LMFDB - Embedded newform 273.2.bn.c.146.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(146,273)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("273.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bn (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.10
Character	$\chi$	$=$	273.146
Dual form			273.2.bn.c.230.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29226 + 0.746087i) q^{2} +(1.56373 - 0.744804i) q^{3} +(0.113292 - 0.196227i) q^{4} -2.73189 q^{5} +(-1.46506 + 2.12916i) q^{6} +(-2.56547 - 0.646794i) q^{7} -2.64625i q^{8} +(1.89053 - 2.32935i) q^{9} +O(q^{10})$	\(q+(-1.29226 + 0.746087i) q^{2} +(1.56373 - 0.744804i) q^{3} +(0.113292 - 0.196227i) q^{4} -2.73189 q^{5} +(-1.46506 + 2.12916i) q^{6} +(-2.56547 - 0.646794i) q^{7} -2.64625i q^{8} +(1.89053 - 2.32935i) q^{9} +(3.53032 - 2.03823i) q^{10} +(4.80144 - 2.77211i) q^{11} +(0.0310075 - 0.391227i) q^{12} +(2.92207 - 2.11223i) q^{13} +(3.79783 - 1.07824i) q^{14} +(-4.27196 + 2.03473i) q^{15} +(2.20091 + 3.81209i) q^{16} +(1.56754 - 2.71505i) q^{17} +(-0.705164 + 4.42063i) q^{18} +(-4.83982 - 2.79427i) q^{19} +(-0.309501 + 0.536071i) q^{20} +(-4.49346 + 0.899361i) q^{21} +(-4.13648 + 7.16459i) q^{22} +(0.778850 - 0.449669i) q^{23} +(-1.97093 - 4.13803i) q^{24} +2.46325 q^{25} +(-2.20017 + 4.90967i) q^{26} +(1.22138 - 5.05057i) q^{27} +(-0.417565 + 0.430138i) q^{28} +(-5.87835 + 3.39386i) q^{29} +(4.00240 - 5.81665i) q^{30} +2.36359i q^{31} +(-1.10487 - 0.637899i) q^{32} +(5.44350 - 7.91098i) q^{33} +4.67808i q^{34} +(7.00860 + 1.76697i) q^{35} +(-0.242900 - 0.634869i) q^{36} +(-1.46680 - 2.54056i) q^{37} +8.33908 q^{38} +(2.99614 - 5.47934i) q^{39} +7.22927i q^{40} +(-1.12250 - 1.94422i) q^{41} +(5.13572 - 4.51472i) q^{42} +(0.910699 - 1.57738i) q^{43} -1.25623i q^{44} +(-5.16474 + 6.36354i) q^{45} +(-0.670985 + 1.16218i) q^{46} -1.03761 q^{47} +(6.28091 + 4.32186i) q^{48} +(6.16332 + 3.31867i) q^{49} +(-3.18316 + 1.83780i) q^{50} +(0.429030 - 5.41313i) q^{51} +(-0.0834302 - 0.812686i) q^{52} -8.97651i q^{53} +(2.18982 + 7.43791i) q^{54} +(-13.1170 + 7.57312i) q^{55} +(-1.71158 + 6.78888i) q^{56} +(-9.64938 - 0.764783i) q^{57} +(5.06424 - 8.77151i) q^{58} +(-1.59559 + 2.76364i) q^{59} +(-0.0847093 + 1.06879i) q^{60} +(-1.62596 - 0.938746i) q^{61} +(-1.76344 - 3.05438i) q^{62} +(-6.35673 + 4.75311i) q^{63} -6.89994 q^{64} +(-7.98278 + 5.77039i) q^{65} +(-1.13214 + 14.2844i) q^{66} +(6.70479 + 11.6130i) q^{67} +(-0.355178 - 0.615186i) q^{68} +(0.882999 - 1.28325i) q^{69} +(-10.3753 + 2.94564i) q^{70} +(-3.21113 - 1.85394i) q^{71} +(-6.16404 - 5.00282i) q^{72} -7.46851i q^{73} +(3.79096 + 2.18871i) q^{74} +(3.85187 - 1.83464i) q^{75} +(-1.09662 + 0.633135i) q^{76} +(-14.1110 + 4.00624i) q^{77} +(0.216261 + 9.31611i) q^{78} +12.5967 q^{79} +(-6.01266 - 10.4142i) q^{80} +(-1.85176 - 8.80744i) q^{81} +(2.90112 + 1.67496i) q^{82} +6.48224 q^{83} +(-0.332592 + 0.983626i) q^{84} +(-4.28235 + 7.41724i) q^{85} +2.71784i q^{86} +(-6.66441 + 9.68532i) q^{87} +(-7.33570 - 12.7058i) q^{88} +(5.08611 + 8.80940i) q^{89} +(1.92643 - 12.0767i) q^{90} +(-8.86267 + 3.52889i) q^{91} -0.203775i q^{92} +(1.76041 + 3.69603i) q^{93} +(1.34086 - 0.774148i) q^{94} +(13.2219 + 7.63365i) q^{95} +(-2.20284 - 0.174591i) q^{96} +(7.68183 + 4.43511i) q^{97} +(-10.4406 + 0.309787i) q^{98} +(2.62006 - 16.4250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 10 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9} - 18 q^{15} - 16 q^{16} + 8 q^{18} - 44 q^{21} - 32 q^{22} + 48 q^{25} + 40 q^{28} - 40 q^{30} - 6 q^{36} + 12 q^{37} - 12 q^{42} + 40 q^{43} - 36 q^{46} - 24 q^{49} - 28 q^{51} - 68 q^{57} - 116 q^{60} + 4 q^{63} - 48 q^{64} - 28 q^{67} - 64 q^{70} + 62 q^{72} - 2 q^{78} + 56 q^{79} + 10 q^{81} + 28 q^{85} + 80 q^{88} - 16 q^{91} + 46 q^{93} - 32 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 10 * q^9 - 18 * q^15 - 16 * q^16 + 8 * q^18 - 44 * q^21 - 32 * q^22 + 48 * q^25 + 40 * q^28 - 40 * q^30 - 6 * q^36 + 12 * q^37 - 12 * q^42 + 40 * q^43 - 36 * q^46 - 24 * q^49 - 28 * q^51 - 68 * q^57 - 116 * q^60 + 4 * q^63 - 48 * q^64 - 28 * q^67 - 64 * q^70 + 62 * q^72 - 2 * q^78 + 56 * q^79 + 10 * q^81 + 28 * q^85 + 80 * q^88 - 16 * q^91 + 46 * q^93 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.29226	+	0.746087i	−0.913766	+	0.527563i	−0.881641	−	0.471921i	$-0.843561\pi$
$2$	−1.29226	+	0.746087i	−0.913766	+	0.527563i	−0.0321252	+	0.999484i	$0.510228\pi$
$3$	1.56373	−	0.744804i	0.902823	−	0.430013i
$3$	1.56373	−	0.744804i	0.902823	−	0.430013i
$4$	0.113292	−	0.196227i	0.0566458	−	0.0981134i
$5$	−2.73189			−1.22174			−0.610870	−	0.791731i	$-0.709180\pi$
$5$	−2.73189			−1.22174			−0.610870	+	0.791731i	$0.709180\pi$
$6$	−1.46506	+	2.12916i	−0.598110	+	0.869227i
$7$	−2.56547	−	0.646794i	−0.969658	−	0.244465i
$7$	−2.56547	−	0.646794i	−0.969658	−	0.244465i
$8$		−	2.64625i		−	0.935589i
$9$	1.89053	−	2.32935i	0.630178	−	0.776451i
$10$	3.53032	−	2.03823i	1.11639	−	0.644545i
$11$	4.80144	−	2.77211i	1.44769	−	0.835824i	0.449346	−	0.893358i	$-0.351657\pi$
$11$	4.80144	−	2.77211i	1.44769	−	0.835824i	0.998344	+	0.0575343i	$0.0183239\pi$
$12$	0.0310075	−	0.391227i	0.00895110	−	0.112937i
$13$	2.92207	−	2.11223i	0.810436	−	0.585827i
$13$	2.92207	−	2.11223i	0.810436	−	0.585827i
$14$	3.79783	−	1.07824i	1.01501	−	0.288172i
$15$	−4.27196	+	2.03473i	−1.10302	+	0.525364i
$16$	2.20091	+	3.81209i	0.550228	+	0.953023i
$17$	1.56754	−	2.71505i	0.380184	−	0.658497i	−0.610905	−	0.791704i	$-0.709194\pi$
$17$	1.56754	−	2.71505i	0.380184	−	0.658497i	0.991088	+	0.133207i	$0.0425274\pi$
$18$	−0.705164	+	4.42063i	−0.166209	+	1.04195i
$19$	−4.83982	−	2.79427i	−1.11033	−	0.641050i	−0.171416	−	0.985199i	$-0.554834\pi$
$19$	−4.83982	−	2.79427i	−1.11033	−	0.641050i	−0.938915	+	0.344149i	$0.888167\pi$
$20$	−0.309501	+	0.536071i	−0.0692064	+	0.119869i
$21$	−4.49346	+	0.899361i	−0.980553	+	0.196257i
$22$	−4.13648	+	7.16459i	−0.881900	+	1.52749i
$23$	0.778850	−	0.449669i	0.162401	−	0.0937625i	−0.416597	−	0.909091i	$-0.636777\pi$
$23$	0.778850	−	0.449669i	0.162401	−	0.0937625i	0.578998	+	0.815329i	$0.303444\pi$
$24$	−1.97093	−	4.13803i	−0.402315	−	0.844671i
$25$	2.46325			0.492649
$26$	−2.20017	+	4.90967i	−0.431488	+	0.962865i
$27$	1.22138	−	5.05057i	0.235055	−	0.971982i
$28$	−0.417565	+	0.430138i	−0.0789124	+	0.0812885i
$29$	−5.87835	+	3.39386i	−1.09158	+	0.630225i	−0.933997	−	0.357281i	$-0.883704\pi$
$29$	−5.87835	+	3.39386i	−1.09158	+	0.630225i	−0.157584	+	0.987506i	$0.550371\pi$
$30$	4.00240	−	5.81665i	0.730735	−	1.06197i
$31$			2.36359i			0.424513i	0.977214	+	0.212257i	$0.0680813\pi$
$31$			2.36359i			0.424513i	−0.977214	+	0.212257i	$0.931919\pi$
$32$	−1.10487	−	0.637899i	−0.195316	−	0.112766i
$33$	5.44350	−	7.91098i	0.947592	−	1.37713i
$34$			4.67808i			0.802284i
$35$	7.00860	+	1.76697i	1.18467	+	0.298673i
$36$	−0.242900	−	0.634869i	−0.0404833	−	0.105812i
$37$	−1.46680	−	2.54056i	−0.241140	−	0.417666i	0.719900	−	0.694078i	$-0.244188\pi$
$37$	−1.46680	−	2.54056i	−0.241140	−	0.417666i	−0.961039	+	0.276412i	$0.910855\pi$
$38$	8.33908			1.35278
$39$	2.99614	−	5.47934i	0.479767	−	0.877396i
$40$			7.22927i			1.14305i
$41$	−1.12250	−	1.94422i	−0.175305	−	0.303637i	0.764962	−	0.644075i	$-0.222758\pi$
$41$	−1.12250	−	1.94422i	−0.175305	−	0.303637i	−0.940267	+	0.340439i	$0.889424\pi$
$42$	5.13572	−	4.51472i	0.792458	−	0.696636i
$43$	0.910699	−	1.57738i	0.138880	−	0.240548i	−0.788193	−	0.615428i	$-0.788983\pi$
$43$	0.910699	−	1.57738i	0.138880	−	0.240548i	0.927073	+	0.374881i	$0.122316\pi$
$44$		−	1.25623i		−	0.189384i
$45$	−5.16474	+	6.36354i	−0.769914	+	0.948621i
$46$	−0.670985	+	1.16218i	−0.0989313	+	0.171354i
$47$	−1.03761			−0.151351			−0.0756756	−	0.997132i	$-0.524111\pi$
$47$	−1.03761			−0.151351			−0.0756756	+	0.997132i	$0.524111\pi$
$48$	6.28091	+	4.32186i	0.906571	+	0.623806i
$49$	6.16332	+	3.31867i	0.880474	+	0.474095i
$50$	−3.18316	+	1.83780i	−0.450166	+	0.259904i
$51$	0.429030	−	5.41313i	0.0600762	−	0.757990i
$52$	−0.0834302	−	0.812686i	−0.0115697	−	0.112699i
$53$		−	8.97651i		−	1.23302i	−0.787348	−	0.616509i	$-0.788546\pi$
$53$		−	8.97651i		−	1.23302i	0.787348	−	0.616509i	$-0.211454\pi$
$54$	2.18982	+	7.43791i	0.297996	+	1.01217i
$55$	−13.1170	+	7.57312i	−1.76870	+	1.02116i
$56$	−1.71158	+	6.78888i	−0.228719	+	0.907202i
$57$	−9.64938	−	0.764783i	−1.27809	−	0.101298i
$58$	5.06424	−	8.77151i	0.664967	−	1.15176i
$59$	−1.59559	+	2.76364i	−0.207728	+	0.359795i	−0.950998	−	0.309196i	$-0.899940\pi$
$59$	−1.59559	+	2.76364i	−0.207728	+	0.359795i	0.743271	+	0.668991i	$0.233274\pi$
$60$	−0.0847093	+	1.06879i	−0.0109359	+	0.137980i
$61$	−1.62596	−	0.938746i	−0.208182	−	0.120194i	0.392284	−	0.919844i	$-0.371685\pi$
$61$	−1.62596	−	0.938746i	−0.208182	−	0.120194i	−0.600466	+	0.799650i	$0.705018\pi$
$62$	−1.76344	−	3.05438i	−0.223958	−	0.387906i
$63$	−6.35673	+	4.75311i	−0.800872	+	0.598835i
$64$	−6.89994			−0.862493
$65$	−7.98278	+	5.77039i	−0.990142	+	0.715729i
$66$	−1.13214	+	14.2844i	−0.139357	+	1.75829i
$67$	6.70479	+	11.6130i	0.819120	+	1.41876i	0.906331	+	0.422568i	$0.138871\pi$
$67$	6.70479	+	11.6130i	0.819120	+	1.41876i	−0.0872108	+	0.996190i	$0.527795\pi$
$68$	−0.355178	−	0.615186i	−0.0430716	−	0.0746022i
$69$	0.882999	−	1.28325i	0.106301	−	0.154486i
$70$	−10.3753	+	2.94564i	−1.24008	+	0.352071i
$71$	−3.21113	−	1.85394i	−0.381091	−	0.220023i	0.297202	−	0.954815i	$-0.403946\pi$
$71$	−3.21113	−	1.85394i	−0.381091	−	0.220023i	−0.678293	+	0.734792i	$0.737280\pi$
$72$	−6.16404	−	5.00282i	−0.726439	−	0.589588i
$73$		−	7.46851i		−	0.874123i	−0.899432	−	0.437062i	$-0.856019\pi$
$73$		−	7.46851i		−	0.874123i	0.899432	−	0.437062i	$-0.143981\pi$
$74$	3.79096	+	2.18871i	0.440691	+	0.254433i
$75$	3.85187	−	1.83464i	0.444775	−	0.211846i
$76$	−1.09662	+	0.633135i	−0.125791	+	0.0726255i
$77$	−14.1110	+	4.00624i	−1.60809	+	0.456554i
$78$	0.216261	+	9.31611i	0.0244868	+	1.05484i
$79$	12.5967			1.41724			0.708620	−	0.705590i	$-0.249318\pi$
$79$	12.5967			1.41724			0.708620	+	0.705590i	$0.249318\pi$
$80$	−6.01266	−	10.4142i	−0.672236	−	1.16435i
$81$	−1.85176	−	8.80744i	−0.205751	−	0.978604i
$82$	2.90112	+	1.67496i	0.320375	+	0.184969i
$83$	6.48224			0.711518			0.355759	−	0.934578i	$-0.384222\pi$
$83$	6.48224			0.711518			0.355759	+	0.934578i	$0.384222\pi$
$84$	−0.332592	+	0.983626i	−0.0362888	+	0.107322i
$85$	−4.28235	+	7.41724i	−0.464486	+	0.804513i
$86$			2.71784i			0.293073i
$87$	−6.66441	+	9.68532i	−0.714500	+	1.03838i
$88$	−7.33570	−	12.7058i	−0.781988	−	1.35444i
$89$	5.08611	+	8.80940i	0.539127	+	0.933795i	0.998951	+	0.0457849i	$0.0145789\pi$
$89$	5.08611	+	8.80940i	0.539127	+	0.933795i	−0.459825	+	0.888010i	$0.652088\pi$
$90$	1.92643	−	12.0767i	0.203064	−	1.27300i
$91$	−8.86267	+	3.52889i	−0.929060	+	0.369929i
$92$		−	0.203775i		−	0.0212450i
$93$	1.76041	+	3.69603i	0.182546	+	0.383260i
$94$	1.34086	−	0.774148i	0.138300	−	0.0798473i
$95$	13.2219	+	7.63365i	1.35654	+	0.783196i
$96$	−2.20284	−	0.174591i	−0.224826	−	0.0178191i
$97$	7.68183	+	4.43511i	0.779972	+	0.450317i	0.836420	−	0.548089i	$-0.184644\pi$
$97$	7.68183	+	4.43511i	0.779972	+	0.450317i	−0.0564485	+	0.998406i	$0.517978\pi$
$98$	−10.4406	+	0.309787i	−1.05466	+	0.0312932i
$99$	2.62006	−	16.4250i	0.263326	−	1.65078i
$100$	0.279065	−	0.483355i	0.0279065	−	0.0483355i
$101$	4.29061	+	7.43156i	0.426932	+	0.739468i	0.996599	−	0.0824081i	$-0.0262611\pi$
$101$	4.29061	+	7.43156i	0.426932	+	0.739468i	−0.569667	+	0.821876i	$0.692928\pi$
$102$	3.48425	+	7.31527i	0.344992	+	0.724320i
$103$			2.58413i			0.254622i	0.991863	+	0.127311i	$0.0406346\pi$
$103$			2.58413i			0.254622i	−0.991863	+	0.127311i	$0.959365\pi$
$104$	−5.58948	−	7.73251i	−0.548094	−	0.758235i
$105$	12.2756	−	2.45696i	1.19798	−	0.239775i
$106$	6.69725	+	11.6000i	0.650495	+	1.12669i
$107$	−6.21163	+	3.58629i	−0.600501	+	0.346699i	−0.769239	−	0.638962i	$-0.779364\pi$
$107$	−6.21163	+	3.58629i	−0.600501	+	0.346699i	0.168738	+	0.985661i	$0.446031\pi$
$108$	−0.852684	−	0.811855i	−0.0820495	−	0.0781208i
$109$	−4.98533			−0.477508			−0.238754	−	0.971080i	$-0.576739\pi$
$109$	−4.98533			−0.477508			−0.238754	+	0.971080i	$0.576739\pi$
$110$	11.3004	−	19.5729i	1.07745	−	1.86620i
$111$	−4.18590	−	2.88029i	−0.397308	−	0.273385i
$112$	−3.18075	−	11.2034i	−0.300552	−	1.05862i
$113$	16.6455	+	9.61026i	1.56587	+	0.904057i	0.996642	+	0.0818789i	$0.0260921\pi$
$113$	16.6455	+	9.61026i	1.56587	+	0.904057i	0.569230	+	0.822178i	$0.307241\pi$
$114$	13.0401	−	6.21098i	1.22132	−	0.581711i
$115$	−2.12774	+	1.22845i	−0.198412	+	0.114553i
$116$			1.53799i			0.142798i
$117$	0.604146	−	10.7998i	0.0558533	−	0.998439i
$118$		−	4.76179i		−	0.438358i
$119$	−5.77756	+	5.95153i	−0.529628	+	0.545576i
$120$	5.38439	+	11.3047i	0.491525	+	1.03197i
$121$	9.86923	−	17.0940i	0.897202	−	1.55400i
$122$	2.80154			0.253640
$123$	−3.20335	−	2.20421i	−0.288837	−	0.198747i
$124$	0.463800	+	0.267775i	0.0416505	+	0.0240469i
$125$	6.93014			0.619851
$126$	4.66832	−	10.8849i	0.415887	−	0.969706i
$127$	−5.59291	−	9.68721i	−0.496291	−	0.859601i	0.503700	−	0.863879i	$-0.331972\pi$
$127$	−5.59291	−	9.68721i	−0.496291	−	0.859601i	−0.999991	+	0.00427785i	$0.998638\pi$
$128$	11.1263	−	6.42375i	0.983432	−	0.567785i
$129$	0.249255	−	3.14489i	0.0219457	−	0.276892i
$130$	6.01063	−	13.4127i	0.527167	−	1.17637i
$131$	−13.2568			−1.15825			−0.579126	−	0.815238i	$-0.696606\pi$
$131$	−13.2568			−1.15825			−0.579126	+	0.815238i	$0.696606\pi$
$132$	−0.935644	−	1.96441i	−0.0814374	−	0.170980i
$133$	10.6091	+	10.2990i	0.919927	+	0.893036i
$134$	−17.3287	−	10.0047i	−1.49697	−	0.864275i
$135$	−3.33669	+	13.7976i	−0.287177	+	1.18751i
$136$	−7.18470	−	4.14809i	−0.616083	−	0.355696i
$137$	−14.7843	−	8.53574i	−1.26311	−	0.729257i	−0.289435	−	0.957198i	$-0.593468\pi$
$137$	−14.7843	−	8.53574i	−1.26311	−	0.729257i	−0.973675	+	0.227940i	$0.926801\pi$
$138$	−0.183646	+	2.31709i	−0.0156330	+	0.197244i
$139$	1.21033	+	0.698786i	0.102659	+	0.0592702i	0.550451	−	0.834868i	$-0.314456\pi$
$139$	1.21033	+	0.698786i	0.102659	+	0.0592702i	−0.447791	+	0.894138i	$0.647789\pi$
$140$	1.14074	−	1.17509i	0.0964104	−	0.0993135i
$141$	−1.62255	+	0.772817i	−0.136643	+	0.0650829i
$142$	5.53282			0.464304
$143$	8.17480	−	18.2421i	0.683611	−	1.52548i
$144$	13.0406	+	2.08019i	1.08672	+	0.173349i
$145$	16.0590	−	9.27168i	1.33363	−	0.769971i
$146$	5.57216	+	9.65126i	0.461155	+	0.798744i
$147$	12.1095	+	0.599054i	0.998779	+	0.0494091i
$148$	−0.664702			−0.0546382
$149$	15.3595	+	8.86783i	1.25830	+	0.726481i	0.972744	−	0.231880i	$-0.0744877\pi$
$149$	15.3595	+	8.86783i	1.25830	+	0.726481i	0.285558	+	0.958361i	$0.407821\pi$
$150$	−3.60882	+	5.24466i	−0.294659	+	0.428224i
$151$	2.09610			0.170578			0.0852891	−	0.996356i	$-0.472819\pi$
$151$	2.09610			0.170578			0.0852891	+	0.996356i	$0.472819\pi$
$152$	−7.39433	+	12.8074i	−0.599759	+	1.03881i
$153$	−3.36083	−	8.78425i	−0.271707	−	0.710164i
$154$	15.2460	−	15.7051i	1.22856	−	1.26555i
$155$		−	6.45708i		−	0.518645i
$156$	−0.735754	−	1.20869i	−0.0589075	−	0.0967724i
$157$		−	10.7453i		−	0.857571i	−0.903406	−	0.428786i	$-0.858942\pi$
$157$		−	10.7453i		−	0.857571i	0.903406	−	0.428786i	$-0.141058\pi$
$158$	−16.2782	+	9.39824i	−1.29503	+	0.747684i
$159$	−6.68574	−	14.0369i	−0.530213	−	1.11320i
$160$	3.01840	+	1.74267i	0.238625	+	0.137770i
$161$	−2.28896	+	0.649859i	−0.180395	+	0.0512161i
$162$	8.96407	+	9.99993i	0.704284	+	0.785669i
$163$	2.58939	−	4.48495i	0.202817	−	0.351289i	−0.746618	−	0.665253i	$-0.768324\pi$
$163$	2.58939	−	4.48495i	0.202817	−	0.351289i	0.949435	+	0.313964i	$0.101657\pi$
$164$	−0.508678			−0.0397211
$165$	−14.8711	+	21.6120i	−1.15771	+	1.68249i
$166$	−8.37674	+	4.83631i	−0.650161	+	0.375371i
$167$	10.2389	+	17.7342i	0.792307	+	1.37232i	0.924535	+	0.381097i	$0.124454\pi$
$167$	10.2389	+	17.7342i	0.792307	+	1.37232i	−0.132228	+	0.991219i	$0.542213\pi$
$168$	2.37993	+	11.8908i	0.183616	+	0.917395i
$169$	4.07697	−	12.3442i	0.313613	−	0.949551i
$170$		−	12.7800i		−	0.980182i
$171$	−15.6587	+	5.99098i	−1.19745	+	0.458141i
$172$	−0.206349	−	0.357407i	−0.0157340	−	0.0272520i
$173$	−0.888921	+	1.53966i	−0.0675834	+	0.117058i	−0.897837	−	0.440328i	$-0.854862\pi$
$173$	−0.888921	+	1.53966i	−0.0675834	+	0.117058i	0.830254	+	0.557386i	$0.188196\pi$
$174$	1.38607	−	17.4882i	0.105077	−	1.32578i
$175$	−6.31940	−	1.59321i	−0.477702	−	0.120436i
$176$	21.1351	+	12.2024i	1.59312	+	0.919788i
$177$	−0.436707	+	5.51000i	−0.0328249	+	0.414157i
$178$	−13.1452	−	7.58936i	−0.985271	−	0.568847i
$179$	−10.8509	+	6.26477i	−0.811035	+	0.468251i	−0.847315	−	0.531091i	$-0.821782\pi$
$179$	−10.8509	+	6.26477i	−0.811035	+	0.468251i	0.0362804	+	0.999342i	$0.488449\pi$
$180$	0.663576	+	1.73440i	0.0494600	+	0.129274i
$181$			20.7938i			1.54559i	0.634656	+	0.772795i	$0.281142\pi$
$181$			20.7938i			1.54559i	−0.634656	+	0.772795i	$0.718858\pi$
$182$	8.82002	−	11.1726i	0.653783	−	0.828166i
$183$	−3.24175	−	0.256932i	−0.239637	−	0.0189929i
$184$	−1.18994	−	2.06103i	−0.0877232	−	0.151941i
$185$	4.00713	+	6.94055i	0.294610	+	0.510280i
$186$	−5.03247	−	3.46281i	−0.368999	−	0.253906i
$187$		−	17.3816i		−	1.27107i
$188$	−0.117553	+	0.203607i	−0.00857341	+	0.0148496i
$189$	−6.40011	+	12.1671i	−0.465539	+	0.885027i
$190$	−22.7815			−1.65274
$191$	−16.9894	−	9.80886i	−1.22931	−	0.709744i	−0.262427	−	0.964952i	$-0.584523\pi$
$191$	−16.9894	−	9.80886i	−1.22931	−	0.709744i	−0.966886	+	0.255207i	$0.917856\pi$
$192$	−10.7897	+	5.13910i	−0.778678	+	0.370883i
$193$	3.49255	+	6.04928i	0.251399	+	0.435437i	0.963911	−	0.266223i	$-0.0857759\pi$
$193$	3.49255	+	6.04928i	0.251399	+	0.435437i	−0.712512	+	0.701660i	$0.752443\pi$
$194$	−13.2359			−0.950282
$195$	−8.18515	+	14.9690i	−0.586151	+	1.07195i
$196$	1.34946	−	0.833430i	0.0963902	−	0.0595307i
$197$	18.7335	−	10.8158i	1.33471	−	0.770594i	0.348691	−	0.937238i	$-0.386626\pi$
$197$	18.7335	−	10.8158i	1.33471	−	0.770594i	0.986017	+	0.166644i	$0.0532930\pi$
$198$	8.86869	+	23.1802i	0.630271	+	1.64735i
$199$	12.5873	+	7.26731i	0.892294	+	0.515166i	0.874692	−	0.484679i	$-0.161064\pi$
$199$	12.5873	+	7.26731i	0.892294	+	0.515166i	0.0176015	+	0.999845i	$0.494397\pi$
$200$		−	6.51836i		−	0.460918i
$201$	19.1339	+	13.1660i	1.34960	+	0.928655i
$202$	−11.0892	−	6.40234i	−0.780232	−	0.450467i
$203$	17.2759	−	4.90479i	1.21253	−	0.344249i
$204$	−1.01360	−	0.697450i	−0.0709659	−	0.0488312i
$205$	3.06655	+	5.31141i	0.214177	+	0.370965i
$206$	−1.92798	−	3.33937i	−0.134329	−	0.232665i
$207$	0.425005	−	2.66433i	0.0295399	−	0.185184i
$208$	14.4832	+	6.49037i	1.00423	+	0.450026i
$209$	−30.9841			−2.14322
$210$	−14.0302	+	12.3337i	−0.968178	+	0.851108i
$211$	−6.98629	−	12.1006i	−0.480956	−	0.833040i	0.518805	−	0.854892i	$-0.326377\pi$
$211$	−6.98629	−	12.1006i	−0.480956	−	0.833040i	−0.999761	+	0.0218526i	$0.993044\pi$
$212$	−1.76143	−	1.01696i	−0.120976	−	0.0698453i
$213$	−6.40218	−	0.507419i	−0.438670	−	0.0347678i
$214$	5.35136	−	9.26883i	0.365812	−	0.633605i
$215$	−2.48793	+	4.30923i	−0.169676	+	0.293887i
$216$	−13.3650	−	3.23208i	−0.909376	−	0.219915i
$217$	1.52876	−	6.06373i	0.103779	−	0.411633i
$218$	6.44234	−	3.71949i	0.436331	−	0.251916i
$219$	−5.56258	−	11.6788i	−0.375884	−	0.789178i
$220$			3.43188i			0.231378i
$221$	−1.15437	−	11.2446i	−0.0776510	−	0.756392i
$222$	7.55823	+	0.599044i	0.507275	+	0.0402052i
$223$	−16.2803	+	9.39944i	−1.09021	+	0.629433i	−0.933632	−	0.358233i	$-0.883379\pi$
$223$	−16.2803	+	9.39944i	−1.09021	+	0.629433i	−0.156577	+	0.987666i	$0.550046\pi$
$224$	2.42193	+	2.35114i	0.161822	+	0.157092i
$225$	4.65685	−	5.73777i	0.310457	−	0.382518i
$226$	−28.6804			−1.90779
$227$	2.91196	−	5.04367i	0.193274	−	0.334760i	−0.753060	−	0.657952i	$-0.771423\pi$
$227$	2.91196	−	5.04367i	0.193274	−	0.334760i	0.946333	+	0.323193i	$0.104756\pi$
$228$	−1.24326	+	1.80682i	−0.0823372	+	0.119660i
$229$			17.2490i			1.13984i	0.821699	+	0.569922i	$0.193027\pi$
$229$			17.2490i			1.13984i	−0.821699	+	0.569922i	$0.806973\pi$
$230$	1.83306	−	3.17495i	0.120868	−	0.209350i
$231$	−19.0819	+	16.7746i	−1.25550	+	1.10369i
$232$	8.98100	+	15.5556i	0.589632	+	1.02127i
$233$		−	15.1362i		−	0.991603i	−0.868436	−	0.495802i	$-0.834874\pi$
$233$		−	15.1362i		−	0.991603i	0.868436	−	0.495802i	$-0.165126\pi$
$234$	7.27685	+	14.4069i	0.475703	+	0.941806i
$235$	2.83464			0.184912
$236$	0.361533	+	0.626194i	0.0235338	+	0.0407618i
$237$	19.6979	−	9.38208i	1.27952	−	0.609431i
$238$	3.02575	−	12.0015i	0.196130	−	0.777941i
$239$			9.13875i			0.591136i	0.955322	+	0.295568i	$0.0955090\pi$
$239$			9.13875i			0.591136i	−0.955322	+	0.295568i	$0.904491\pi$
$240$	−17.1588	−	11.8069i	−1.10759	−	0.762129i
$241$	16.2277	+	9.36906i	1.04532	+	0.603514i	0.921335	−	0.388770i	$-0.127100\pi$
$241$	16.2277	+	9.36906i	1.04532	+	0.603514i	0.123982	+	0.992284i	$0.460433\pi$
$242$			29.4532i			1.89332i
$243$	−9.45548	−	12.3933i	−0.606569	−	0.795031i
$244$	−0.368414	+	0.212704i	−0.0235853	+	0.0136170i
$245$	−16.8375	−	9.06625i	−1.07571	−	0.579221i
$246$	5.78410	+	0.458432i	0.368781	+	0.0292285i
$247$	−20.0444	+	2.05776i	−1.27540	+	0.130932i
$248$	6.25464			0.397170
$249$	10.1365	−	4.82800i	0.642375	−	0.305962i
$250$	−8.95555	+	5.17049i	−0.566399	+	0.327010i
$251$	5.72137	−	9.90971i	0.361130	−	0.625495i	−0.627017	−	0.779005i	$-0.715724\pi$
$251$	5.72137	−	9.90971i	0.361130	−	0.625495i	0.988147	+	0.153510i	$0.0490578\pi$
$252$	0.212523	+	1.78585i	0.0133877	+	0.112498i
$253$	2.49307	−	4.31812i	0.156738	−	0.271478i
$254$	14.4550	+	8.34560i	0.906987	+	0.523649i
$255$	−1.17206	+	14.7881i	−0.0733975	+	0.926067i
$256$	−2.68542	+	4.65128i	−0.167839	+	0.290705i
$257$	6.64490	+	11.5093i	0.414498	+	0.717931i	0.995376	−	0.0960597i	$-0.0306240\pi$
$257$	6.64490	+	11.5093i	0.414498	+	0.717931i	−0.580878	+	0.813991i	$0.697291\pi$
$258$	2.02426	+	4.24999i	0.126025	+	0.264593i
$259$	2.11980	+	7.46647i	0.131718	+	0.463944i
$260$	0.227922	+	2.22017i	0.0141351	+	0.137689i
$261$	−3.20771	+	20.1090i	−0.198552	+	1.24471i
$262$	17.1312	−	9.89073i	1.05837	−	0.611051i
$263$	9.59512	−	5.53975i	0.591661	−	0.341595i	−0.174093	−	0.984729i	$-0.555699\pi$
$263$	9.59512	−	5.53975i	0.591661	−	0.341595i	0.765754	+	0.643134i	$0.222366\pi$
$264$	−20.9344	−	14.4048i	−1.28842	−	0.886557i
$265$			24.5229i			1.50643i
$266$	−21.3937	−	5.39366i	−1.31173	−	0.330707i
$267$	14.5146	+	9.98741i	0.888279	+	0.611220i
$268$	3.03838			0.185599
$269$	12.8859	−	22.3191i	0.785668	−	1.36082i	−0.142931	−	0.989733i	$-0.545653\pi$
$269$	12.8859	−	22.3191i	0.785668	−	1.36082i	0.928599	−	0.371085i	$-0.121014\pi$
$270$	−5.98234	−	20.3196i	−0.364074	−	1.23661i
$271$	−23.0734	+	13.3214i	−1.40161	+	0.809218i	−0.994558	−	0.104188i	$-0.966776\pi$
$271$	−23.0734	+	13.3214i	−1.40161	+	0.809218i	−0.407049	+	0.913406i	$0.633442\pi$
$272$	13.8001			0.836751
$273$	−11.2305	+	12.1192i	−0.679703	+	0.733488i
$274$	25.4736			1.53892
$275$	11.8271	−	6.82840i	0.713203	−	0.411768i
$276$	−0.151772	−	0.318650i	−0.00913562	−	0.0191805i
$277$	5.64884	−	9.78407i	0.339406	−	0.587868i	−0.644915	−	0.764254i	$-0.723107\pi$
$277$	5.64884	−	9.78407i	0.339406	−	0.587868i	0.984321	+	0.176386i	$0.0564407\pi$
$278$	−2.08542			−0.125075
$279$	5.50563	+	4.46845i	0.329614	+	0.267519i
$280$	4.67585	−	18.5465i	0.279435	−	1.10837i
$281$		−	13.4298i		−	0.801153i	−0.916263	−	0.400576i	$-0.868810\pi$
$281$		−	13.4298i		−	0.801153i	0.916263	−	0.400576i	$-0.131190\pi$
$282$	1.52017	−	2.20924i	0.0905246	−	0.131559i
$283$	1.72819	−	0.997772i	0.102730	−	0.0593114i	−0.447755	−	0.894156i	$-0.647776\pi$
$283$	1.72819	−	0.997772i	0.102730	−	0.0593114i	0.550485	+	0.834845i	$0.314443\pi$
$284$	−0.727587	+	0.420073i	−0.0431744	+	0.0249267i
$285$	26.3611	+	2.08931i	1.56150	+	0.123760i
$286$	3.04618	+	29.6726i	0.180125	+	1.75458i
$287$	1.62223	+	5.71388i	0.0957570	+	0.337280i
$288$	−3.57469	+	1.36767i	−0.210641	+	0.0805907i
$289$	3.58565	+	6.21053i	0.210921	+	0.365325i
$290$	−13.8350	+	23.9629i	−0.812417	+	1.40715i
$291$	15.3156	+	1.21387i	0.897818	+	0.0711586i
$292$	−1.46552	−	0.846120i	−0.0857632	−	0.0495154i
$293$	13.4902	−	23.3658i	0.788109	−	1.36504i	−0.139016	−	0.990290i	$-0.544394\pi$
$293$	13.4902	−	23.3658i	0.788109	−	1.36504i	0.927124	−	0.374754i	$-0.122273\pi$
$294$	−16.0956	+	8.26064i	−0.938717	+	0.481770i
$295$	4.35898	−	7.54997i	0.253790	−	0.439576i
$296$	−6.72296	+	3.88150i	−0.390764	+	0.225608i
$297$	−8.13634	−	27.6358i	−0.472118	−	1.60359i
$298$	−26.4647			−1.53306
$299$	1.32605	−	2.95907i	0.0766874	−	0.171128i
$300$	0.0763792	−	0.963688i	0.00440976	−	0.0556386i
$301$	−3.35661	+	3.45769i	−0.193472	+	0.199298i
$302$	−2.70871	+	1.56387i	−0.155869	+	0.0899908i
$303$	12.2444	+	8.42532i	0.703424	+	0.484022i
$304$		−	24.5998i		−	1.41089i
$305$	4.44194	+	2.56456i	0.254345	+	0.146846i
$306$	10.8969	+	8.84406i	0.622934	+	0.505582i
$307$		−	22.9472i		−	1.30966i	−0.755775	−	0.654832i	$-0.772739\pi$
$307$		−	22.9472i		−	1.30966i	0.755775	−	0.654832i	$-0.227261\pi$
$308$	−0.812521	+	3.22282i	−0.0462977	+	0.183637i
$309$	1.92467	+	4.04089i	0.109491	+	0.229878i
$310$	4.81754	+	8.34423i	0.273618	+	0.473920i
$311$	−14.0205			−0.795030			−0.397515	−	0.917596i	$-0.630127\pi$
$311$	−14.0205			−0.795030			−0.397515	+	0.917596i	$0.630127\pi$
$312$	−14.4997	−	7.92854i	−0.820882	−	0.448865i
$313$			0.982717i			0.0555465i	0.999614	+	0.0277732i	$0.00884163\pi$
$313$			0.982717i			0.0555465i	−0.999614	+	0.0277732i	$0.991158\pi$
$314$	8.01696	+	13.8858i	0.452423	+	0.783620i
$315$	17.3659	−	12.9850i	0.978458	−	0.731621i
$316$	1.42710	−	2.47181i	0.0802807	−	0.139050i
$317$		−	9.12747i		−	0.512650i	−0.966591	−	0.256325i	$-0.917488\pi$
$317$		−	9.12747i		−	0.512650i	0.966591	−	0.256325i	$-0.0825117\pi$
$318$	19.1124	+	13.1512i	1.07177	+	0.737480i
$319$	−18.8164	+	32.5909i	−1.05351	+	1.82474i
$320$	18.8499			1.05374
$321$	−7.04226	+	10.2345i	−0.393061	+	0.571231i
$322$	2.47308	−	2.54755i	0.137820	−	0.141970i
$323$	−15.1732	+	8.76025i	−0.844259	+	0.487433i
$324$	−1.93804	−	0.634444i	−0.107669	−	0.0352469i
$325$	7.19778	−	5.20294i	0.399261	−	0.288607i
$326$			7.72764i			0.427994i
$327$	−7.79573	+	3.71309i	−0.431105	+	0.205334i
$328$	−5.14489	+	2.97041i	−0.284079	+	0.164013i
$329$	2.66196	+	0.671121i	0.146759	+	0.0370001i
$330$	3.09289	−	39.0234i	0.170258	−	2.14817i
$331$	−14.4100	+	24.9588i	−0.792043	+	1.37186i	0.132657	+	0.991162i	$0.457649\pi$
$331$	−14.4100	+	24.9588i	−0.792043	+	1.37186i	−0.924700	+	0.380697i	$0.875684\pi$
$332$	0.734383	−	1.27199i	0.0403045	−	0.0698095i
$333$	−8.69090	−	1.38634i	−0.476258	−	0.0759710i
$334$	−26.4626	−	15.2782i	−1.44797	−	0.835984i
$335$	−18.3168	−	31.7256i	−1.00075	−	1.73335i
$336$	−13.3182	−	15.1501i	−0.726565	−	0.826504i
$337$	11.4930			0.626066			0.313033	−	0.949742i	$-0.398655\pi$
$337$	11.4930			0.626066			0.313033	+	0.949742i	$0.398655\pi$
$338$	3.94131	+	18.9936i	0.214379	+	1.03312i
$339$	33.1868	+	2.63030i	1.80246	+	0.142858i
$340$	0.970308	+	1.68062i	0.0526223	+	0.0911445i
$341$	6.55214	+	11.3486i	0.354818	+	0.614563i
$342$	15.7653	−	19.4246i	0.852490	−	1.05036i
$343$	−13.6653	−	12.5003i	−0.737859	−	0.674955i
$344$	−4.17413	−	2.40993i	−0.225054	−	0.129935i
$345$	−2.41226	+	3.50571i	−0.129872	+	0.188741i
$346$		−	2.65285i		−	0.142618i
$347$	−19.8548	−	11.4631i	−1.06586	−	0.615374i	−0.138812	−	0.990319i	$-0.544328\pi$
$347$	−19.8548	−	11.4631i	−1.06586	−	0.615374i	−0.927047	+	0.374945i	$0.877662\pi$
$348$	1.14550	+	2.40500i	0.0614051	+	0.128922i
$349$	18.2528	−	10.5383i	0.977052	−	0.564101i	0.0756733	−	0.997133i	$-0.475889\pi$
$349$	18.2528	−	10.5383i	0.977052	−	0.564101i	0.901379	+	0.433031i	$0.142556\pi$
$350$	9.35498	−	2.65597i	0.500045	−	0.141968i
$351$	−7.09899	−	17.3379i	−0.378916	−	0.925431i
$352$	−7.07331			−0.377009
$353$	8.26451	+	14.3146i	0.439876	+	0.761887i	0.997679	−	0.0680859i	$-0.0216892\pi$
$353$	8.26451	+	14.3146i	0.439876	+	0.761887i	−0.557804	+	0.829973i	$0.688356\pi$
$354$	−3.54660	−	7.44618i	−0.188500	−	0.395760i
$355$	8.77246	+	5.06478i	0.465594	+	0.268811i
$356$	2.30485			0.122157
$357$	−4.60185	+	13.6098i	−0.243556	+	0.720305i
$358$	9.34813	−	16.1914i	0.494064	−	0.855744i
$359$			4.77131i			0.251820i	0.992042	+	0.125910i	$0.0401851\pi$
$359$			4.77131i			0.251820i	−0.992042	+	0.125910i	$0.959815\pi$
$360$	16.8395	+	13.6672i	0.887520	+	0.720323i
$361$	6.11590	+	10.5930i	0.321889	+	0.557529i
$362$	−15.5140	−	26.8710i	−0.815396	−	1.41231i
$363$	2.70118	−	34.0811i	0.141775	−	1.78880i
$364$	−0.311602	+	2.13889i	−0.0163324	+	0.112108i
$365$			20.4032i			1.06795i
$366$	4.38087	−	2.08660i	0.228992	−	0.109068i
$367$	−0.192629	+	0.111214i	−0.0100551	+	0.00580533i	−0.505019	−	0.863108i	$-0.668515\pi$
$367$	−0.192629	+	0.111214i	−0.0100551	+	0.00580533i	0.494964	+	0.868913i	$0.335181\pi$
$368$	3.42836	+	1.97937i	0.178716	+	0.103182i
$369$	−6.65090	−	1.06093i	−0.346232	−	0.0552297i
$370$	−10.3565	−	5.97934i	−0.538410	−	0.310851i
$371$	−5.80595	+	23.0290i	−0.301430	+	1.19561i
$372$	0.924700	+	0.0732891i	0.0479435	+	0.00379986i
$373$	−1.16748	+	2.02213i	−0.0604496	+	0.104702i	−0.894666	−	0.446735i	$-0.852587\pi$
$373$	−1.16748	+	2.02213i	−0.0604496	+	0.104702i	0.834217	+	0.551436i	$0.185920\pi$
$374$	12.9682	+	22.4615i	0.670568	+	1.16146i
$375$	10.8369	−	5.16160i	0.559615	−	0.266544i
$376$			2.74577i			0.141603i
$377$	−10.0083	+	22.3335i	−0.515454	+	1.15023i
$378$	−0.807121	−	20.4981i	−0.0415138	−	1.05431i
$379$	−1.58669	−	2.74823i	−0.0815030	−	0.141167i	0.822393	−	0.568920i	$-0.192639\pi$
$379$	−1.58669	−	2.74823i	−0.0815030	−	0.141167i	−0.903896	+	0.427753i	$0.859305\pi$
$380$	2.99585	−	1.72966i	0.153684	−	0.0887295i
$381$	−15.9609	−	10.9826i	−0.817702	−	0.562656i
$382$	29.2731			1.49774
$383$	−11.5345	+	19.9784i	−0.589386	+	1.02085i	0.404927	+	0.914349i	$0.367297\pi$
$383$	−11.5345	+	19.9784i	−0.589386	+	1.02085i	−0.994313	+	0.106498i	$0.966036\pi$
$384$	12.6141	−	18.3319i	0.643710	−	0.935498i
$385$	38.5497	−	10.9446i	1.96467	−	0.557790i
$386$	−9.02658	−	5.21150i	−0.459441	−	0.265258i
$387$	−1.95256	−	5.10342i	−0.0992541	−	0.259422i
$388$	1.74057	−	1.00492i	0.0883642	−	0.0510171i
$389$			36.7393i			1.86276i	0.364051	+	0.931379i	$0.381393\pi$
$389$			36.7393i			1.86276i	−0.364051	+	0.931379i	$0.618607\pi$
$390$	−0.590803	−	25.4506i	−0.0299165	−	1.28874i
$391$		−	2.81949i		−	0.142588i
$392$	8.78201	−	16.3097i	0.443558	−	0.823762i
$393$	−20.7301	+	9.87372i	−1.04570	+	0.498063i
$394$	−16.1391	+	27.9537i	−0.813074	+	1.40829i
$395$	−34.4129			−1.73150
$396$	−2.92620	−	2.37494i	−0.147047	−	0.119345i
$397$	9.72327	+	5.61373i	0.487997	+	0.281745i	0.723743	−	0.690070i	$-0.242420\pi$
$397$	9.72327	+	5.61373i	0.487997	+	0.281745i	−0.235746	+	0.971815i	$0.575753\pi$
$398$	−21.6882			−1.08713
$399$	24.2606	+	8.20319i	1.21455	+	0.410673i
$400$	5.42139	+	9.39013i	0.271070	+	0.469506i
$401$	−12.8082	+	7.39483i	−0.639612	+	0.369280i	−0.784465	−	0.620173i	$-0.787062\pi$
$401$	−12.8082	+	7.39483i	−0.639612	+	0.369280i	0.144853	+	0.989453i	$0.453729\pi$
$402$	−34.5490	−	2.73826i	−1.72315	−	0.136572i
$403$	4.99245	+	6.90658i	0.248691	+	0.344041i
$404$	1.94436			0.0967356
$405$	5.05881	+	24.0610i	0.251375	+	1.19560i
$406$	−18.6655	+	19.2276i	−0.926355	+	0.954249i
$407$	−14.0855	−	8.13225i	−0.698191	−	0.403101i
$408$	−14.3245	−	1.13532i	−0.709168	−	0.0562067i
$409$	−10.3595	−	5.98106i	−0.512244	−	0.295744i	0.221512	−	0.975158i	$-0.428901\pi$
$409$	−10.3595	−	5.98106i	−0.512244	−	0.295744i	−0.733756	+	0.679413i	$0.762234\pi$
$410$	−7.92555	−	4.57582i	−0.391415	−	0.225984i
$411$	−29.4762	−	2.33620i	−1.45395	−	0.115236i
$412$	0.507075	+	0.292760i	0.0249818	+	0.0144232i
$413$	5.88095	−	6.05803i	0.289382	−	0.298096i
$414$	1.43861	+	3.76010i	0.0707036	+	0.184799i
$415$	−17.7088			−0.869291
$416$	−4.57591	+	0.469761i	−0.224352	+	0.0230319i
$417$	2.41310	+	0.191255i	0.118170	+	0.00936581i
$418$	40.0396	−	23.1169i	1.95840	−	1.13068i
$419$	−5.08405	−	8.80583i	−0.248372	−	0.430193i	0.714702	−	0.699429i	$-0.246562\pi$
$419$	−5.08405	−	8.80583i	−0.248372	−	0.430193i	−0.963074	+	0.269236i	$0.913229\pi$
$420$	0.908607	−	2.68716i	0.0443355	−	0.131120i
$421$	1.53126			0.0746289			0.0373145	−	0.999304i	$-0.488120\pi$
$421$	1.53126			0.0746289			0.0373145	+	0.999304i	$0.488120\pi$
$422$	18.0562	+	10.4248i	0.878962	+	0.507469i
$423$	−1.96164	+	2.41696i	−0.0953782	+	0.117517i
$424$	−23.7540			−1.15360
$425$	3.86123	−	6.68785i	0.187297	−	0.324408i
$426$	8.65186	−	4.12086i	0.419184	−	0.199656i
$427$	3.56417	+	3.45999i	0.172482	+	0.167441i
$428$			1.62518i			0.0785563i
$429$	−0.803527	−	34.6144i	−0.0387947	−	1.67120i
$430$		−	7.42486i		−	0.358059i
$431$	26.7372	−	15.4367i	1.28788	−	0.743560i	0.309607	−	0.950865i	$-0.399802\pi$
$431$	26.7372	−	15.4367i	1.28788	−	0.743560i	0.978276	+	0.207305i	$0.0664691\pi$
$432$	21.9414	−	6.45983i	1.05566	−	0.310799i
$433$	7.30929	+	4.22002i	0.351262	+	0.202801i	0.665241	−	0.746629i	$-0.268329\pi$
$433$	7.30929	+	4.22002i	0.351262	+	0.202801i	−0.313979	+	0.949430i	$0.601662\pi$
$434$	2.54852	+	8.97651i	0.122333	+	0.430886i
$435$	18.2065	−	26.4593i	0.872933	−	1.26862i
$436$	−0.564796	+	0.978255i	−0.0270488	+	0.0468499i
$437$	−5.02599			−0.240426
$438$	15.9017	+	10.9419i	0.759812	+	0.522822i
$439$	−15.2471	+	8.80294i	−0.727706	+	0.420142i	−0.817583	−	0.575811i	$-0.804686\pi$
$439$	−15.2471	+	8.80294i	−0.727706	+	0.420142i	0.0898761	+	0.995953i	$0.471353\pi$
$440$	20.0403	+	34.7109i	0.955386	+	1.65478i
$441$	19.3823	−	8.08248i	0.922967	−	0.384880i
$442$	9.88117	+	13.6697i	0.469999	+	0.650200i
$443$			14.0924i			0.669551i	0.942298	+	0.334776i	$0.108661\pi$
$443$			14.0924i			0.669551i	−0.942298	+	0.334776i	$0.891339\pi$
$444$	−1.03942	+	0.495073i	−0.0493286	+	0.0234951i
$445$	−13.8947	−	24.0664i	−0.658673	−	1.14085i
$446$	14.0256	−	24.2930i	0.664131	−	1.15031i
$447$	30.6230	+	2.42710i	1.44842	+	0.114798i
$448$	17.7016	+	4.46284i	0.836323	+	0.210849i
$449$	−17.2357	−	9.95103i	−0.813402	−	0.469618i	0.0347338	−	0.999397i	$-0.488942\pi$
$449$	−17.2357	−	9.95103i	−0.813402	−	0.469618i	−0.848136	+	0.529779i	$0.822275\pi$
$450$	−1.73699	+	10.8891i	−0.0818826	+	0.513318i
$451$	−10.7792	−	6.22338i	−0.507573	−	0.293048i
$452$	3.77158	−	2.17752i	0.177400	−	0.102422i
$453$	3.27775	−	1.56118i	0.154002	−	0.0733508i
$454$			8.69031i			0.407856i
$455$	24.2119	−	9.64056i	1.13507	−	0.451957i
$456$	−2.02380	+	25.5346i	−0.0947733	+	1.19577i
$457$	12.3601	+	21.4083i	0.578181	+	1.00144i	0.995688	+	0.0927651i	$0.0295706\pi$
$457$	12.3601	+	21.4083i	0.578181	+	1.00144i	−0.417507	+	0.908674i	$0.637096\pi$
$458$	−12.8692	−	22.2902i	−0.601340	−	1.04155i
$459$	−11.7980	−	11.2331i	−0.550683	−	0.524315i
$460$			0.556692i			0.0259559i
$461$	13.0742	−	22.6451i	0.608925	−	1.05469i	−0.382493	−	0.923958i	$-0.624934\pi$
$461$	13.0742	−	22.6451i	0.608925	−	1.05469i	0.991418	−	0.130730i	$-0.0417322\pi$
$462$	12.1435	−	35.9139i	0.564968	−	1.67087i
$463$	22.7832			1.05883			0.529413	−	0.848364i	$-0.322412\pi$
$463$	22.7832			1.05883			0.529413	+	0.848364i	$0.322412\pi$
$464$	−25.8755	−	14.9392i	−1.20124	−	0.693535i
$465$	−4.80926	−	10.0972i	−0.223024	−	0.468245i
$466$	11.2929	+	19.5599i	0.523133	+	0.906094i
$467$	11.7468			0.543578			0.271789	−	0.962357i	$-0.412385\pi$
$467$	11.7468			0.543578			0.271789	+	0.962357i	$0.412385\pi$
$468$	−2.05076	−	1.34207i	−0.0947964	−	0.0620373i
$469$	−9.68972	−	34.1296i	−0.447430	−	1.57596i
$470$	−3.66310	+	2.11489i	−0.168966	+	0.0975527i
$471$	−8.00317	−	16.8029i	−0.368767	−	0.774235i
$472$	7.31327	+	4.22232i	0.336621	+	0.194348i
$473$		−	10.0982i		−	0.464318i
$474$	−18.4550	+	26.8204i	−0.847666	+	1.23190i
$475$	−11.9217	−	6.88298i	−0.547004	−	0.315813i
$476$	0.513301	+	1.80797i	0.0235271	+	0.0828681i
$477$	−20.9094	−	16.9704i	−0.957378	−	0.777021i
$478$	−6.81830	−	11.8096i	−0.311862	−	0.540161i
$479$	3.81589	+	6.60932i	0.174353	+	0.301988i	0.939937	−	0.341348i	$-0.110883\pi$
$479$	3.81589	+	6.60932i	0.174353	+	0.301988i	−0.765584	+	0.643335i	$0.777550\pi$
$480$	6.01792	+	0.476964i	0.274679	+	0.0217703i
$481$	−9.65233	−	4.32550i	−0.440108	−	0.197226i
$482$	−27.9605			−1.27357
$483$	−3.09531	+	2.72104i	−0.140842	+	0.123811i
$484$	−2.23620	−	3.87321i	−0.101645	−	0.176055i
$485$	−20.9860	−	12.1162i	−0.952923	−	0.550170i
$486$	21.4654	+	8.96077i	0.973691	+	0.406469i
$487$	10.7128	−	18.5552i	0.485446	−	0.840816i	−0.514415	−	0.857542i	$-0.671991\pi$
$487$	10.7128	−	18.5552i	0.485446	−	0.840816i	0.999860	+	0.0167253i	$0.00532408\pi$
$488$	−2.48415	+	4.30268i	−0.112452	+	0.194773i
$489$	0.708707	−	8.94186i	0.0320488	−	0.404365i
$490$	28.5227	−	0.846306i	1.28852	−	0.0382322i
$491$	2.74421	−	1.58437i	0.123845	−	0.0715017i	−0.436798	−	0.899560i	$-0.643888\pi$
$491$	2.74421	−	1.58437i	0.123845	−	0.0715017i	0.560643	+	0.828058i	$0.310554\pi$
$492$	−0.795438	+	0.378866i	−0.0358611	+	0.0170806i
$493$			21.2800i			0.958405i
$494$	24.3674	−	17.6140i	1.09634	−	0.792493i
$495$	−7.15773	+	44.8714i	−0.321716	+	2.01682i
$496$	−9.01023	+	5.20206i	−0.404571	+	0.233579i
$497$	7.03894	+	6.83318i	0.315740	+	0.306510i
$498$	−9.49690	+	13.8017i	−0.425566	+	0.618471i
$499$	1.64154			0.0734852			0.0367426	−	0.999325i	$-0.488302\pi$
$499$	1.64154			0.0734852			0.0367426	+	0.999325i	$0.488302\pi$
$500$	0.785127	−	1.35988i	0.0351119	−	0.0608156i
$501$	29.2194	+	20.1057i	1.30543	+	0.898256i
$502$			17.0746i			0.762075i
$503$	−11.4570	+	19.8441i	−0.510843	+	0.884805i	0.489079	+	0.872240i	$0.337333\pi$
$503$	−11.4570	+	19.8441i	−0.510843	+	0.884805i	−0.999921	+	0.0125654i	$0.996000\pi$
$504$	12.5779	+	16.8215i	0.560264	+	0.749288i
$505$	−11.7215	−	20.3022i	−0.521600	−	0.903437i
$506$			7.44018i			0.330756i
$507$	−2.81867	−	22.3395i	−0.125182	−	0.992134i
$508$	−2.53452			−0.112451
$509$	−13.5701	−	23.5041i	−0.601485	−	1.04180i	−0.992596	−	0.121459i	$-0.961243\pi$
$509$	−13.5701	−	23.5041i	−0.601485	−	1.04180i	0.391112	−	0.920343i	$-0.372091\pi$
$510$	−9.51860	−	19.9846i	−0.421491	−	0.884931i
$511$	−4.83059	+	19.1603i	−0.213693	+	0.847601i
$512$			17.6808i			0.781388i
$513$	−20.0239	+	21.0309i	−0.884078	+	0.928539i
$514$	−17.1739	−	9.91535i	−0.757508	−	0.437347i
$515$		−	7.05956i		−	0.311082i
$516$	−0.588873	−	0.405200i	−0.0259237	−	0.0178380i
$517$	−4.98203	+	2.87638i	−0.219109	+	0.126503i
$518$	−8.30997	−	8.06706i	−0.365119	−	0.354446i
$519$	−0.243295	+	3.06969i	−0.0106795	+	0.134744i
$520$	15.2699	+	21.1244i	0.669628	+	0.926367i
$521$	29.5173			1.29318			0.646588	−	0.762839i	$-0.276195\pi$
$521$	29.5173			1.29318			0.646588	+	0.762839i	$0.276195\pi$
$522$	−10.8578	−	28.3792i	−0.475234	−	1.24213i
$523$	22.2430	−	12.8420i	0.972619	−	0.561542i	0.0725853	−	0.997362i	$-0.476875\pi$
$523$	22.2430	−	12.8420i	0.972619	−	0.561542i	0.900034	+	0.435820i	$0.143542\pi$
$524$	−1.50188	+	2.60134i	−0.0656101	+	0.113640i
$525$	−11.0685	+	2.21535i	−0.483069	+	0.0966857i
$526$	−8.26627	+	14.3176i	−0.360426	+	0.624277i
$527$	6.41728	+	3.70502i	0.279541	+	0.161393i
$528$	42.1381	+	3.33975i	1.83382	+	0.145344i
$529$	−11.0956	+	19.2181i	−0.482417	+	0.835571i
$530$	−18.2962	−	31.6899i	−0.794736	−	1.37652i
$531$	3.42098	+	8.94144i	0.148458	+	0.388026i
$532$	3.22286	−	0.915002i	0.139729	−	0.0396704i
$533$	−7.38666	−	3.31018i	−0.319952	−	0.143380i
$534$	−26.2081	−	2.07718i	−1.13414	−	0.0898885i
$535$	16.9695	−	9.79736i	0.733656	−	0.423577i
$536$	30.7310	−	17.7425i	1.32737	−	0.766360i
$537$	−12.3019	+	17.8782i	−0.530867	+	0.771503i
$538$			38.4561i			1.65796i
$539$	38.7925	−	1.15103i	1.67091	−	0.0495782i
$540$	2.32944	+	2.21790i	0.100243	+	0.0954433i
$541$	8.86441			0.381111			0.190555	−	0.981676i	$-0.438971\pi$
$541$	8.86441			0.381111			0.190555	+	0.981676i	$0.438971\pi$
$542$	19.8779	−	34.4295i	0.853827	−	1.47887i
$543$	15.4873	+	32.5160i	0.664623	+	1.39539i
$544$	−3.46386	+	1.99986i	−0.148512	+	0.0857433i
$545$	13.6194			0.583391
$546$	5.47079	−	24.0401i	0.234128	−	1.02882i
$547$	−9.77953			−0.418143			−0.209071	−	0.977900i	$-0.567044\pi$
$547$	−9.77953			−0.418143			−0.209071	+	0.977900i	$0.567044\pi$
$548$	−3.34988	+	1.93405i	−0.143100	+	0.0826187i
$549$	−5.26060	+	2.01269i	−0.224517	+	0.0858996i
$550$	−10.1892	+	17.6481i	−0.434467	+	0.752520i
$551$	37.9335			1.61602
$552$	−3.39581	−	2.33663i	−0.144535	−	0.0994537i
$553$	−32.3165	−	8.14748i	−1.37424	−	0.346466i
$554$			16.8581i			0.716232i
$555$	11.4354	+	7.86866i	0.485407	+	0.334006i
$556$	0.274241	−	0.158333i	0.0116304	−	0.00671482i
$557$	−2.45545	+	1.41766i	−0.104041	+	0.0600680i	−0.551118	−	0.834428i	$-0.685798\pi$
$557$	−2.45545	+	1.41766i	−0.104041	+	0.0600680i	0.447077	+	0.894496i	$0.352465\pi$
$558$	−10.4486	−	1.66672i	−0.442323	−	0.0705578i
$559$	−0.670657	−	6.53281i	−0.0283658	−	0.276308i
$560$	8.68946	+	30.6064i	0.367197	+	1.29336i
$561$	−12.9459	−	27.1802i	−0.546575	−	1.14755i
$562$	10.0198	+	17.3548i	0.422659	+	0.732066i
$563$	−15.0972	+	26.1492i	−0.636273	+	1.10206i	0.349971	+	0.936761i	$0.386191\pi$
$563$	−15.0972	+	26.1492i	−0.636273	+	1.10206i	−0.986244	+	0.165296i	$0.947142\pi$
$564$	−0.0321738	+	0.405941i	−0.00135476	+	0.0170932i
$565$	−45.4736	−	26.2542i	−1.91309	−	1.10452i
$566$	−1.48885	+	2.57876i	−0.0625810	+	0.108393i
$567$	−0.945955	+	23.7930i	−0.0397264	+	0.999211i
$568$	−4.90599	+	8.49743i	−0.205851	+	0.356544i
$569$	−6.05199	+	3.49412i	−0.253712	+	0.146481i	−0.621463	−	0.783444i	$-0.713461\pi$
$569$	−6.05199	+	3.49412i	−0.253712	+	0.146481i	0.367750	+	0.929924i	$0.380128\pi$
$570$	−35.6242	+	16.9677i	−1.49213	+	0.710700i
$571$	−0.691674			−0.0289457			−0.0144728	−	0.999895i	$-0.504607\pi$
$571$	−0.691674			−0.0289457			−0.0144728	+	0.999895i	$0.504607\pi$
$572$	−2.65344	−	3.67079i	−0.110946	−	0.153483i
$573$	−33.8727	−	2.68465i	−1.41505	−	0.112153i
$574$	−6.35939	−	6.17350i	−0.265436	−	0.257677i
$575$	1.91850	−	1.10765i	0.0800070	−	0.0461920i
$576$	−13.0446	+	16.0724i	−0.543524	+	0.669683i
$577$			28.5220i			1.18739i	0.804691	+	0.593693i	$0.202331\pi$
$577$			28.5220i			1.18739i	−0.804691	+	0.593693i	$0.797669\pi$
$578$	−9.26720	−	5.35042i	−0.385465	−	0.222548i
$579$	9.96695	+	6.85820i	0.414213	+	0.285017i
$580$		−	4.20161i		−	0.174462i
$581$	−16.6300	−	4.19267i	−0.689929	−	0.173941i
$582$	−20.6974	+	9.85815i	−0.857937	+	0.408634i
$583$	−24.8839	−	43.1002i	−1.03059	−	1.78503i
$584$	−19.7635			−0.817820
$585$	−1.65046	+	29.5038i	−0.0682382	+	1.21983i
$586$			40.2596i			1.66311i
$587$	7.10897	+	12.3131i	0.293418	+	0.508216i	0.974616	−	0.223884i	$-0.0718738\pi$
$587$	7.10897	+	12.3131i	0.293418	+	0.508216i	−0.681197	+	0.732100i	$0.738540\pi$
$588$	1.48946	−	2.30835i	0.0614243	−	0.0951947i
$589$	6.60451	−	11.4394i	0.272134	−	0.471350i
$590$			13.0087i			0.535560i
$591$	21.2386	−	30.8658i	0.873640	−	1.26965i
$592$	6.45658	−	11.1831i	0.265364	−	0.459624i
$593$	11.0169			0.452412			0.226206	−	0.974080i	$-0.427368\pi$
$593$	11.0169			0.452412			0.226206	+	0.974080i	$0.427368\pi$
$594$	31.1330	+	29.6423i	1.27740	+	1.21624i
$595$	15.7837	−	16.2589i	0.647068	−	0.666552i
$596$	3.48021	−	2.00930i	0.142555	−	0.0823042i
$597$	25.0960	+	1.98904i	1.02711	+	0.0814059i
$598$	0.494126	+	4.81324i	0.0202063	+	0.196828i
$599$		−	9.21125i		−	0.376362i	−0.982134	−	0.188181i	$-0.939741\pi$
$599$		−	9.21125i		−	0.376362i	0.982134	−	0.188181i	$-0.0602591\pi$
$600$	−4.85490	−	10.1930i	−0.198200	−	0.416127i
$601$	−14.6701	+	8.46981i	−0.598407	+	0.345491i	−0.768415	−	0.639952i	$-0.778954\pi$
$601$	−14.6701	+	8.46981i	−0.598407	+	0.345491i	0.170007	+	0.985443i	$0.445621\pi$
$602$	1.75788	−	6.97256i	0.0716460	−	0.284180i
$603$	39.7265	+	6.33703i	1.61779	+	0.258064i
$604$	0.237471	−	0.411311i	0.00966254	−	0.0167360i
$605$	−26.9617	+	46.6990i	−1.09615	+	1.89858i
$606$	−22.1090	−	1.75230i	−0.898118	−	0.0711823i
$607$	−19.8418	−	11.4557i	−0.805354	−	0.464971i	0.0399857	−	0.999200i	$-0.487269\pi$
$607$	−19.8418	−	11.4557i	−0.805354	−	0.464971i	−0.845340	+	0.534229i	$0.820602\pi$
$608$	3.56492	+	6.17463i	0.144577	+	0.250414i
$609$	23.3618	−	20.5369i	0.946667	−	0.832199i
$610$	−7.65353			−0.309882
$611$	−3.03197	+	2.19167i	−0.122660	+	0.0886656i
$612$	−2.10446	−	0.335696i	−0.0850677	−	0.0135697i
$613$	−20.3388	−	35.2278i	−0.821477	−	1.42284i	−0.904583	−	0.426299i	$-0.859817\pi$
$613$	−20.3388	−	35.2278i	−0.821477	−	1.42284i	0.0831059	−	0.996541i	$-0.473516\pi$
$614$	17.1206	+	29.6537i	0.690930	+	1.19673i
$615$	8.75123	+	6.02167i	0.352883	+	0.242817i
$616$	10.6015	+	37.3411i	0.427147	+	1.50451i
$617$	−18.7586	−	10.8303i	−0.755195	−	0.436012i	0.0723732	−	0.997378i	$-0.476943\pi$
$617$	−18.7586	−	10.8303i	−0.755195	−	0.436012i	−0.827568	+	0.561366i	$0.810276\pi$
$618$	−5.50203	−	3.78591i	−0.221324	−	0.152292i
$619$			13.0520i			0.524605i	0.964986	+	0.262302i	$0.0844817\pi$
$619$			13.0520i			0.524605i	−0.964986	+	0.262302i	$0.915518\pi$
$620$	−1.26705	−	0.731533i	−0.0508860	−	0.0293791i
$621$	−1.31981	−	4.48285i	−0.0529621	−	0.179891i
$622$	18.1181	−	10.4605i	0.726471	−	0.419428i
$623$	−7.35042	−	25.8900i	−0.294488	−	1.03726i
$624$	27.4820	−	0.637958i	1.10016	−	0.0255388i
$625$	−31.2486			−1.24995
$626$	−0.733193	−	1.26993i	−0.0293043	−	0.0507565i
$627$	−48.4510	+	23.0771i	−1.93495	+	0.921611i
$628$	−2.10852	−	1.21736i	−0.0841392	−	0.0485778i
$629$	−9.19703			−0.366709
$630$	−12.7534	+	29.7365i	−0.508106	+	1.18473i
$631$	−3.42275	+	5.92838i	−0.136258	+	0.236005i	−0.926077	−	0.377334i	$-0.876841\pi$
$631$	−3.42275	+	5.92838i	−0.136258	+	0.236005i	0.789820	+	0.613339i	$0.210174\pi$
$632$		−	33.3340i		−	1.32596i
$633$	−19.9373	−	13.7187i	−0.792436	−	0.545270i
$634$	6.80989	+	11.7951i	0.270455	+	0.468442i
$635$	15.2792	+	26.4644i	0.606338	+	1.05021i
$636$	−3.51185	−	0.278339i	−0.139254	−	0.0110369i
$637$	25.0194	−	3.32096i	0.991305	−	0.131581i
$638$		−	56.1546i		−	2.22318i
$639$	−10.3892	+	3.97490i	−0.410992	+	0.157245i
$640$	−30.3958	+	17.5490i	−1.20150	+	0.693686i
$641$	32.2373	+	18.6122i	1.27330	+	0.735138i	0.975607	−	0.219525i	$-0.0704506\pi$
$641$	32.2373	+	18.6122i	1.27330	+	0.735138i	0.297690	+	0.954663i	$0.403784\pi$
$642$	1.46465	−	18.4797i	0.0578052	−	0.729336i
$643$	−25.6103	−	14.7861i	−1.00997	−	0.583107i	−0.0987882	−	0.995108i	$-0.531497\pi$
$643$	−25.6103	−	14.7861i	−1.00997	−	0.583107i	−0.911183	+	0.412001i	$0.864830\pi$
$644$	−0.131800	+	0.522779i	−0.00519366	+	0.0206004i
$645$	−0.680939	+	8.59151i	−0.0268120	+	0.338290i
$646$	13.0718	−	22.6410i	0.514304	−	0.890800i
$647$	12.1062	+	20.9686i	0.475944	+	0.824360i	0.999620	−	0.0275577i	$-0.00877300\pi$
$647$	12.1062	+	20.9686i	0.475944	+	0.824360i	−0.523676	+	0.851918i	$0.675440\pi$
$648$	−23.3067	+	4.90022i	−0.915572	+	0.192499i
$649$			17.6926i			0.694496i
$650$	−5.41956	+	12.0937i	−0.212573	+	0.474355i
$651$	−2.12572	−	10.6207i	−0.0833136	−	0.416258i
$652$	−0.586712	−	1.01621i	−0.0229774	−	0.0397980i
$653$	13.1479	−	7.59096i	0.514518	−	0.297057i	−0.220171	−	0.975461i	$-0.570661\pi$
$653$	13.1479	−	7.59096i	0.514518	−	0.297057i	0.734689	+	0.678404i	$0.237328\pi$
$654$	7.30383	−	10.6146i	0.285602	−	0.415063i
$655$	36.2162			1.41508
$656$	4.94104	−	8.55813i	0.192915	−	0.334139i
$657$	−17.3968	−	14.1195i	−0.678714	−	0.550853i
$658$	−3.94067	+	1.11879i	−0.153623	+	0.0436151i
$659$	15.5162	+	8.95828i	0.604425	+	0.348965i	0.770780	−	0.637101i	$-0.219867\pi$
$659$	15.5162	+	8.95828i	0.604425	+	0.348965i	−0.166355	+	0.986066i	$0.553200\pi$
$660$	2.55608	+	5.36656i	0.0994953	+	0.208893i
$661$	8.15101	−	4.70599i	0.317037	−	0.183042i	−0.333034	−	0.942915i	$-0.608072\pi$
$661$	8.15101	−	4.70599i	0.317037	−	0.183042i	0.650071	+	0.759873i	$0.274739\pi$
$662$		−	43.0043i		−	1.67141i
$663$	−10.1801	−	16.7238i	−0.395363	−	0.649497i
$664$		−	17.1536i		−	0.665689i
$665$	−28.9830	−	28.1358i	−1.12391	−	1.09106i
$666$	12.2652	−	4.69265i	0.475268	−	0.181837i
$667$	−3.05223	+	5.28662i	−0.118183	+	0.204699i
$668$	4.63991			0.179523
$669$	−18.4573	+	26.8239i	−0.713602	+	1.03707i
$670$	47.3401	+	27.3318i	1.82891	+	1.05592i
$671$	−10.4092			−0.401844
$672$	5.53840	+	1.87269i	0.213648	+	0.0722406i
$673$	−4.30087	−	7.44933i	−0.165786	−	0.287151i	0.771148	−	0.636656i	$-0.219683\pi$
$673$	−4.30087	−	7.44933i	−0.165786	−	0.287151i	−0.936934	+	0.349506i	$0.886350\pi$
$674$	−14.8520	+	8.57481i	−0.572078	+	0.330289i
$675$	3.00857	−	12.4408i	0.115800	−	0.478846i
$676$	−1.96037	−	2.19850i	−0.0753988	−	0.0845577i
$677$	−0.179419			−0.00689562			−0.00344781	−	0.999994i	$-0.501097\pi$
$677$	−0.179419			−0.00689562			−0.00344781	+	0.999994i	$0.501097\pi$
$678$	−44.8485	+	21.3612i	−1.72240	+	0.820373i
$679$	−16.8389	−	16.3467i	−0.646219	−	0.627329i
$680$	19.6279	+	11.3321i	0.752694	+	0.434568i
$681$	0.796994	−	10.0558i	0.0305409	−	0.385339i
$682$	−16.9342	−	9.77694i	−0.648442	−	0.374378i
$683$	−7.02462	−	4.05566i	−0.268789	−	0.155186i	0.359548	−	0.933127i	$-0.382931\pi$
$683$	−7.02462	−	4.05566i	−0.268789	−	0.155186i	−0.628337	+	0.777941i	$0.716264\pi$
$684$	−0.598407	+	3.75138i	−0.0228807	+	0.143438i
$685$	40.3892	+	23.3187i	1.54319	+	0.890963i
$686$	26.9855	+	5.95818i	1.03031	+	0.227484i
$687$	12.8471	+	26.9728i	0.490148	+	1.02908i
$688$	8.01748			0.305664
$689$	−18.9604	−	26.2300i	−0.722335	−	0.999282i
$690$	0.501702	−	6.33005i	0.0190995	−	0.240981i
$691$	39.8678	−	23.0177i	1.51664	−	0.875633i	0.516832	−	0.856087i	$-0.327111\pi$
$691$	39.8678	−	23.0177i	1.51664	−	0.875633i	0.999809	−	0.0195462i	$-0.00622215\pi$
$692$	0.201415	+	0.348860i	0.00765664	+	0.0132617i
$693$	−17.3453	+	40.4433i	−0.658894	+	1.53632i
$694$	34.2100			1.29859
$695$	−3.30650	−	1.90901i	−0.125423	−	0.0724128i
$696$	25.6297	+	17.6357i	0.971493	+	0.668479i
$697$	−7.03823			−0.266592
$698$	−15.7250	+	27.2364i	−0.595198	+	1.03091i
$699$	−11.2735	−	23.6690i	−0.426402	−	0.895242i
$700$	−1.02857	+	1.05954i	−0.0388761	+	0.0400467i
$701$		−	13.7239i		−	0.518344i	−0.965831	−	0.259172i	$-0.916550\pi$
$701$		−	13.7239i		−	0.518344i	0.965831	−	0.259172i	$-0.0834497\pi$
$702$	22.1094	+	17.1087i	0.834464	+	0.645726i
$703$			16.3945i			0.618330i
$704$	−33.1297	+	19.1274i	−1.24862	+	0.720892i
$705$	4.43263	−	2.11125i	0.166943	−	0.0795144i
$706$	−21.3598	−	12.3321i	−0.803887	−	0.464124i
$707$	−6.20077	−	21.8406i	−0.233204	−	0.821401i
$708$	1.03173	+	0.709930i	0.0387750	+	0.0266808i
$709$	19.8771	−	34.4282i	0.746502	−	1.29298i	−0.202988	−	0.979181i	$-0.565065\pi$
$709$	19.8771	−	34.4282i	0.746502	−	1.29298i	0.949490	−	0.313798i	$-0.101601\pi$
$710$	−15.1151			−0.567258
$711$	23.8145	−	29.3422i	0.893114	−	1.10042i
$712$	23.3118	−	13.4591i	0.873648	−	0.504401i
$713$	1.06283	+	1.84088i	0.0398034	+	0.0689416i
$714$	−4.20728	−	21.0207i	−0.157453	−	0.786681i
$715$	−22.3327	+	49.8354i	−0.835196	+	1.86374i
$716$			2.83898i			0.106098i
$717$	6.80658	+	14.2906i	0.254196	+	0.533692i
$718$	−3.55982	−	6.16578i	−0.132851	−	0.230105i
$719$	−1.45563	+	2.52122i	−0.0542858	+	0.0940258i	−0.891891	−	0.452250i	$-0.850622\pi$
$719$	−1.45563	+	2.52122i	−0.0542858	+	0.0940258i	0.837605	+	0.546276i	$0.183955\pi$
$720$	−35.6256	−	5.68286i	−1.32769	−	0.211788i
$721$	1.67140	−	6.62951i	0.0622461	−	0.246896i
$722$	−15.8067	−	9.12598i	−0.588263	−	0.339634i
$723$	32.3539	+	2.56428i	1.20325	+	0.0953666i
$724$	4.08030	+	2.35576i	0.151643	+	0.0875512i
$725$	−14.4798	+	8.35993i	−0.537767	+	0.310480i
$726$	21.9369	+	46.0570i	0.814153	+	1.70934i
$727$			16.3030i			0.604645i	0.953206	+	0.302322i	$0.0977619\pi$
$727$			16.3030i			0.604645i	−0.953206	+	0.302322i	$0.902238\pi$
$728$	9.33832	+	23.4528i	0.346101	+	0.869219i
$729$	−24.0164	−	12.3374i	−0.889498	−	0.456939i
$730$	−15.2226	−	26.3662i	−0.563412	−	0.975858i
$731$	−2.85511	−	4.94520i	−0.105600	−	0.182905i
$732$	−0.417679	+	0.607009i	−0.0154379	+	0.0224357i
$733$			1.06305i			0.0392646i	0.999807	+	0.0196323i	$0.00624956\pi$
$733$			1.06305i			0.0392646i	−0.999807	+	0.0196323i	$0.993750\pi$
$734$	0.165951	−	0.287435i	0.00612536	−	0.0106094i
$735$	−33.0820	−	1.63655i	−1.22025	−	0.0603651i
$736$	−1.14737			−0.0422928
$737$	64.3853	+	37.1729i	2.37166	+	1.36928i
$738$	9.38624	−	3.59115i	0.345512	−	0.132192i
$739$	14.5653	+	25.2279i	0.535794	+	0.928022i	0.999124	+	0.0418368i	$0.0133209\pi$
$739$	14.5653	+	25.2279i	0.535794	+	0.928022i	−0.463331	+	0.886186i	$0.653346\pi$
$740$	1.81590			0.0667537
$741$	−29.8115	+	18.1470i	−1.09515	+	0.666645i
$742$	−9.67883	−	34.0912i	−0.355321	−	1.25153i
$743$	−4.35485	+	2.51427i	−0.159764	+	0.0922397i	−0.577750	−	0.816214i	$-0.696069\pi$
$743$	−4.35485	+	2.51427i	−0.159764	+	0.0922397i	0.417987	+	0.908453i	$0.362736\pi$
$744$	9.78061	−	4.65848i	0.358574	−	0.170788i
$745$	−41.9606	−	24.2260i	−1.53732	−	0.887572i
$746$		−	3.48415i		−	0.127564i
$747$	12.2549	−	15.0994i	0.448383	−	0.552459i
$748$	−3.41073	−	1.96919i	−0.124709	−	0.0720005i
$749$	18.2554	−	5.18288i	0.667037	−	0.189378i
$750$	−10.1531	+	14.7554i	−0.370739	+	0.538791i
$751$	21.4022	+	37.0697i	0.780977	+	1.35269i	0.931373	+	0.364066i	$0.118612\pi$
$751$	21.4022	+	37.0697i	0.780977	+	1.35269i	−0.150396	+	0.988626i	$0.548055\pi$
$752$	−2.28369	−	3.95547i	−0.0832777	−	0.144241i
$753$	1.56592	−	19.7575i	0.0570653	−	0.720002i
$754$	−3.72940	−	36.3278i	−0.135817	−	1.32298i
$755$	−5.72633			−0.208402
$756$	1.66244	+	2.63430i	0.0604622	+	0.0958087i
$757$	−12.1617	−	21.0646i	−0.442024	−	0.765607i	0.555816	−	0.831305i	$-0.312406\pi$
$757$	−12.1617	−	21.0646i	−0.442024	−	0.765607i	−0.997840	+	0.0656980i	$0.979073\pi$
$758$	4.10084	+	2.36762i	0.148949	+	0.0859959i
$759$	0.682345	−	8.60924i	0.0247675	−	0.312496i
$760$	20.2005	−	34.9883i	0.732750	−	1.26916i
$761$	20.5036	−	35.5132i	0.743253	−	1.28735i	−0.207753	−	0.978181i	$-0.566615\pi$
$761$	20.5036	−	35.5132i	0.743253	−	1.28735i	0.951006	−	0.309171i	$-0.100052\pi$
$762$	28.8196	+	2.28416i	1.04402	+	0.0827465i
$763$	12.7897	+	3.22448i	0.463019	+	0.116734i
$764$	−3.84952	+	2.22252i	−0.139271	+	0.0804081i
$765$	9.18144	+	23.9976i	0.331956	+	0.867637i
$766$		−	34.4230i		−	1.24375i
$767$	1.17502	+	11.4458i	0.0424276	+	0.413284i
$768$	−0.734990	+	9.27348i	−0.0265217	+	0.334628i
$769$	19.8423	−	11.4560i	0.715533	−	0.413113i	−0.0975737	−	0.995228i	$-0.531108\pi$
$769$	19.8423	−	11.4560i	0.715533	−	0.413113i	0.813106	+	0.582115i	$0.197775\pi$
$770$	−41.6506	+	42.9047i	−1.50098	+	1.54618i
$771$	18.9630	+	13.0484i	0.682937	+	0.469925i
$772$	1.58271			0.0569629
$773$	−19.7617	+	34.2283i	−0.710780	+	1.23111i	0.253784	+	0.967261i	$0.418325\pi$
$773$	−19.7617	+	34.2283i	−0.710780	+	1.23111i	−0.964565	+	0.263847i	$0.915009\pi$
$774$	6.33081	+	5.13818i	0.227556	+	0.184688i
$775$			5.82211i			0.209136i
$776$	11.7364	−	20.3280i	0.421312	−	0.729733i
$777$	8.87587	+	10.0967i	0.318420	+	0.362218i
$778$	−27.4107	−	47.4768i	−0.982722	−	1.70213i
$779$			12.5463i			0.449516i
$780$	2.01000	+	3.30200i	0.0719697	+	0.118231i
$781$	−20.5574			−0.735601
$782$	2.10359	+	3.64352i	0.0752241	+	0.130292i
$783$	9.96122	+	33.8342i	0.355985	+	1.20914i
$784$	0.913854	+	30.7992i	0.0326376	+	1.09997i
$785$			29.3551i			1.04773i
$786$	19.4221	−	28.2259i	0.692762	−	1.00678i
$787$	−1.33472	−	0.770603i	−0.0475778	−	0.0274690i	0.476022	−	0.879433i	$-0.342078\pi$
$787$	−1.33472	−	0.770603i	−0.0475778	−	0.0274690i	−0.523600	+	0.851964i	$0.675411\pi$
$788$		−	4.90136i		−	0.174604i
$789$	10.8782	−	15.8092i	0.387274	−	0.562822i
$790$	44.4704	−	25.6750i	1.58219	−	0.913476i
$791$	−36.4876	−	35.4210i	−1.29735	−	1.25943i
$792$	−43.4647	−	6.93333i	−1.54445	−	0.246365i
$793$	−6.73400	+	0.691311i	−0.239131	+	0.0245492i
$794$	−16.7533			−0.594553
$795$	18.2647	+	38.3473i	0.647783	+	1.36004i
$796$	2.85208	−	1.64665i	0.101089	−	0.0583640i
$797$	24.6129	−	42.6309i	0.871835	−	1.51006i	0.0117386	−	0.999931i	$-0.496263\pi$
$797$	24.6129	−	42.6309i	0.871835	−	1.51006i	0.860096	−	0.510132i	$-0.170403\pi$
$798$	−37.4713	+	7.49984i	−1.32647	+	0.265491i
$799$	−1.62649	+	2.81717i	−0.0575412	+	0.0996643i
$800$	−2.72158	−	1.57130i	−0.0962223	−	0.0555539i
$801$	30.1357	+	4.80713i	1.06479	+	0.169852i
$802$	11.0344	−	19.1121i	0.389637	−	0.674872i
$803$	−20.7036	−	35.8596i	−0.730613	−	1.26546i
$804$	4.75123	−	2.26300i	0.167563	−	0.0798099i
$805$	6.25320	−	1.77535i	0.220396	−	0.0625727i
$806$	−11.6044	−	5.20030i	−0.408749	−	0.183173i
$807$	3.52683	−	44.4986i	0.124150	−	1.56642i
$808$	19.6657	−	11.3540i	0.691838	−	0.399433i
$809$	−27.9253	+	16.1227i	−0.981801	+	0.566843i	−0.902813	−	0.430033i	$-0.858502\pi$
$809$	−27.9253	+	16.1227i	−0.981801	+	0.566843i	−0.0789874	+	0.996876i	$0.525169\pi$
$810$	−24.4889	−	27.3188i	−0.860452	−	0.959883i
$811$		−	46.2744i		−	1.62492i	−0.583020	−	0.812458i	$-0.698129\pi$
$811$		−	46.2744i		−	1.62492i	0.583020	−	0.812458i	$-0.301871\pi$
$812$	0.994760	−	3.94566i	0.0349092	−	0.138466i
$813$	−26.1588	+	38.0163i	−0.917428	+	1.33329i
$814$	24.2695			0.850644
$815$	−7.07394	+	12.2524i	−0.247789	+	0.429183i
$816$	21.5796	−	10.2783i	0.755438	−	0.359814i
$817$	−8.81524	+	5.08948i	−0.308406	+	0.178058i
$818$	17.8496			0.624095
$819$	−8.53515	+	27.3158i	−0.298242	+	0.954490i
$820$	1.38966			0.0485289
$821$	−13.4915	+	7.78933i	−0.470857	+	0.271849i	−0.716598	−	0.697486i	$-0.754302\pi$
$821$	−13.4915	+	7.78933i	−0.470857	+	0.271849i	0.245741	+	0.969335i	$0.420969\pi$
$822$	39.8340	−	18.9728i	1.38937	−	0.661754i
$823$	−11.0357	+	19.1143i	−0.384679	+	0.666283i	−0.991725	−	0.128384i	$-0.959021\pi$
$823$	−11.0357	+	19.1143i	−0.384679	+	0.666283i	0.607046	+	0.794667i	$0.292354\pi$
$824$	6.83824			0.238221
$825$	13.4087	−	19.4867i	0.466831	−	0.678440i
$826$	−3.07990	+	12.2163i	−0.107163	+	0.425058i
$827$			43.0278i			1.49622i	0.663573	+	0.748112i	$0.269039\pi$
$827$			43.0278i			1.49622i	−0.663573	+	0.748112i	$0.730961\pi$
$828$	−0.474663	−	0.385243i	−0.0164957	−	0.0133881i
$829$	−10.0663	+	5.81180i	−0.349618	+	0.201852i	−0.664517	−	0.747273i	$-0.731363\pi$
$829$	−10.0663	+	5.81180i	−0.349618	+	0.201852i	0.314899	+	0.949125i	$0.398029\pi$
$830$	22.8844	−	13.2123i	0.794328	−	0.458606i
$831$	1.54607	−	19.5070i	0.0536325	−	0.676690i
$832$	−20.1621	+	14.5743i	−0.698995	+	0.505271i
$833$	18.6716	−	11.5316i	0.646932	−	0.399546i
$834$	−3.26104	+	1.55323i	−0.112921	+	0.0537839i
$835$	−27.9715	−	48.4481i	−0.967994	−	1.67661i
$836$	−3.51024	+	6.07992i	−0.121404	+	0.210278i
$837$	11.9375	+	2.88685i	0.412619	+	0.0997842i
$838$	13.1398	+	7.58628i	0.453908	+	0.262064i
$839$	20.5689	−	35.6264i	0.710117	−	1.22996i	−0.254695	−	0.967021i	$-0.581975\pi$
$839$	20.5689	−	35.6264i	0.710117	−	1.22996i	0.964813	−	0.262938i	$-0.0846915\pi$
$840$	−6.50172	−	32.4844i	−0.224331	−	1.12082i
$841$	8.53663	−	14.7859i	0.294367	−	0.509858i
$842$	−1.97878	+	1.14245i	−0.0681934	+	0.0393715i
$843$	−10.0025	−	21.0006i	−0.344506	−	0.723299i
$844$	−3.16595			−0.108976
$845$	−11.1379	+	33.7229i	−0.383154	+	1.16010i
$846$	0.731686	−	4.58690i	0.0251559	−	0.157701i
$847$	−36.3755	+	37.4709i	−1.24988	+	1.28751i
$848$	34.2193	−	19.7565i	1.17509	−	0.678441i
$849$	1.95929	−	2.84741i	0.0672426	−	0.0977230i
$850$			11.5233i			0.395245i
$851$	−2.28483	−	1.31915i	−0.0783229	−	0.0452197i
$852$	−0.824882	+	1.19879i	−0.0282600	+	0.0410699i
$853$		−	23.2038i		−	0.794482i	−0.917714	−	0.397241i	$-0.869968\pi$
$853$		−	23.2038i		−	0.794482i	0.917714	−	0.397241i	$-0.130032\pi$
$854$	−7.18729	−	1.81202i	−0.245944	−	0.0620061i
$855$	42.7779	−	16.3667i	1.46297	−	0.559730i
$856$	9.49020	+	16.4375i	0.324368	+	0.561822i
$857$	17.3181			0.591575			0.295788	−	0.955254i	$-0.404418\pi$
$857$	17.3181			0.591575			0.295788	+	0.955254i	$0.404418\pi$
$858$	26.8637	+	44.1313i	0.917111	+	1.50662i
$859$		−	1.05148i		−	0.0358759i	−0.999839	−	0.0179379i	$-0.994290\pi$
$859$		−	1.05148i		−	0.0358759i	0.999839	−	0.0179379i	$-0.00571013\pi$
$860$	0.563724	+	0.976398i	0.0192228	+	0.0332949i
$861$	6.79245	+	7.72675i	0.231486	+	0.263327i
$862$	−23.0343	+	39.8965i	−0.784550	+	1.35888i
$863$		−	18.0952i		−	0.615968i	−0.951392	−	0.307984i	$-0.900346\pi$
$863$		−	18.0952i		−	0.615968i	0.951392	−	0.307984i	$-0.0996543\pi$
$864$	−4.57123	+	4.80112i	−0.155516	+	0.163337i
$865$	2.42844	−	4.20618i	0.0825694	−	0.143014i
$866$	−12.5940			−0.427962
$867$	10.2326	+	7.04102i	0.347519	+	0.239126i
$868$	−1.01667	−	0.986953i	−0.0345081	−	0.0334994i
$869$	60.4824	−	34.9195i	2.05172	−	1.18456i
$870$	−3.78658	+	47.7759i	−0.128377	+	1.61975i
$871$	44.1212	+	19.7720i	1.49499	+	0.669950i
$872$			13.1924i			0.446751i
$873$	24.8537	−	9.50897i	0.841170	−	0.321830i
$874$	6.49489	−	3.74983i	0.219693	−	0.126840i
$875$	−17.7791	−	4.48237i	−0.601043	−	0.151532i
$876$	−2.92188	−	0.231580i	−0.0987212	−	0.00782437i
$877$	2.08989	−	3.61980i	0.0705707	−	0.122232i	−0.828581	−	0.559869i	$-0.810851\pi$
$877$	2.08989	−	3.61980i	0.0705707	−	0.122232i	0.899152	+	0.437637i	$0.144185\pi$
$878$	13.1355	−	22.7514i	0.443302	−	0.767822i
$879$	3.69224	−	46.5855i	0.124536	−	1.57129i
$880$	−57.7389	−	33.3356i	−1.94638	−	1.12374i
$881$	22.0623	+	38.2129i	0.743296	+	1.28743i	0.950987	+	0.309232i	$0.100072\pi$
$881$	22.0623	+	38.2129i	0.743296	+	1.28743i	−0.207690	+	0.978195i	$0.566595\pi$
$882$	−19.0168	+	24.9055i	−0.640327	+	0.838613i
$883$	15.3513			0.516612			0.258306	−	0.966063i	$-0.416836\pi$
$883$	15.3513			0.516612			0.258306	+	0.966063i	$0.416836\pi$
$884$	−2.33727	−	1.04740i	−0.0786108	−	0.0352278i
$885$	1.19304	−	15.0527i	0.0401035	−	0.505992i
$886$	−10.5142	−	18.2111i	−0.353231	−	0.611813i
$887$	−16.8966	−	29.2658i	−0.567333	−	0.982650i	−0.996828	−	0.0795811i	$-0.974642\pi$
$887$	−16.8966	−	29.2658i	−0.567333	−	0.982650i	0.429495	−	0.903069i	$-0.358692\pi$
$888$	−7.62197	+	11.0769i	−0.255777	+	0.371717i
$889$	8.08284	+	28.4697i	0.271090	+	0.954845i
$890$	35.9112	+	20.7333i	1.20375	+	0.694983i
$891$	−33.3063	−	37.1551i	−1.11580	−	1.24474i
$892$			4.25951i			0.142619i
$893$	5.02185	+	2.89937i	0.168050	+	0.0970236i
$894$	−41.3838	+	19.7110i	−1.38408	+	0.659235i
$895$	29.6435	−	17.1147i	0.990874	−	0.572081i
$896$	−32.6990	+	9.28357i	−1.09240	+	0.310142i
$897$	−0.130341	−	5.61485i	−0.00435197	−	0.187474i
$898$	29.6973			0.991013
$899$	−8.02171	−	13.8940i	−0.267539	−	0.463391i
$900$	−0.598322	−	1.56384i	−0.0199441	−	0.0521280i
$901$	−24.3717	−	14.0710i	−0.811939	−	0.468773i
$902$	18.5727			0.618405
$903$	−2.67356	+	7.90692i	−0.0889704	+	0.263126i
$904$	25.4311	−	44.0480i	0.845826	−	1.46501i
$905$		−	56.8064i		−	1.88831i
$906$	−3.07092	+	4.46294i	−0.102025	+	0.148271i
$907$	−0.313363	−	0.542760i	−0.0104050	−	0.0180220i	0.860776	−	0.508984i	$-0.169979\pi$
$907$	−0.313363	−	0.542760i	−0.0104050	−	0.0180220i	−0.871181	+	0.490962i	$0.836645\pi$
$908$	−0.659801	−	1.14281i	−0.0218963	−	0.0379255i
$909$	25.4223	+	4.05527i	0.843203	+	0.134505i
$910$	−24.0954	+	30.5223i	−0.798753	+	1.01180i
$911$			7.90527i			0.261913i	0.991388	+	0.130957i	$0.0418049\pi$
$911$			7.90527i			0.261913i	−0.991388	+	0.130957i	$0.958195\pi$
$912$	−18.3220	−	38.4676i	−0.606703	−	1.27379i
$913$	31.1241	−	17.9695i	1.03006	−	0.594704i
$914$	−31.9449	−	18.4434i	−1.05664	−	0.610054i
$915$	8.85611	+	0.701910i	0.292774	+	0.0232044i
$916$	3.38471	+	1.95416i	0.111834	+	0.0645674i
$917$	34.0100	+	8.57442i	1.12311	+	0.283152i
$918$	23.6269	+	5.71373i	0.779805	+	0.188581i
$919$	8.11060	−	14.0480i	0.267544	−	0.463400i	−0.700683	−	0.713473i	$-0.747121\pi$
$919$	8.11060	−	14.0480i	0.267544	−	0.463400i	0.968227	+	0.250073i	$0.0804546\pi$
$920$	3.25078	+	5.63051i	0.107175	+	0.185632i
$921$	−17.0911	−	35.8833i	−0.563172	−	1.18239i
$922$			39.0179i			1.28499i
$923$	−13.2991	+	1.36528i	−0.437745	+	0.0449388i
$924$	1.12980	+	5.64481i	0.0371678	+	0.185701i
$925$	−3.61308	−	6.25804i	−0.118797	−	0.205763i
$926$	−29.4419	+	16.9983i	−0.967520	+	0.558598i
$927$	6.01934	+	4.88538i	0.197701	+	0.160457i
$928$	8.65977			0.284271
$929$	−12.4689	+	21.5967i	−0.409091	+	0.708566i	−0.994788	−	0.101964i	$-0.967487\pi$
$929$	−12.4689	+	21.5967i	−0.409091	+	0.708566i	0.585697	+	0.810530i	$0.300821\pi$
$930$	13.7482	+	9.46004i	0.450821	+	0.310207i
$931$	−20.5561	−	33.2837i	−0.673698	−	1.09083i
$932$	−2.97012	−	1.71480i	−0.0972896	−	0.0561701i
$933$	−21.9243	+	10.4425i	−0.717771	+	0.341873i
$934$	−15.1799	+	8.76414i	−0.496703	+	0.286772i
$935$			47.4846i			1.55291i
$936$	−28.5789	−	1.59872i	−0.934129	−	0.0522557i
$937$		−	17.5533i		−	0.573440i	−0.958014	−	0.286720i	$-0.907435\pi$
$937$		−	17.5533i		−	0.573440i	0.958014	−	0.286720i	$-0.0925649\pi$
$938$	37.9853	+	36.8749i	1.24026	+	1.20401i
$939$	0.731932	+	1.53671i	0.0238857	+	0.0501486i
$940$	0.321141	−	0.556233i	0.0104745	−	0.0181423i
$941$	−16.1819			−0.527514			−0.263757	−	0.964589i	$-0.584962\pi$
$941$	−16.1819			−0.527514			−0.263757	+	0.964589i	$0.584962\pi$
$942$	22.8786	+	15.7426i	0.745424	+	0.512922i
$943$	−1.74851	−	1.00951i	−0.0569395	−	0.0328740i
$944$	−14.0470			−0.457191
$945$	17.4844	−	33.2393i	0.568768	−	1.08127i
$946$	7.53417	+	13.0496i	0.244957	+	0.424278i
$947$	4.78591	−	2.76314i	0.155521	−	0.0897901i	−0.420220	−	0.907422i	$-0.638047\pi$
$947$	4.78591	−	2.76314i	0.155521	−	0.0897901i	0.575741	+	0.817632i	$0.304714\pi$
$948$	0.390593	−	4.92817i	0.0126859	−	0.160059i
$949$	−15.7752	−	21.8235i	−0.512085	−	0.708421i
$950$	20.5412			0.666445
$951$	−6.79818	−	14.2729i	−0.220446	−	0.462832i
$952$	15.7492	+	15.2888i	0.510435	+	0.495514i
$953$	38.2971	+	22.1108i	1.24056	+	0.716240i	0.969209	−	0.246239i	$-0.0791948\pi$
$953$	38.2971	+	22.1108i	1.24056	+	0.716240i	0.271355	+	0.962479i	$0.412528\pi$
$954$	39.6818	+	6.32991i	1.28475	+	0.204938i
$955$	46.4134	+	26.7968i	1.50190	+	0.867123i
$956$	1.79327	+	1.03534i	0.0579984	+	0.0334854i
$957$	−5.14998	+	64.9780i	−0.166475	+	2.10044i
$958$	−9.86225	−	5.69398i	−0.318635	−	0.183964i
$959$	32.4080	+	31.4606i	1.04651	+	1.01592i
$960$	29.4763	−	14.0395i	0.951342	−	0.453122i
$961$	25.4134			0.819788
$962$	15.7005	−	1.61181i	0.506205	−	0.0519669i
$963$	−3.38958	+	21.2491i	−0.109228	+	0.684742i
$964$	3.67692	−	2.12287i	0.118426	−	0.0683731i
$965$	−9.54129	−	16.5260i	−0.307145	−	0.531991i
$966$	1.96982	−	5.82566i	0.0633780	−	0.187438i
$967$	−44.0147			−1.41542			−0.707709	−	0.706504i	$-0.750271\pi$
$967$	−44.0147			−1.41542			−0.707709	+	0.706504i	$0.750271\pi$
$968$	−45.2349	−	26.1164i	−1.45391	−	0.839413i
$969$	−17.2022	+	24.9998i	−0.552614	+	0.803108i
$970$	36.1591			1.16100
$971$	−1.59883	+	2.76926i	−0.0513090	+	0.0888698i	−0.890539	−	0.454907i	$-0.849673\pi$
$971$	−1.59883	+	2.76926i	−0.0513090	+	0.0888698i	0.839230	+	0.543776i	$0.183006\pi$
$972$	−3.50312	+	0.451361i	−0.112363	+	0.0144774i
$973$	−2.65311	−	2.57555i	−0.0850547	−	0.0825684i
$974$			31.9709i			1.02441i
$975$	7.38025	−	13.4970i	0.236357	−	0.432249i
$976$		−	8.26439i		−	0.264537i
$977$	−43.7474	+	25.2576i	−1.39960	+	0.808061i	−0.994351	−	0.106144i	$-0.966150\pi$
$977$	−43.7474	+	25.2576i	−1.39960	+	0.808061i	−0.405252	+	0.914205i	$0.632816\pi$
$978$	5.75557	+	12.0840i	0.184043	+	0.386403i
$979$	48.8413	+	28.1985i	1.56098	+	0.901229i
$980$	−3.68659	+	2.27684i	−0.117764	+	0.0727311i
$981$	−9.42493	+	11.6126i	−0.300915	+	0.370761i
$982$	−2.36416	+	4.09484i	−0.0754433	+	0.130672i
$983$	−23.2037			−0.740083			−0.370041	−	0.929015i	$-0.620657\pi$
$983$	−23.2037			−0.740083			−0.370041	+	0.929015i	$0.620657\pi$
$984$	−5.83288	+	8.47686i	−0.185945	+	0.270233i
$985$	−51.1780	+	29.5476i	−1.63067	+	0.941466i
$986$	−15.8768	−	27.4994i	−0.505619	−	0.875758i
$987$	4.66246	−	0.933187i	0.148408	−	0.0297037i
$988$	−1.86708	+	4.16638i	−0.0593997	+	0.132550i
$989$		−	1.63805i		−	0.0520871i
$990$	−24.2283	−	63.3259i	−0.770027	−	2.01263i
$991$	−2.83645	−	4.91288i	−0.0901029	−	0.156063i	0.817451	−	0.575998i	$-0.195386\pi$
$991$	−2.83645	−	4.91288i	−0.0901029	−	0.156063i	−0.907554	+	0.419935i	$0.862053\pi$
$992$	1.50773	−	2.61147i	0.0478705	−	0.0829142i
$993$	−3.94396	+	49.7615i	−0.125158	+	1.57913i
$994$	−14.1943	−	3.57859i	−0.450216	−	0.113506i
$995$	−34.3873	−	19.8535i	−1.09015	−	0.629399i
$996$	0.200998	−	2.53603i	0.00636887	−	0.0803570i
$997$	2.89159	+	1.66946i	0.0915777	+	0.0528724i	0.545089	−	0.838378i	$-0.316496\pi$
$997$	2.89159	+	1.66946i	0.0915777	+	0.0528724i	−0.453512	+	0.891250i	$0.649829\pi$
$998$	−2.12129	+	1.22473i	−0.0671483	+	0.0387681i
$999$	−14.6228	+	4.30514i	−0.462645	+	0.136209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bn.c.146.10	yes	64
3.2	odd	2	inner	273.2.bn.c.146.24	yes	64
7.6	odd	2	inner	273.2.bn.c.146.9	✓	64
13.9	even	3	inner	273.2.bn.c.230.23	yes	64
21.20	even	2	inner	273.2.bn.c.146.23	yes	64
39.35	odd	6	inner	273.2.bn.c.230.9	yes	64
91.48	odd	6	inner	273.2.bn.c.230.24	yes	64
273.230	even	6	inner	273.2.bn.c.230.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bn.c.146.9	✓	64	7.6	odd	2	inner
273.2.bn.c.146.10	yes	64	1.1	even	1	trivial
273.2.bn.c.146.23	yes	64	21.20	even	2	inner
273.2.bn.c.146.24	yes	64	3.2	odd	2	inner
273.2.bn.c.230.9	yes	64	39.35	odd	6	inner
273.2.bn.c.230.10	yes	64	273.230	even	6	inner
273.2.bn.c.230.23	yes	64	13.9	even	3	inner
273.2.bn.c.230.24	yes	64	91.48	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29226 + 0.746087i) q^{2} +(1.56373 - 0.744804i) q^{3} +(0.113292 - 0.196227i) q^{4} -2.73189 q^{5} +(-1.46506 + 2.12916i) q^{6} +(-2.56547 - 0.646794i) q^{7} -2.64625i q^{8} +(1.89053 - 2.32935i) q^{9} +O(q^{10})\)	\(q+(-1.29226 + 0.746087i) q^{2} +(1.56373 - 0.744804i) q^{3} +(0.113292 - 0.196227i) q^{4} -2.73189 q^{5} +(-1.46506 + 2.12916i) q^{6} +(-2.56547 - 0.646794i) q^{7} -2.64625i q^{8} +(1.89053 - 2.32935i) q^{9} +(3.53032 - 2.03823i) q^{10} +(4.80144 - 2.77211i) q^{11} +(0.0310075 - 0.391227i) q^{12} +(2.92207 - 2.11223i) q^{13} +(3.79783 - 1.07824i) q^{14} +(-4.27196 + 2.03473i) q^{15} +(2.20091 + 3.81209i) q^{16} +(1.56754 - 2.71505i) q^{17} +(-0.705164 + 4.42063i) q^{18} +(-4.83982 - 2.79427i) q^{19} +(-0.309501 + 0.536071i) q^{20} +(-4.49346 + 0.899361i) q^{21} +(-4.13648 + 7.16459i) q^{22} +(0.778850 - 0.449669i) q^{23} +(-1.97093 - 4.13803i) q^{24} +2.46325 q^{25} +(-2.20017 + 4.90967i) q^{26} +(1.22138 - 5.05057i) q^{27} +(-0.417565 + 0.430138i) q^{28} +(-5.87835 + 3.39386i) q^{29} +(4.00240 - 5.81665i) q^{30} +2.36359i q^{31} +(-1.10487 - 0.637899i) q^{32} +(5.44350 - 7.91098i) q^{33} +4.67808i q^{34} +(7.00860 + 1.76697i) q^{35} +(-0.242900 - 0.634869i) q^{36} +(-1.46680 - 2.54056i) q^{37} +8.33908 q^{38} +(2.99614 - 5.47934i) q^{39} +7.22927i q^{40} +(-1.12250 - 1.94422i) q^{41} +(5.13572 - 4.51472i) q^{42} +(0.910699 - 1.57738i) q^{43} -1.25623i q^{44} +(-5.16474 + 6.36354i) q^{45} +(-0.670985 + 1.16218i) q^{46} -1.03761 q^{47} +(6.28091 + 4.32186i) q^{48} +(6.16332 + 3.31867i) q^{49} +(-3.18316 + 1.83780i) q^{50} +(0.429030 - 5.41313i) q^{51} +(-0.0834302 - 0.812686i) q^{52} -8.97651i q^{53} +(2.18982 + 7.43791i) q^{54} +(-13.1170 + 7.57312i) q^{55} +(-1.71158 + 6.78888i) q^{56} +(-9.64938 - 0.764783i) q^{57} +(5.06424 - 8.77151i) q^{58} +(-1.59559 + 2.76364i) q^{59} +(-0.0847093 + 1.06879i) q^{60} +(-1.62596 - 0.938746i) q^{61} +(-1.76344 - 3.05438i) q^{62} +(-6.35673 + 4.75311i) q^{63} -6.89994 q^{64} +(-7.98278 + 5.77039i) q^{65} +(-1.13214 + 14.2844i) q^{66} +(6.70479 + 11.6130i) q^{67} +(-0.355178 - 0.615186i) q^{68} +(0.882999 - 1.28325i) q^{69} +(-10.3753 + 2.94564i) q^{70} +(-3.21113 - 1.85394i) q^{71} +(-6.16404 - 5.00282i) q^{72} -7.46851i q^{73} +(3.79096 + 2.18871i) q^{74} +(3.85187 - 1.83464i) q^{75} +(-1.09662 + 0.633135i) q^{76} +(-14.1110 + 4.00624i) q^{77} +(0.216261 + 9.31611i) q^{78} +12.5967 q^{79} +(-6.01266 - 10.4142i) q^{80} +(-1.85176 - 8.80744i) q^{81} +(2.90112 + 1.67496i) q^{82} +6.48224 q^{83} +(-0.332592 + 0.983626i) q^{84} +(-4.28235 + 7.41724i) q^{85} +2.71784i q^{86} +(-6.66441 + 9.68532i) q^{87} +(-7.33570 - 12.7058i) q^{88} +(5.08611 + 8.80940i) q^{89} +(1.92643 - 12.0767i) q^{90} +(-8.86267 + 3.52889i) q^{91} -0.203775i q^{92} +(1.76041 + 3.69603i) q^{93} +(1.34086 - 0.774148i) q^{94} +(13.2219 + 7.63365i) q^{95} +(-2.20284 - 0.174591i) q^{96} +(7.68183 + 4.43511i) q^{97} +(-10.4406 + 0.309787i) q^{98} +(2.62006 - 16.4250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 10 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9} - 18 q^{15} - 16 q^{16} + 8 q^{18} - 44 q^{21} - 32 q^{22} + 48 q^{25} + 40 q^{28} - 40 q^{30} - 6 q^{36} + 12 q^{37} - 12 q^{42} + 40 q^{43} - 36 q^{46} - 24 q^{49} - 28 q^{51} - 68 q^{57} - 116 q^{60} + 4 q^{63} - 48 q^{64} - 28 q^{67} - 64 q^{70} + 62 q^{72} - 2 q^{78} + 56 q^{79} + 10 q^{81} + 28 q^{85} + 80 q^{88} - 16 q^{91} + 46 q^{93} - 32 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 10 * q^9 - 18 * q^15 - 16 * q^16 + 8 * q^18 - 44 * q^21 - 32 * q^22 + 48 * q^25 + 40 * q^28 - 40 * q^30 - 6 * q^36 + 12 * q^37 - 12 * q^42 + 40 * q^43 - 36 * q^46 - 24 * q^49 - 28 * q^51 - 68 * q^57 - 116 * q^60 + 4 * q^63 - 48 * q^64 - 28 * q^67 - 64 * q^70 + 62 * q^72 - 2 * q^78 + 56 * q^79 + 10 * q^81 + 28 * q^85 + 80 * q^88 - 16 * q^91 + 46 * q^93 - 32 * q^99

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