LMFDB - Embedded newform 840.2.cf.a.101.105

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			101.105
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.105

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16593 - 0.800386i) q^{2} +(1.64343 + 0.546941i) q^{3} +(0.718765 - 1.86638i) 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} +(2.40171 + 1.79772i) q^{9} +(0.609528 - 1.27612i) q^{10} +(-0.791910 + 1.37163i) q^{11} +(2.20204 - 2.67414i) q^{12} -2.55381 q^{13} +(3.72864 + 0.311895i) q^{14} +(1.69672 - 0.348049i) q^{15} +(-2.96675 - 2.68298i) q^{16} +(-0.000650046 + 0.00112591i) q^{17} +(4.23908 + 0.173708i) 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} +(0.427070 - 4.88033i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.97755 + 2.04403i) q^{26} +(2.96379 + 4.26801i) q^{27} +(4.59695 - 2.62070i) q^{28} -2.84802 q^{29} +(1.69968 - 1.76383i) q^{30} +(-2.05487 - 1.18638i) q^{31} +(-5.60643 - 0.753606i) q^{32} +(-2.05165 + 1.82104i) 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} +(-1.23226 - 0.588578i) q^{38} +(-4.19700 - 1.39678i) q^{39} +(-1.94361 - 2.05484i) q^{40} +1.33074 q^{41} +(5.95716 + 2.55192i) q^{42} +5.61460i q^{43} +(1.99078 + 2.46388i) q^{44} +(2.97880 + 0.356013i) q^{45} +(1.96484 - 4.11362i) 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} +(-0.00168411 + 0.00149482i) q^{51} +(-1.83559 + 4.76638i) q^{52} +(4.58699 - 7.94490i) q^{53} +(6.87162 + 2.60401i) q^{54} +1.58382i q^{55} +(3.26213 - 6.73487i) q^{56} +(-0.336086 - 1.63840i) q^{57} +(-3.32058 + 2.27952i) q^{58} +(-3.29646 - 1.90321i) q^{59} +(0.569952 - 3.41689i) 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} +(-0.934530 + 3.76531i) q^{66} +(6.97977 + 4.02977i) q^{67} +(0.00163415 + 0.00202250i) q^{68} +(5.46946 - 1.12195i) q^{69} +(3.38504 - 1.59421i) q^{70} -9.45233i q^{71} +(3.37111 - 7.78689i) q^{72} +(-7.92146 - 4.57346i) q^{73} +(-6.31810 + 13.2277i) q^{74} +(1.29538 - 1.14978i) 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} +(-3.91077 - 0.840151i) q^{80} +(2.53643 + 8.63519i) q^{81} +(1.55154 - 1.06510i) q^{82} -9.94503i q^{83} +(8.98812 - 1.79267i) q^{84} +0.00130009i q^{85} +(4.49385 + 6.54621i) q^{86} +(-4.68052 - 1.55770i) q^{87} +(4.29316 + 1.27931i) 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} +(-2.72815 - 3.07362i) q^{93} +(-14.7814 - 7.06024i) q^{94} +(-0.836259 - 0.482815i) q^{95} +(-8.80159 - 4.30489i) q^{96} +10.1286i q^{97} +(7.11726 + 6.88075i) 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 $

$2$	1.16593	−	0.800386i	0.824434	−	0.565958i
$2$	1.16593	−	0.800386i	0.824434	−	0.565958i
$3$	1.64343	+	0.546941i	0.948834	+	0.315777i
$3$	1.64343	+	0.546941i	0.948834	+	0.315777i
$4$	0.718765	−	1.86638i	0.359383	−	0.933190i
$5$	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
$9$	2.40171	+	1.79772i	0.800570	+	0.599239i
$10$	0.609528	−	1.27612i	0.192750	−	0.403544i
$11$	−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	$0.243411\pi$
$12$	2.20204	−	2.67414i	0.635674	−	0.771958i
$13$	−2.55381			−0.708299			−0.354149	−	0.935189i	$-0.615230\pi$
$13$	−2.55381			−0.708299			−0.354149	+	0.935189i	$0.615230\pi$
$14$	3.72864	+	0.311895i	0.996520	+	0.0833575i
$15$	1.69672	−	0.348049i	0.438091	−	0.0898659i
$16$	−2.96675	−	2.68298i	−0.741688	−	0.670745i
$17$	−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	$0.166717\pi$
$18$	4.23908	+	0.173708i	0.999161	+	0.0409434i
$19$	−0.482815	−	0.836259i	−0.110765	−	0.191851i	0.805314	−	0.592849i	$-0.201997\pi$
$19$	−0.482815	−	0.836259i	−0.110765	−	0.191851i	−0.916079	+	0.400998i	$0.868664\pi$
$20$	−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	$0.224233\pi$
$24$	0.427070	−	4.88033i	0.0871753	−	0.996193i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.97755	+	2.04403i	−0.583946	+	0.400868i
$27$	2.96379	+	4.26801i	0.570382	+	0.821379i
$28$	4.59695	−	2.62070i	0.868741	−	0.495266i
$29$	−2.84802			−0.528864			−0.264432	−	0.964404i	$-0.585185\pi$
$29$	−2.84802			−0.528864			−0.264432	+	0.964404i	$0.585185\pi$
$30$	1.69968	−	1.76383i	0.310317	−	0.322030i
$31$	−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	$0.735016\pi$
$32$	−5.60643	−	0.753606i	−0.991086	−	0.133220i
$33$	−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
$36$	5.08149	−	3.19037i	0.846915	−	0.531728i
$37$	−8.97684	+	5.18278i	−1.47578	+	0.852044i	−0.999627	−	0.0273169i	$-0.991304\pi$
$37$	−8.97684	+	5.18278i	−1.47578	+	0.852044i	−0.476156	+	0.879361i	$0.657970\pi$
$38$	−1.23226	−	0.588578i	−0.199898	−	0.0954800i
$39$	−4.19700	−	1.39678i	−0.672058	−	0.223664i
$40$	−1.94361	−	2.05484i	−0.307312	−	0.324899i
$41$	1.33074			0.207826			0.103913	−	0.994586i	$-0.466864\pi$
$41$	1.33074			0.207826			0.103913	+	0.994586i	$0.466864\pi$
$42$	5.95716	+	2.55192i	0.919209	+	0.393770i
$43$			5.61460i			0.856219i	0.903727	+	0.428109i	$0.140820\pi$
$43$			5.61460i			0.856219i	−0.903727	+	0.428109i	$0.859180\pi$
$44$	1.99078	+	2.46388i	0.300122	+	0.371445i
$45$	2.97880	+	0.356013i	0.444053	+	0.0530712i
$46$	1.96484	−	4.11362i	0.289700	−	0.606520i
$47$	−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	$-0.486939\pi$
$48$	−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
$51$	−0.00168411	+	0.00149482i	−0.000235823	+	0.000209317i
$52$	−1.83559	+	4.76638i	−0.254550	+	0.660978i
$53$	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	$-0.0503077\pi$
$54$	6.87162	+	2.60401i	0.935109	+	0.354360i
$55$			1.58382i			0.213562i
$56$	3.26213	−	6.73487i	0.435920	−	0.899985i
$57$	−0.336086	−	1.63840i	−0.0445157	−	0.217012i
$58$	−3.32058	+	2.27952i	−0.436014	+	0.299315i
$59$	−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	$0.746367\pi$
$60$	0.569952	−	3.41689i	0.0735804	−	0.441119i
$61$	−4.28404	−	7.42017i	−0.548515	−	0.950055i	−0.998377	−	0.0569573i	$-0.981860\pi$
$61$	−4.28404	−	7.42017i	−0.548515	−	0.950055i	0.449862	−	0.893098i	$-0.351473\pi$
$62$	−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
$66$	−0.934530	+	3.76531i	−0.115033	+	0.463478i
$67$	6.97977	+	4.02977i	0.852714	+	0.492315i	0.861566	−	0.507646i	$-0.169484\pi$
$67$	6.97977	+	4.02977i	0.852714	+	0.492315i	−0.00885142	+	0.999961i	$0.502818\pi$
$68$	0.00163415	+	0.00202250i	0.000198170	+	0.000245264i
$69$	5.46946	−	1.12195i	0.658445	−	0.135067i
$70$	3.38504	−	1.59421i	0.404590	−	0.190544i
$71$		−	9.45233i		−	1.12178i	−0.827889	−	0.560892i	$-0.810458\pi$
$71$		−	9.45233i		−	1.12178i	0.827889	−	0.560892i	$-0.189542\pi$
$72$	3.37111	−	7.78689i	0.397289	−	0.917693i
$73$	−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	$0.846462\pi$
$74$	−6.31810	+	13.2277i	−0.734464	+	1.53769i
$75$	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
$78$	−6.01135	+	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	$0.534792\pi$
$80$	−3.91077	−	0.840151i	−0.437238	−	0.0939317i
$81$	2.53643	+	8.63519i	0.281826	+	0.959466i
$82$	1.55154	−	1.06510i	0.171339	−	0.117621i
$83$		−	9.94503i		−	1.09161i	−0.837912	−	0.545805i	$-0.816224\pi$
$83$		−	9.94503i		−	1.09161i	0.837912	−	0.545805i	$-0.183776\pi$
$84$	8.98812	−	1.79267i	0.980684	−	0.195597i
$85$			0.00130009i			0.000141015i
$86$	4.49385	+	6.54621i	0.484584	+	0.705896i
$87$	−4.68052	−	1.55770i	−0.501804	−	0.167003i
$88$	4.29316	+	1.27931i	0.457653	+	0.136375i
$89$	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	$0.523250\pi$
$90$	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
$93$	−2.72815	−	3.07362i	−0.282896	−	0.318719i
$94$	−14.7814	−	7.06024i	−1.52459	−	0.728208i
$95$	−0.836259	−	0.482815i	−0.0857984	−	0.0495357i
$96$	−8.80159	−	4.30489i	−0.898308	−	0.439365i
$97$			10.1286i			1.02841i	0.857669	+	0.514203i	$0.171912\pi$
$97$			10.1286i			1.02841i	−0.857669	+	0.514203i	$0.828088\pi$
$98$	7.11726	+	6.88075i	0.718951	+	0.695060i
$99$	−4.36774	+	1.87063i	−0.438974	+	0.188005i
$100$	−1.25695	−	1.55566i	−0.125695	−	0.155566i
$101$	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	$0.603501\pi$
$102$	−0.000767117		0.00309079i	−7.59559e−5		0.000306034i
$103$	−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	0.923228	−	0.384252i	$-0.125541\pi$
$107$	1.33275	+	2.30839i	0.128842	+	0.223161i	−0.794386	+	0.607413i	$0.792207\pi$
$108$	10.0960	−	2.46387i	0.971489	−	0.237086i
$109$	5.84319	+	3.37357i	0.559676	+	0.323129i	0.753015	−	0.658003i	$-0.228599\pi$
$109$	5.84319	+	3.37357i	0.559676	+	0.323129i	−0.193339	+	0.981132i	$0.561932\pi$
$110$	1.26767	+	1.84662i	0.120867	+	0.176068i
$111$	−17.5875	+	3.60772i	−1.66933	+	0.342430i
$112$	−1.58710	−	10.4633i	−0.149967	−	0.988691i
$113$			5.09463i			0.479262i	0.970864	+	0.239631i	$0.0770265\pi$
$113$			5.09463i			0.479262i	−0.970864	+	0.239631i	$0.922974\pi$
$114$	−1.70321	−	1.64126i	−0.159520	−	0.153718i
$115$	1.61177	−	2.79167i	0.150299	−	0.260325i
$116$	−2.04706	+	5.31549i	−0.190065	+	0.493531i
$117$	−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
$120$	−2.07031	−	4.44002i	−0.188993	−	0.405317i
$121$	4.24576	+	7.35387i	0.385978	+	0.668533i
$122$	−10.9339	−	5.22248i	−0.989906	−	0.472821i
$123$	2.18697	+	0.727834i	0.197192	+	0.0656266i
$124$	−3.69120	+	2.98244i	−0.331480	+	0.267831i
$125$		−	1.00000i		−	0.0894427i
$126$	8.39441	+	7.45211i	0.747833	+	0.663887i
$127$	−2.78021			−0.246704			−0.123352	−	0.992363i	$-0.539364\pi$
$127$	−2.78021			−0.246704			−0.123352	+	0.992363i	$0.539364\pi$
$128$	−5.43622	+	9.92207i	−0.480499	+	0.876995i
$129$	−3.07086	+	9.22719i	−0.270374	+	0.812409i
$130$	−1.55662	+	3.25896i	−0.136524	+	0.285830i
$131$	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
$135$	4.70073	+	2.21431i	0.404574	+	0.190577i
$136$	0.00352408	+	0.00105013i	0.000302187	+	9.00482e-5i
$137$	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	$0.547785\pi$
$138$	5.47898	−	5.68579i	0.466402	−	0.484006i
$139$	−13.1724			−1.11727			−0.558633	−	0.829415i	$-0.688674\pi$
$139$	−13.1724			−1.11727			−0.558633	+	0.829415i	$0.688674\pi$
$140$	2.67072	−	4.56807i	0.225717	−	0.386072i
$141$	−4.03149	−	19.6533i	−0.339513	−	1.65511i
$142$	−7.56551	−	11.0207i	−0.634883	−	0.924837i
$143$	2.02239	−	3.50288i	0.169120	−	0.292925i
$144$	−2.30205	−	11.7771i	−0.191837	−	0.981427i
$145$	−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	$-0.918975\pi$
$149$	−8.56852	−	14.8411i	−0.701961	−	1.21583i	0.265816	−	0.964024i	$-0.414359\pi$
$150$	0.590048	−	2.37736i	0.0481772	−	0.194111i
$151$	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	$0.0702259\pi$
$152$	−1.98421	+	1.87681i	−0.160941	+	0.152229i
$153$	−0.00358530	+	0.00153552i	−0.000289854	+	0.000124139i
$154$	−3.38055	+	4.86731i	−0.272412	+	0.392219i
$155$	−2.37276			−0.190584
$156$	−5.62358	+	6.82924i	−0.450247	+	0.546777i
$157$	−11.4441	+	19.8218i	−0.913338	+	1.58195i	−0.104022	+	0.994575i	$0.533171\pi$
$157$	−11.4441	+	19.8218i	−0.913338	+	1.58195i	−0.809316	+	0.587374i	$0.800162\pi$
$158$	18.2911	+	8.73660i	1.45516	+	0.695046i
$159$	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
$162$	9.86877	+	8.03787i	0.775364	+	0.631514i
$163$	9.51457	−	5.49324i	0.745238	−	0.430264i	−0.0787325	−	0.996896i	$-0.525087\pi$
$163$	9.51457	−	5.49324i	0.745238	−	0.430264i	0.823971	+	0.566632i	$0.191754\pi$
$164$	0.956487	−	2.48366i	0.0746891	−	0.193941i
$165$	−0.866256	+	2.60289i	−0.0674380	+	0.202635i
$166$	−7.95986	−	11.5952i	−0.617805	−	0.899960i
$167$	−22.2823			−1.72426			−0.862128	−	0.506690i	$-0.830869\pi$
$167$	−22.2823			−1.72426			−0.862128	+	0.506690i	$0.830869\pi$
$168$	9.04465	−	9.28409i	0.697810	−	0.716283i
$169$	−6.47806			−0.498313
$170$	0.00104058	+	0.00151581i	7.98085e−5	+	0.000116257i
$171$	0.343776	−	2.87642i	0.0262892	−	0.219965i
$172$	10.4790	+	4.03558i	0.799015	+	0.307710i
$173$	−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
$177$	−4.37655	−	4.93076i	−0.328962	−	0.370619i
$178$	19.9178	+	9.51358i	1.49290	+	0.713073i
$179$	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	$-0.0620772\pi$
$180$	2.80551	−	5.30369i	0.209111	−	0.395313i
$181$	7.54524			0.560833			0.280417	−	0.959878i	$-0.409527\pi$
$181$	7.54524			0.560833			0.280417	+	0.959878i	$0.409527\pi$
$182$	−9.52222	−	0.796520i	−0.705834	−	0.0590420i
$183$	−2.98211	−	14.5376i	−0.220444	−	1.07465i
$184$	−6.26532	−	6.62387i	−0.461886	−	0.488318i
$185$	−5.18278	+	8.97684i	−0.381046	+	0.659990i
$186$	−5.64090	−	1.40004i	−0.413611	−	0.102656i
$187$	−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	$0.515208\pi$
$192$	−13.7076	+	2.02549i	−0.989258	+	0.146177i
$193$	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	$0.123018\pi$
$194$	8.10681	+	11.8092i	0.582035	+	0.847853i
$195$	−4.33310	+	0.888851i	−0.310300	+	0.0636519i
$196$	13.8054	+	2.32589i	0.986103	+	0.166135i
$197$	18.1418			1.29255			0.646276	−	0.763104i	$-0.276326\pi$
$197$	18.1418			1.29255			0.646276	+	0.763104i	$0.276326\pi$
$198$	−3.59524	+	5.67689i	−0.255502	+	0.403439i
$199$	−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	$0.829750\pi$
$200$	−2.71064	−	0.807738i	−0.191671	−	0.0571157i
$201$	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
$204$	0.00157942	+	0.00421762i	0.000110582	+	0.000295292i
$205$	1.15245	−	0.665368i	0.0804907	−	0.0464713i
$206$	−2.10398	+	4.40493i	−0.146591	+	0.306906i
$207$	9.60230	+	1.14762i	0.667406	+	0.0797653i
$208$	7.57652	+	6.85181i	0.525337	+	0.475088i
$209$	1.52938			0.105790
$210$	6.43501	−	0.768549i	0.444058	−	0.0530349i
$211$		−	9.20943i		−	0.634003i	−0.948425	−	0.317002i	$-0.897324\pi$
$211$		−	9.20943i		−	0.634003i	0.948425	−	0.317002i	$-0.102676\pi$
$212$	−11.5312	−	14.2716i	−0.791968	−	0.980176i
$213$	5.16987	−	15.5342i	0.354233	−	1.06439i
$214$	3.40149	+	1.62470i	0.232521	+	0.111062i
$215$	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
$219$	−10.5169	−	11.8487i	−0.710669	−	0.800662i
$220$	2.95601	+	1.13839i	0.199294	+	0.0767506i
$221$	0.00166009	−	0.00287537i	0.000111670	−	0.000193418i
$222$	−17.6181	+	18.2831i	−1.18245	+	1.22708i
$223$		−	17.0765i		−	1.14353i	−0.820418	−	0.571764i	$-0.806259\pi$
$223$		−	17.0765i		−	1.14353i	0.820418	−	0.571764i	$-0.193741\pi$
$224$	−10.2251	−	10.9292i	−0.683195	−	0.730236i
$225$	2.75772	−	1.18108i	0.183848	−	0.0787390i
$226$	4.07767	+	5.93995i	0.271242	+	0.395120i
$227$	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	$0.335811\pi$
$228$	−3.29945	−	0.550362i	−0.218512	−	0.0364486i
$229$	10.8195	+	18.7399i	0.714971	+	1.23837i	0.962971	+	0.269606i	$0.0868936\pi$
$229$	10.8195	+	18.7399i	0.714971	+	1.23837i	−0.247999	+	0.968760i	$0.579773\pi$
$230$	−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	$0.518423\pi$
$234$	−10.8258	−	0.443618i	−0.707705	−	0.0290002i
$235$	−10.0313	−	5.79156i	−0.654368	−	0.377800i
$236$	−5.92150	+	4.78449i	−0.385457	+	0.311444i
$237$	4.98872	+	24.3197i	0.324052	+	1.57974i
$238$	−0.00277495	+	0.00399537i	−0.000179873	+	0.000258982i
$239$		−	7.53787i		−	0.487584i	−0.969827	−	0.243792i	$-0.921609\pi$
$239$		−	7.53787i		−	0.487584i	0.969827	−	0.243792i	$-0.0783915\pi$
$240$	−5.96756	−	3.51969i	−0.385204	−	0.227195i
$241$	−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	$0.825029\pi$
$242$	10.8362	+	5.17582i	0.696575	+	0.332714i
$243$	−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
$246$	3.13239	−	0.901819i	0.199714	−	0.0574979i
$247$	1.23302	+	2.13565i	0.0784549	+	0.135888i
$248$	−1.91656	+	6.43169i	−0.121702	+	0.408412i
$249$	5.43935	−	16.3439i	0.344705	−	1.03576i
$250$	−0.800386	−	1.16593i	−0.0506208	−	0.0737396i
$251$		−	12.7580i		−	0.805281i	−0.915358	−	0.402640i	$-0.868092\pi$
$251$		−	12.7580i		−	0.805281i	0.915358	−	0.402640i	$-0.131908\pi$
$252$	15.7518	+	1.96984i	0.992271	+	0.124089i
$253$			5.10552i			0.320981i
$254$	−3.24152	+	2.22524i	−0.203391	+	0.139624i
$255$	−0.000711074		0.00213661i	−4.45292e−5		0.000133800i
$256$	1.60325	+	15.9195i	0.100203	+	0.994967i
$257$	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	$0.509561\pi$
$258$	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
$261$	−6.84013	−	5.11994i	−0.423393	−	0.316916i
$262$	0.703603	−	1.47307i	0.0434688	−	0.0910068i
$263$	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	$0.494690\pi$
$264$	6.35580	+	4.45056i	0.391172	+	0.273913i
$265$		−	9.17398i		−	0.563553i
$266$	−1.53941	−	3.26869i	−0.0943876	−	0.200416i
$267$	5.43239	+	26.4826i	0.332457	+	1.62071i
$268$	12.5379	−	10.1304i	0.765874	−	0.618815i
$269$	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	$0.635723\pi$
$270$	7.25300	−	1.18067i	0.441404	−	0.0718536i
$271$	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
$276$	1.83726	−	11.0145i	0.110590	−	0.662995i
$277$	21.0161	+	12.1337i	1.26274	+	0.729041i	0.973603	−	0.228248i	$-0.0732996\pi$
$277$	21.0161	+	12.1337i	1.26274	+	0.729041i	0.289133	+	0.957289i	$0.406633\pi$
$278$	−15.3580	+	10.5430i	−0.921112	+	0.632326i
$279$	−2.80243	−	6.54341i	−0.167777	−	0.391744i
$280$	−0.542351	−	7.46364i	−0.0324117	−	0.446038i
$281$		−	8.11655i		−	0.484193i	−0.970252	−	0.242096i	$-0.922165\pi$
$281$		−	8.11655i		−	0.484193i	0.970252	−	0.242096i	$-0.0778350\pi$
$282$	−20.4307	−	19.6876i	−1.21663	−	1.17238i
$283$	4.25172	−	7.36420i	0.252739	−	0.437756i	−0.711540	−	0.702645i	$-0.752002\pi$
$283$	4.25172	−	7.36420i	0.252739	−	0.437756i	0.964279	+	0.264889i	$0.0853354\pi$
$284$	−17.6416	−	6.79400i	−1.04684	−	0.403150i
$285$	−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
$288$	−12.1103	−	11.8887i	−0.713604	−	0.700549i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−1.73595	+	3.63441i	−0.101938	+	0.213420i
$291$	−5.53976	+	16.6457i	−0.324746	+	0.975786i
$292$	−14.2295	+	11.4972i	−0.832717	+	0.672824i
$293$		−	9.79161i		−	0.572032i	−0.958225	−	0.286016i	$-0.907669\pi$
$293$		−	9.79161i		−	0.572032i	0.958225	−	0.286016i	$-0.0923311\pi$
$294$	7.93334	+	15.2007i	0.462682	+	0.886525i
$295$	−3.80642			−0.221619
$296$	20.1466	+	21.2996i	1.17100	+	1.23801i
$297$	−8.20119	+	0.685343i	−0.475881	+	0.0397676i
$298$	−21.8689	−	10.4455i	−1.26683	−	0.605092i
$299$	−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
$303$	4.55597	+	5.13290i	0.261733	+	0.294877i
$304$	−0.811274	+	3.77636i	−0.0465298	+	0.216589i
$305$	−7.42017	−	4.28404i	−0.424878	−	0.245303i
$306$	−0.00295118	+	0.00465992i	−0.000168708	+	0.000266390i
$307$	−20.0331			−1.14335			−0.571676	−	0.820479i	$-0.693707\pi$
$307$	−20.0331			−1.14335			−0.571676	+	0.820479i	$0.693707\pi$
$308$	−0.0457421	+	8.38066i	−0.00260640	+	0.477533i
$309$	−5.85678	+	1.20140i	−0.333181	+	0.0683455i
$310$	−2.76646	+	1.89912i	−0.157124	+	0.107863i
$311$	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	$-0.0130624\pi$
$312$	−1.09065	+	12.4634i	−0.0617461	+	0.705602i
$313$	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	$0.0645695\pi$
$317$	11.8261	+	20.4834i	0.664220	+	1.15046i	−0.315276	+	0.949000i	$0.602097\pi$
$318$	5.41309	−	21.8099i	0.303551	−	1.22304i
$319$	2.25538	−	3.90643i	0.126277	−	0.218718i
$320$	−4.37897	+	6.69512i	−0.244792	+	0.374269i
$321$	0.927725	+	4.52261i	0.0517806	+	0.252428i
$322$	10.9118	−	5.13900i	0.608092	−	0.286385i
$323$	0.00125541			6.98527e−5
$324$	17.9397	+	1.47273i	0.996647	+	0.0818182i
$325$	−1.27690	+	2.21166i	−0.0708299	+	0.122681i
$326$	6.69657	−	14.0200i	0.370889	−	0.776498i
$327$	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
$330$	1.07333	+	3.72812i	0.0590848	+	0.205226i
$331$	29.0623	−	16.7791i	1.59741	−	0.922264i	0.605424	−	0.795903i	$-0.293004\pi$
$331$	29.0623	−	16.7791i	1.59741	−	0.922264i	0.991984	−	0.126361i	$-0.0403298\pi$
$332$	−18.5612	−	7.14814i	−1.01868	−	0.392305i
$333$	−30.8769	−	3.69027i	−1.69205	−	0.202226i
$334$	−25.9795	+	17.8344i	−1.42154	+	0.975857i
$335$	8.05954			0.440340
$336$	3.11454	−	18.0638i	0.169912	−	0.985459i
$337$	−11.9306			−0.649902			−0.324951	−	0.945731i	$-0.605348\pi$
$337$	−11.9306			−0.649902			−0.324951	+	0.945731i	$0.605348\pi$
$338$	−7.55294	+	5.18495i	−0.410826	+	0.282024i
$339$	−2.78646	+	8.37265i	−0.151340	+	0.454740i
$340$	0.00242647		0.000934461i	0.000131594		5.06783e-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
$345$	4.17571	−	3.70637i	0.224813	−	0.199544i
$346$	−3.14766	+	6.58998i	−0.169219	+	0.354279i
$347$	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	$0.0938821\pi$
$348$	−6.27146	+	7.61601i	−0.336185	+	0.408261i
$349$	22.2036			1.18853			0.594266	−	0.804268i	$-0.297443\pi$
$349$	22.2036			1.18853			0.594266	+	0.804268i	$0.297443\pi$
$350$	2.13443	−	3.07315i	0.114090	−	0.164267i
$351$	−7.56896	−	10.8997i	−0.404001	−	0.581782i
$352$	5.47346	−	7.09315i	0.291736	−	0.378066i
$353$	−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	$0.291707\pi$
$354$	−9.04924	−	2.24597i	−0.480962	−	0.119372i
$355$	−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	$0.406494\pi$
$360$	−0.973976	−	8.42920i	−0.0513330	−	0.444258i
$361$	9.03378	−	15.6470i	0.475462	−	0.823525i
$362$	8.79719	−	6.03911i	0.462370	−	0.317408i
$363$	2.95546	+	14.4077i	0.155122	+	0.756210i
$364$	−11.7397	+	6.69277i	−0.615329	+	0.350796i
$365$	−9.14691			−0.478771
$366$	−15.1126	−	14.5630i	−0.789950	−	0.761218i
$367$	−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	$0.693513\pi$
$368$	−12.6066	−	2.70826i	−0.657162	−	0.141178i
$369$	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
$372$	−7.69744	+	2.88255i	−0.399094	+	0.149453i
$373$	−16.6643	+	9.62113i	−0.862844	+	0.498163i	−0.864964	−	0.501835i	$-0.832659\pi$
$373$	−16.6643	+	9.62113i	−0.862844	+	0.498163i	0.00211985	+	0.999998i	$0.499325\pi$
$374$	−0.00262767	−	0.00125509i	−0.000135874	−	6.48990e-5i
$375$	0.546941	−	1.64343i	0.0282439	−	0.0848663i
$376$	−23.8015	+	22.5131i	−1.22747	+	1.16102i
$377$	7.27330			0.374594
$378$	9.71973	+	16.8383i	0.499929	+	0.866066i
$379$		−	28.2338i		−	1.45027i	−0.688604	−	0.725137i	$-0.741776\pi$
$379$		−	28.2338i		−	1.45027i	0.688604	−	0.725137i	$-0.258224\pi$
$380$	−1.50219	+	1.21375i	−0.0770607	+	0.0622640i
$381$	−4.56908	−	1.52061i	−0.234081	−	0.0779033i
$382$	−9.11108	+	19.0751i	−0.466163	+	0.975967i
$383$	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	$0.800927\pi$
$384$	−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
$387$	−10.0935	+	13.4846i	−0.513079	+	0.685463i
$388$	18.9039	+	7.28010i	0.959698	+	0.369591i
$389$	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	$-0.111696\pi$
$390$	−4.34065	+	4.50449i	−0.219797	+	0.228093i
$391$			0.00419091i			0.000211943i
$392$	17.9577	−	8.33787i	0.907002	−	0.421126i
$393$	1.95859	−	0.401767i	0.0987980	−	0.0202665i
$394$	21.1520	−	14.5205i	1.06562	−	0.731530i
$395$	12.4131	+	7.16669i	0.624569	+	0.360595i
$396$	0.351921	+	9.49640i	0.0176847	+	0.477212i
$397$	−9.36263	−	16.2166i	−0.469897	−	0.813886i	0.529510	−	0.848303i	$-0.322376\pi$
$397$	−9.36263	−	16.2166i	−0.469897	−	0.813886i	−0.999408	+	0.0344178i	$0.989042\pi$
$398$	−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	$0.101950\pi$
$402$	19.1604	+	4.75552i	0.955636	+	0.237184i
$403$	5.24774	+	3.02978i	0.261408	+	0.150924i
$404$	6.16425	−	4.98063i	0.306683	−	0.247795i
$405$	6.51421	+	6.21008i	0.323694	+	0.308581i
$406$	−10.6192	−	0.888284i	−0.527024	−	0.0440848i
$407$		−	16.4172i		−	0.813770i
$408$	0.00521721	+	0.00365328i	0.000258290	+	0.000180864i
$409$	−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	$0.913924\pi$
$410$	0.811122	−	1.69818i	0.0400584	−	0.0838669i
$411$	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
$414$	12.1141	−	6.34750i	0.595376	−	0.311963i
$415$	−4.97252	−	8.61265i	−0.244091	−	0.422778i
$416$	14.3178	+	1.92457i	0.701986	+	0.0943596i
$417$	−21.6478	−	7.20451i	−1.06010	−	0.352806i
$418$	1.78315	−	1.22410i	0.0872166	−	0.0598725i
$419$		−	29.6942i		−	1.45066i	−0.688403	−	0.725329i	$-0.741688\pi$
$419$		−	29.6942i		−	1.45066i	0.688403	−	0.725329i	$-0.258312\pi$
$420$	6.88761	−	6.04656i	0.336081	−	0.295042i
$421$		−	13.9615i		−	0.680442i	−0.940346	−	0.340221i	$-0.889498\pi$
$421$		−	13.9615i		−	0.680442i	0.940346	−	0.340221i	$-0.110502\pi$
$422$	−7.37110	−	10.7375i	−0.358819	−	0.522694i
$423$	4.12374	−	34.5038i	0.200503	−	1.67763i
$424$	−24.8673	−	7.41017i	−1.20766	−	0.359869i
$425$	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
$429$	5.23951	−	4.65060i	0.252966	−	0.224533i
$430$	7.16489	+	3.42226i	0.345522	+	0.165036i
$431$	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	$0.456864\pi$
$432$	2.65814	−	20.6139i	0.127890	−	0.991788i
$433$		−	32.4681i		−	1.56032i	−0.625581	−	0.780159i	$-0.715138\pi$
$433$		−	32.4681i		−	1.56032i	0.625581	−	0.780159i	$-0.284862\pi$
$434$	−7.29183	−	5.06448i	−0.350019	−	0.243103i
$435$	−4.83230	+	0.991252i	−0.231691	+	0.0475269i
$436$	10.4962	−	8.48081i	0.502679	−	0.406157i
$437$	−2.69572	−	1.55637i	−0.128954	−	0.0744515i
$438$	−21.7455	−	5.39712i	−1.03904	−	0.257884i
$439$	−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	0.986160	−	0.165796i	$-0.0530194\pi$
$443$	7.35604	+	12.7410i	0.349496	+	0.605345i	−0.636664	+	0.771141i	$0.719686\pi$
$444$	−5.90787	+	35.4180i	−0.280375	+	1.68086i
$445$	13.5170	+	7.80405i	0.640768	+	0.369948i
$446$	−13.6678	−	19.9099i	−0.647189	−	0.942763i
$447$	−5.96453	−	29.0768i	−0.282113	−	1.37528i
$448$	−20.6693	−	4.55854i	−0.976532	−	0.215371i
$449$		−	22.4699i		−	1.06042i	−0.847866	−	0.530211i	$-0.822113\pi$
$449$		−	22.4699i		−	1.06042i	0.847866	−	0.530211i	$-0.177887\pi$
$450$	2.26998	−	3.58430i	0.107008	−	0.168965i
$451$	−1.05382	+	1.82528i	−0.0496226	+	0.0859489i
$452$	9.50851	+	3.66184i	0.447243	+	0.172238i
$453$	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
$456$	−4.28742	+	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	$0.696377\pi$
$458$	27.6138	+	13.1896i	1.29031	+	0.616308i
$459$	−0.00673201		0.000562569i	−0.000314223		2.62585e-5i
$460$	−4.05184	−	5.01474i	−0.188918	−	0.233813i
$461$		−	24.2057i		−	1.12737i	−0.825989	−	0.563686i	$-0.809383\pi$
$461$		−	24.2057i		−	1.12737i	0.825989	−	0.563686i	$-0.190617\pi$
$462$	−8.21782	+	6.15011i	−0.382328	+	0.286129i
$463$	32.9835			1.53287			0.766436	−	0.642321i	$-0.222028\pi$
$463$	32.9835			1.53287			0.766436	+	0.642321i	$0.222028\pi$
$464$	8.44938	+	7.64118i	0.392253	+	0.354733i
$465$	−3.89946	−	1.29776i	−0.180833	−	0.0601821i
$466$	−10.2207	+	21.3981i	−0.473463	+	0.991250i
$467$	−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
$471$	−29.6489	+	26.3164i	−1.36615	+	1.21260i
$472$	−3.07459	+	10.3178i	−0.141520	+	0.474917i
$473$	−7.70115	−	4.44626i	−0.354099	−	0.204439i
$474$	25.2816	+	24.3621i	1.16122	+	1.11899i
$475$	−0.965629			−0.0443061
$476$	−3.75478e−5		0.00687934i	−1.72100e−6		0.000315314i
$477$	25.2993	−	10.8352i	1.15838	−	0.496112i
$478$	−6.03321	−	8.78860i	−0.275952	−	0.401981i
$479$	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	$0.158572\pi$
$480$	−9.77484	+	0.672655i	−0.446158	+	0.0307023i
$481$	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
$486$	11.8224	+	18.6073i	0.536274	+	0.844044i
$487$	−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	$0.290969\pi$
$488$	−17.6060	+	16.6530i	−0.796987	+	0.753847i
$489$	18.6410	−	3.82383i	0.842974	−	0.172920i
$490$	9.60410	+	2.40027i	0.433869	+	0.108433i
$491$	−24.9428			−1.12565			−0.562826	−	0.826575i	$-0.690286\pi$
$491$	−24.9428			−1.12565			−0.562826	+	0.826575i	$0.690286\pi$
$492$	2.93033	−	3.55858i	0.132110	−	0.160433i
$493$	0.00185135	−	0.00320663i	8.33804e−5	−	0.000144419i
$494$	3.14695	+	1.50312i	0.141588	+	0.0676284i
$495$	−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
$498$	−6.73959	−	23.4094i	−0.302008	−	1.04900i
$499$	28.6360	−	16.5330i	1.28192	−	0.740118i	0.304723	−	0.952441i	$-0.401436\pi$
$499$	28.6360	−	16.5330i	1.28192	−	0.740118i	0.977200	+	0.212323i	$0.0681028\pi$
$500$	−1.86638	−	0.718765i	−0.0834671	−	0.0321442i
$501$	−36.6194	−	12.1871i	−1.63603	−	0.544480i
$502$	−10.2114	−	14.8749i	−0.455755	−	0.663901i
$503$	−14.4817			−0.645709			−0.322854	−	0.946449i	$-0.604642\pi$
$503$	−14.4817			−0.645709			−0.322854	+	0.946449i	$0.604642\pi$
$504$	19.9421	−	10.3108i	0.888291	−	0.459281i
$505$	3.96247			0.176328
$506$	4.08638	+	5.95265i	0.181662	+	0.264628i
$507$	−10.6462	−	3.54312i	−0.472816	−	0.157355i
$508$	−1.99832	+	5.18893i	−0.0886611	+	0.230222i
$509$	−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
$513$	2.13820	−	4.53916i	0.0944039	−	0.200409i
$514$	34.8034	+	16.6236i	1.53511	+	0.733236i
$515$	−1.72591	+	2.98937i	−0.0760527	+	0.131727i
$516$	15.0142	+	12.3636i	0.660965	+	0.544276i
$517$	18.3456			0.806837
$518$	−35.0878	+	16.5249i	−1.54167	+	0.726061i
$519$	−8.76201	+	1.79736i	−0.384610	+	0.0788951i
$520$	4.96361	+	5.24767i	0.217669	+	0.230125i
$521$	−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	$0.254111\pi$
$522$	−12.0730	−	0.494725i	−0.528421	−	0.0216535i
$523$	10.2725	+	17.7925i	0.449185	+	0.778012i	0.998333	−	0.0577132i	$-0.0183809\pi$
$523$	10.2725	+	17.7925i	0.449185	+	0.778012i	−0.549148	+	0.835725i	$0.685048\pi$
$524$	−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
$528$	10.9726	+	0.101935i	0.477519	+	0.00443616i
$529$	−6.30438	+	10.9195i	−0.274103	+	0.474761i
$530$	−7.34272	−	10.6962i	−0.318947	−	0.464612i
$531$	−4.49571	−	10.4971i	−0.195097	−	0.455534i
$532$	−4.41106	−	2.57893i	−0.191244	−	0.111811i
$533$	−3.39845			−0.147203
$534$	27.5301	+	26.5287i	1.19134	+	1.14801i
$535$	2.30839	+	1.33275i	0.0998005	+	0.0576198i
$536$	6.50999	−	21.8465i	0.281189	−	0.943625i
$537$	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
$540$	7.51146	−	7.18178i	0.323242	−	0.309054i
$541$	−16.3217	+	9.42333i	−0.701724	+	0.405140i	−0.807989	−	0.589197i	$-0.799444\pi$
$541$	−16.3217	+	9.42333i	−0.701724	+	0.405140i	0.106265	+	0.994338i	$0.466111\pi$
$542$	14.3222	−	29.9851i	0.615190	−	1.28797i
$543$	12.4001	+	4.12680i	0.532138	+	0.177098i
$544$	0.00449293	−	0.00582248i	0.000192633	−	0.000249637i
$545$	6.74713			0.289015
$546$	−15.2134	−	6.51712i	−0.651075	−	0.278907i
$547$			13.4614i			0.575569i	0.957695	+	0.287785i	$0.0929188\pi$
$547$			13.4614i			0.575569i	−0.957695	+	0.287785i	$0.907081\pi$
$548$	13.2869	−	10.7357i	0.567590	−	0.458604i
$549$	3.05034	−	25.5226i	0.130185	−	1.08928i
$550$	2.02114	+	0.965383i	0.0861817	+	0.0411641i
$551$	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
$555$	−13.4273	+	11.9181i	−0.569958	+	0.505896i
$556$	−9.46784	+	24.5846i	−0.401526	+	1.04262i
$557$	−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	$0.968239\pi$
$558$	−8.50467	−	5.38610i	−0.360031	−	0.228012i
$559$		−	14.3386i		−	0.606459i
$560$	−6.60613	−	8.26795i	−0.279160	−	0.349385i
$561$	−0.000716672	−	0.00349374i	−3.02579e−5	−	0.000147506i
$562$	−6.49637	−	9.46329i	−0.274033	−	0.399185i
$563$	−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	$0.920288\pi$
$564$	−39.5783	−	6.60181i	−1.66655	−	0.277987i
$565$	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	$0.355043\pi$
$570$	−2.29565	−	0.569768i	−0.0961542	−	0.0238649i
$571$	20.8343	+	12.0287i	0.871890	+	0.503386i	0.867976	−	0.496607i	$-0.165421\pi$
$571$	20.8343	+	12.0287i	0.871890	+	0.503386i	0.00391387	+	0.999992i	$0.498754\pi$
$572$	−5.08408	−	6.29229i	−0.212576	−	0.263094i
$573$	−25.3622	+	5.20255i	−1.05952	+	0.217340i
$574$	4.96183	+	0.415050i	0.207103	+	0.0173239i
$575$		−	3.22354i		−	0.134431i
$576$	−23.6352	−	4.16848i	−0.984801	−	0.173687i
$577$	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	$0.582153\pi$
$578$	21.6940	+	10.3620i	0.902351	+	0.431002i
$579$	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
$582$	6.86400	+	23.8415i	0.284522	+	0.988264i
$583$	7.26497	+	12.5833i	0.300884	+	0.521147i
$584$	−7.38831	+	24.7940i	−0.305730	+	1.02598i
$585$	−7.60729	−	0.909188i	−0.314523	−	0.0375903i
$586$	−7.83707	−	11.4163i	−0.323746	−	0.471603i
$587$			8.47618i			0.349850i	0.984582	+	0.174925i	$0.0559682\pi$
$587$			8.47618i			0.349850i	−0.984582	+	0.174925i	$0.944032\pi$
$588$	21.4161	+	11.3732i	0.883186	+	0.469022i
$589$			2.29120i			0.0944074i
$590$	−4.43801	+	3.04661i	−0.182710	+	0.125427i
$591$	29.8148	+	9.92251i	1.22642	+	0.408157i
$592$	40.5374	+	8.70863i	1.66607	+	0.357923i
$593$	−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	$0.958327\pi$
$594$	−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
$597$	−15.9024	−	17.9162i	−0.650842	−	0.733259i
$598$	−5.01783	+	10.5054i	−0.205194	+	0.429598i
$599$	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	$0.433449\pi$
$600$	−4.01295	−	2.81002i	−0.163828	−	0.114718i
$601$		−	6.71478i		−	0.273902i	−0.990578	−	0.136951i	$-0.956270\pi$
$601$		−	6.71478i		−	0.273902i	0.990578	−	0.136951i	$-0.0437302\pi$
$602$	−1.75117	+	20.9348i	−0.0713722	+	0.853239i
$603$	9.51900	+	22.2260i	0.387644	+	0.905112i
$604$	−9.21685	−	11.4072i	−0.375028	−	0.464152i
$605$	7.35387	+	4.24576i	0.298977	+	0.172615i
$606$	9.42022	+	2.33805i	0.382670	+	0.0949766i
$607$	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
$612$	0.000288877		0.00779520i	1.16772e−5		0.000315102i
$613$	−26.1540	−	15.1000i	−1.05635	−	0.609884i	−0.131930	−	0.991259i	$-0.542117\pi$
$613$	−26.1540	−	15.1000i	−1.05635	−	0.609884i	−0.924421	+	0.381375i	$0.875451\pi$
$614$	−23.3572	+	16.0342i	−0.942618	+	0.647089i
$615$	2.25789	−	0.463162i	0.0910468	−	0.0186765i
$616$	6.65443	+	9.80784i	0.268115	+	0.395169i
$617$		−	8.88102i		−	0.357536i	−0.983891	−	0.178768i	$-0.942789\pi$
$617$		−	8.88102i		−	0.357536i	0.983891	−	0.178768i	$-0.0572112\pi$
$618$	−5.86698	+	6.08843i	−0.236005	+	0.244913i
$619$	2.72170	−	4.71412i	0.109394	−	0.189477i	−0.806131	−	0.591738i	$-0.798442\pi$
$619$	2.72170	−	4.71412i	0.109394	−	0.189477i	0.915525	+	0.402261i	$0.131776\pi$
$620$	−1.70545	+	4.42847i	−0.0684927	+	0.177852i
$621$	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
$624$	8.70393	+	15.4044i	0.348436	+	0.616668i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	9.75548	−	20.4242i	0.389907	−	0.816316i
$627$	2.51343	+	0.836483i	0.100377	+	0.0334059i
$628$	28.7693	+	35.6062i	1.14802	+	1.42084i
$629$		−	0.0134762i		−	0.000537331i
$630$	10.9958	+	2.25651i	0.438084	+	0.0899017i
$631$	−27.6620			−1.10121			−0.550603	−	0.834767i	$-0.685602\pi$
$631$	−27.6620			−1.10121			−0.550603	+	0.834767i	$0.685602\pi$
$632$	29.4528	−	27.8585i	1.17157	−	1.10815i
$633$	5.03702	−	15.1350i	0.200203	−	0.601564i
$634$	30.1830	+	14.4167i	1.19872	+	0.572560i
$635$	−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
$639$	16.9926	−	22.7018i	0.672217	−	0.898068i
$640$	0.253128	+	11.3109i	0.0100057	+	0.447102i
$641$	−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	$0.953447\pi$
$642$	4.70149	+	4.53049i	0.185553	+	0.178804i
$643$	49.5521			1.95415			0.977073	−	0.212905i	$-0.0682925\pi$
$643$	49.5521			1.95415			0.977073	+	0.212905i	$0.0682925\pi$
$644$	8.60920	−	14.7254i	0.339250	−	0.580261i
$645$	1.95416	+	9.52641i	0.0769448	+	0.375102i
$646$	0.00146371	−	0.00100481i	5.75890e−5	−	3.95337e-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	$0.105241\pi$
$648$	22.0950	−	12.6416i	0.867976	−	0.496607i
$649$	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	0.843753	−	0.536731i	$-0.180341\pi$
$653$	−1.09745	−	1.90084i	−0.0429465	−	0.0743855i	−0.886700	+	0.462346i	$0.847008\pi$
$654$	16.0404	+	3.98113i	0.627228	+	0.155675i
$655$	0.577170	−	0.999689i	0.0225519	−	0.0390611i
$656$	−3.94797	−	3.57034i	−0.154142	−	0.139398i
$657$	−10.8033	−	25.2247i	−0.421476	−	0.984108i
$658$	−18.4659	−	39.2093i	−0.719876	−	1.52854i
$659$	−10.0050			−0.389739			−0.194869	−	0.980829i	$-0.562428\pi$
$659$	−10.0050			−0.389739			−0.194869	+	0.980829i	$0.562428\pi$
$660$	4.23536	+	3.48763i	0.164861	+	0.135756i
$661$	−10.8267	+	18.7524i	−0.421109	+	0.729382i	−0.996048	−	0.0888140i	$-0.971692\pi$
$661$	−10.8267	+	18.7524i	−0.421109	+	0.729382i	0.574939	+	0.818196i	$0.305026\pi$
$662$	20.4547	−	42.8243i	0.794995	−	1.66441i
$663$	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
$666$	−38.9539	+	20.4109i	−1.50943	+	0.790906i
$667$	−7.95074	+	4.59036i	−0.307854	+	0.177740i
$668$	−16.0157	+	41.5873i	−0.619668	+	1.60906i
$669$	9.33985	−	28.0640i	0.361099	−	1.08502i
$670$	9.39683	−	6.45074i	0.363031	−	0.249214i
$671$	13.5703			0.523875
$672$	−10.8267	−	23.5538i	−0.417648	−	0.908609i
$673$	22.8109			0.879296			0.439648	−	0.898170i	$-0.355103\pi$
$673$	22.8109			0.879296			0.439648	+	0.898170i	$0.355103\pi$
$674$	−13.9102	+	9.54909i	−0.535801	+	0.367817i
$675$	5.17810	−	0.432715i	0.199305	−	0.0166552i
$676$	−4.65621	+	12.0905i	−0.179085	+	0.465021i
$677$	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
$681$	29.8689	+	33.6512i	1.14458	+	1.28952i
$682$	2.29062	−	4.79567i	0.0877124	−	0.183636i
$683$	−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	$0.895902\pi$
$684$	−5.12140	−	2.70909i	−0.195821	−	0.103584i
$685$	8.54103			0.326336
$686$	3.06376	+	26.0118i	0.116975	+	0.993135i
$687$	7.53142	+	36.7153i	0.287342	+	1.40077i
$688$	15.0639	−	16.6571i	0.574304	−	0.635047i
$689$	−11.7143	+	20.2897i	−0.446279	+	0.772978i
$690$	1.90205	−	7.66353i	0.0724096	−	0.291746i
$691$	14.3163	+	24.7966i	0.544619	+	0.943308i	0.998631	+	0.0523123i	$0.0166591\pi$
$691$	14.3163	+	24.7966i	0.544619	+	0.943308i	−0.454012	+	0.890996i	$0.650008\pi$
$692$	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
$696$	−1.21630	+	13.8993i	−0.0461039	+	0.526851i
$697$	−0.000865040		0.00149829i	−3.27657e−5		5.67519e-5i
$698$	25.8878	−	17.7715i	0.979866	−	0.672660i
$699$	−28.4509	+	5.83614i	−1.07611	+	0.220743i
$700$	0.0288809	−	5.29142i	0.00109159	−	0.199997i
$701$	−12.4837			−0.471503			−0.235752	−	0.971813i	$-0.575755\pi$
$701$	−12.4837			−0.471503			−0.235752	+	0.971813i	$0.575755\pi$
$702$	−17.5488	−	6.65013i	−0.662337	−	0.250993i
$703$	8.66830	+	5.00464i	0.326931	+	0.188754i
$704$	0.704385	−	12.6510i	0.0265475	−	0.476801i
$705$	−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
$708$	−12.3484	+	4.62425i	−0.464081	+	0.173790i
$709$	20.2803	−	11.7089i	0.761644	−	0.439735i	−0.0682416	−	0.997669i	$-0.521739\pi$
$709$	20.2803	−	11.7089i	0.761644	−	0.439735i	0.829886	+	0.557933i	$0.188406\pi$
$710$	−12.0623	−	5.76146i	−0.452689	−	0.216224i
$711$	−5.10286	+	42.6963i	−0.191372	+	1.60123i
$712$	32.0722	−	30.3361i	1.20196	−	1.13689i
$713$	−7.64869			−0.286446
$714$	−0.00674567	+	0.00504837i	−0.000252450	+	0.000188931i
$715$		−	4.04477i		−	0.151266i
$716$	−22.1426	−	27.4047i	−0.827509	−	1.02416i
$717$	4.12277	−	12.3880i	0.153968	−	0.462637i
$718$	−5.26221	+	11.0170i	−0.196384	+	0.411152i
$719$	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	$0.708747\pi$
$720$	−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
$723$	−17.0368	−	19.1942i	−0.633606	−	0.713841i
$724$	5.42326	−	14.0823i	0.201554	−	0.523364i
$725$	−1.42401	+	2.46646i	−0.0528864	+	0.0916020i
$726$	14.9776	+	14.4328i	0.555871	+	0.535652i
$727$			26.7145i			0.990787i	0.868669	+	0.495393i	$0.164976\pi$
$727$			26.7145i			0.990787i	−0.868669	+	0.495393i	$0.835024\pi$
$728$	−8.33085	+	17.1996i	−0.308762	+	0.637459i
$729$	−9.43185	+	25.2990i	−0.349328	+	0.937001i
$730$	−10.6646	+	7.32106i	−0.394715	+	0.270965i
$731$	−0.00632155	−	0.00364975i	−0.000233811	−	0.000134991i
$732$	−29.2762	−	4.88339i	−1.08208	−	0.180495i
$733$	−9.50542	−	16.4639i	−0.351091	−	0.608107i	0.635350	−	0.772224i	$-0.280856\pi$
$733$	−9.50542	−	16.4639i	−0.351091	−	0.608107i	−0.986441	+	0.164117i	$0.947522\pi$
$734$	−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
$738$	5.64110	+	0.231160i	0.207652	+	0.00850912i
$739$	−40.1985	−	23.2086i	−1.47873	−	0.853742i	−0.479015	−	0.877807i	$-0.659006\pi$
$739$	−40.1985	−	23.2086i	−1.47873	−	0.853742i	−0.999710	+	0.0240645i	$0.992339\pi$
$740$	13.0290	+	16.1253i	0.478955	+	0.592777i
$741$	0.858300	+	4.18417i	0.0315304	+	0.153709i
$742$	19.5812	−	28.1930i	0.718848	−	1.03500i
$743$			43.2496i			1.58668i	0.608782	+	0.793338i	$0.291658\pi$
$743$			43.2496i			1.58668i	−0.608782	+	0.793338i	$0.708342\pi$
$744$	−6.66749	+	9.52176i	−0.244442	+	0.349085i
$745$	−14.8411	−	8.56852i	−0.543737	−	0.313926i
$746$	−11.7287	+	24.5554i	−0.429418	+	0.899036i
$747$	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
$750$	−0.677684	−	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	$0.772139\pi$
$752$	−9.73156	+	45.2989i	−0.354874	+	1.65188i
$753$	6.97790	−	20.9669i	0.254289	−	0.764078i
$754$	8.48013	−	5.82145i	0.308828	−	0.212005i
$755$		−	7.33270i		−	0.266864i
$756$	24.8096	+	11.8526i	0.902316	+	0.431075i
$757$		−	16.3077i		−	0.592713i	−0.955077	−	0.296356i	$-0.904228\pi$
$757$		−	16.3077i		−	0.592713i	0.955077	−	0.296356i	$-0.0957716\pi$
$758$	−22.5980	−	32.9186i	−0.820795	−	1.19566i
$759$	−2.79242	+	8.39055i	−0.101358	+	0.304558i
$760$	−0.779975	+	2.61747i	−0.0282927	+	0.0949457i
$761$	−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	$-0.395395\pi$
$762$	−6.54428	+	1.88410i	−0.237074	+	0.0682539i
$763$	6.32441	+	16.6934i	0.228959	+	0.604341i
$764$	4.64459	+	29.5325i	0.168035	+	1.06845i
$765$	−0.00233720	+	0.00312245i	−8.45016e−5	+	0.000112892i
$766$	5.07630	+	2.42466i	0.183414	+	0.0876065i
$767$	8.41853	+	4.86044i	0.303975	+	0.175500i
$768$	−6.07218	+	27.0394i	−0.219111	+	0.975700i
$769$			19.2160i			0.692948i	0.938060	+	0.346474i	$0.112621\pi$
$769$			19.2160i			0.692948i	−0.938060	+	0.346474i	$0.887379\pi$
$770$	−0.493986	+	5.90549i	−0.0178020	+	0.212819i
$771$	9.49231	+	46.2745i	0.341857	+	1.66654i
$772$	−4.77404	−	5.90858i	−0.171822	−	0.212654i
$773$	−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	$0.793610\pi$
$774$	−0.975303	+	23.8008i	−0.0350565	+	0.855501i
$775$	−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
$780$	−1.45555	+	8.72609i	−0.0521169	+	0.312444i
$781$	12.9651	+	7.48539i	0.463927	+	0.267848i
$782$	0.00335434	+	0.00488628i	0.000119951	+	0.000174733i
$783$	−8.44095	−	12.1554i	−0.301655	−	0.434398i
$784$	14.2639	−	24.0944i	0.509424	−	0.860516i
$785$			22.8882i			0.816915i
$786$	1.96201	−	2.03606i	0.0699825	−	0.0726239i
$787$	12.2472	−	21.2127i	0.436564	−	0.756151i	−0.560858	−	0.827912i	$-0.689529\pi$
$787$	12.2472	−	21.2127i	0.436564	−	0.756151i	0.997422	+	0.0717612i	$0.0228619\pi$
$788$	13.0397	−	33.8595i	0.464520	−	1.20620i
$789$	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
$792$	8.01110	+	10.7904i	0.284662	+	0.383421i
$793$	10.9406	+	18.9497i	0.388512	+	0.672923i
$794$	−23.8956	−	11.4136i	−0.848024	−	0.405053i
$795$	5.01762	−	15.0768i	0.177957	−	0.534718i
$796$	−21.5160	+	17.3847i	−0.762616	+	0.616183i
$797$			19.6298i			0.695322i	0.937620	+	0.347661i	$0.113024\pi$
$797$			19.6298i			0.695322i	−0.937620	+	0.347661i	$0.886976\pi$
$798$	−0.742134	−	6.21383i	−0.0262713	−	0.219967i
$799$	0.0150591			0.000532753
$800$	−3.45586	+	4.47851i	−0.122183	+	0.158339i
$801$	−5.55668	+	46.4934i	−0.196336	+	1.64277i
$802$	16.2231	−	33.9649i	0.572858	−	1.19934i
$803$	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
$807$	3.66063	+	4.12419i	0.128860	+	0.145178i
$808$	3.20063	−	10.7408i	0.112598	−	0.377861i
$809$	−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	$-0.761296\pi$
$810$	12.5655	+	2.02661i	0.441508	+	0.0712078i
$811$	−19.9803			−0.701602			−0.350801	−	0.936450i	$-0.614091\pi$
$811$	−19.9803			−0.701602			−0.350801	+	0.936450i	$0.614091\pi$
$812$	−13.0922	+	7.46381i	−0.459446	+	0.261928i
$813$	39.8681	−	8.17816i	1.39823	−	0.286820i
$814$	−13.1401	−	19.1412i	−0.460560	−	0.670899i
$815$	5.49324	−	9.51457i	0.192420	−	0.333281i
$816$	0.00900692		8.36744e-5i	0.000315305		2.92919e-6i
$817$	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	$0.143711\pi$
$821$	23.7175	+	41.0799i	0.827746	+	1.43370i	−0.0720557	+	0.997401i	$0.522956\pi$
$822$	20.3051	+	5.03962i	0.708222	+	0.175777i
$823$	−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	$0.843426\pi$
$824$	6.70901	+	7.09294i	0.233719	+	0.247094i
$825$	0.551247	+	2.68730i	0.0191920	+	0.0935598i
$826$	−11.6977	−	8.12453i	−0.407015	−	0.282689i
$827$	21.8780			0.760771			0.380386	−	0.924828i	$-0.375791\pi$
$827$	21.8780			0.760771			0.380386	+	0.924828i	$0.375791\pi$
$828$	9.04370	−	17.0967i	0.314290	−	0.594150i
$829$	−1.75742	+	3.04395i	−0.0610379	+	0.105721i	−0.894930	−	0.446207i	$-0.852774\pi$
$829$	−1.75742	+	3.04395i	−0.0610379	+	0.105721i	0.833892	+	0.551928i	$0.186108\pi$
$830$	−12.6910	−	6.06178i	−0.440512	−	0.210407i
$831$	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
$834$	−31.0062	+	8.92670i	−1.07366	+	0.309106i
$835$	−19.2970	+	11.1412i	−0.667802	+	0.385555i
$836$	1.09927	−	2.85441i	0.0380190	−	0.0987219i
$837$	−1.02673	−	12.2864i	−0.0354889	−	0.424679i
$838$	−23.7668	−	34.6212i	−0.821011	−	1.19597i
$839$	0.0334897			0.00115619			0.000578097	−	1.00000i	$-0.499816\pi$
$839$	0.0334897			0.00115619			0.000578097		1.00000i	$0.499816\pi$
$840$	3.19085	−	12.5626i	0.110095	−	0.433450i
$841$	−20.8888			−0.720302
$842$	−11.1746	−	16.2781i	−0.385102	−	0.560979i
$843$	4.43927	−	13.3390i	0.152897	−	0.459418i
$844$	−17.1883	−	6.61942i	−0.591646	−	0.227850i
$845$	−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
$849$	11.0152	−	9.77709i	0.378040	−	0.335549i
$850$	0.00165907		0.000792443i	5.69056e−5		2.71806e-5i
$851$	−16.7069	+	28.9372i	−0.572706	+	0.991956i
$852$	−25.2768	−	20.8144i	−0.865970	−	0.713089i
$853$	−22.8091			−0.780969			−0.390484	−	0.920610i	$-0.627692\pi$
$853$	−22.8091			−0.780969			−0.390484	+	0.920610i	$0.627692\pi$
$854$	−13.6593	−	29.0033i	−0.467412	−	0.992472i
$855$	−1.14049	−	2.66294i	−0.0390039	−	0.0910706i
$856$	5.47718	−	5.18070i	0.187206	−	0.177073i
$857$	−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	$0.239312\pi$
$858$	2.38661	−	9.61588i	0.0814775	−	0.328281i
$859$	−12.3708	−	21.4269i	−0.422088	−	0.731077i	0.574056	−	0.818816i	$-0.305369\pi$
$859$	−12.3708	−	21.4269i	−0.422088	−	0.731077i	−0.996144	+	0.0877388i	$0.972036\pi$
$860$	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	$0.390915\pi$
$864$	−13.3999	−	26.1619i	−0.455874	−	0.890044i
$865$	−2.58204	+	4.47223i	−0.0877921	+	0.152060i
$866$	−25.9870	−	37.8554i	−0.883075	−	1.28638i
$867$	5.91683	+	28.8443i	0.200946	+	0.979602i
$868$	−12.5553	−	0.0685273i	−0.426153	−	0.00232597i
$869$	−22.7015			−0.770095
$870$	−4.84072	+	5.02343i	−0.164116	+	0.170310i
$871$	−17.8250	−	10.2913i	−0.603977	−	0.348706i
$872$	5.44991	−	18.2890i	0.184557	−	0.619345i
$873$	−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
$876$	−29.6734	+	11.1122i	−1.00257	+	0.375445i
$877$	−36.4434	+	21.0406i	−1.23061	+	0.710490i	−0.967156	−	0.254183i	$-0.918193\pi$
$877$	−36.4434	+	21.0406i	−1.23061	+	0.710490i	−0.263449	+	0.964673i	$0.584860\pi$
$878$	−4.82567	+	10.1031i	−0.162858	+	0.340963i
$879$	5.35544	−	16.0918i	0.180634	−	0.542763i
$880$	4.24936	−	4.69880i	0.143246	−	0.158397i
$881$	3.56867			0.120232			0.0601158	−	0.998191i	$-0.480853\pi$
$881$	3.56867			0.120232			0.0601158	+	0.998191i	$0.480853\pi$
$882$	4.72396	+	29.3204i	0.159064	+	0.987268i
$883$		−	49.6285i		−	1.67013i	−0.550150	−	0.835066i	$-0.685429\pi$
$883$		−	49.6285i		−	1.67013i	0.550150	−	0.835066i	$-0.314571\pi$
$884$	−0.00417331	−	0.00516508i	−0.000140364	−	0.000173720i
$885$	−6.25559	−	2.08189i	−0.210279	−	0.0699820i
$886$	18.7743	+	8.96743i	0.630736	+	0.301267i
$887$	−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	$-0.384699\pi$
$888$	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
$891$	−13.8529	−	3.35925i	−0.464090	−	0.112539i
$892$	−31.8713	−	12.2740i	−1.06713	−	0.410964i
$893$	−5.59250	+	9.68649i	−0.187146	+	0.324146i
$894$	−30.2269	−	29.1274i	−1.01094	−	0.974167i
$895$		−	17.6162i		−	0.588843i
$896$	−27.7475	+	11.2285i	−0.926977	+	0.375118i
$897$	−13.9679	+	2.86525i	−0.466376	+	0.0956679i
$898$	−17.9846	−	26.1983i	−0.600154	−	0.874247i
$899$	5.85231	+	3.37883i	0.195185	+	0.112690i
$900$	−0.222198	−	5.99588i	−0.00740659	−	0.199863i
$901$	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
$906$	4.32665	−	17.4325i	0.143743	−	0.579155i
$907$	3.48443	+	2.01173i	0.115698	+	0.0667985i	0.556732	−	0.830692i	$-0.312055\pi$
$907$	3.48443	+	2.01173i	0.115698	+	0.0667985i	−0.441034	+	0.897490i	$0.645388\pi$
$908$	40.4128	−	32.6530i	1.34115	−	1.08363i
$909$	4.68001	+	10.9274i	0.155226	+	0.362439i
$910$	−8.64474	+	4.07130i	−0.286570	+	0.134962i
$911$			9.23822i			0.306076i	0.988220	+	0.153038i	$0.0489057\pi$
$911$			9.23822i			0.306076i	−0.988220	+	0.153038i	$0.951094\pi$
$912$	−3.39872	+	5.76245i	−0.112543	+	0.190814i
$913$	13.6409	+	7.87557i	0.451448	+	0.260643i
$914$	22.7577	+	10.8700i	0.752757	+	0.359549i
$915$	−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
$918$	−0.00739875	+	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	$0.707193\pi$
$920$	−8.73786	−	2.60378i	−0.288079	−	0.0858440i
$921$	−32.9230	−	10.9569i	−1.08485	−	0.361044i
$922$	−19.3739	−	28.2220i	−0.638045	−	0.929443i
$923$			24.1394i			0.794559i
$924$	−4.65890	+	13.7480i	−0.153267	+	0.452276i
$925$			10.3656i			0.340818i
$926$	38.4563	−	26.3995i	1.26375	−	0.867541i
$927$	−10.2823	−	1.22889i	−0.337715	−	0.0403621i
$928$	15.9672	+	2.14629i	0.524150	+	0.0704553i
$929$	−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	$0.874776\pi$
$930$	−5.58518	+	1.60798i	−0.183145	+	0.0527277i
$931$	5.06256	−	4.47884i	0.165919	−	0.146788i
$932$	5.21023	+	33.1291i	0.170667	+	1.08518i
$933$	24.4483	−	21.7003i	0.800401	−	0.710437i
$934$	−11.7689	+	24.6396i	−0.385090	+	0.806231i
$935$	−0.00178324	−	0.00102956i	−5.83183e−5	−	3.36701e-5i
$936$	−8.60917	+	19.8862i	−0.281400	+	0.650001i
$937$			50.5634i			1.65184i	0.563791	+	0.825918i	$0.309342\pi$
$937$			50.5634i			1.65184i	−0.563791	+	0.825918i	$0.690658\pi$
$938$	24.7681	+	17.2025i	0.808709	+	0.561682i
$939$	27.1560	−	5.57051i	0.886201	−	0.181787i
$940$	−18.0194	+	14.5594i	−0.587727	+	0.474875i
$941$	−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	$0.817683\pi$
$942$	−13.5051	+	54.4135i	−0.440021	+	1.77289i
$943$	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	0.889661	−	0.456621i	$-0.150940\pi$
$947$	1.51976	+	2.63230i	0.0493855	+	0.0855381i	−0.840276	+	0.542159i	$0.817607\pi$
$948$	48.9756	+	8.16933i	1.59065	+	0.265327i
$949$	20.2299	+	11.6797i	0.656690	+	0.379140i
$950$	−1.12585	+	0.772876i	−0.0365275	+	0.0250754i
$951$	8.23213	+	40.1312i	0.266945	+	1.30134i
$952$	0.00546235	+	0.00805085i	0.000177036	+	0.000260930i
$953$			2.46246i			0.0797670i	0.999204	+	0.0398835i	$0.0126987\pi$
$953$			2.46246i			0.0797670i	−0.999204	+	0.0398835i	$0.987301\pi$
$954$	20.8247	−	32.8823i	0.674225	−	1.06460i
$955$	−7.47388	+	12.9451i	−0.241849	+	0.418895i
$956$	−14.0685	−	5.41796i	−0.455009	−	0.175229i
$957$	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
$960$	−10.8584	+	8.60791i	−0.350452	+	0.277819i
$961$	−12.6850	−	21.9711i	−0.409194	−	0.708745i
$962$	16.1352	−	33.7809i	0.520220	−	1.08914i
$963$	−0.948952	+	7.94000i	−0.0305796	+	0.255863i
$964$	−23.0509	+	18.6248i	−0.742420	+	0.599865i
$965$		−	3.79812i		−	0.122266i
$966$	20.7435	−	2.47745i	0.667412	−	0.0797108i
$967$	−31.6944			−1.01922			−0.509611	−	0.860405i	$-0.670211\pi$
$967$	−31.6944			−1.01922			−0.509611	+	0.860405i	$0.670211\pi$
$968$	17.4487	−	16.5042i	0.560823	−	0.530466i
$969$	0.00206317		0.000686634i	6.62786e−5		2.20579e-5i
$970$	12.9253	+	6.17368i	0.415007	+	0.198225i
$971$	−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
$975$	−3.30815	+	2.93632i	−0.105946	+	0.0940374i
$976$	−7.19847	+	33.5078i	−0.230418	+	1.07256i
$977$	−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	$0.794094\pi$
$978$	18.6735	−	19.3783i	0.597111	−	0.619649i
$979$	−24.7204			−0.790069
$980$	13.1188	−	4.88845i	0.419065	−	0.156156i
$981$	7.96894	+	18.6067i	0.254429	+	0.594067i
$982$	−29.0814	+	19.9639i	−0.928026	+	0.637072i
$983$	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	$0.108033\pi$
$984$	0.568317	−	6.49443i	0.0181173	−	0.207035i
$985$	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
$990$	−0.275123	+	6.71395i	−0.00874398	+	0.213383i
$991$	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	$0.00645526\pi$
$992$	10.6264	+	8.19991i	0.337389	+	0.260347i
$993$	56.9390	−	11.6799i	1.80690	−	0.370651i
$994$	2.94813	−	35.2443i	0.0935091	−	1.11788i
$995$	−13.8308			−0.438466
$996$	−26.5944	−	21.8994i	−0.842676	−	0.693908i
$997$	−8.22424	+	14.2448i	−0.260464	+	0.451137i	−0.966365	−	0.257173i	$-0.917209\pi$
$997$	−8.22424	+	14.2448i	−0.260464	+	0.451137i	0.705901	+	0.708310i	$0.250542\pi$
$998$	20.1547	−	42.1961i	0.637984	−	1.33569i
$999$	−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.101.105	yes	256
3.2	odd	2	inner	840.2.cf.a.101.24	yes	256
7.5	odd	6	inner	840.2.cf.a.341.19	yes	256
8.5	even	2	inner	840.2.cf.a.101.110	yes	256
21.5	even	6	inner	840.2.cf.a.341.110	yes	256
24.5	odd	2	inner	840.2.cf.a.101.19	✓	256
56.5	odd	6	inner	840.2.cf.a.341.24	yes	256
168.5	even	6	inner	840.2.cf.a.341.105	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.19	✓	256	24.5	odd	2	inner
840.2.cf.a.101.24	yes	256	3.2	odd	2	inner
840.2.cf.a.101.105	yes	256	1.1	even	1	trivial
840.2.cf.a.101.110	yes	256	8.5	even	2	inner
840.2.cf.a.341.19	yes	256	7.5	odd	6	inner
840.2.cf.a.341.24	yes	256	56.5	odd	6	inner
840.2.cf.a.341.105	yes	256	168.5	even	6	inner
840.2.cf.a.341.110	yes	256	21.5	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+(1.16593 - 0.800386i) q^{2} +(1.64343 + 0.546941i) q^{3} +(0.718765 - 1.86638i) 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} +(2.40171 + 1.79772i) q^{9} +(0.609528 - 1.27612i) q^{10} +(-0.791910 + 1.37163i) q^{11} +(2.20204 - 2.67414i) q^{12} -2.55381 q^{13} +(3.72864 + 0.311895i) q^{14} +(1.69672 - 0.348049i) q^{15} +(-2.96675 - 2.68298i) q^{16} +(-0.000650046 + 0.00112591i) q^{17} +(4.23908 + 0.173708i) 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} +(0.427070 - 4.88033i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.97755 + 2.04403i) q^{26} +(2.96379 + 4.26801i) q^{27} +(4.59695 - 2.62070i) q^{28} -2.84802 q^{29} +(1.69968 - 1.76383i) q^{30} +(-2.05487 - 1.18638i) q^{31} +(-5.60643 - 0.753606i) q^{32} +(-2.05165 + 1.82104i) 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} +(-1.23226 - 0.588578i) q^{38} +(-4.19700 - 1.39678i) q^{39} +(-1.94361 - 2.05484i) q^{40} +1.33074 q^{41} +(5.95716 + 2.55192i) q^{42} +5.61460i q^{43} +(1.99078 + 2.46388i) q^{44} +(2.97880 + 0.356013i) q^{45} +(1.96484 - 4.11362i) 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} +(-0.00168411 + 0.00149482i) q^{51} +(-1.83559 + 4.76638i) q^{52} +(4.58699 - 7.94490i) q^{53} +(6.87162 + 2.60401i) q^{54} +1.58382i q^{55} +(3.26213 - 6.73487i) q^{56} +(-0.336086 - 1.63840i) q^{57} +(-3.32058 + 2.27952i) q^{58} +(-3.29646 - 1.90321i) q^{59} +(0.569952 - 3.41689i) 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} +(-0.934530 + 3.76531i) q^{66} +(6.97977 + 4.02977i) q^{67} +(0.00163415 + 0.00202250i) q^{68} +(5.46946 - 1.12195i) q^{69} +(3.38504 - 1.59421i) q^{70} -9.45233i q^{71} +(3.37111 - 7.78689i) q^{72} +(-7.92146 - 4.57346i) q^{73} +(-6.31810 + 13.2277i) q^{74} +(1.29538 - 1.14978i) 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} +(-3.91077 - 0.840151i) q^{80} +(2.53643 + 8.63519i) q^{81} +(1.55154 - 1.06510i) q^{82} -9.94503i q^{83} +(8.98812 - 1.79267i) q^{84} +0.00130009i q^{85} +(4.49385 + 6.54621i) q^{86} +(-4.68052 - 1.55770i) q^{87} +(4.29316 + 1.27931i) 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} +(-2.72815 - 3.07362i) q^{93} +(-14.7814 - 7.06024i) q^{94} +(-0.836259 - 0.482815i) q^{95} +(-8.80159 - 4.30489i) q^{96} +10.1286i q^{97} +(7.11726 + 6.88075i) 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

L-functions

Modular forms

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