.0787400	−	0.0540535i
$551$	1.37507	+	2.38169i	0.0585798	+	0.101463i
$552$	−0.499975	+	15.7842i	−0.0212803	+	0.671819i
$553$	−6.09605	+	37.4294i	−0.259231	+	1.59166i
$554$	−34.2148	−	2.67406i	−1.45365	−	0.113610i
$555$	13.4273	−	11.9181i	0.569958	−	0.505896i
$556$	16.5570	−	20.4917i	0.702174	−	0.869042i
$557$	13.7778	−	23.8638i	0.583783	−	1.01114i	−0.411243	−	0.911526i	$-0.634905\pi$
$557$	13.7778	−	23.8638i	0.583783	−	1.01114i	0.995026	−	0.0996161i	$-0.0317615\pi$
$558$	−7.56462	−	6.64200i	−0.320236	−	0.281178i
$559$		−	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	$-0.0797120\pi$
$563$	29.3890	+	16.9677i	1.23860	+	0.715105i	0.269791	+	0.962919i	$0.413045\pi$
$564$	35.6412	+	18.4316i	1.50077	+	0.776111i
$565$	−2.54731	−	4.41208i	−0.107166	−	0.185617i
$566$	−0.937009	+	11.9891i	−0.0393854	+	0.503941i
$567$	−9.25855	+	21.9381i	−0.388822	+	0.921313i
$568$	−26.0067	−	6.19882i	−1.09122	−	0.260097i
$569$	−2.81569	+	1.62564i	−0.118040	+	0.0681503i	−0.557857	−	0.829937i	$-0.688376\pi$
$569$	−2.81569	+	1.62564i	−0.118040	+	0.0681503i	0.439818	+	0.898087i	$0.355043\pi$
$570$	2.17926	+	0.919503i	0.0912790	+	0.0385137i
$571$	−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
$576$	−10.6605	−	21.5024i	−0.444189	−	0.895933i
$577$	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
$579$	−4.92000	+	4.36700i	−0.204468	+	0.181486i
$580$	−0.884942	+	5.62688i	−0.0367452	+	0.233644i
$581$	−16.6480	+	20.3758i	−0.690674	+	0.845329i
$582$	−3.07662	−	24.6185i	−0.127530	−	1.02047i
$583$	7.26497	+	12.5833i	0.300884	+	0.521147i
$584$	−17.7781	+	18.7954i	−0.735661	+	0.777761i
$585$	−7.60729	−	0.909188i	−0.314523	−	0.0375903i
$586$	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	$-0.0559682\pi$
$588$	−16.8913	−	17.3978i	−0.696586	−	0.717474i
$589$		−	2.29120i		−	0.0944074i
$590$	−4.85744	+	2.32012i	−0.199978	+	0.0955180i
$591$	29.8148	+	9.92251i	1.22642	+	0.408157i
$592$	−27.8106	−	30.7521i	−1.14301	−	1.26390i
$593$	−9.31853	−	16.1402i	−0.382666	−	0.662797i	0.608776	−	0.793342i	$-0.291661\pi$
$593$	−9.31853	−	16.1402i	−0.382666	−	0.662797i	−0.991442	+	0.130545i	$0.958327\pi$
$594$	−10.0479	+	5.87343i	−0.412272	+	0.240990i
$595$	0.00217635	−	0.00266368i	8.92217e−5	−	0.000109200i
$596$	33.8579	+	5.32485i	1.38687	+	0.218114i
$597$	15.9024	+	17.9162i	0.650842	+	0.733259i
$598$	6.58903	−	9.59827i	0.269445	−	0.392502i
$599$	28.3537	+	16.3700i	1.15850	+	0.668861i	0.950944	−	0.309362i	$-0.100115\pi$
$599$	28.3537	+	16.3700i	1.15850	+	0.668861i	0.207557	+	0.978223i	$0.433449\pi$
$600$	2.31394	+	4.31806i	0.0944662	+	0.176284i
$601$		−	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
$606$	8.94259	+	3.77319i	0.363268	+	0.153275i
$607$	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
$609$	−6.98204	−	11.0266i	−0.282926	−	0.446822i
$610$	−12.0802	−	0.944130i	−0.489115	−	0.0382267i
$611$	−14.7905	−	25.6179i	−0.598361	−	1.03639i
$612$	−0.00211779	+	0.00750757i	−8.56068e−5	+	0.000303475i
$613$	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	$-0.942789\pi$
$617$		−	8.88102i		−	0.357536i	0.983891	−	0.178768i	$-0.0572112\pi$
$618$	6.74165	−	5.10300i	0.271189	−	0.205273i
$619$	−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
$621$	−15.1530	−	7.13793i	−0.608069	−	0.286435i
$622$	2.07970	−	26.6100i	0.0833883	−	1.06696i
$623$	−6.63820	+	40.7581i	−0.265954	+	1.63294i
$624$	−1.93639	+	17.5870i	−0.0775175	+	0.704044i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	12.8101	−	18.6606i	0.511996	−	0.745828i
$627$	−2.51343	−	0.836483i	−0.100377	−	0.0334059i
$628$	−16.4512	−	42.7181i	−0.656476	−	1.70464i
$629$			0.0134762i			0.000537331i
$630$	−10.5117	−	3.93744i	−0.418798	−	0.156871i
$631$	−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
$633$	5.03702	−	15.1350i	0.200203	−	0.601564i
$634$	−27.5767	−	18.9309i	−1.09521	−	0.751842i
$635$	2.40773	−	1.39011i	0.0955480	−	0.0551647i
$636$	−1.47186	−	31.7455i	−0.0583630	−	1.25879i
$637$	3.56376	+	17.5178i	0.141201	+	0.694082i
$638$	0.497048	−	6.35978i	0.0196783	−	0.251786i
$639$	16.9926	−	22.7018i	0.672217	−	0.898068i
$640$	9.92207	−	5.43622i	0.392204	−	0.214886i
$641$	−34.3763	−	19.8472i	−1.35778	−	0.783916i	−0.368458	−	0.929645i	$-0.620114\pi$
$641$	−34.3763	−	19.8472i	−1.35778	−	0.783916i	−0.989325	+	0.145729i	$0.953447\pi$
$642$	3.94055	+	5.20591i	0.155521	+	0.205461i
$643$	−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	$-0.771908\pi$
$647$	4.87813	−	8.44917i	0.191779	−	0.332171i	0.945840	+	0.324634i	$0.105241\pi$
$648$	25.4218	−	1.31567i	0.998663	−	0.0516844i
$649$	5.22100	−	3.01435i	0.204942	−	0.118323i
$650$	0.281408	−	3.60065i	0.0110377	−	0.141229i
$651$	0.444304	+	10.8643i	0.0174136	+	0.425804i
$652$	−3.41373	+	21.7061i	−0.133692	+	0.850078i
$653$	1.09745	+	1.90084i	0.0429465	+	0.0743855i	0.886700	−	0.462346i	$-0.152992\pi$
$653$	1.09745	+	1.90084i	0.0429465	+	0.0743855i	−0.843753	+	0.536731i	$0.819659\pi$
$654$	15.2271	+	6.42484i	0.595427	+	0.251231i
$655$	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	$-0.437572\pi$
$659$	10.0050			0.389739			0.194869	+	0.980829i	$0.437572\pi$
$660$	−2.96038	−	4.61931i	−0.115232	−	0.179806i
$661$	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
$663$	0.00430090	−	0.00381748i	0.000167033	−	0.000148259i
$664$	27.3623	+	6.52193i	1.06186	+	0.253100i
$665$	−0.905130	−	2.38910i	−0.0350994	−	0.0926455i
$666$	41.6519	−	14.1112i	1.61398	−	0.546796i
$667$	7.95074	−	4.59036i	0.307854	−	0.177740i
$668$	−28.0077	+	34.6637i	−1.08365	+	1.34118i
$669$	−9.33985	+	28.0640i	−0.361099	+	1.08502i
$670$	10.2849	−	4.91252i	0.397341	−	0.189787i
$671$	13.5703			0.523875
$672$	−8.86721	+	24.3592i	−0.342060	+	0.939678i
$673$	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
$675$	−5.17810	+	0.432715i	−0.199305	+	0.0166552i
$676$	−8.14261	+	10.0777i	−0.313177	+	0.387602i
$677$	−18.1134	+	10.4578i	−0.696154	+	0.401925i	−0.805913	−	0.592034i	$-0.798325\pi$
$677$	−18.1134	+	10.4578i	−0.696154	+	0.401925i	0.109759	+	0.993958i	$0.464992\pi$
$678$	−1.54752	−	12.3829i	−0.0594321	−	0.475563i
$679$	−16.9553	+	20.7519i	−0.650684	+	0.796385i
$680$	−0.00357701		0.000852598i	−0.000137172		3.26956e-5i
$681$	29.8689	+	33.6512i	1.14458	+	1.28952i
$682$	−3.00787	+	4.38157i	−0.115177	+	0.167779i
$683$	19.6451	−	34.0263i	0.751698	−	1.30198i	−0.195301	−	0.980743i	$-0.562568\pi$
$683$	19.6451	−	34.0263i	0.751698	−	1.30198i	0.946999	−	0.321236i	$-0.104098\pi$
$684$	4.04262	+	4.15031i	0.154573	+	0.158691i
$685$	−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
$690$	3.06956	−	7.27497i	0.116856	−	0.276953i
$691$	−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
$693$	12.0802	+	3.47897i	0.458889	+	0.132155i
$694$	−0.930554	+	11.9065i	−0.0353233	+	0.451966i
$695$	−11.4076	+	6.58618i	−0.432715	+	0.249828i
$696$	−7.35525	+	11.8562i	−0.278800	+	0.449409i
$697$	−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	$-0.424245\pi$
$701$	12.4837			0.471503			0.235752	+	0.971813i	$0.424245\pi$
$702$	−16.3025	−	9.29578i	−0.615300	−	0.350847i
$703$	8.66830	+	5.00464i	0.326931	+	0.188754i
$704$	−10.6039	+	6.93550i	−0.399648	+	0.261391i
$705$	−13.3180	−	15.0045i	−0.501586	−	0.565103i
$706$	−1.58503	+	20.2807i	−0.0596535	+	0.763273i
$707$	−3.71421	−	9.80371i	−0.139687	−	0.368707i
$708$	−13.1717	+	0.610697i	−0.495023	+	0.0229514i
$709$	−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
$711$	−5.10286	+	42.6963i	−0.191372	+	1.60123i
$712$	42.3079	−	12.6073i	1.58556	−	0.472477i
$713$	−7.64869			−0.286446
$714$	0.00744808	−	0.00393906i	0.000278737	−	0.000147416i
$715$			4.04477i			0.151266i
$716$	12.6619	+	32.8784i	0.473197	+	1.22873i
$717$	−4.12277	+	12.3880i	−0.153968	+	0.462637i
$718$	−6.90993	+	10.0657i	−0.257876	+	0.375649i
$719$	10.2291	+	17.7174i	0.381482	+	0.660746i	0.991274	−	0.131815i	$-0.0420806\pi$
$719$	10.2291	+	17.7174i	0.381482	+	0.660746i	−0.609793	+	0.792561i	$0.708747\pi$
$720$	1.11036	+	11.9485i	0.0413806	+	0.445295i
$721$	−9.01389	−	1.46808i	−0.335695	−	0.0546740i
$722$	1.99089	−	25.4737i	0.0740934	−	0.948033i
$723$	17.0368	+	19.1942i	0.633606	+	0.713841i
$724$	−9.48400	+	11.7378i	−0.352470	+	0.436233i
$725$	1.42401	−	2.46646i	0.0528864	−	0.0916020i
$726$	−12.5534	−	16.5845i	−0.465902	−	0.615509i
$727$			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
$732$	−26.3640	−	13.6339i	−0.974440	−	0.503925i
$733$	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
$735$	4.75516	+	11.1530i	0.175397	+	0.411383i
$736$	−16.8660	−	6.93247i	−0.621687	−	0.255534i
$737$	−11.0547	+	6.38243i	−0.407205	+	0.235100i
$738$	5.53669	+	1.10476i	0.203809	+	0.0406667i
$739$	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	$0.291658\pi$
$743$			43.2496i			1.58668i	−0.608782	+	0.793338i	$0.708342\pi$
$744$	10.2457	−	5.49042i	0.375626	−	0.201288i
$745$	−14.8411	−	8.56852i	−0.543737	−	0.313926i
$746$	15.4012	−	22.4350i	0.563879	−	0.821405i
$747$	−17.8784	+	23.8851i	−0.654135	+	0.873910i
$748$	0.00406822		0.000639811i	0.000148749		2.33938e-5i
$749$	1.13365	−	6.96054i	0.0414227	−	0.254333i
$750$	−0.303755	−	2.43058i	−0.0110916	−	0.0887523i
$751$	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
$753$	6.97790	−	20.9669i	0.254289	−	0.764078i
$754$	9.28159	−	4.43328i	0.338015	−	0.161451i
$755$			7.33270i			0.266864i
$756$	−19.9738	−	18.8957i	−0.726440	−	0.687230i
$757$			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
$759$	−2.79242	+	8.39055i	−0.101358	+	0.304558i
$760$	−1.87681	+	1.98421i	−0.0680790	+	0.0719750i
$761$	−18.1603	−	31.4546i	−0.658310	−	1.14023i	−0.981053	−	0.193740i	$-0.937938\pi$
$761$	−18.1603	−	31.4546i	−0.658310	−	1.14023i	0.322742	−	0.946487i	$-0.395395\pi$
$762$	6.75754	−	0.844503i	0.244800	−	0.0305931i
$763$	−6.32441	−	16.6934i	−0.228959	−	0.604341i
$764$	−4.64459	+	29.5325i	−0.168035	+	1.06845i
$765$	0.00233720	−	0.00312245i	8.45016e−5	−	0.000112892i
$766$	4.63797	+	3.18388i	0.167577	+	0.115038i
$767$	8.41853	+	4.86044i	0.303975	+	0.175500i
$768$	27.5689	−	2.82049i	0.994807	−	0.101776i
$769$			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	0.797055	−	0.603907i	$-0.206390\pi$
$773$	18.6998	+	10.7963i	0.672584	+	0.388316i	−0.124471	+	0.992223i	$0.539723\pi$
$774$	4.66116	−	23.3602i	0.167542	−	0.839666i
$775$	−2.05487	+	1.18638i	−0.0738130	+	0.0426160i
$776$	27.8674	+	6.64233i	1.00038	+	0.238446i
$777$	−42.0732	−	22.0497i	−1.50937	−	0.791029i
$778$	−3.33485	+	42.6698i	−0.119560	+	1.52979i
$779$	0.642499	+	1.11284i	0.0230199	+	0.0398717i
$780$	4.06374	−	7.85807i	0.145505	−	0.281364i
$781$	−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
$786$	2.25451	−	1.70652i	0.0804156	−	0.0608696i
$787$	−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
$789$	−19.1824	−	21.6115i	−0.682911	−	0.769390i
$790$	−20.2088	−	1.57942i	−0.718998	−	0.0561932i
$791$	−8.52839	+	10.4381i	−0.303235	+	0.371135i
$792$	−2.28239	−	13.2439i	−0.0811013	−	0.470603i
$793$	10.9406	+	18.9497i	0.388512	+	0.672923i
$794$	21.8323	+	14.9874i	0.774798	+	0.531884i
$795$	−5.01762	+	15.0768i	−0.177957	+	0.534718i
$796$	−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	$-0.113024\pi$
$798$	0.232263	−	6.25368i	0.00822202	−	0.221378i
$799$	0.0150591			0.000532753
$800$	−5.60643	+	0.753606i	−0.198217	+	0.0266440i
$801$	−5.55668	+	46.4934i	−0.196336	+	1.64277i
$802$	21.3029	−	31.0321i	0.752233	−	1.09578i
$803$	−12.5462	+	7.24353i	−0.442745	+	0.255619i
$804$	27.8891	−	1.29306i	0.983573	−	0.0456027i
$805$	−7.97551	+	3.02158i	−0.281100	+	0.106497i
$806$	−8.54347	−	0.667713i	−0.300931	−	0.0235192i
$807$	3.66063	+	4.12419i	0.128860	+	0.145178i
$808$	−7.70150	+	8.14224i	−0.270938	+	0.286443i
$809$	−48.0084	−	27.7176i	−1.68788	−	0.974500i	−0.956135	−	0.292926i	$-0.905371\pi$
$809$	−48.0084	−	27.7176i	−1.68788	−	0.974500i	−0.731749	−	0.681574i	$-0.761296\pi$
$810$	−12.0981	−	3.95419i	−0.425084	−	0.138936i
$811$	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
$816$	−0.00726081	−	0.00533031i	−0.000254179	−	0.000186598i
$817$	4.69526	−	2.71081i	0.164266	−	0.0948393i
$818$	−39.9756	−	3.12429i	−1.39771	−	0.109238i
$819$	4.88121	+	19.6737i	0.170563	+	0.687456i
$820$	−0.413488	+	2.62916i	−0.0144396	+	0.0918141i
$821$	−23.7175	−	41.0799i	−0.827746	−	1.43370i	−0.899802	−	0.436298i	$-0.856289\pi$
$821$	−23.7175	−	41.0799i	−0.827746	−	1.43370i	0.0720557	−	0.997401i	$-0.477044\pi$
$822$	−19.2756	−	8.13304i	−0.672314	−	0.283672i
$823$	−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	$-0.624209\pi$
$827$	−21.8780			−0.760771			−0.380386	+	0.924828i	$0.624209\pi$
$828$	13.8549	−	13.4954i	0.481492	−	0.468998i
$829$	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
$831$	27.9021	+	31.4354i	0.967912	+	1.09048i
$832$	−18.2338	−	9.21582i	−0.632144	−	0.319501i
$833$	−0.00863031	−	0.00288781i	−0.000299023	−	0.000100057i
$834$	−32.0165	+	4.00117i	−1.10864	+	0.138549i
$835$	19.2970	−	11.1412i	0.667802	−	0.385555i
$836$	1.92236	−	2.37920i	0.0664862	−	0.0822863i
$837$	1.02673	+	12.2864i	0.0354889	+	0.424679i
$838$	18.0995	+	37.8933i	0.625236	+	1.30900i
$839$	0.0334897			0.00115619			0.000578097	−	1.00000i	$-0.499816\pi$
$839$	0.0334897			0.00115619			0.000578097		1.00000i	$0.499816\pi$
$840$	8.51454	−	9.77254i	0.293780	−	0.337185i
$841$	−20.8888			−0.720302
$842$	8.50993	+	17.8165i	0.293272	+	0.613997i
$843$	−4.43927	+	13.3390i	−0.152897	+	0.459418i
$844$	14.3267	+	11.5758i	0.493147	+	0.398455i
$845$	5.61017	−	3.23903i	0.192996	−	0.111426i
$846$	−15.7687	−	46.5444i	−0.542138	−	1.60023i
$847$	−3.61148	+	22.1743i	−0.124092	+	0.761917i
$848$	34.9245	+	11.2638i	1.19931	+	0.386799i
$849$	11.0152	−	9.77709i	0.378040	−	0.335549i
$850$	0.00151581	+	0.00104058i	5.19919e−5	+	3.56914e-5i
$851$	16.7069	−	28.9372i	0.572706	−	0.991956i
$852$	17.6677	+	27.5683i	0.605285	+	0.944474i
$853$	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	$-0.905978\pi$
$857$	−6.62323	+	11.4718i	−0.226245	+	0.391868i	0.730447	+	0.682969i	$0.239312\pi$
$858$	−3.85156	+	9.12834i	−0.131490	+	0.311636i
$859$	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
$861$	−3.26235	−	5.15219i	−0.111181	−	0.175586i
$862$	35.8516	+	2.80198i	1.22111	+	0.0954358i
$863$	−9.15443	+	5.28531i	−0.311620	+	0.179914i	−0.647651	−	0.761937i	$-0.724249\pi$
$863$	−9.15443	+	5.28531i	−0.311620	+	0.179914i	0.336031	+	0.941851i	$0.390915\pi$
$864$	−8.87188	+	28.0230i	−0.301827	+	0.953363i
$865$	−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
$870$	5.56238	−	4.21038i	0.188582	−	0.142745i
$871$	−17.8250	−	10.2913i	−0.603977	−	0.348706i
$872$	−13.1138	+	13.8643i	−0.444090	+	0.469504i
$873$	−18.2084	+	24.3260i	−0.616261	+	0.823311i
$874$	4.38871	+	0.342999i	0.148450	+	0.0116021i
$875$	−1.67400	+	2.04884i	−0.0565914	+	0.0692634i
$876$	31.6518	−	1.46752i	1.06942	−	0.0495828i
$877$	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
$879$	5.35544	−	16.0918i	0.180634	−	0.542763i
$880$	6.19396	−	1.33065i	0.208798	−	0.0448561i
$881$	3.56867			0.120232			0.0601158	−	0.998191i	$-0.480853\pi$
$881$	3.56867			0.120232			0.0601158	+	0.998191i	$0.480853\pi$
$882$	0.111370	+	29.6983i	0.00375002	+	0.999993i
$883$			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
$885$	6.25559	+	2.08189i	0.210279	+	0.0699820i
$886$	−17.1532	−	11.7753i	−0.576273	−	0.395600i
$887$	−18.8419	−	32.6351i	−0.632649	−	1.09578i	−0.987008	−	0.160671i	$-0.948634\pi$
$887$	−18.8419	−	32.6351i	−0.632649	−	1.09578i	0.354359	−	0.935109i	$-0.384699\pi$
$888$	−1.60771	+	50.7552i	−0.0539512	+	1.70323i
$889$	−5.69620	−	4.65407i	−0.191045	−	0.156092i
$890$	−22.0061	−	1.71988i	−0.737646	−	0.0576506i
$891$	13.8529	+	3.35925i	0.464090	+	0.112539i
$892$	−26.5652	−	21.4643i	−0.889470	−	0.718679i
$893$	5.59250	−	9.68649i	0.187146	−	0.324146i
$894$	−25.3346	−	33.4698i	−0.847315	−	1.11940i
$895$		−	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
$900$	1.62896	−	5.77464i	0.0542986	−	0.192488i
$901$	−0.00596351	−	0.0103291i	−0.000198673	−	0.000344112i
$902$	0.232245	−	2.97160i	0.00773292	−	0.0989435i
$903$	−21.7380	+	13.7644i	−0.723394	+	0.458051i
$904$	14.0171	+	3.34105i	0.466202	+	0.111122i
$905$	6.53437	−	3.77262i	0.217210	−	0.125406i
$906$	−6.98244	+	16.5486i	−0.231976	+	0.549791i
$907$	−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	$0.0489057\pi$
$911$			9.23822i			0.306076i	−0.988220	+	0.153038i	$0.951094\pi$
$912$	−6.12506	+	2.69086i	−0.202821	+	0.0891034i
$913$	13.6409	+	7.87557i	0.451448	+	0.260643i
$914$	20.7926	+	14.2737i	0.687757	+	0.472132i
$915$	9.85140	+	11.0989i	0.325677	+	0.366918i
$916$	−42.7524	−	6.72369i	−1.41258	−	0.222157i
$917$	−3.01438	−	0.490947i	−0.0995436	−	0.0162125i
$918$	0.00824794	−	0.00482126i	0.000272222	−	0.000159125i
$919$	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
$921$	−32.9230	−	10.9569i	−1.08485	−	0.361044i
$922$	14.7541	+	30.8893i	0.485899	+	1.01729i
$923$		−	24.1394i		−	0.794559i
$924$	−8.65393	+	11.6543i	−0.284693	+	0.383398i
$925$		−	10.3656i		−	0.340818i
$926$	42.0908	−	20.1044i	1.38319	−	0.660670i
$927$	−10.2823	−	1.22889i	−0.337715	−	0.0403621i
$928$	−9.84236	−	12.7549i	−0.323091	−	0.418700i
$929$	−3.95711	−	6.85391i	−0.129828	−	0.224870i	0.793782	−	0.608203i	$-0.208109\pi$
$929$	−3.95711	−	6.85391i	−0.129828	−	0.224870i	−0.923610	+	0.383333i	$0.874776\pi$
$930$	−5.76718	+	0.720737i	−0.189113	+	0.0236339i
$931$	−5.06256	+	4.47884i	−0.165919	+	0.146788i
$932$	−5.21023	+	33.1291i	−0.170667	+	1.08518i
$933$	−24.4483	+	21.7003i	−0.800401	+	0.710437i
$934$	15.4540	−	22.5120i	0.505671	−	0.736614i
$935$	−0.00178324	−	0.00102956i	−5.83183e−5	−	3.36701e-5i
$936$	16.6539	−	13.8646i	0.544348	−	0.453180i
$937$			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	0.840406	−	0.541958i	$-0.182317\pi$
$941$	24.2724	+	14.0137i	0.791259	+	0.456834i	−0.0491464	+	0.998792i	$0.515650\pi$
$942$	−21.7949	+	51.6546i	−0.710115	+	1.68300i
$943$	3.71498	−	2.14484i	0.120976	−	0.0698457i
$944$	4.67351	−	14.4907i	0.152110	−	0.471632i
$945$	5.92428	+	12.4058i	0.192717	+	0.403559i
$946$	−12.5377	−	0.979881i	−0.407635	−	0.0318587i
$947$	−1.51976	−	2.63230i	−0.0493855	−	0.0855381i	0.840276	−	0.542159i	$-0.182393\pi$
$947$	−1.51976	−	2.63230i	−0.0493855	−	0.0855381i	−0.889661	+	0.456621i	$0.849060\pi$
$948$	−44.1038	−	22.8080i	−1.43242	−	0.740768i
$949$	−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	$0.987301\pi$
$954$	−25.6805	+	29.2477i	−0.831436	+	0.946928i
$955$	7.47388	−	12.9451i	0.241849	−	0.418895i
$956$	−11.7264	−	9.47473i	−0.379258	−	0.306435i
$957$	−5.84314	+	5.18638i	−0.188882	+	0.167652i
$958$	0.122644	−	1.56925i	0.00396246	−	0.0507001i
$959$	8.00591	+	21.1317i	0.258524	+	0.682379i
$960$	−13.3703	−	3.63787i	−0.431526	−	0.117412i
$961$	−12.6850	−	21.9711i	−0.409194	−	0.708745i
$962$	21.1875	−	30.8640i	0.683114	−	0.995095i
$963$	0.948952	−	7.94000i	0.0305796	−	0.255863i
$964$	−27.6550	+	10.6503i	−0.890708	+	0.343022i
$965$			3.79812i			0.122266i
$966$	−20.8766	−	0.775360i	−0.671692	−	0.0249468i
$967$	−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
$969$	0.00206317		0.000686634i	6.62786e−5		2.20579e-5i
$970$	−11.8092	−	8.10681i	−0.379171	−	0.260294i
$971$	12.1432	−	7.01086i	0.389693	−	0.224989i	−0.292334	−	0.956316i	$-0.594432\pi$
$971$	12.1432	−	7.01086i	0.389693	−	0.224989i	0.682027	+	0.731327i	$0.261099\pi$
$972$	−23.5380	−	20.4441i	−0.754982	−	0.655746i
$973$	26.9880	+	22.0505i	0.865197	+	0.706906i
$974$	−1.85130	+	23.6876i	−0.0593195	+	0.758999i
$975$	−3.30815	+	2.93632i	−0.105946	+	0.0940374i
$976$	25.4194	−	22.9880i	0.813654	−	0.735827i
$977$	−21.0989	−	12.1814i	−0.675013	−	0.389719i	0.122961	−	0.992412i	$-0.460761\pi$
$977$	−21.0989	−	12.1814i	−0.675013	−	0.389719i	−0.797973	+	0.602693i	$0.794094\pi$
$978$	21.4573	−	16.2419i	0.686130	−	0.519358i
$979$	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	$-0.774700\pi$
$983$	5.74265	−	9.94656i	0.183162	−	0.317246i	0.942956	+	0.332918i	$0.108033\pi$
$984$	−3.43674	+	5.53981i	−0.109559	+	0.176603i
$985$	15.7113	−	9.07091i	0.500603	−	0.289023i
$986$	−0.000408006		0.00522048i	−1.29935e−5		0.000166254i
$987$	−24.6397	+	47.0151i	−0.784290	+	1.49651i
$988$	4.87218	+	0.766249i	0.155005	+	0.0243776i
$989$	−9.04946	−	15.6741i	−0.287756	−	0.498408i
$990$	−1.31487	+	6.58968i	−0.0417892	+	0.209434i
$991$	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
$996$	−18.5886	−	29.0053i	−0.589003	−	0.919068i
$997$	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
$999$	−48.7257	−	22.9526i	−1.54161	−	0.726187i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(-1.64343 - 0.546941i) q^{3} +(1.25695 - 1.55566i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-2.43058 + 0.303755i) q^{6} +(2.04884 + 1.67400i) q^{7} +(0.655798 - 2.75135i) q^{8} +(2.40171 + 1.79772i) q^{9} +(-0.800386 + 1.16593i) q^{10} +(0.791910 - 1.37163i) q^{11} +(-2.91656 + 1.86914i) 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} +(4.16062 + 0.830186i) q^{18} +(0.482815 + 0.836259i) q^{19} +(-0.310721 + 1.97572i) q^{20} +(-2.45154 - 3.87169i) q^{21} +(0.174524 - 2.23305i) q^{22} +(2.79167 - 1.61177i) q^{23} +(-2.58258 + 4.16296i) 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} +(1.95307 - 1.47835i) q^{30} +(-2.05487 - 1.18638i) q^{31} +(-3.45586 - 4.47851i) q^{32} +(-2.05165 + 1.82104i) q^{33} +(-0.000143259 + 0.00183302i) q^{34} +(-2.61134 - 0.425305i) q^{35} +(5.81547 - 1.47660i) q^{36} +(8.97684 - 5.18278i) q^{37} +(1.12585 + 0.772876i) q^{38} +(-4.19700 - 1.39678i) q^{39} +(0.807738 + 2.71064i) q^{40} +1.33074 q^{41} +(-5.48835 - 3.44644i) q^{42} -5.61460i q^{43} +(-1.13839 - 2.95601i) q^{44} +(-2.97880 - 0.356013i) q^{45} +(2.58008 - 3.75841i) q^{46} +(-5.79156 - 10.0313i) q^{47} +(-0.758235 + 6.88659i) q^{48} +(1.39547 + 6.85949i) q^{49} +(0.110192 - 1.40991i) q^{50} +(0.00168411 - 0.00149482i) q^{51} +(3.21001 - 3.97285i) q^{52} +(-4.58699 + 7.94490i) q^{53} +(-6.38362 - 3.63997i) 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} +(1.59125 - 3.07700i) q^{60} +(4.28404 + 7.42017i) q^{61} +(-3.34538 - 0.261458i) q^{62} +(1.91134 + 7.70369i) q^{63} +(-7.13986 - 3.60866i) q^{64} +(-2.21166 + 1.27690i) q^{65} +(-1.50816 + 3.57440i) 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} +(6.52119 - 5.42901i) q^{72} +(-7.92146 - 4.57346i) q^{73} +(8.29645 - 12.0855i) q^{74} +(-1.29538 + 1.14978i) q^{75} +(1.90781 + 0.300042i) q^{76} +(3.91860 - 1.48459i) q^{77} +(-6.20724 + 0.775732i) q^{78} +(7.16669 + 12.4131i) q^{79} +(2.68298 + 2.96675i) q^{80} +(2.53643 + 8.63519i) q^{81} +(1.69818 - 0.811122i) q^{82} +9.94503i q^{83} +(-9.10449 - 1.05276i) q^{84} -0.00130009i q^{85} +(-3.42226 - 7.16489i) q^{86} +(-4.68052 - 1.55770i) q^{87} +(-3.25450 - 3.07833i) q^{88} +(7.80405 + 13.5170i) q^{89} +(-4.01830 + 1.36135i) q^{90} +(5.23234 + 4.27507i) q^{91} +(1.00162 - 6.36881i) q^{92} +(2.72815 + 3.07362i) q^{93} +(-13.5050 - 9.27096i) q^{94} +(-0.836259 - 0.482815i) q^{95} +(3.22997 + 9.25026i) 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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