LMFDB - Embedded newform 84.2.n.a.23.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [84,2,Mod(11,84)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(84, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("84.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.n (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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.10
Character	$\chi$	$=$	84.23
Dual form			84.2.n.a.11.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09645 + 0.893190i) q^{2} +(1.03264 - 1.39056i) q^{3} +(0.404424 + 1.95868i) q^{4} +(-1.79791 - 1.03802i) q^{5} +(2.37428 - 0.602344i) q^{6} +(-2.61347 + 0.412056i) q^{7} +(-1.30604 + 2.50883i) q^{8} +(-0.867316 - 2.87189i) q^{9} +(-1.04417 - 2.74402i) q^{10} +(1.99399 + 3.45368i) q^{11} +(3.14129 + 1.46024i) q^{12} -1.30998 q^{13} +(-3.23359 - 1.88252i) q^{14} +(-3.30003 + 1.42820i) q^{15} +(-3.67288 + 1.58428i) q^{16} +(2.54752 - 1.47081i) q^{17} +(1.61417 - 3.92358i) q^{18} +(0.949883 + 0.548415i) q^{19} +(1.30604 - 3.94134i) q^{20} +(-2.12578 + 4.05969i) q^{21} +(-0.898482 + 5.56781i) q^{22} +(3.75063 - 6.49627i) q^{23} +(2.14001 + 4.40685i) q^{24} +(-0.345008 - 0.597572i) q^{25} +(-1.43634 - 1.17006i) q^{26} +(-4.88916 - 1.75957i) q^{27} +(-1.86404 - 4.95231i) q^{28} +0.865568i q^{29} +(-4.89399 - 1.38160i) q^{30} +(3.18742 - 1.84026i) q^{31} +(-5.44221 - 1.54349i) q^{32} +(6.86162 + 0.793650i) q^{33} +(4.10695 + 0.662741i) q^{34} +(5.12651 + 1.97200i) q^{35} +(5.27436 - 2.86026i) q^{36} +(-2.08850 + 3.61738i) q^{37} +(0.551664 + 1.44974i) q^{38} +(-1.35274 + 1.82161i) q^{39} +(4.95238 - 3.15496i) q^{40} +7.01712i q^{41} +(-5.95689 + 2.55254i) q^{42} +4.27597i q^{43} +(-5.95826 + 5.30234i) q^{44} +(-1.42174 + 6.06370i) q^{45} +(9.91479 - 3.77285i) q^{46} +(-3.75063 + 6.49627i) q^{47} +(-1.58973 + 6.74335i) q^{48} +(6.66042 - 2.15379i) q^{49} +(0.155459 - 0.963368i) q^{50} +(0.585414 - 5.06129i) q^{51} +(-0.529789 - 2.56584i) q^{52} +(4.27909 - 2.47053i) q^{53} +(-3.78911 - 6.29624i) q^{54} -8.27923i q^{55} +(2.37952 - 7.09492i) q^{56} +(1.74349 - 0.754555i) q^{57} +(-0.773117 + 0.949056i) q^{58} +(-2.44458 - 4.23414i) q^{59} +(-4.13200 - 5.88611i) q^{60} +(-2.05347 + 3.55672i) q^{61} +(5.13856 + 0.829212i) q^{62} +(3.45008 + 7.14821i) q^{63} +(-4.58850 - 6.55330i) q^{64} +(2.35524 + 1.35980i) q^{65} +(6.81457 + 6.99893i) q^{66} +(-2.09778 + 1.21116i) q^{67} +(3.91113 + 4.39495i) q^{68} +(-5.16042 - 11.9238i) q^{69} +(3.85961 + 6.74116i) q^{70} -0.901192 q^{71} +(8.33785 + 1.57487i) q^{72} +(-6.50543 - 11.2677i) q^{73} +(-5.52095 + 2.10087i) q^{74} +(-1.18723 - 0.137321i) q^{75} +(-0.690016 + 2.08231i) q^{76} +(-6.63432 - 8.20446i) q^{77} +(-3.11026 + 0.789060i) q^{78} +(8.97336 + 5.18077i) q^{79} +(8.24804 + 0.964154i) q^{80} +(-7.49553 + 4.98167i) q^{81} +(-6.26762 + 7.69395i) q^{82} -12.4386 q^{83} +(-8.81136 - 2.52189i) q^{84} -6.10695 q^{85} +(-3.81926 + 4.68841i) q^{86} +(1.20363 + 0.893819i) q^{87} +(-11.2690 + 0.491915i) q^{88} +(-7.38393 - 4.26311i) q^{89} +(-6.97491 + 5.37869i) q^{90} +(3.42360 - 0.539786i) q^{91} +(14.2410 + 4.71904i) q^{92} +(0.732462 - 6.33262i) q^{93} +(-9.91479 + 3.77285i) q^{94} +(-1.13854 - 1.97200i) q^{95} +(-7.76615 + 5.97385i) q^{96} +15.3909 q^{97} +(9.22659 + 3.58749i) q^{98} +(8.18919 - 8.72195i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.09645	+	0.893190i	0.775310	+	0.631581i
$2$	1.09645	+	0.893190i	0.775310	+	0.631581i
$3$	1.03264	−	1.39056i	0.596194	−	0.802840i
$3$	1.03264	−	1.39056i	0.596194	−	0.802840i
$4$	0.404424	+	1.95868i	0.202212	+	0.979342i
$5$	−1.79791	−	1.03802i	−0.804051	−	0.464219i	0.0408349	−	0.999166i	$-0.486998\pi$
$5$	−1.79791	−	1.03802i	−0.804051	−	0.464219i	−0.844886	+	0.534947i	$0.820332\pi$
$6$	2.37428	−	0.602344i	0.969294	−	0.245906i
$7$	−2.61347	+	0.412056i	−0.987798	+	0.155742i
$7$	−2.61347	+	0.412056i	−0.987798	+	0.155742i
$8$	−1.30604	+	2.50883i	−0.461756	+	0.887007i
$9$	−0.867316	−	2.87189i	−0.289105	−	0.957297i
$10$	−1.04417	−	2.74402i	−0.330197	−	0.867736i
$11$	1.99399	+	3.45368i	0.601209	+	1.04132i	0.992638	+	0.121117i	$0.0386475\pi$
$11$	1.99399	+	3.45368i	0.601209	+	1.04132i	−0.391429	+	0.920208i	$0.628019\pi$
$12$	3.14129	+	1.46024i	0.906813	+	0.421534i
$13$	−1.30998			−0.363324			−0.181662	−	0.983361i	$-0.558148\pi$
$13$	−1.30998			−0.363324			−0.181662	+	0.983361i	$0.558148\pi$
$14$	−3.23359	−	1.88252i	−0.864214	−	0.503125i
$15$	−3.30003	+	1.42820i	−0.852064	+	0.368760i
$16$	−3.67288	+	1.58428i	−0.918221	+	0.396069i
$17$	2.54752	−	1.47081i	0.617863	−	0.356724i	−0.158173	−	0.987411i	$-0.550560\pi$
$17$	2.54752	−	1.47081i	0.617863	−	0.356724i	0.776037	+	0.630688i	$0.217227\pi$
$18$	1.61417	−	3.92358i	0.380464	−	0.924796i
$19$	0.949883	+	0.548415i	0.217918	+	0.125815i	0.604986	−	0.796236i	$-0.293179\pi$
$19$	0.949883	+	0.548415i	0.217918	+	0.125815i	−0.387068	+	0.922051i	$0.626512\pi$
$20$	1.30604	−	3.94134i	0.292040	−	0.881311i
$21$	−2.12578	+	4.05969i	−0.463883	+	0.885897i
$22$	−0.898482	+	5.56781i	−0.191557	+	1.18706i
$23$	3.75063	−	6.49627i	0.782059	−	1.35457i	−0.148681	−	0.988885i	$-0.547503\pi$
$23$	3.75063	−	6.49627i	0.782059	−	1.35457i	0.930740	−	0.365681i	$-0.119164\pi$
$24$	2.14001	+	4.40685i	0.436829	+	0.899545i
$25$	−0.345008	−	0.597572i	−0.0690016	−	0.119514i
$26$	−1.43634	−	1.17006i	−0.281689	−	0.229468i
$27$	−4.88916	−	1.75957i	−0.940920	−	0.338630i
$28$	−1.86404	−	4.95231i	−0.352270	−	0.935899i
$29$			0.865568i			0.160732i	0.996765	+	0.0803660i	$0.0256089\pi$
$29$			0.865568i			0.160732i	−0.996765	+	0.0803660i	$0.974391\pi$
$30$	−4.89399	−	1.38160i	−0.893515	−	0.252244i
$31$	3.18742	−	1.84026i	0.572477	−	0.330520i	−0.185661	−	0.982614i	$-0.559443\pi$
$31$	3.18742	−	1.84026i	0.572477	−	0.330520i	0.758138	+	0.652094i	$0.226109\pi$
$32$	−5.44221	−	1.54349i	−0.962055	−	0.272854i
$33$	6.86162	+	0.793650i	1.19445	+	0.138157i
$34$	4.10695	+	0.662741i	0.704336	+	0.113659i
$35$	5.12651	+	1.97200i	0.866538	+	0.333330i
$36$	5.27436	−	2.86026i	0.879061	−	0.476710i
$37$	−2.08850	+	3.61738i	−0.343347	+	0.594694i	−0.985052	−	0.172257i	$-0.944894\pi$
$37$	−2.08850	+	3.61738i	−0.343347	+	0.594694i	0.641705	+	0.766952i	$0.278227\pi$
$38$	0.551664	+	1.44974i	0.0894918	+	0.235179i
$39$	−1.35274	+	1.82161i	−0.216612	+	0.291691i
$40$	4.95238	−	3.15496i	0.783041	−	0.498842i
$41$			7.01712i			1.09589i	0.836514	+	0.547945i	$0.184590\pi$
$41$			7.01712i			1.09589i	−0.836514	+	0.547945i	$0.815410\pi$
$42$	−5.95689	+	2.55254i	−0.919168	+	0.393865i
$43$			4.27597i			0.652080i	0.945356	+	0.326040i	$0.105714\pi$
$43$			4.27597i			0.652080i	−0.945356	+	0.326040i	$0.894286\pi$
$44$	−5.95826	+	5.30234i	−0.898241	+	0.799358i
$45$	−1.42174	+	6.06370i	−0.211940	+	0.903924i
$46$	9.91479	−	3.77285i	1.46186	−	0.556276i
$47$	−3.75063	+	6.49627i	−0.547085	+	0.947579i	0.451388	+	0.892328i	$0.350929\pi$
$47$	−3.75063	+	6.49627i	−0.547085	+	0.947579i	−0.998473	+	0.0552509i	$0.982404\pi$
$48$	−1.58973	+	6.74335i	−0.229457	+	0.973319i
$49$	6.66042	−	2.15379i	0.951489	−	0.307684i
$50$	0.155459	−	0.963368i	0.0219853	−	0.136241i
$51$	0.585414	−	5.06129i	0.0819744	−	0.708722i
$52$	−0.529789	−	2.56584i	−0.0734685	−	0.355818i
$53$	4.27909	−	2.47053i	0.587778	−	0.339354i	−0.176440	−	0.984311i	$-0.556458\pi$
$53$	4.27909	−	2.47053i	0.587778	−	0.339354i	0.764218	+	0.644957i	$0.223125\pi$
$54$	−3.78911	−	6.29624i	−0.515633	−	0.856810i
$55$		−	8.27923i		−	1.11637i
$56$	2.37952	−	7.09492i	0.317977	−	0.948098i
$57$	1.74349	−	0.754555i	0.230931	−	0.0999432i
$58$	−0.773117	+	0.949056i	−0.101515	+	0.124617i
$59$	−2.44458	−	4.23414i	−0.318257	−	0.551238i	0.661867	−	0.749621i	$-0.269764\pi$
$59$	−2.44458	−	4.23414i	−0.318257	−	0.551238i	−0.980125	+	0.198383i	$0.936431\pi$
$60$	−4.13200	−	5.88611i	−0.533439	−	0.759894i
$61$	−2.05347	+	3.55672i	−0.262920	+	0.455391i	−0.967017	−	0.254713i	$-0.918019\pi$
$61$	−2.05347	+	3.55672i	−0.262920	+	0.455391i	0.704096	+	0.710104i	$0.251352\pi$
$62$	5.13856	+	0.829212i	0.652597	+	0.105310i
$63$	3.45008	+	7.14821i	0.434669	+	0.900590i
$64$	−4.58850	−	6.55330i	−0.573562	−	0.819162i
$65$	2.35524	+	1.35980i	0.292131	+	0.168662i
$66$	6.81457	+	6.99893i	0.838816	+	0.861509i
$67$	−2.09778	+	1.21116i	−0.256285	+	0.147966i	−0.622639	−	0.782509i	$-0.713939\pi$
$67$	−2.09778	+	1.21116i	−0.256285	+	0.147966i	0.366354	+	0.930476i	$0.380606\pi$
$68$	3.91113	+	4.39495i	0.474294	+	0.532966i
$69$	−5.16042	−	11.9238i	−0.621242	−	1.43545i
$70$	3.85961	+	6.74116i	0.461311	+	0.805722i
$71$	−0.901192			−0.106952			−0.0534759	−	0.998569i	$-0.517030\pi$
$71$	−0.901192			−0.106952			−0.0534759	+	0.998569i	$0.517030\pi$
$72$	8.33785	+	1.57487i	0.982625	+	0.185600i
$73$	−6.50543	−	11.2677i	−0.761403	−	1.31879i	−0.942128	−	0.335255i	$-0.891178\pi$
$73$	−6.50543	−	11.2677i	−0.761403	−	1.31879i	0.180725	−	0.983534i	$-0.442156\pi$
$74$	−5.52095	+	2.10087i	−0.641798	+	0.244221i
$75$	−1.18723	−	0.137321i	−0.137089	−	0.0158564i
$76$	−0.690016	+	2.08231i	−0.0791503	+	0.238858i
$77$	−6.63432	−	8.20446i	−0.756051	−	0.934985i
$78$	−3.11026	+	0.789060i	−0.352168	+	0.0893435i
$79$	8.97336	+	5.18077i	1.00958	+	0.582882i	0.911069	−	0.412254i	$-0.135258\pi$
$79$	8.97336	+	5.18077i	1.00958	+	0.582882i	0.0985123	+	0.995136i	$0.468592\pi$
$80$	8.24804	+	0.964154i	0.922159	+	0.107796i
$81$	−7.49553	+	4.98167i	−0.832836	+	0.553519i
$82$	−6.26762	+	7.69395i	−0.692143	+	0.849654i
$83$	−12.4386			−1.36531			−0.682657	−	0.730739i	$-0.739176\pi$
$83$	−12.4386			−1.36531			−0.682657	+	0.730739i	$0.739176\pi$
$84$	−8.81136	−	2.52189i	−0.961398	−	0.275161i
$85$	−6.10695			−0.662391
$86$	−3.81926	+	4.68841i	−0.411841	+	0.505564i
$87$	1.20363	+	0.893819i	0.129042	+	0.0958275i
$88$	−11.2690	+	0.491915i	−1.20127	+	0.0524384i
$89$	−7.38393	−	4.26311i	−0.782695	−	0.451889i	0.0546896	−	0.998503i	$-0.482583\pi$
$89$	−7.38393	−	4.26311i	−0.782695	−	0.451889i	−0.837385	+	0.546614i	$0.815916\pi$
$90$	−6.97491	+	5.37869i	−0.735220	+	0.566964i
$91$	3.42360	−	0.539786i	0.358891	−	0.0565850i
$92$	14.2410	+	4.71904i	1.48473	+	0.491994i
$93$	0.732462	−	6.33262i	0.0759528	−	0.656662i
$94$	−9.91479	+	3.77285i	−1.02263	+	0.389139i
$95$	−1.13854	−	1.97200i	−0.116811	−	0.202323i
$96$	−7.76615	+	5.97385i	−0.792630	+	0.609703i
$97$	15.3909			1.56271			0.781354	−	0.624088i	$-0.214529\pi$
$97$	15.3909			1.56271			0.781354	+	0.624088i	$0.214529\pi$
$98$	9.22659	+	3.58749i	0.932026	+	0.362391i
$99$	8.18919	−	8.72195i	0.823045	−	0.876588i
$100$	1.03092	−	0.917434i	0.103092	−	0.0917434i
$101$	−5.28731	+	3.05263i	−0.526107	+	0.303748i	−0.739430	−	0.673234i	$-0.764905\pi$
$101$	−5.28731	+	3.05263i	−0.526107	+	0.303748i	0.213322	+	0.976982i	$0.431572\pi$
$102$	5.16257	−	5.02659i	0.511171	−	0.497706i
$103$	−6.17682	−	3.56619i	−0.608620	−	0.351387i	0.163805	−	0.986493i	$-0.447623\pi$
$103$	−6.17682	−	3.56619i	−0.608620	−	0.351387i	−0.772425	+	0.635106i	$0.780956\pi$
$104$	1.71090	−	3.28653i	0.167767	−	0.322271i
$105$	8.03602	−	5.09235i	0.784235	−	0.496963i
$106$	6.89848	+	1.11321i	0.670040	+	0.108125i
$107$	1.20838	−	2.09297i	0.116818	−	0.202335i	−0.801687	−	0.597744i	$-0.796064\pi$
$107$	1.20838	−	2.09297i	0.116818	−	0.202335i	0.918505	+	0.395409i	$0.129397\pi$
$108$	1.46915	−	10.2879i	0.141369	−	0.989957i
$109$	3.39848	+	5.88634i	0.325516	+	0.563809i	0.981617	−	0.190864i	$-0.0611288\pi$
$109$	3.39848	+	5.88634i	0.325516	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$110$	7.39492	−	9.07779i	0.705078	−	0.865534i
$111$	2.87353	+	6.63963i	0.272743	+	0.630206i
$112$	8.94615	−	5.65389i	0.845332	−	0.534242i
$113$		−	3.16365i		−	0.297611i	−0.988867	−	0.148805i	$-0.952457\pi$
$113$		−	3.16365i		−	0.297611i	0.988867	−	0.148805i	$-0.0475428\pi$
$114$	2.58562	+	0.729933i	0.242165	+	0.0683644i
$115$	−13.4866	+	7.78649i	−1.25763	+	0.726094i
$116$	−1.69537	+	0.350057i	−0.157412	+	0.0325019i
$117$	1.13617	+	3.76213i	0.105039	+	0.347809i
$118$	1.10152	−	6.82601i	0.101403	−	0.628386i
$119$	−6.05179	+	4.89363i	−0.554767	+	0.448598i
$120$	0.726865	−	10.1445i	0.0663534	−	0.926064i
$121$	−2.45196	+	4.24691i	−0.222905	+	0.386083i
$122$	−5.42837	+	2.06564i	−0.491461	+	0.187014i
$123$	9.75772	+	7.24614i	0.879824	+	0.653363i
$124$	4.89355	+	5.49890i	0.439454	+	0.493816i
$125$			11.8128i			1.05657i
$126$	−2.60186	+	10.9193i	−0.231792	+	0.972765i
$127$		−	15.0889i		−	1.33892i	−0.742848	−	0.669460i	$-0.766526\pi$
$127$		−	15.0889i		−	1.33892i	0.742848	−	0.669460i	$-0.233474\pi$
$128$	0.822259	−	11.2838i	0.0726781	−	0.997355i
$129$	5.94600	+	4.41553i	0.523516	+	0.388766i
$130$	1.36785	+	3.59463i	0.119969	+	0.315270i
$131$	3.70488	−	6.41704i	0.323697	−	0.560660i	−0.657551	−	0.753410i	$-0.728407\pi$
$131$	3.70488	−	6.41704i	0.323697	−	0.560660i	0.981248	+	0.192751i	$0.0617408\pi$
$132$	1.22049	+	13.7607i	0.106230	+	1.19772i
$133$	−2.70847	−	1.04186i	−0.234854	−	0.0903407i
$134$	−3.38192	−	0.545742i	−0.292153	−	0.0471449i
$135$	6.96381	+	8.23863i	0.599349	+	0.709068i
$136$	0.362848	+	8.31224i	0.0311140	+	0.712768i
$137$	13.0764	−	7.54965i	1.11719	−	0.645010i	0.176508	−	0.984299i	$-0.443520\pi$
$137$	13.0764	−	7.54965i	1.11719	−	0.645010i	0.940682	+	0.339290i	$0.110187\pi$
$138$	4.99203	−	17.6831i	0.424950	−	1.50529i
$139$			14.4761i			1.22785i	0.789364	+	0.613925i	$0.210410\pi$
$139$			14.4761i			1.22785i	−0.789364	+	0.613925i	$0.789590\pi$
$140$	−1.78925	+	10.8387i	−0.151219	+	0.916040i
$141$	5.16042	+	11.9238i	0.434586	+	1.00416i
$142$	−0.988116	−	0.804935i	−0.0829208	−	0.0675487i
$143$	−2.61209	−	4.52427i	−0.218434	−	0.378338i
$144$	7.73542	+	9.17405i	0.644618	+	0.764504i
$145$	0.898482	−	1.55622i	0.0746148	−	0.129237i
$146$	2.93132	−	18.1651i	0.242598	−	1.50336i
$147$	3.88283	−	11.4858i	0.320251	−	0.947333i
$148$	−7.92995	−	2.62775i	−0.651838	−	0.216000i
$149$	9.86511	+	5.69562i	0.808181	+	0.466604i	0.846324	−	0.532669i	$-0.178811\pi$
$149$	9.86511	+	5.69562i	0.808181	+	0.466604i	−0.0381428	+	0.999272i	$0.512144\pi$
$150$	−1.17909	−	1.21099i	−0.0962721	−	0.0988766i
$151$	−0.795186	+	0.459101i	−0.0647113	+	0.0373611i	−0.532007	−	0.846740i	$-0.678562\pi$
$151$	−0.795186	+	0.459101i	−0.0647113	+	0.0373611i	0.467295	+	0.884101i	$0.345229\pi$
$152$	−2.61647	+	1.66684i	−0.212224	+	0.135199i
$153$	−6.43351	−	6.04054i	−0.520118	−	0.488348i
$154$	0.0539032	−	14.9215i	0.00434364	−	1.20241i
$155$	−7.64093			−0.613734
$156$	−4.11504	−	1.91289i	−0.329467	−	0.153153i
$157$	4.36346	+	7.55773i	0.348242	+	0.603172i	0.985937	−	0.167116i	$-0.0534455\pi$
$157$	4.36346	+	7.55773i	0.348242	+	0.603172i	−0.637695	+	0.770289i	$0.720112\pi$
$158$	5.21146	+	13.6954i	0.414602	+	1.08955i
$159$	0.983326	−	8.50150i	0.0779829	−	0.674213i
$160$	8.18242	+	8.42422i	0.646877	+	0.665993i
$161$	−7.12531	+	18.5233i	−0.561553	+	1.45984i
$162$	−12.6681	−	1.23275i	−0.995299	−	0.0968540i
$163$	−7.78729	−	4.49599i	−0.609948	−	0.352153i	0.162997	−	0.986627i	$-0.447884\pi$
$163$	−7.78729	−	4.49599i	−0.609948	−	0.352153i	−0.772945	+	0.634473i	$0.781217\pi$
$164$	−13.7443	+	2.83789i	−1.07325	+	0.221602i
$165$	−11.5128	−	8.54945i	−0.896267	−	0.665574i
$166$	−13.6384	−	11.1100i	−1.05854	−	0.862306i
$167$	16.1830			1.25228			0.626141	−	0.779710i	$-0.284633\pi$
$167$	16.1830			1.25228			0.626141	+	0.779710i	$0.284633\pi$
$168$	−7.40872	−	10.6354i	−0.571595	−	0.820536i
$169$	−11.2839			−0.867996
$170$	−6.69599	−	5.45466i	−0.513559	−	0.418354i
$171$	0.751141	−	3.20361i	0.0574412	−	0.244986i
$172$	−8.37528	+	1.72931i	−0.638609	+	0.131858i
$173$	3.66216	+	2.11435i	0.278429	+	0.160751i	0.632712	−	0.774387i	$-0.281942\pi$
$173$	3.66216	+	2.11435i	0.278429	+	0.160751i	−0.354283	+	0.935138i	$0.615275\pi$
$174$	0.521370	+	2.05510i	0.0395249	+	0.155797i
$175$	1.14790	+	1.41957i	0.0867731	+	0.107310i
$176$	−12.7953	−	9.52595i	−0.964479	−	0.718046i
$177$	−8.41219	−	0.972997i	−0.632299	−	0.0731349i
$178$	−4.28837	−	11.2696i	−0.321427	−	0.844689i
$179$	−3.27593	−	5.67408i	−0.244855	−	0.424101i	0.717236	−	0.696830i	$-0.245407\pi$
$179$	−3.27593	−	5.67408i	−0.244855	−	0.424101i	−0.962091	+	0.272729i	$0.912074\pi$
$180$	−12.4519	−	0.332428i	−0.928107	−	0.0247777i
$181$	−12.2839			−0.913058			−0.456529	−	0.889708i	$-0.650908\pi$
$181$	−12.2839			−0.913058			−0.456529	+	0.889708i	$0.650908\pi$
$182$	4.23595	+	2.46607i	0.313990	+	0.182797i
$183$	2.82534	+	6.52828i	0.208855	+	0.482585i
$184$	11.3996	+	17.8941i	0.840389	+	1.31917i
$185$	7.50987	−	4.33583i	0.552137	−	0.318776i
$186$	6.45934	−	6.28919i	0.473622	−	0.461146i
$187$	10.1594	+	5.86554i	0.742930	+	0.428931i
$188$	−14.2410	−	4.71904i	−1.03863	−	0.344171i
$189$	13.5027	+	2.58397i	0.982177	+	0.187956i
$190$	0.513020	−	3.17914i	0.0372184	−	0.230639i
$191$	−11.8662	+	20.5529i	−0.858611	+	1.48716i	0.0146426	+	0.999893i	$0.495339\pi$
$191$	−11.8662	+	20.5529i	−0.858611	+	1.48716i	−0.873254	+	0.487266i	$0.837994\pi$
$192$	−13.8510	−	0.386602i	−0.999611	−	0.0279006i
$193$	1.98698	+	3.44155i	0.143026	+	0.247728i	0.928635	−	0.370995i	$-0.120983\pi$
$193$	1.98698	+	3.44155i	0.143026	+	0.247728i	−0.785609	+	0.618724i	$0.787650\pi$
$194$	16.8754	+	13.7470i	1.21158	+	0.986976i
$195$	4.32298	−	1.87092i	0.309575	−	0.133979i
$196$	6.91222	+	12.1746i	0.493730	+	0.869615i
$197$		−	19.7720i		−	1.40870i	−0.709853	−	0.704350i	$-0.751239\pi$
$197$		−	19.7720i		−	1.40870i	0.709853	−	0.704350i	$-0.248761\pi$
$198$	16.7694	−	2.24871i	1.19175	−	0.159809i
$199$	6.63939	−	3.83325i	0.470654	−	0.271732i	−0.245859	−	0.969305i	$-0.579070\pi$
$199$	6.63939	−	3.83325i	0.470654	−	0.271732i	0.716513	+	0.697573i	$0.245737\pi$
$200$	1.94980	−	0.0851134i	0.137872	−	0.00601843i
$201$	−0.482067	+	4.16778i	−0.0340024	+	0.293973i
$202$	−8.52388	−	1.37550i	−0.599738	−	0.0967801i
$203$	−0.356662	−	2.26213i	−0.0250328	−	0.158771i
$204$	10.1502	−	0.900265i	0.710657	−	0.0630311i
$205$	7.28394	−	12.6162i	0.508733	−	0.881151i
$206$	−3.58732	−	9.42723i	−0.249940	−	0.656826i
$207$	−21.9096	−	5.13707i	−1.52282	−	0.357051i
$208$	4.81142	−	2.07538i	0.333612	−	0.143901i
$209$			4.37413i			0.302565i
$210$	13.3596	+	1.59416i	0.921898	+	0.110008i
$211$			11.7483i			0.808789i	0.914585	+	0.404395i	$0.132518\pi$
$211$			11.7483i			0.808789i	−0.914585	+	0.404395i	$0.867482\pi$
$212$	6.56956	+	7.38224i	0.451199	+	0.507014i
$213$	−0.930605	+	1.25316i	−0.0637640	+	0.0858652i
$214$	3.19435	−	1.21554i	0.218361	−	0.0830923i
$215$	4.43857	−	7.68782i	0.302708	−	0.524305i
$216$	10.7999	−	9.96802i	0.734842	−	0.678238i
$217$	−7.57192	+	6.12284i	−0.514016	+	0.415646i
$218$	−1.53134	+	9.48959i	−0.103716	+	0.642716i
$219$	−22.3862	−	2.58930i	−1.51272	−	0.174969i
$220$	16.2164	−	3.34832i	1.09331	−	0.225743i
$221$	−3.33720	+	1.92674i	−0.224485	+	0.129606i
$222$	−2.77976	+	9.84666i	−0.186565	+	0.660865i
$223$		−	14.5202i		−	0.972345i	−0.873863	−	0.486173i	$-0.838393\pi$
$223$		−	14.5202i		−	0.972345i	0.873863	−	0.486173i	$-0.161607\pi$
$224$	14.8590	+	1.79138i	0.992811	+	0.119692i
$225$	−1.41693	+	1.50911i	−0.0944620	+	0.100607i
$226$	2.82574	−	3.46879i	0.187965	−	0.230741i
$227$	10.7314	+	18.5874i	0.712271	+	1.23369i	0.964003	+	0.265892i	$0.0856665\pi$
$227$	10.7314	+	18.5874i	0.712271	+	1.23369i	−0.251732	+	0.967797i	$0.581000\pi$
$228$	2.18304	+	3.10978i	0.144576	+	0.205951i
$229$	9.81541	−	17.0008i	0.648621	−	1.12344i	−0.334832	−	0.942278i	$-0.608680\pi$
$229$	9.81541	−	17.0008i	0.648621	−	1.12344i	0.983453	−	0.181166i	$-0.0579872\pi$
$230$	−21.7422	−	3.50856i	−1.43364	−	0.231348i
$231$	−18.2596	+	0.753192i	−1.20140	+	0.0495564i
$232$	−2.17157	−	1.13047i	−0.142570	−	0.0742190i
$233$	−12.3530	−	7.13202i	−0.809273	−	0.467234i	0.0374302	−	0.999299i	$-0.488083\pi$
$233$	−12.3530	−	7.13202i	−0.809273	−	0.467234i	−0.846703	+	0.532065i	$0.821416\pi$
$234$	−2.11454	+	5.13982i	−0.138232	+	0.336001i
$235$	13.4866	−	7.78649i	0.879768	−	0.507934i
$236$	7.30469	−	6.50055i	0.475495	−	0.423150i
$237$	16.4704	−	7.12813i	1.06987	−	0.463022i
$238$	−11.0065	−	0.0397602i	−0.713443	−	0.00257727i
$239$	15.2819			0.988501			0.494251	−	0.869320i	$-0.335443\pi$
$239$	15.2819			0.988501			0.494251	+	0.869320i	$0.335443\pi$
$240$	9.85796	−	10.4738i	0.636328	−	0.676079i
$241$	2.95196	+	5.11294i	0.190152	+	0.329353i	0.945301	−	0.326201i	$-0.105769\pi$
$241$	2.95196	+	5.11294i	0.190152	+	0.329353i	−0.755148	+	0.655554i	$0.772435\pi$
$242$	−6.48175	+	2.46648i	−0.416663	+	0.158551i
$243$	−0.812849	+	15.5673i	−0.0521443	+	0.998640i
$244$	−7.79696	−	2.58368i	−0.499149	−	0.165403i
$245$	−14.2105	−	3.04136i	−0.907878	−	0.194305i
$246$	4.22672	+	16.6606i	0.269486	+	1.06224i
$247$	−1.24433	−	0.718415i	−0.0791749	−	0.0457116i
$248$	0.453991	+	10.4002i	0.0288284	+	0.660411i
$249$	−12.8446	+	17.2966i	−0.813992	+	1.09613i
$250$	−10.5510	+	12.9521i	−0.667306	+	0.819166i
$251$	23.7400			1.49845			0.749226	−	0.662314i	$-0.230425\pi$
$251$	23.7400			1.49845			0.749226	+	0.662314i	$0.230425\pi$
$252$	−12.6058	+	9.64852i	−0.794090	+	0.607800i
$253$	29.9148			1.88073
$254$	13.4772	−	16.5442i	0.845636	−	1.03808i
$255$	−6.30627	+	8.49208i	−0.394914	+	0.531795i
$256$	10.9801	−	11.6377i	0.686258	−	0.727358i
$257$	−12.8177	−	7.40033i	−0.799549	−	0.461620i	0.0437643	−	0.999042i	$-0.486065\pi$
$257$	−12.8177	−	7.40033i	−0.799549	−	0.461620i	−0.843314	+	0.537422i	$0.819398\pi$
$258$	2.57560	+	10.1523i	0.160350	+	0.632057i
$259$	3.96766	−	10.3145i	0.246538	−	0.640911i
$260$	−1.71090	+	5.16309i	−0.106105	+	0.320202i
$261$	2.48582	−	0.750721i	0.153868	−	0.0464685i
$262$	9.79387	−	3.72683i	0.605067	−	0.230244i
$263$	−6.95299	−	12.0429i	−0.428740	−	0.742599i	0.568022	−	0.823013i	$-0.307709\pi$
$263$	−6.95299	−	12.0429i	−0.428740	−	0.742599i	−0.996761	+	0.0804148i	$0.974376\pi$
$264$	−10.9527	+	16.1781i	−0.674093	+	0.995695i
$265$	−10.2579			−0.630138
$266$	−2.03913	−	3.56153i	−0.125027	−	0.218371i
$267$	−13.5530	+	5.86554i	−0.829433	+	0.358965i
$268$	−3.22066	−	3.61907i	−0.196733	−	0.221070i
$269$	7.15156	−	4.12896i	0.436039	−	0.251747i	−0.265877	−	0.964007i	$-0.585662\pi$
$269$	7.15156	−	4.12896i	0.436039	−	0.251747i	0.701916	+	0.712260i	$0.252328\pi$
$270$	0.276837	+	15.2533i	0.0168477	+	0.928285i
$271$	−4.59472	−	2.65276i	−0.279109	−	0.161144i	0.353911	−	0.935279i	$-0.384852\pi$
$271$	−4.59472	−	2.65276i	−0.279109	−	0.161144i	−0.633020	+	0.774135i	$0.718185\pi$
$272$	−7.02656	+	9.43808i	−0.426048	+	0.572268i
$273$	2.78473	−	5.31812i	0.168540	−	0.321868i
$274$	21.0809	+	3.40184i	1.27354	+	0.205513i
$275$	1.37588	−	2.38310i	0.0829688	−	0.143706i
$276$	21.2679	−	14.9299i	1.28018	−	0.898674i
$277$	−6.30239	−	10.9161i	−0.378674	−	0.655883i	0.612196	−	0.790706i	$-0.290287\pi$
$277$	−6.30239	−	10.9161i	−0.378674	−	0.655883i	−0.990870	+	0.134824i	$0.956953\pi$
$278$	−12.9299	+	15.8724i	−0.775486	+	0.951965i
$279$	−8.04951	−	7.55783i	−0.481912	−	0.452476i
$280$	−11.6429	+	10.2860i	−0.695795	+	0.614708i
$281$			2.02977i			0.121086i	0.998166	+	0.0605428i	$0.0192832\pi$
$281$			2.02977i			0.121086i	−0.998166	+	0.0605428i	$0.980717\pi$
$282$	−4.99203	+	17.6831i	−0.297271	+	1.05301i
$283$	6.64918	−	3.83891i	0.395253	−	0.228199i	−0.289181	−	0.957274i	$-0.593383\pi$
$283$	6.64918	−	3.83891i	0.395253	−	0.228199i	0.684434	+	0.729075i	$0.260050\pi$
$284$	−0.364463	−	1.76515i	−0.0216269	−	0.104742i
$285$	−3.91789	−	0.453163i	−0.232076	−	0.0268430i
$286$	1.17700	−	7.29374i	0.0695972	−	0.431288i
$287$	−2.89144	−	18.3390i	−0.170676	−	1.08252i
$288$	0.287363	+	16.9681i	0.0169331	+	0.999857i
$289$	−4.17344	+	7.22861i	−0.245497	+	0.425212i
$290$	2.37514	−	0.903805i	0.139473	−	0.0530732i
$291$	15.8932	−	21.4020i	0.931677	−	1.25461i
$292$	19.4390	−	17.2990i	1.13758	−	1.01235i
$293$			1.55539i			0.0908671i	0.998967	+	0.0454336i	$0.0144669\pi$
$293$			1.55539i			0.0908671i	−0.998967	+	0.0454336i	$0.985533\pi$
$294$	14.5163	−	9.12555i	0.846611	−	0.532213i
$295$			10.1501i			0.590964i
$296$	−6.34775	−	9.96416i	−0.368955	−	0.579155i
$297$	−3.67192	−	20.3942i	−0.213066	−	1.18339i
$298$	5.72937	+	15.0564i	0.331893	+	0.872194i
$299$	−4.91326	+	8.51001i	−0.284141	+	0.492147i
$300$	−0.211175	−	2.38094i	−0.0121922	−	0.137464i
$301$	−1.76194	−	11.1751i	−0.101556	−	0.644123i
$302$	−1.28195	−	0.206869i	−0.0737679	−	0.0119040i
$303$	−1.21501	+	10.5046i	−0.0698008	+	0.603473i
$304$	−4.35765	−	0.509387i	−0.249928	−	0.0292154i
$305$	7.38393	−	4.26311i	0.422803	−	0.244105i
$306$	−1.65870	−	12.3695i	−0.0948216	−	0.707118i
$307$			31.5800i			1.80237i	0.433437	+	0.901184i	$0.357301\pi$
$307$			31.5800i			1.80237i	−0.433437	+	0.901184i	$0.642699\pi$
$308$	13.3869	−	16.3126i	0.762787	−	0.929498i
$309$	−11.3374	+	4.90665i	−0.644963	+	0.279130i
$310$	−8.37793	−	6.82480i	−0.475834	−	0.387623i
$311$	9.13857	+	15.8285i	0.518201	+	0.897550i	0.999776	+	0.0211458i	$0.00673141\pi$
$311$	9.13857	+	15.8285i	0.518201	+	0.897550i	−0.481575	+	0.876405i	$0.659935\pi$
$312$	−2.80338	−	5.77290i	−0.158710	−	0.326826i
$313$	−14.8909	+	25.7918i	−0.841683	+	1.45784i	0.0467882	+	0.998905i	$0.485101\pi$
$313$	−14.8909	+	25.7918i	−0.841683	+	1.45784i	−0.888471	+	0.458933i	$0.848232\pi$
$314$	−1.96616	+	12.1841i	−0.110957	+	0.687589i
$315$	1.21708	−	16.4331i	0.0685748	−	0.925902i
$316$	−6.51845	+	19.6712i	−0.366691	+	1.10659i
$317$	15.3252	+	8.84800i	0.860748	+	0.496953i	0.864263	−	0.503041i	$-0.167785\pi$
$317$	15.3252	+	8.84800i	0.860748	+	0.496953i	−0.00351474	+	0.999994i	$0.501119\pi$
$318$	8.67163	−	8.44321i	0.486281	−	0.473472i
$319$	−2.98940	+	1.72593i	−0.167374	+	0.0966336i
$320$	1.44723	+	16.5452i	0.0809027	+	0.924906i
$321$	−1.66258	−	3.84160i	−0.0927964	−	0.214417i
$322$	−24.3574	+	13.9457i	−1.35738	+	0.777161i
$323$	3.22646			0.179525
$324$	−12.7889	−	12.6667i	−0.710494	−	0.703703i
$325$	0.451955	+	0.782809i	0.0250700	+	0.0434224i
$326$	−4.52263	−	11.8852i	−0.250485	−	0.658259i
$327$	11.6947	+	1.35267i	0.646719	+	0.0748028i
$328$	−17.6048	−	9.16466i	−0.972062	−	0.506034i
$329$	7.12531	−	18.5233i	0.392831	−	1.02122i
$330$	−4.98694	−	19.6572i	−0.274522	−	1.08209i
$331$	−30.3818	−	17.5410i	−1.66994	−	0.964138i	−0.967668	−	0.252225i	$-0.918838\pi$
$331$	−30.3818	−	17.5410i	−1.66994	−	0.964138i	−0.702268	−	0.711913i	$-0.747829\pi$
$332$	−5.03047	−	24.3633i	−0.276083	−	1.33711i
$333$	12.2001	+	2.86053i	0.668563	+	0.156756i
$334$	17.7440	+	14.4545i	0.970907	+	0.790917i
$335$	5.02884			0.274755
$336$	1.37607	−	18.2786i	0.0750705	−	0.997178i
$337$	−0.132987			−0.00724428			−0.00362214	−	0.999993i	$-0.501153\pi$
$337$	−0.132987			−0.00724428			−0.00362214	+	0.999993i	$0.501153\pi$
$338$	−12.3723	−	10.0787i	−0.672966	−	0.548209i
$339$	−4.39924	−	3.26690i	−0.238934	−	0.177434i
$340$	−2.46979	−	11.9616i	−0.133943	−	0.648708i
$341$	12.7113	+	7.33889i	0.688357	+	0.397423i
$342$	3.68502	−	2.84170i	0.199263	−	0.153662i
$343$	−16.5193	+	8.37332i	−0.891959	+	0.452117i
$344$	−10.7277	−	5.58461i	−0.578399	−	0.301102i
$345$	−3.09919	+	26.7945i	−0.166855	+	1.44257i
$346$	2.12688	+	5.58930i	0.114342	+	0.300482i
$347$	−0.0976681	−	0.169166i	−0.00524310	−	0.00908131i	0.863392	−	0.504534i	$-0.168336\pi$
$347$	−0.0976681	−	0.169166i	−0.00524310	−	0.00908131i	−0.868635	+	0.495452i	$0.835002\pi$
$348$	−1.26393	+	2.71900i	−0.0677540	+	0.145754i
$349$	5.80782			0.310885			0.155443	−	0.987845i	$-0.450320\pi$
$349$	5.80782			0.310885			0.155443	+	0.987845i	$0.450320\pi$
$350$	−0.00932657	+	2.58179i	−0.000498526	+	0.138002i
$351$	6.40472	+	2.30501i	0.341859	+	0.123032i
$352$	−5.52094	−	21.8734i	−0.294267	−	1.16585i
$353$	−17.3154	+	9.99704i	−0.921604	+	0.532089i	−0.884147	−	0.467210i	$-0.845259\pi$
$353$	−17.3154	+	9.99704i	−0.921604	+	0.532089i	−0.0374578	+	0.999298i	$0.511926\pi$
$354$	−8.35451	−	8.58053i	−0.444037	−	0.456050i
$355$	1.62026	+	0.935460i	0.0859947	+	0.0496490i
$356$	5.36385	−	16.1869i	0.284284	−	0.857903i
$357$	0.555572	+	13.4687i	0.0294040	+	0.712841i
$358$	1.47612	−	9.14741i	0.0780155	−	0.483455i
$359$	−6.95299	+	12.0429i	−0.366965	+	0.635601i	−0.989089	−	0.147317i	$-0.952936\pi$
$359$	−6.95299	+	12.0429i	−0.366965	+	0.635601i	0.622125	+	0.782918i	$0.286270\pi$
$360$	−13.3560	−	11.4864i	−0.703922	−	0.605385i
$361$	−8.89848	−	15.4126i	−0.468341	−	0.811191i
$362$	−13.4688	−	10.9719i	−0.707903	−	0.576670i
$363$	3.37360	+	7.79511i	0.177068	+	0.409137i
$364$	2.44186	+	6.48744i	0.127988	+	0.340034i
$365$			27.0112i			1.41383i
$366$	−2.73314	+	9.68153i	−0.142864	+	0.506062i
$367$	16.2929	−	9.40672i	0.850483	−	0.491027i	−0.0103306	−	0.999947i	$-0.503288\pi$
$367$	16.2929	−	9.40672i	0.850483	−	0.491027i	0.860814	+	0.508920i	$0.169955\pi$
$368$	−3.48371	+	29.8021i	−0.181601	+	1.55354i
$369$	20.1524	−	6.08606i	1.04909	−	0.316827i
$370$	12.1069	+	1.95371i	0.629410	+	0.101568i
$371$	−10.1653	+	8.21988i	−0.527754	+	0.426755i
$372$	12.6998	−	1.12640i	0.658455	−	0.0584011i
$373$	−2.91150	+	5.04287i	−0.150752	+	0.261110i	−0.931504	−	0.363731i	$-0.881503\pi$
$373$	−2.91150	+	5.04287i	−0.150752	+	0.261110i	0.780752	+	0.624841i	$0.214836\pi$
$374$	5.90030	+	15.5056i	0.305097	+	0.801775i
$375$	16.4264	+	12.1983i	0.848253	+	0.629918i
$376$	−11.3996	−	17.8941i	−0.587889	−	0.922819i
$377$		−	1.13388i		−	0.0583978i
$378$	12.4971	+	14.8937i	0.642783	+	0.766049i
$379$			12.0598i			0.619469i	0.950823	+	0.309735i	$0.100240\pi$
$379$			12.0598i			0.619469i	−0.950823	+	0.309735i	$0.899760\pi$
$380$	3.40208	−	3.02756i	0.174523	−	0.155311i
$381$	−20.9820	−	15.5813i	−1.07494	−	0.798256i
$382$	−31.3685	+	11.9365i	−1.60495	+	0.610727i
$383$	6.07589	−	10.5237i	0.310463	−	0.537738i	−0.667999	−	0.744162i	$-0.732849\pi$
$383$	6.07589	−	10.5237i	0.310463	−	0.537738i	0.978463	+	0.206423i	$0.0661824\pi$
$384$	−14.8417	−	12.7955i	−0.757387	−	0.652966i
$385$	3.41150	+	21.6375i	0.173866	+	1.10275i
$386$	−0.895325	+	5.54825i	−0.0455708	+	0.282399i
$387$	12.2801	−	3.70862i	0.624234	−	0.188520i
$388$	6.22444	+	30.1459i	0.315998	+	1.53043i
$389$	1.04831	−	0.605241i	0.0531513	−	0.0306869i	−0.473189	−	0.880961i	$-0.656897\pi$
$389$	1.04831	−	0.605241i	0.0531513	−	0.0306869i	0.526340	+	0.850274i	$0.323564\pi$
$390$	6.41104	+	1.80987i	0.324636	+	0.0916462i
$391$		−	22.0658i		−	1.11592i
$392$	−3.29531	+	19.5228i	−0.166438	+	0.986052i
$393$	−5.09748	−	11.7783i	−0.257134	−	0.594139i
$394$	17.6602	−	21.6791i	0.889708	−	1.09218i
$395$	−10.7555	−	18.6291i	−0.541170	−	0.937334i
$396$	20.3954	+	12.5127i	1.02491	+	0.628785i
$397$	4.77851	−	8.27663i	0.239827	−	0.415392i	−0.720838	−	0.693104i	$-0.756243\pi$
$397$	4.77851	−	8.27663i	0.239827	−	0.415392i	0.960664	+	0.277712i	$0.0895760\pi$
$398$	10.7036	+	1.72725i	0.536524	+	0.0865792i
$399$	−4.24563	+	2.69042i	−0.212548	+	0.134689i
$400$	2.21389	+	1.64822i	0.110695	+	0.0824111i
$401$	9.73916	+	5.62291i	0.486351	+	0.280795i	0.723059	−	0.690786i	$-0.242735\pi$
$401$	9.73916	+	5.62291i	0.486351	+	0.280795i	−0.236709	+	0.971581i	$0.576069\pi$
$402$	−4.25118	+	4.13920i	−0.212030	+	0.206445i
$403$	−4.17546	+	2.41071i	−0.207995	+	0.120086i
$404$	−8.11746	−	9.12162i	−0.403859	−	0.453817i
$405$	18.6474	−	1.17607i	0.926597	−	0.0584393i
$406$	1.62945	−	2.79889i	0.0808683	−	0.138907i
$407$	−16.6577			−0.825693
$408$	11.9334	+	8.07897i	0.590789	+	0.399969i
$409$	7.78394	+	13.4822i	0.384891	+	0.666651i	0.991754	−	0.128155i	$-0.0409056\pi$
$409$	7.78394	+	13.4822i	0.384891	+	0.666651i	−0.606863	+	0.794807i	$0.707572\pi$
$410$	19.2551	−	7.32710i	0.950943	−	0.361860i
$411$	3.00492	−	25.9795i	0.148222	−	1.28148i
$412$	4.48698	−	13.5407i	0.221058	−	0.667101i
$413$	8.13353	+	10.0585i	0.400225	+	0.494945i
$414$	−19.4345	−	25.2020i	−0.955152	−	1.23861i
$415$	22.3635	+	12.9116i	1.09778	+	0.633805i
$416$	7.12920	+	2.02195i	0.349538	+	0.0991344i
$417$	20.1299	+	14.9486i	0.985768	+	0.732037i
$418$	−3.90693	+	4.79603i	−0.191094	+	0.234582i
$419$	−18.0336			−0.881000			−0.440500	−	0.897753i	$-0.645199\pi$
$419$	−18.0336			−0.881000			−0.440500	+	0.897753i	$0.645199\pi$
$420$	13.2243	+	13.6806i	0.645278	+	0.667543i
$421$	−12.4978			−0.609107			−0.304554	−	0.952495i	$-0.598507\pi$
$421$	−12.4978			−0.609107			−0.304554	+	0.952495i	$0.598507\pi$
$422$	−10.4935	+	12.8815i	−0.510816	+	0.627063i
$423$	21.9096	+	5.13707i	1.06528	+	0.249773i
$424$	0.609480	+	13.9622i	0.0295990	+	0.678062i
$425$	−1.75783	−	1.01488i	−0.0852672	−	0.0492290i
$426$	−2.13968	+	0.542827i	−0.103668	+	0.0263001i
$427$	3.90112	−	10.1415i	0.188788	−	0.490782i
$428$	4.58816	+	1.52038i	0.221777	+	0.0734903i
$429$	−8.98861	−	1.03967i	−0.433974	−	0.0501957i
$430$	11.7334	−	4.46486i	0.565833	−	0.215315i
$431$	6.22304	+	10.7786i	0.299753	+	0.519188i	0.976079	−	0.217415i	$-0.0697624\pi$
$431$	6.22304	+	10.7786i	0.299753	+	0.519188i	−0.676326	+	0.736602i	$0.736429\pi$
$432$	20.7450	−	1.28309i	0.998093	−	0.0617326i
$433$	−0.497837			−0.0239245			−0.0119623	−	0.999928i	$-0.503808\pi$
$433$	−0.497837			−0.0239245			−0.0119623	+	0.999928i	$0.503808\pi$
$434$	−13.7711	−	0.0497474i	−0.661035	−	0.00238795i
$435$	−1.23621	−	2.85640i	−0.0592715	−	0.136954i
$436$	−10.1551	+	9.03713i	−0.486339	+	0.432800i
$437$	7.12531	−	4.11380i	0.340850	−	0.196790i
$438$	−22.2327	−	22.8342i	−1.06232	−	1.09106i
$439$	4.03571	+	2.33002i	0.192614	+	0.111206i	0.593206	−	0.805051i	$-0.297862\pi$
$439$	4.03571	+	2.33002i	0.192614	+	0.111206i	−0.400592	+	0.916257i	$0.631195\pi$
$440$	20.7712	+	10.8130i	0.990228	+	0.515491i
$441$	−11.9621	−	17.2600i	−0.569625	−	0.821904i
$442$	−5.38003	−	0.868179i	−0.255902	−	0.0412951i
$443$	11.0349	−	19.1130i	0.524283	−	0.908086i	−0.475317	−	0.879815i	$-0.657667\pi$
$443$	11.0349	−	19.1130i	0.524283	−	0.908086i	0.999600	−	0.0282709i	$-0.00900011\pi$
$444$	−11.8428	+	8.31356i	−0.562035	+	0.394544i
$445$	8.85044	+	15.3294i	0.419551	+	0.726684i
$446$	12.9693	−	15.9207i	0.614114	−	0.753869i
$447$	18.1072	−	7.83651i	0.856441	−	0.370654i
$448$	14.6922	+	15.2361i	0.694142	+	0.719838i
$449$		−	6.02866i		−	0.284510i	−0.989830	−	0.142255i	$-0.954565\pi$
$449$		−	6.02866i		−	0.284510i	0.989830	−	0.142255i	$-0.0454353\pi$
$450$	−2.90152	+	0.389082i	−0.136779	+	0.0183415i
$451$	−24.2349	+	13.9920i	−1.14118	+	0.658859i
$452$	6.19658	−	1.27945i	0.291463	−	0.0601804i
$453$	−0.182732	+	1.57984i	−0.00858551	+	0.0742273i
$454$	−4.83554	+	29.9654i	−0.226943	+	1.40635i
$455$	−6.71564	−	2.58329i	−0.314834	−	0.121107i
$456$	−0.384021	+	5.35961i	−0.0179834	+	0.250987i
$457$	19.1308	−	33.1356i	0.894902	−	1.55002i	0.0609766	−	0.998139i	$-0.480578\pi$
$457$	19.1308	−	33.1356i	0.894902	−	1.55002i	0.833926	−	0.551877i	$-0.186088\pi$
$458$	25.9471	−	9.87356i	1.21243	−	0.461361i
$459$	−15.0432	+	2.70849i	−0.702157	+	0.126421i
$460$	−20.7056	−	23.2669i	−0.965402	−	1.08483i
$461$		−	12.4563i		−	0.580148i	−0.957004	−	0.290074i	$-0.906320\pi$
$461$		−	12.4563i		−	0.580148i	0.957004	−	0.290074i	$-0.0936799\pi$
$462$	−20.6936	−	15.4835i	−0.962754	−	0.720357i
$463$		−	28.0609i		−	1.30410i	−0.758176	−	0.652050i	$-0.773909\pi$
$463$		−	28.0609i		−	1.30410i	0.758176	−	0.652050i	$-0.226091\pi$
$464$	−1.37130	−	3.17913i	−0.0636610	−	0.147587i
$465$	−7.89032	+	10.6252i	−0.365905	+	0.492731i
$466$	−7.17427	−	18.8535i	−0.332342	−	0.873373i
$467$	−8.54830	+	14.8061i	−0.395568	+	0.685144i	−0.993174	−	0.116646i	$-0.962786\pi$
$467$	−8.54830	+	14.8061i	−0.395568	+	0.685144i	0.597605	+	0.801790i	$0.296119\pi$
$468$	−6.90933	+	3.74689i	−0.319384	+	0.173200i
$469$	4.98342	−	4.02972i	0.230113	−	0.186075i
$470$	21.7422	+	3.50856i	1.00289	+	0.161838i
$471$	15.0154	+	1.73675i	0.691871	+	0.0800253i
$472$	13.8155	−	0.603077i	0.635909	−	0.0277589i
$473$	−14.7679	+	8.52623i	−0.679027	+	0.392036i
$474$	24.4258	+	6.89553i	1.12191	+	0.316722i
$475$		−	0.756831i		−	0.0347258i
$476$	−12.0326	−	9.87445i	−0.551512	−	0.452595i
$477$	−10.8064	−	10.1464i	−0.494792	−	0.464569i
$478$	16.7559	+	13.6496i	0.766395	+	0.624318i
$479$	−8.21329	−	14.2258i	−0.375275	−	0.649995i	0.615093	−	0.788454i	$-0.289118\pi$
$479$	−8.21329	−	14.2258i	−0.375275	−	0.649995i	−0.990368	+	0.138459i	$0.955785\pi$
$480$	20.1639	−	2.67899i	0.920350	−	0.122278i
$481$	2.73590	−	4.73871i	0.124746	−	0.216067i
$482$	−1.33014	+	8.24276i	−0.0605862	+	0.375447i
$483$	18.3998	+	29.0360i	0.837222	+	1.32118i
$484$	−9.30998	−	3.08505i	−0.423181	−	0.140230i
$485$	−27.6715	−	15.9761i	−1.25650	−	0.725439i
$486$	−14.7958	+	16.3427i	−0.671149	+	0.741322i
$487$	−27.7018	+	15.9937i	−1.25529	+	0.724742i	−0.972155	−	0.234339i	$-0.924708\pi$
$487$	−27.7018	+	15.9937i	−1.25529	+	0.724742i	−0.283134	+	0.959080i	$0.591374\pi$
$488$	−6.24129	−	9.79706i	−0.282530	−	0.443492i
$489$	−14.2934	+	6.18596i	−0.646370	+	0.279739i
$490$	−12.8647	−	16.0274i	−0.581167	−	0.724045i
$491$	−2.03844			−0.0919935			−0.0459968	−	0.998942i	$-0.514646\pi$
$491$	−2.03844			−0.0919935			−0.0459968	+	0.998942i	$0.514646\pi$
$492$	−10.2466	+	22.0428i	−0.461955	+	0.993767i
$493$	1.27309	+	2.20505i	0.0573369	+	0.0993104i
$494$	−0.722671	−	1.89913i	−0.0325145	−	0.0854460i
$495$	−23.7770	+	7.18070i	−1.06870	+	0.322749i
$496$	−8.79153	+	11.8088i	−0.394752	+	0.530231i
$497$	2.35524	−	0.371341i	0.105647	−	0.0166569i
$498$	−29.5327	+	7.49231i	−1.32339	+	0.335739i
$499$	3.71805	+	2.14662i	0.166443	+	0.0960957i	0.580907	−	0.813970i	$-0.302698\pi$
$499$	3.71805	+	2.14662i	0.166443	+	0.0960957i	−0.414465	+	0.910065i	$0.636031\pi$
$500$	−23.1375	+	4.77736i	−1.03474	+	0.213650i
$501$	16.7112	−	22.5035i	0.746603	−	1.00538i
$502$	26.0298	+	21.2043i	1.16177	+	0.946394i
$503$	−26.3039			−1.17283			−0.586415	−	0.810010i	$-0.699461\pi$
$503$	−26.3039			−1.17283			−0.586415	+	0.810010i	$0.699461\pi$
$504$	−22.4396	−	0.680200i	−0.999541	−	0.0302985i
$505$	12.6748			0.564023
$506$	32.8002	+	26.7196i	1.45815	+	1.18783i
$507$	−11.6522	+	15.6910i	−0.517494	+	0.696862i
$508$	29.5543	−	6.10229i	1.31126	−	0.270746i
$509$	−35.3140	−	20.3886i	−1.56527	−	0.903707i	−0.996709	−	0.0810631i	$-0.974168\pi$
$509$	−35.3140	−	20.3886i	−1.56527	−	0.903707i	−0.568557	−	0.822644i	$-0.692498\pi$
$510$	−14.4996	+	3.67848i	−0.642052	+	0.162886i
$511$	21.6447	+	26.7673i	0.957503	+	1.18411i
$512$	22.4339	−	2.95289i	0.991448	−	0.130500i
$513$	−3.67916	−	4.35268i	−0.162439	−	0.192175i
$514$	−7.44418	−	19.5628i	−0.328348	−	0.862878i
$515$	7.40358	+	12.8234i	0.326241	+	0.565066i
$516$	−6.24393	+	13.4321i	−0.274874	+	0.591314i
$517$	−29.9148			−1.31565
$518$	13.5632	−	7.76550i	0.595931	−	0.341196i
$519$	6.72182	−	2.90910i	0.295055	−	0.127695i
$520$	−6.48754	+	4.13294i	−0.284498	+	0.181241i
$521$	6.01740	−	3.47415i	0.263627	−	0.152205i	−0.362361	−	0.932038i	$-0.618029\pi$
$521$	6.01740	−	3.47415i	0.263627	−	0.152205i	0.625988	+	0.779833i	$0.284696\pi$
$522$	3.39612	+	1.39718i	0.148644	+	0.0611528i
$523$	6.54296	+	3.77758i	0.286104	+	0.165182i	0.636183	−	0.771538i	$-0.280512\pi$
$523$	6.54296	+	3.77758i	0.286104	+	0.165182i	−0.350080	+	0.936720i	$0.613846\pi$
$524$	14.0673	+	4.66149i	0.614533	+	0.203638i
$525$	3.15937	−	0.130321i	0.137886	−	0.00568766i
$526$	3.13299	−	19.4149i	0.136605	−	0.846528i
$527$	5.41333	−	9.37617i	0.235808	−	0.408432i
$528$	−26.4593	+	7.95572i	−1.15149	+	0.346228i
$529$	−16.6344	−	28.8116i	−0.723234	−	1.25268i
$530$	−11.2473	−	9.16225i	−0.488552	−	0.397983i
$531$	−10.0398	+	10.6929i	−0.435689	+	0.464033i
$532$	0.945307	−	5.72638i	0.0409842	−	0.248270i
$533$		−	9.19231i		−	0.398163i
$534$	−20.0993	−	5.67414i	−0.869783	−	0.245544i
$535$	−4.34511	+	2.50865i	−0.187855	+	0.108458i
$536$	−0.298792	−	6.84481i	−0.0129058	−	0.295651i
$537$	−11.2730	−	1.30389i	−0.486466	−	0.0562672i
$538$	11.5293	+	1.86049i	0.497064	+	0.0802115i
$539$	20.7193	+	18.7084i	0.892443	+	0.805826i
$540$	−13.3205	+	16.9718i	−0.573224	+	0.730349i
$541$	−5.57548	+	9.65701i	−0.239709	+	0.415187i	−0.960631	−	0.277829i	$-0.910385\pi$
$541$	−5.57548	+	9.65701i	−0.239709	+	0.415187i	0.720922	+	0.693016i	$0.243719\pi$
$542$	−2.66848	−	7.01259i	−0.114621	−	0.301216i
$543$	−12.6849	+	17.0816i	−0.544360	+	0.733040i
$544$	−16.1343	+	4.07237i	−0.691752	+	0.174601i
$545$		−	14.1108i		−	0.604442i
$546$	7.80343	−	3.34378i	0.333956	−	0.143101i
$547$		−	39.2870i		−	1.67979i	−0.542748	−	0.839896i	$-0.682616\pi$
$547$		−	39.2870i		−	1.67979i	0.542748	−	0.839896i	$-0.317384\pi$
$548$	20.0758	+	22.5592i	0.857594	+	0.963682i
$549$	11.9955	+	2.81255i	0.511957	+	0.120037i
$550$	3.63715	−	1.38403i	0.155089	−	0.0590154i
$551$	−0.474691	+	0.822189i	−0.0202225	+	0.0350264i
$552$	36.6545	+	2.62633i	1.56012	+	0.111784i
$553$	−25.5863	−	9.84225i	−1.08804	−	0.418535i
$554$	2.83983	−	17.5982i	0.120653	−	0.747676i
$555$	1.72575	−	14.9203i	0.0732542	−	0.633330i
$556$	−28.3542	+	5.85450i	−1.20249	+	0.248286i
$557$	−25.5152	+	14.7312i	−1.08112	+	0.624182i	−0.931197	−	0.364516i	$-0.881234\pi$
$557$	−25.5152	+	14.7312i	−1.08112	+	0.624182i	−0.149919	+	0.988698i	$0.547901\pi$
$558$	−2.07534	−	15.4766i	−0.0878563	−	0.655175i
$559$		−	5.60145i		−	0.236916i
$560$	−21.9533	+	0.878866i	−0.927695	+	0.0371389i
$561$	18.6474	−	8.07030i	0.787294	−	0.340728i
$562$	−1.81297	+	2.22554i	−0.0764753	+	0.0938789i
$563$	−20.3385	−	35.2274i	−0.857167	−	1.48466i	−0.874620	−	0.484808i	$-0.838889\pi$
$563$	−20.3385	−	35.2274i	−0.857167	−	1.48466i	0.0174537	−	0.999848i	$-0.494444\pi$
$564$	−21.2679	+	14.9299i	−0.895540	+	0.628662i
$565$	−3.28394	+	5.68796i	−0.138157	+	0.239294i
$566$	10.7194	+	1.72980i	0.450570	+	0.0727087i
$567$	17.5366	−	16.1080i	0.736467	−	0.676473i
$568$	1.17700	−	2.26094i	0.0493857	−	0.0948670i
$569$	4.30534	+	2.48569i	0.180489	+	0.104206i	0.587523	−	0.809208i	$-0.300103\pi$
$569$	4.30534	+	2.48569i	0.180489	+	0.104206i	−0.407033	+	0.913413i	$0.633437\pi$
$570$	−3.89102	−	3.99629i	−0.162977	−	0.167386i
$571$	30.2952	−	17.4909i	1.26781	−	0.731973i	0.293240	−	0.956039i	$-0.405266\pi$
$571$	30.2952	−	17.4909i	1.26781	−	0.731973i	0.974574	+	0.224066i	$0.0719331\pi$
$572$	7.80522	−	6.94598i	0.326353	−	0.290426i
$573$	16.3266	+	37.7245i	0.682052	+	1.57596i
$574$	13.2099	−	22.6905i	0.551370	−	0.947083i
$575$	−5.17599			−0.215854
$576$	−14.8407	+	18.8614i	−0.618362	+	0.785894i
$577$	7.33386	+	12.7026i	0.305313	+	0.528817i	0.977331	−	0.211718i	$-0.0679057\pi$
$577$	7.33386	+	12.7026i	0.305313	+	0.528817i	−0.672018	+	0.740535i	$0.734572\pi$
$578$	−11.0325	+	4.19817i	−0.458892	+	0.174621i
$579$	6.83751	+	0.790861i	0.284157	+	0.0328671i
$580$	3.41150	+	1.13047i	0.141655	+	0.0469402i
$581$	32.5079	−	5.12540i	1.34865	−	0.212637i
$582$	36.5422	−	9.27060i	1.51472	−	0.384279i
$583$	17.0649	+	9.85242i	0.706755	+	0.408045i
$584$	36.7652	−	1.60489i	1.52136	−	0.0664107i
$585$	1.86245	−	7.94335i	0.0770030	−	0.328417i
$586$	−1.38926	+	1.70542i	−0.0573899	+	0.0704502i
$587$	−18.7469			−0.773769			−0.386885	−	0.922128i	$-0.626449\pi$
$587$	−18.7469			−0.773769			−0.386885	+	0.922128i	$0.626449\pi$
$588$	24.0674	+	2.96011i	0.992521	+	0.122073i
$589$	4.03690			0.166337
$590$	−9.06601	+	11.1292i	−0.373242	+	0.458181i
$591$	−27.4942	−	20.4174i	−1.13096	−	0.839859i
$592$	1.93987	−	16.5950i	0.0797282	−	0.682050i
$593$	38.8836	+	22.4494i	1.59676	+	0.921888i	0.992107	+	0.125398i	$0.0400207\pi$
$593$	38.8836	+	22.4494i	1.59676	+	0.921888i	0.604651	+	0.796491i	$0.293313\pi$
$594$	14.1898	−	25.6410i	0.582214	−	1.05206i
$595$	15.9603	−	2.51640i	0.654309	−	0.103162i
$596$	−7.16624	+	21.6261i	−0.293541	+	0.885838i
$597$	1.52572	−	13.1908i	0.0624435	−	0.539865i
$598$	−12.9882	+	4.94237i	−0.531128	+	0.202108i
$599$	−0.596454	−	1.03309i	−0.0243704	−	0.0422108i	0.853583	−	0.520957i	$-0.174425\pi$
$599$	−0.596454	−	1.03309i	−0.0243704	−	0.0422108i	−0.877953	+	0.478746i	$0.841091\pi$
$600$	1.89509	−	2.79921i	0.0773666	−	0.114277i
$601$	37.4089			1.52594			0.762970	−	0.646434i	$-0.223741\pi$
$601$	37.4089			1.52594			0.762970	+	0.646434i	$0.223741\pi$
$602$	8.04961	−	13.8267i	0.328078	−	0.563536i
$603$	5.29775	+	4.97415i	0.215741	+	0.202563i
$604$	−1.22083	−	1.37185i	−0.0496747	−	0.0558196i
$605$	8.81680	−	5.09038i	0.358454	−	0.206953i
$606$	−10.7148	+	10.4326i	−0.435259	+	0.423794i
$607$	−18.5588	−	10.7149i	−0.753279	−	0.434906i	0.0735982	−	0.997288i	$-0.476552\pi$
$607$	−18.5588	−	10.7149i	−0.753279	−	0.434906i	−0.826878	+	0.562382i	$0.809885\pi$
$608$	−4.32298	−	4.45073i	−0.175320	−	0.180501i
$609$	−3.51394	−	1.84001i	−0.142392	−	0.0745608i
$610$	11.9039	+	1.92094i	0.481975	+	0.0777766i
$611$	4.91326	−	8.51001i	0.198769	−	0.344278i
$612$	9.22963	−	15.0441i	0.373086	−	0.608123i
$613$	20.2674	+	35.1041i	0.818591	+	1.41784i	0.906720	+	0.421733i	$0.138578\pi$
$613$	20.2674	+	35.1041i	0.818591	+	1.41784i	−0.0881290	+	0.996109i	$0.528089\pi$
$614$	−28.2070	+	34.6261i	−1.13834	+	1.39739i
$615$	−10.0219	−	23.1567i	−0.404120	−	0.933768i
$616$	29.2483	−	5.92904i	1.17845	−	0.238888i
$617$			46.2548i			1.86215i	0.364830	+	0.931074i	$0.381127\pi$
$617$			46.2548i			1.86215i	−0.364830	+	0.931074i	$0.618873\pi$
$618$	−16.8135	−	4.74654i	−0.676339	−	0.190934i
$619$	22.3403	−	12.8982i	0.897932	−	0.518421i	0.0214035	−	0.999771i	$-0.493187\pi$
$619$	22.3403	−	12.8982i	0.897932	−	0.518421i	0.876529	+	0.481349i	$0.159853\pi$
$620$	−3.09017	−	14.9662i	−0.124104	−	0.601055i
$621$	−29.7681	+	25.1618i	−1.19455	+	1.00971i
$622$	−4.11780	+	25.5177i	−0.165109	+	1.02317i
$623$	21.0543	+	8.09892i	0.843523	+	0.324476i
$624$	2.08252	−	8.83368i	0.0833674	−	0.353630i
$625$	10.5369	−	18.2504i	0.421476	−	0.730018i
$626$	−39.3641	+	14.9791i	−1.57331	+	0.598686i
$627$	6.08249	+	4.51689i	0.242911	+	0.180387i
$628$	−13.0385	+	11.6032i	−0.520293	+	0.463016i
$629$			12.2871i			0.489920i
$630$	16.0124	−	16.9311i	0.637948	−	0.674551i
$631$			26.5913i			1.05858i	0.848440	+	0.529291i	$0.177542\pi$
$631$			26.5913i			1.05858i	−0.848440	+	0.529291i	$0.822458\pi$
$632$	−24.7173	+	15.7463i	−0.983201	+	0.626356i
$633$	16.3368	+	12.1318i	0.649329	+	0.482195i
$634$	8.90042	+	23.3897i	0.353481	+	0.928924i
$635$	−15.6626	+	27.1284i	−0.621552	+	1.07656i
$636$	17.0494	−	1.51218i	0.676054	−	0.0599620i
$637$	−8.72504	+	2.82143i	−0.345699	+	0.111789i
$638$	−4.81932	−	0.777697i	−0.190799	−	0.0307893i
$639$	0.781618	+	2.58813i	0.0309203	+	0.102385i
$640$	−13.1912	+	19.4337i	−0.521428	+	0.768186i
$641$	−5.24154	+	3.02620i	−0.207028	+	0.119528i	−0.599930	−	0.800053i	$-0.704805\pi$
$641$	−5.24154	+	3.02620i	−0.207028	+	0.119528i	0.392901	+	0.919581i	$0.371471\pi$
$642$	1.60833	−	5.69714i	0.0634757	−	0.224848i
$643$			9.95426i			0.392558i	0.980548	+	0.196279i	$0.0628858\pi$
$643$			9.95426i			0.392558i	−0.980548	+	0.196279i	$0.937114\pi$
$644$	−39.1629	−	6.46498i	−1.54323	−	0.254756i
$645$	−6.10695	−	14.1108i	−0.240461	−	0.555614i
$646$	3.53766	+	2.88184i	0.139187	+	0.113384i
$647$	15.4951	+	26.8383i	0.609175	+	1.05512i	0.991377	+	0.131044i	$0.0418328\pi$
$647$	15.4951	+	26.8383i	0.609175	+	1.05512i	−0.382201	+	0.924079i	$0.624834\pi$
$648$	−2.70871	−	25.3113i	−0.106408	−	0.994323i
$649$	9.74892	−	16.8856i	0.382679	−	0.662819i
$650$	−0.203649	+	1.26200i	−0.00798778	+	0.0494996i
$651$	0.695124	+	16.8519i	0.0272440	+	0.660478i
$652$	5.65686	−	17.0711i	0.221540	−	0.668557i
$653$	−7.01889	−	4.05236i	−0.274670	−	0.158581i	0.356338	−	0.934357i	$-0.384025\pi$
$653$	−7.01889	−	4.05236i	−0.274670	−	0.158581i	−0.631008	+	0.775776i	$0.717359\pi$
$654$	11.6145	+	11.9287i	0.454164	+	0.466451i
$655$	−13.3221	+	7.69152i	−0.520538	+	0.300533i
$656$	−11.1171	−	25.7730i	−0.434048	−	1.00627i
$657$	−26.7174	+	28.4556i	−1.04235	+	1.11016i
$658$	24.3574	−	13.9457i	0.949549	−	0.543658i
$659$	38.3085			1.49229			0.746143	−	0.665785i	$-0.231903\pi$
$659$	38.3085			1.49229			0.746143	+	0.665785i	$0.231903\pi$
$660$	12.0896	−	26.0075i	0.470588	−	1.01234i
$661$	−3.32843	−	5.76501i	−0.129461	−	0.224233i	0.794007	−	0.607909i	$-0.207991\pi$
$661$	−3.32843	−	5.76501i	−0.129461	−	0.224233i	−0.923468	+	0.383676i	$0.874658\pi$
$662$	−17.6449	−	46.3696i	−0.685788	−	1.80221i
$663$	−0.766883	+	6.63021i	−0.0297833	+	0.257496i
$664$	16.2454	−	31.2064i	0.630442	−	1.21104i
$665$	3.78811	+	4.68463i	0.146896	+	0.181662i
$666$	10.8219	+	14.0335i	0.419340	+	0.543786i
$667$	5.62297	+	3.24642i	0.217722	+	0.125702i
$668$	6.54481	+	31.6975i	0.253226	+	1.22641i
$669$	−20.1912	−	14.9941i	−0.780638	−	0.579706i
$670$	5.51389	+	4.49171i	0.213020	+	0.173530i
$671$	−16.3784			−0.632280
$672$	17.8350	−	18.8125i	0.688001	−	0.725709i
$673$	−22.0809			−0.851156			−0.425578	−	0.904922i	$-0.639929\pi$
$673$	−22.0809			−0.851156			−0.425578	+	0.904922i	$0.639929\pi$
$674$	−0.145815	−	0.118783i	−0.00561657	−	0.00457535i
$675$	0.635331	+	3.52869i	0.0244539	+	0.135819i
$676$	−4.56350	−	22.1017i	−0.175519	−	0.850064i
$677$	39.0358	+	22.5373i	1.50027	+	0.866180i	1.00000		0.000308342i	$9.81484e-5\pi$
$677$	39.0358	+	22.5373i	1.50027	+	0.866180i	0.500267	+	0.865871i	$0.333235\pi$
$678$	−1.90560	−	7.51136i	−0.0731842	−	0.288472i
$679$	−40.2236	+	6.34190i	−1.54364	+	0.243380i
$680$	7.97594	−	15.3213i	0.305863	−	0.587546i
$681$	36.9286	+	4.27135i	1.41511	+	0.163678i
$682$	7.38237	+	19.4004i	0.282685	+	0.742879i
$683$	7.80843	+	13.5246i	0.298781	+	0.517505i	0.975857	−	0.218408i	$-0.0700865\pi$
$683$	7.80843	+	13.5246i	0.298781	+	0.517505i	−0.677076	+	0.735913i	$0.736753\pi$
$684$	6.57864	+	0.175630i	0.251541	+	0.00671539i
$685$	−31.3469			−1.19770
$686$	−25.5916	−	5.57392i	−0.977093	−	0.212813i
$687$	−13.5049	−	31.2046i	−0.515242	−	1.19053i
$688$	−6.77432	−	15.7051i	−0.258269	−	0.598753i
$689$	−5.60554	+	3.23636i	−0.213554	+	0.123295i
$690$	−27.3307	+	26.6108i	−1.04046	+	1.01306i
$691$	−33.1799	−	19.1564i	−1.26222	−	0.728744i	−0.288718	−	0.957414i	$-0.593229\pi$
$691$	−33.1799	−	19.1564i	−1.26222	−	0.728744i	−0.973504	+	0.228670i	$0.926562\pi$
$692$	−2.66028	+	8.02811i	−0.101129	+	0.305183i
$693$	−17.8083	+	26.1689i	−0.676480	+	0.994075i
$694$	0.0440088	−	0.272719i	0.00167055	−	0.0103523i
$695$	15.0266	−	26.0268i	0.569991	−	0.987254i
$696$	−3.81443	+	1.85233i	−0.144586	+	0.0702123i
$697$	10.3208	+	17.8762i	0.390930	+	0.677110i
$698$	6.36801	+	5.18749i	0.241033	+	0.196349i
$699$	−22.6737	+	9.81282i	−0.857598	+	0.371155i
$700$	−2.31625	+	2.82248i	−0.0875461	+	0.106680i
$701$		−	36.6488i		−	1.38420i	−0.721799	−	0.692102i	$-0.756685\pi$
$701$		−	36.6488i		−	1.38420i	0.721799	−	0.692102i	$-0.243315\pi$
$702$	4.96367	+	8.24797i	0.187342	+	0.311300i
$703$	−3.96766	+	2.29073i	−0.149643	+	0.0863964i
$704$	13.4836	−	28.9144i	0.508183	−	1.08975i
$705$	3.09919	−	26.7945i	0.116722	−	1.00914i
$706$	−27.9148	−	4.50462i	−1.05059	−	0.169534i
$707$	12.5604	−	10.1566i	0.472381	−	0.381979i
$708$	−1.49630	−	16.8703i	−0.0562344	−	0.634026i
$709$	−18.2674	+	31.6400i	−0.686045	+	1.18827i	0.287062	+	0.957912i	$0.407322\pi$
$709$	−18.2674	+	31.6400i	−0.686045	+	1.18827i	−0.973107	+	0.230353i	$0.926012\pi$
$710$	0.941002	+	2.47289i	0.0353152	+	0.0928060i
$711$	7.09588	−	30.2639i	0.266116	−	1.13498i
$712$	20.3392	−	12.9572i	0.762243	−	0.485593i
$713$		−	27.6084i		−	1.03394i
$714$	−11.4210	+	15.2641i	−0.427419	+	0.571244i
$715$			10.8457i			0.405604i
$716$	9.78887	−	8.71125i	0.365827	−	0.325555i
$717$	15.7806	−	21.2503i	0.589338	−	0.793609i
$718$	−18.3803	+	6.99418i	−0.685945	+	0.261020i
$719$	12.2687	−	21.2499i	0.457543	−	0.792488i	−0.541287	−	0.840838i	$-0.682063\pi$
$719$	12.2687	−	21.2499i	0.457543	−	0.792488i	0.998830	+	0.0483494i	$0.0153961\pi$
$720$	−4.38471	−	24.5237i	−0.163408	−	0.913944i
$721$	17.6124	+	6.77492i	0.655919	+	0.252311i
$722$	4.00962	−	24.8473i	0.149223	−	0.924720i
$723$	10.1581	+	1.17494i	0.377786	+	0.0436966i
$724$	−4.96792	−	24.0604i	−0.184631	−	0.894196i
$725$	0.517239	−	0.298628i	0.0192098	−	0.0110908i
$726$	−3.26352	+	11.5603i	−0.121120	+	0.429041i
$727$			7.89691i			0.292880i	0.989220	+	0.146440i	$0.0467816\pi$
$727$			7.89691i			0.292880i	−0.989220	+	0.146440i	$0.953218\pi$
$728$	−3.11714	+	9.29423i	−0.115529	+	0.344467i
$729$	20.8078	+	17.2057i	0.770660	+	0.637247i
$730$	−24.1261	+	29.6165i	−0.892948	+	1.09616i
$731$	6.28914	+	10.8931i	0.232612	+	0.402896i
$732$	−11.6442	+	8.17414i	−0.430382	+	0.302125i
$733$	−2.92236	+	5.06167i	−0.107940	+	0.186957i	−0.914935	−	0.403600i	$-0.867759\pi$
$733$	−2.92236	+	5.06167i	−0.107940	+	0.186957i	0.806996	+	0.590557i	$0.201092\pi$
$734$	26.2664	+	4.23863i	0.969511	+	0.156451i
$735$	−18.9035	+	16.6200i	−0.697268	+	0.613037i
$736$	−30.4386	+	29.5650i	−1.12198	+	1.08978i
$737$	−8.36590	−	4.83005i	−0.308162	−	0.177917i
$738$	27.5322	+	11.3268i	1.01347	+	0.416947i
$739$	1.22939	−	0.709786i	0.0452237	−	0.0261099i	−0.477218	−	0.878785i	$-0.658355\pi$
$739$	1.22939	−	0.709786i	0.0452237	−	0.0261099i	0.522441	+	0.852675i	$0.325021\pi$
$740$	11.5297	+	12.9560i	0.423840	+	0.476270i
$741$	−2.28394	+	0.988455i	−0.0839027	+	0.0363118i
$742$	−18.4877	−	0.0667857i	−0.678703	−	0.00245178i
$743$	1.70600			0.0625872			0.0312936	−	0.999510i	$-0.490037\pi$
$743$	1.70600			0.0625872			0.0312936	+	0.999510i	$0.490037\pi$
$744$	14.9309	+	10.1083i	0.547392	+	0.370588i
$745$	−11.8244	−	20.4805i	−0.433212	−	0.750346i
$746$	−7.69657	+	2.92875i	−0.281791	+	0.107229i
$747$	10.7882	+	35.7223i	0.394720	+	1.30701i
$748$	−7.38003	+	22.2713i	−0.269841	+	0.814318i
$749$	−2.29563	+	5.96782i	−0.0838805	+	0.218059i
$750$	7.11534	+	28.0467i	0.259815	+	1.02412i
$751$	23.1969	+	13.3927i	0.846466	+	0.488707i	0.859457	−	0.511208i	$-0.170802\pi$
$751$	23.1969	+	13.3927i	0.846466	+	0.488707i	−0.0129912	+	0.999916i	$0.504135\pi$
$752$	3.48371	−	29.8021i	0.127038	−	1.08677i
$753$	24.5148	−	33.0118i	0.893369	−	1.20302i
$754$	1.01277	−	1.24325i	0.0368829	−	0.0452764i
$755$	1.90623			0.0693749
$756$	0.399630	+	27.4925i	0.0145344	+	0.999894i
$757$	−23.8816			−0.867992			−0.433996	−	0.900915i	$-0.642897\pi$
$757$	−23.8816			−0.867992			−0.433996	+	0.900915i	$0.642897\pi$
$758$	−10.7717	+	13.2230i	−0.391245	+	0.480281i
$759$	30.8911	−	41.5983i	1.12128	−	1.50992i
$760$	6.43441	−	0.280877i	0.233401	−	0.0101885i
$761$	−13.0696	−	7.54576i	−0.473774	−	0.273533i	0.244044	−	0.969764i	$-0.421526\pi$
$761$	−13.0696	−	7.54576i	−0.473774	−	0.273533i	−0.717818	+	0.696231i	$0.754859\pi$
$762$	−9.08868	−	35.8251i	−0.329248	−	1.29781i
$763$	−11.3073	−	13.9834i	−0.409352	−	0.506233i
$764$	−45.0557	−	14.9301i	−1.63006	−	0.540153i
$765$	5.29665	+	17.5385i	0.191501	+	0.634105i
$766$	16.0616	−	6.11189i	0.580331	−	0.220831i
$767$	3.20236	+	5.54665i	0.115631	+	0.200278i
$768$	−4.84445	−	27.2861i	−0.174809	−	0.984602i
$769$	12.6792			0.457222			0.228611	−	0.973518i	$-0.426582\pi$
$769$	12.6792			0.457222			0.228611	+	0.973518i	$0.426582\pi$
$770$	−15.5858	+	26.7716i	−0.561674	+	0.964783i
$771$	−23.5267	+	10.1820i	−0.847294	+	0.366695i
$772$	−5.93733	+	5.28371i	−0.213689	+	0.190165i
$773$	−33.5367	+	19.3624i	−1.20623	+	0.696417i	−0.961934	−	0.273283i	$-0.911890\pi$
$773$	−33.5367	+	19.3624i	−1.20623	+	0.696417i	−0.244296	+	0.969701i	$0.578557\pi$
$774$	16.7771	+	6.90216i	0.603041	+	0.248093i
$775$	−2.19937	−	1.26981i	−0.0790037	−	0.0456128i
$776$	−20.1012	+	38.6132i	−0.721590	+	1.38613i
$777$	−10.2458	−	16.1684i	−0.367565	−	0.580038i
$778$	1.69002	+	0.272719i	0.0605900	+	0.00977745i
$779$	−3.84829	+	6.66544i	−0.137879	+	0.238814i
$780$	5.41286	+	7.71071i	0.193811	+	0.276088i
$781$	−1.79696	−	3.11243i	−0.0643004	−	0.111372i
$782$	19.7090	−	24.1942i	0.704791	−	0.865181i
$783$	1.52303	−	4.23190i	0.0544286	−	0.151236i
$784$	−21.0507	+	18.4626i	−0.751812	+	0.659377i
$785$		−	18.1175i		−	0.646642i
$786$	4.93114	−	17.4674i	0.175888	−	0.623043i
$787$	−17.6523	+	10.1915i	−0.629235	+	0.363289i	−0.780456	−	0.625211i	$-0.785013\pi$
$787$	−17.6523	+	10.1915i	−0.629235	+	0.363289i	0.151221	+	0.988500i	$0.451680\pi$
$788$	38.7272	−	7.99629i	1.37960	−	0.284856i
$789$	−23.9263	−	2.76744i	−0.851800	−	0.0985235i
$790$	4.84640	−	30.0327i	0.172427	−	1.06852i
$791$	1.30360	+	8.26808i	0.0463506	+	0.293979i
$792$	11.1865	+	31.9366i	0.397494	+	1.13482i
$793$	2.69002	−	4.65925i	0.0955253	−	0.165455i
$794$	12.6320	−	4.80683i	0.448294	−	0.170588i
$795$	−10.5927	+	14.2642i	−0.375685	+	0.505900i
$796$	10.1933	+	11.4542i	0.361291	+	0.405984i
$797$		−	27.9005i		−	0.988287i	−0.869380	−	0.494143i	$-0.835482\pi$
$797$		−	27.9005i		−	0.988287i	0.869380	−	0.494143i	$-0.164518\pi$
$798$	−7.05820	−	0.842236i	−0.249858	−	0.0298148i
$799$			22.0658i			0.780632i
$800$	0.955258	+	3.78463i	0.0337735	+	0.133807i
$801$	−5.83900	+	24.9033i	−0.206311	+	0.879915i
$802$	5.65622	+	14.8642i	0.199728	+	0.524873i
$803$	25.9435	−	44.9354i	0.915525	−	1.58574i
$804$	−8.35832	+	0.741334i	−0.294775	+	0.0261448i
$805$	32.0383	−	25.9069i	1.12920	−	0.913100i
$806$	−6.73142	−	1.08625i	−0.237104	−	0.0382617i
$807$	1.64342	−	14.2084i	0.0578510	−	0.500159i
$808$	−0.753083	−	17.2519i	−0.0264934	−	0.606918i
$809$	12.3530	−	7.13202i	0.434309	−	0.250748i	−0.266872	−	0.963732i	$-0.585990\pi$
$809$	12.3530	−	7.13202i	0.434309	−	0.250748i	0.701181	+	0.712984i	$0.252657\pi$
$810$	21.4965	+	15.3662i	0.755309	+	0.539912i
$811$		−	38.4069i		−	1.34865i	−0.738435	−	0.674325i	$-0.764435\pi$
$811$		−	38.4069i		−	1.34865i	0.738435	−	0.674325i	$-0.235565\pi$
$812$	4.28656	−	1.61345i	0.150429	−	0.0566210i
$813$	−8.43351	+	3.64989i	−0.295776	+	0.128007i
$814$	−18.2644	−	14.8785i	−0.640169	−	0.521492i
$815$	9.33391	+	16.1668i	0.326953	+	0.566299i
$816$	5.86832	+	19.5170i	0.205432	+	0.683231i
$817$	−2.34501	+	4.06167i	−0.0820415	+	0.142100i
$818$	−3.50741	+	21.7351i	−0.122634	+	0.759951i
$819$	−4.51955	−	9.36404i	−0.157926	−	0.327206i
$820$	27.6569	+	9.16466i	0.965820	+	0.320044i
$821$	−45.7169	−	26.3947i	−1.59553	−	0.921181i	−0.992333	−	0.123589i	$-0.960559\pi$
$821$	−45.7169	−	26.3947i	−1.59553	−	0.921181i	−0.603198	−	0.797591i	$-0.706107\pi$
$822$	26.4994	−	25.8014i	0.924273	−	0.899927i
$823$	−4.96238	+	2.86503i	−0.172978	+	0.0998687i	−0.583989	−	0.811761i	$-0.698509\pi$
$823$	−4.96238	+	2.86503i	−0.172978	+	0.0998687i	0.411012	+	0.911630i	$0.365176\pi$
$824$	17.0142	−	10.8390i	0.592717	−	0.377595i
$825$	−1.89305	−	4.37413i	−0.0659077	−	0.152288i
$826$	−0.0660841	+	18.2935i	−0.00229936	+	0.636511i
$827$	−44.5253			−1.54830			−0.774149	−	0.633003i	$-0.781822\pi$
$827$	−44.5253			−1.54830			−0.774149	+	0.633003i	$0.781822\pi$
$828$	1.20114	−	44.9915i	0.0417425	−	1.56356i
$829$	−13.0293	−	22.5674i	−0.452526	−	0.783799i	0.546016	−	0.837775i	$-0.316144\pi$
$829$	−13.0293	−	22.5674i	−0.452526	−	0.783799i	−0.998542	+	0.0539760i	$0.982811\pi$
$830$	12.9881	+	34.1318i	0.450823	+	1.18473i
$831$	−21.6875	−	2.50849i	−0.752332	−	0.0870186i
$832$	6.01086	+	8.58471i	0.208389	+	0.297621i
$833$	13.7997	−	15.2830i	0.478132	−	0.529525i
$834$	8.71961	+	34.3703i	0.301935	+	1.19015i
$835$	−29.0957	−	16.7984i	−1.00690	−	0.581333i
$836$	−8.56753	+	1.76900i	−0.296314	+	0.0611822i
$837$	−18.8219	+	3.38883i	−0.650579	+	0.117135i
$838$	−19.7730	−	16.1074i	−0.683048	−	0.556423i
$839$	46.0533			1.58994			0.794968	−	0.606652i	$-0.207488\pi$
$839$	46.0533			1.58994			0.794968	+	0.606652i	$0.207488\pi$
$840$	2.28047	+	26.8119i	0.0786836	+	0.925098i
$841$	28.2508			0.974165
$842$	−13.7033	−	11.1629i	−0.472247	−	0.384700i
$843$	2.82251	+	2.09601i	0.0972124	+	0.0721905i
$844$	−23.0113	+	4.75131i	−0.792081	+	0.163547i
$845$	20.2875	+	11.7130i	0.697912	+	0.402940i
$846$	19.4345	+	25.2020i	0.668171	+	0.866462i
$847$	4.65814	−	12.1095i	0.160056	−	0.416087i
$848$	−11.8026	+	15.8532i	−0.405302	+	0.544403i
$849$	1.52797	−	13.2103i	0.0524397	−	0.453376i
$850$	−1.02090	−	2.68285i	−0.0350164	−	0.0920209i
$851$	15.6663	+	27.1349i	0.537035	+	0.930173i
$852$	−2.83091	−	1.31595i	−0.0969852	−	0.0450838i
$853$	46.3274			1.58622			0.793109	−	0.609079i	$-0.208461\pi$
$853$	46.3274			1.58622			0.793109	+	0.609079i	$0.208461\pi$
$854$	13.3357	−	7.63527i	0.456338	−	0.261274i
$855$	−4.67591	+	4.98011i	−0.159913	+	0.170316i
$856$	3.67272	+	5.76512i	0.125531	+	0.197048i
$857$	−35.6333	+	20.5729i	−1.21721	+	0.702756i	−0.964320	−	0.264739i	$-0.914714\pi$
$857$	−35.6333	+	20.5729i	−1.21721	+	0.702756i	−0.252890	+	0.967495i	$0.581381\pi$
$858$	−8.92698	−	9.16848i	−0.304762	−	0.313007i
$859$	49.7193	+	28.7054i	1.69640	+	0.979417i	0.949123	+	0.314905i	$0.101973\pi$
$859$	49.7193	+	28.7054i	1.69640	+	0.979417i	0.747277	+	0.664512i	$0.231361\pi$
$860$	16.8531	+	5.58461i	0.574685	+	0.190434i
$861$	−28.4873	−	14.9168i	−0.970845	−	0.508364i
$862$	−2.80407	+	17.3766i	−0.0955072	+	0.591850i
$863$	−12.7433	+	22.0721i	−0.433788	+	0.751343i	−0.997196	−	0.0748356i	$-0.976157\pi$
$863$	−12.7433	+	22.0721i	−0.433788	+	0.751343i	0.563408	+	0.826179i	$0.309490\pi$
$864$	23.8919	+	17.1223i	0.812821	+	0.582514i
$865$	−4.38950	−	7.60283i	−0.149247	−	0.258504i
$866$	−0.545855	−	0.444663i	−0.0185489	−	0.0151103i
$867$	5.74216	+	13.2680i	0.195014	+	0.450604i
$868$	−15.0550	−	12.3548i	−0.510999	−	0.419348i
$869$			41.3215i			1.40174i
$870$	1.19587	−	4.23608i	0.0405437	−	0.143617i
$871$	2.74806	−	1.58659i	0.0931145	−	0.0537597i
$872$	−19.2064	+	0.838404i	−0.650412	+	0.0283919i
$873$	−13.3488	−	44.2010i	−0.451787	−	1.49598i
$874$	11.4870	+	1.85366i	0.388553	+	0.0627010i
$875$	−4.86751	−	30.8723i	−0.164552	−	1.04367i
$876$	−3.98189	−	44.8947i	−0.134536	−	1.51685i
$877$	−20.9313	+	36.2541i	−0.706801	+	1.22422i	0.259236	+	0.965814i	$0.416529\pi$
$877$	−20.9313	+	36.2541i	−0.706801	+	1.22422i	−0.966038	+	0.258402i	$0.916804\pi$
$878$	2.34382	+	6.15942i	0.0791002	+	0.207870i
$879$	2.16287	+	1.60616i	0.0729518	+	0.0541744i
$880$	13.1166	+	30.4086i	0.442160	+	1.02507i
$881$		−	38.5556i		−	1.29897i	−0.760373	−	0.649486i	$-0.774984\pi$
$881$		−	38.5556i		−	1.29897i	0.760373	−	0.649486i	$-0.225016\pi$
$882$	2.30052	−	29.6092i	0.0774625	−	0.996995i
$883$		−	4.56420i		−	0.153597i	−0.997047	−	0.0767987i	$-0.975530\pi$
$883$		−	4.56420i		−	0.153597i	0.997047	−	0.0767987i	$-0.0244699\pi$
$884$	−5.12351	−	5.75731i	−0.172322	−	0.193639i
$885$	14.1144	+	10.4814i	0.474450	+	0.352329i
$886$	29.1708	−	11.1003i	0.980012	−	0.372921i
$887$	−20.2446	+	35.0647i	−0.679747	+	1.17736i	0.295310	+	0.955401i	$0.404577\pi$
$887$	−20.2446	+	35.0647i	−0.679747	+	1.17736i	−0.975057	+	0.221955i	$0.928756\pi$
$888$	−20.4107	−	1.46245i	−0.684938	−	0.0490765i
$889$	6.21745	+	39.4342i	0.208527	+	1.32258i
$890$	−3.98797	+	24.7131i	−0.133677	+	0.828385i
$891$	−32.1511	−	15.9538i	−1.07710	−	0.534472i
$892$	28.4405	−	5.87232i	0.952258	−	0.196620i
$893$	−7.12531	+	4.11380i	−0.238439	+	0.137663i
$894$	26.8532	+	7.58079i	0.898105	+	0.253540i
$895$			13.6020i			0.454665i
$896$	2.50060	+	29.8286i	0.0835393	+	0.996504i
$897$	6.76007	+	15.6199i	0.225712	+	0.521535i
$898$	5.38474	−	6.61015i	0.179691	−	0.220584i
$899$	1.59287	+	2.75893i	0.0531251	+	0.0920154i
$900$	−3.52891	−	2.16500i	−0.117630	−	0.0721666i
$901$	7.26737	−	12.5874i	0.242111	−	0.419349i
$902$	−39.0700	−	6.30475i	−1.30089	−	0.209925i
$903$	−17.3591	−	9.08977i	−0.577675	−	0.302489i
$904$	7.93706	+	4.13186i	0.263983	+	0.137424i
$905$	22.0854	+	12.7510i	0.734145	+	0.423859i
$906$	−1.61145	+	1.56901i	−0.0535370	+	0.0521268i
$907$	−2.36697	+	1.36657i	−0.0785940	+	0.0453763i	−0.538782	−	0.842445i	$-0.681115\pi$
$907$	−2.36697	+	1.36657i	−0.0785940	+	0.0453763i	0.460188	+	0.887822i	$0.347782\pi$
$908$	−32.0668	+	28.5367i	−1.06417	+	0.947023i
$909$	13.3526	+	12.5370i	0.442878	+	0.415826i
$910$	−5.05602	−	8.83081i	−0.167605	−	0.292738i
$911$	5.16105			0.170993			0.0854966	−	0.996338i	$-0.472752\pi$
$911$	5.16105			0.170993			0.0854966	+	0.996338i	$0.472752\pi$
$912$	−5.20821	+	5.53356i	−0.172461	+	0.183235i
$913$	−24.8024	−	42.9590i	−0.820839	−	1.42174i
$914$	50.5724	−	19.2442i	1.67279	−	0.636540i
$915$	1.69681	−	14.6701i	0.0560949	−	0.484977i
$916$	37.2688	+	12.3498i	1.23139	+	0.408048i
$917$	−7.03841	+	18.2973i	−0.232429	+	0.604232i
$918$	−18.9134	−	10.4667i	−0.624235	−	0.345453i
$919$	−34.5011	−	19.9192i	−1.13809	−	0.657074i	−0.192130	−	0.981370i	$-0.561539\pi$
$919$	−34.5011	−	19.9192i	−1.13809	−	0.657074i	−0.945956	+	0.324296i	$0.894873\pi$
$920$	−1.92092	−	44.0051i	−0.0633310	−	1.45081i
$921$	43.9139	+	32.6108i	1.44701	+	1.07456i
$922$	11.1258	−	13.6578i	0.366410	−	0.449794i
$923$	1.18055			0.0388582
$924$	−8.85990	−	35.4603i	−0.291469	−	1.16656i
$925$	2.88220			0.0947660
$926$	25.0637	−	30.7675i	0.823644	−	1.01108i
$927$	−4.88445	+	20.8322i	−0.160426	+	0.684218i
$928$	1.33600	−	4.71060i	0.0438564	−	0.154633i
$929$	22.2777	+	12.8621i	0.730909	+	0.421990i	0.818754	−	0.574144i	$-0.194665\pi$
$929$	22.2777	+	12.8621i	0.730909	+	0.421990i	−0.0878459	+	0.996134i	$0.527998\pi$
$930$	−18.1417	+	4.60246i	−0.594889	+	0.150921i
$931$	7.50779	+	1.60683i	0.246058	+	0.0526617i
$932$	8.97351	−	27.0800i	0.293937	−	0.887035i
$933$	31.4473	+	3.63735i	1.02954	+	0.119082i
$934$	−22.5975	+	8.59895i	−0.739412	+	0.281366i
$935$	−12.1772	−	21.0915i	−0.398236	−	0.689765i
$936$	−10.9225	−	2.06305i	−0.357011	−	0.0674328i
$937$	20.2068			0.660127			0.330063	−	0.943959i	$-0.392930\pi$
$937$	20.2068			0.660127			0.330063	+	0.943959i	$0.392930\pi$
$938$	9.06340	+	0.0327410i	0.295931	+	0.00106903i
$939$	20.4881	+	47.3403i	0.668604	+	1.54489i
$940$	20.7056	+	23.2669i	0.675341	+	0.758883i
$941$	41.4712	−	23.9434i	1.35192	−	0.780533i	0.363403	−	0.931632i	$-0.381615\pi$
$941$	41.4712	−	23.9434i	1.35192	−	0.780533i	0.988519	+	0.151099i	$0.0482813\pi$
$942$	14.9124	+	15.3158i	0.485872	+	0.499017i
$943$	45.5851	+	26.3186i	1.48446	+	0.857051i
$944$	15.6867	+	11.6786i	0.510559	+	0.380106i
$945$	−21.5944	−	18.6619i	−0.702467	−	0.607072i
$946$	−23.8078	−	3.84188i	−0.774059	−	0.124910i
$947$	3.16035	−	5.47389i	0.102698	−	0.177878i	−0.810098	−	0.586295i	$-0.800586\pi$
$947$	3.16035	−	5.47389i	0.102698	−	0.177878i	0.912795	+	0.408418i	$0.133919\pi$
$948$	20.6228	+	29.3775i	0.669797	+	0.954138i
$949$	8.52200	+	14.7605i	0.276636	+	0.479148i
$950$	0.675994	−	0.829830i	0.0219321	−	0.0269233i
$951$	28.1290	−	12.1738i	0.912147	−	0.394763i
$952$	−4.37340	−	21.5742i	−0.141743	−	0.699225i
$953$		−	3.70027i		−	0.119863i	−0.998202	−	0.0599317i	$-0.980912\pi$
$953$		−	3.70027i		−	0.119863i	0.998202	−	0.0599317i	$-0.0190883\pi$
$954$	−2.78614	−	20.7772i	−0.0902045	−	0.672687i
$955$	42.6689	−	24.6349i	1.38073	−	0.797167i
$956$	6.18035	+	29.9323i	0.199887	+	0.968080i
$957$	−0.686958	+	5.93920i	−0.0222062	+	0.191987i
$958$	3.70087	−	22.9340i	0.119570	−	0.740964i
$959$	−31.0638	+	25.1189i	−1.00310	+	0.811133i
$960$	24.5016	+	15.0728i	0.790786	+	0.486472i
$961$	−8.72691	+	15.1155i	−0.281513	+	0.487595i
$962$	7.23236	−	2.75211i	0.233181	−	0.0887315i
$963$	−7.05882	−	1.65506i	−0.227467	−	0.0533336i
$964$	−8.82078	+	7.84974i	−0.284098	+	0.252823i
$965$		−	8.25014i		−	0.265581i
$966$	−5.76008	+	48.2712i	−0.185327	+	1.55310i
$967$			14.5970i			0.469409i	0.972067	+	0.234705i	$0.0754123\pi$
$967$			14.5970i			0.469409i	−0.972067	+	0.234705i	$0.924588\pi$
$968$	−7.45243	−	11.6982i	−0.239530	−	0.375994i
$969$	3.33176	−	4.48658i	0.107032	−	0.144130i
$970$	−16.0708	−	42.2330i	−0.516002	−	1.35602i
$971$	4.10729	−	7.11403i	0.131809	−	0.228300i	−0.792565	−	0.609788i	$-0.791255\pi$
$971$	4.10729	−	7.11403i	0.131809	−	0.228300i	0.924374	+	0.381488i	$0.124588\pi$
$972$	−30.8201	+	4.70365i	−0.988554	+	0.150870i
$973$	−5.96498	−	37.8329i	−0.191228	−	1.21287i
$974$	−44.6592	−	7.20668i	−1.43097	−	0.230917i
$975$	1.55525	+	0.179888i	0.0498078	+	0.00576103i
$976$	1.90734	−	16.3167i	0.0610524	−	0.522284i
$977$	−30.8426	+	17.8070i	−0.986744	+	0.569697i	−0.904299	−	0.426899i	$-0.859606\pi$
$977$	−30.8426	+	17.8070i	−0.986744	+	0.569697i	−0.0824443	+	0.996596i	$0.526273\pi$
$978$	−21.1973	−	5.98410i	−0.677815	−	0.191351i
$979$		−	34.0023i		−	1.08672i
$980$	0.209987	−	29.0639i	0.00670777	−	0.928414i
$981$	13.9574	−	14.8654i	0.445625	−	0.474615i
$982$	−2.23506	−	1.82071i	−0.0713235	−	0.0581013i
$983$	−15.5749	−	26.9764i	−0.496761	−	0.860415i	0.503232	−	0.864151i	$-0.332144\pi$
$983$	−15.5749	−	26.9764i	−0.496761	−	0.860415i	−0.999993	+	0.00373618i	$0.998811\pi$
$984$	−30.9234	+	15.0167i	−0.985802	+	0.478716i
$985$	−20.5239	+	35.5484i	−0.653945	+	1.13267i
$986$	−0.573647	+	3.55484i	−0.0182687	+	0.113209i
$987$	−18.3998	−	29.0360i	−0.585674	−	0.924226i
$988$	0.903910	−	2.72779i	0.0287572	−	0.0867827i
$989$	27.7779	+	16.0376i	0.883285	+	0.509965i
$990$	−32.4842	−	13.3641i	−1.03241	−	0.424739i
$991$	30.1606	−	17.4132i	0.958083	−	0.553149i	0.0625004	−	0.998045i	$-0.480093\pi$
$991$	30.1606	−	17.4132i	0.958083	−	0.553149i	0.895582	+	0.444896i	$0.146759\pi$
$992$	−20.1870	+	5.09530i	−0.640938	+	0.161776i
$993$	−55.7652	+	24.1343i	−1.76966	+	0.765879i
$994$	2.91409	+	1.69651i	0.0924292	+	0.0538101i
$995$	−15.9161			−0.504573
$996$	−39.0733	−	18.1633i	−1.23808	−	0.575526i
$997$	−4.22860	−	7.32414i	−0.133921	−	0.231958i	0.791264	−	0.611475i	$-0.209424\pi$
$997$	−4.22860	−	7.32414i	−0.133921	−	0.231958i	−0.925185	+	0.379517i	$0.876090\pi$
$998$	2.15933	+	5.67459i	0.0683525	+	0.179626i
$999$	16.5761	−	14.0111i	0.524443	−	0.443292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.n.a.23.10	yes	24
3.2	odd	2	inner	84.2.n.a.23.3	yes	24
4.3	odd	2	inner	84.2.n.a.23.12	yes	24
7.2	even	3		588.2.e.e.491.7		12
7.3	odd	6		588.2.n.e.263.1		24
7.4	even	3	inner	84.2.n.a.11.1	✓	24
7.5	odd	6		588.2.e.d.491.7		12
7.6	odd	2		588.2.n.e.275.10		24
12.11	even	2	inner	84.2.n.a.23.1	yes	24
21.2	odd	6		588.2.e.e.491.6		12
21.5	even	6		588.2.e.d.491.6		12
21.11	odd	6	inner	84.2.n.a.11.12	yes	24
21.17	even	6		588.2.n.e.263.12		24
21.20	even	2		588.2.n.e.275.3		24
28.3	even	6		588.2.n.e.263.3		24
28.11	odd	6	inner	84.2.n.a.11.3	yes	24
28.19	even	6		588.2.e.d.491.5		12
28.23	odd	6		588.2.e.e.491.5		12
28.27	even	2		588.2.n.e.275.12		24
84.11	even	6	inner	84.2.n.a.11.10	yes	24
84.23	even	6		588.2.e.e.491.8		12
84.47	odd	6		588.2.e.d.491.8		12
84.59	odd	6		588.2.n.e.263.10		24
84.83	odd	2		588.2.n.e.275.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.1	✓	24	7.4	even	3	inner
84.2.n.a.11.3	yes	24	28.11	odd	6	inner
84.2.n.a.11.10	yes	24	84.11	even	6	inner
84.2.n.a.11.12	yes	24	21.11	odd	6	inner
84.2.n.a.23.1	yes	24	12.11	even	2	inner
84.2.n.a.23.3	yes	24	3.2	odd	2	inner
84.2.n.a.23.10	yes	24	1.1	even	1	trivial
84.2.n.a.23.12	yes	24	4.3	odd	2	inner
588.2.e.d.491.5		12	28.19	even	6
588.2.e.d.491.6		12	21.5	even	6
588.2.e.d.491.7		12	7.5	odd	6
588.2.e.d.491.8		12	84.47	odd	6
588.2.e.e.491.5		12	28.23	odd	6
588.2.e.e.491.6		12	21.2	odd	6
588.2.e.e.491.7		12	7.2	even	3
588.2.e.e.491.8		12	84.23	even	6
588.2.n.e.263.1		24	7.3	odd	6
588.2.n.e.263.3		24	28.3	even	6
588.2.n.e.263.10		24	84.59	odd	6
588.2.n.e.263.12		24	21.17	even	6
588.2.n.e.275.1		24	84.83	odd	2
588.2.n.e.275.3		24	21.20	even	2
588.2.n.e.275.10		24	7.6	odd	2
588.2.n.e.275.12		24	28.27	even	2

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09645 + 0.893190i) q^{2} +(1.03264 - 1.39056i) q^{3} +(0.404424 + 1.95868i) q^{4} +(-1.79791 - 1.03802i) q^{5} +(2.37428 - 0.602344i) q^{6} +(-2.61347 + 0.412056i) q^{7} +(-1.30604 + 2.50883i) q^{8} +(-0.867316 - 2.87189i) q^{9} +(-1.04417 - 2.74402i) q^{10} +(1.99399 + 3.45368i) q^{11} +(3.14129 + 1.46024i) q^{12} -1.30998 q^{13} +(-3.23359 - 1.88252i) q^{14} +(-3.30003 + 1.42820i) q^{15} +(-3.67288 + 1.58428i) q^{16} +(2.54752 - 1.47081i) q^{17} +(1.61417 - 3.92358i) q^{18} +(0.949883 + 0.548415i) q^{19} +(1.30604 - 3.94134i) q^{20} +(-2.12578 + 4.05969i) q^{21} +(-0.898482 + 5.56781i) q^{22} +(3.75063 - 6.49627i) q^{23} +(2.14001 + 4.40685i) q^{24} +(-0.345008 - 0.597572i) q^{25} +(-1.43634 - 1.17006i) q^{26} +(-4.88916 - 1.75957i) q^{27} +(-1.86404 - 4.95231i) q^{28} +0.865568i q^{29} +(-4.89399 - 1.38160i) q^{30} +(3.18742 - 1.84026i) q^{31} +(-5.44221 - 1.54349i) q^{32} +(6.86162 + 0.793650i) q^{33} +(4.10695 + 0.662741i) q^{34} +(5.12651 + 1.97200i) q^{35} +(5.27436 - 2.86026i) q^{36} +(-2.08850 + 3.61738i) q^{37} +(0.551664 + 1.44974i) q^{38} +(-1.35274 + 1.82161i) q^{39} +(4.95238 - 3.15496i) q^{40} +7.01712i q^{41} +(-5.95689 + 2.55254i) q^{42} +4.27597i q^{43} +(-5.95826 + 5.30234i) q^{44} +(-1.42174 + 6.06370i) q^{45} +(9.91479 - 3.77285i) q^{46} +(-3.75063 + 6.49627i) q^{47} +(-1.58973 + 6.74335i) q^{48} +(6.66042 - 2.15379i) q^{49} +(0.155459 - 0.963368i) q^{50} +(0.585414 - 5.06129i) q^{51} +(-0.529789 - 2.56584i) q^{52} +(4.27909 - 2.47053i) q^{53} +(-3.78911 - 6.29624i) q^{54} -8.27923i q^{55} +(2.37952 - 7.09492i) q^{56} +(1.74349 - 0.754555i) q^{57} +(-0.773117 + 0.949056i) q^{58} +(-2.44458 - 4.23414i) q^{59} +(-4.13200 - 5.88611i) q^{60} +(-2.05347 + 3.55672i) q^{61} +(5.13856 + 0.829212i) q^{62} +(3.45008 + 7.14821i) q^{63} +(-4.58850 - 6.55330i) q^{64} +(2.35524 + 1.35980i) q^{65} +(6.81457 + 6.99893i) q^{66} +(-2.09778 + 1.21116i) q^{67} +(3.91113 + 4.39495i) q^{68} +(-5.16042 - 11.9238i) q^{69} +(3.85961 + 6.74116i) q^{70} -0.901192 q^{71} +(8.33785 + 1.57487i) q^{72} +(-6.50543 - 11.2677i) q^{73} +(-5.52095 + 2.10087i) q^{74} +(-1.18723 - 0.137321i) q^{75} +(-0.690016 + 2.08231i) q^{76} +(-6.63432 - 8.20446i) q^{77} +(-3.11026 + 0.789060i) q^{78} +(8.97336 + 5.18077i) q^{79} +(8.24804 + 0.964154i) q^{80} +(-7.49553 + 4.98167i) q^{81} +(-6.26762 + 7.69395i) q^{82} -12.4386 q^{83} +(-8.81136 - 2.52189i) q^{84} -6.10695 q^{85} +(-3.81926 + 4.68841i) q^{86} +(1.20363 + 0.893819i) q^{87} +(-11.2690 + 0.491915i) q^{88} +(-7.38393 - 4.26311i) q^{89} +(-6.97491 + 5.37869i) q^{90} +(3.42360 - 0.539786i) q^{91} +(14.2410 + 4.71904i) q^{92} +(0.732462 - 6.33262i) q^{93} +(-9.91479 + 3.77285i) q^{94} +(-1.13854 - 1.97200i) q^{95} +(-7.76615 + 5.97385i) q^{96} +15.3909 q^{97} +(9.22659 + 3.58749i) q^{98} +(8.18919 - 8.72195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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