LMFDB - Embedded newform 504.2.cc.b.293.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.16
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21170 - 0.729232i) q^{2} +(1.13327 - 1.30985i) q^{3} +(0.936442 + 1.76722i) q^{4} +(2.78508 + 1.60797i) q^{5} +(-2.32837 + 0.760729i) q^{6} +(-0.187474 + 2.63910i) q^{7} +(0.154027 - 2.82423i) q^{8} +(-0.431402 - 2.96882i) q^{9} +O(q^{10})$	\(q+(-1.21170 - 0.729232i) q^{2} +(1.13327 - 1.30985i) q^{3} +(0.936442 + 1.76722i) q^{4} +(2.78508 + 1.60797i) q^{5} +(-2.32837 + 0.760729i) q^{6} +(-0.187474 + 2.63910i) q^{7} +(0.154027 - 2.82423i) q^{8} +(-0.431402 - 2.96882i) q^{9} +(-2.20210 - 3.97934i) q^{10} +(0.246781 + 0.427438i) q^{11} +(3.37603 + 0.776143i) q^{12} +(-0.618157 + 1.07068i) q^{13} +(2.15168 - 3.06109i) q^{14} +(5.26243 - 1.82577i) q^{15} +(-2.24615 + 3.30980i) q^{16} +2.09784 q^{17} +(-1.64223 + 3.91192i) q^{18} +0.616370 q^{19} +(-0.233569 + 6.42762i) q^{20} +(3.24436 + 3.23637i) q^{21} +(0.0126759 - 0.697888i) q^{22} +(2.78836 + 1.60986i) q^{23} +(-3.52476 - 3.40236i) q^{24} +(2.67111 + 4.62649i) q^{25} +(1.52980 - 0.846565i) q^{26} +(-4.37760 - 2.79940i) q^{27} +(-4.83944 + 2.14006i) q^{28} +(5.17425 + 8.96207i) q^{29} +(-7.70791 - 1.62524i) q^{30} +(-3.17049 - 1.83048i) q^{31} +(5.13528 - 2.37253i) q^{32} +(0.839548 + 0.161156i) q^{33} +(-2.54196 - 1.52981i) q^{34} +(-4.76571 + 7.04865i) q^{35} +(4.84258 - 3.54251i) q^{36} -2.67605i q^{37} +(-0.746856 - 0.449476i) q^{38} +(0.701889 + 2.02306i) q^{39} +(4.97024 - 7.61803i) q^{40} +(5.96422 - 10.3303i) q^{41} +(-1.57113 - 6.28741i) q^{42} +(-5.92731 + 3.42214i) q^{43} +(-0.524282 + 0.836389i) q^{44} +(3.57227 - 8.96207i) q^{45} +(-2.20470 - 3.98403i) q^{46} +(-4.61268 - 7.98939i) q^{47} +(1.78984 + 6.69302i) q^{48} +(-6.92971 - 0.989525i) q^{49} +(0.137201 - 7.55378i) q^{50} +(2.37742 - 2.74785i) q^{51} +(-2.47100 - 0.0897922i) q^{52} +8.87141 q^{53} +(3.26293 + 6.58432i) q^{54} +1.58726i q^{55} +(7.42455 + 0.935962i) q^{56} +(0.698513 - 0.807351i) q^{57} +(0.265775 - 14.6326i) q^{58} +(-1.46977 - 0.848571i) q^{59} +(8.15451 + 7.59016i) q^{60} +(-3.88555 - 6.72997i) q^{61} +(2.50684 + 4.53002i) q^{62} +(7.91589 - 0.581938i) q^{63} +(-7.95255 - 0.870014i) q^{64} +(-3.44323 + 1.98795i) q^{65} +(-0.899762 - 0.807498i) q^{66} +(4.18454 + 2.41594i) q^{67} +(1.96451 + 3.70735i) q^{68} +(5.26863 - 1.82792i) q^{69} +(10.9147 - 5.06555i) q^{70} -9.17377i q^{71} +(-8.45108 + 0.761102i) q^{72} +8.40778i q^{73} +(-1.95146 + 3.24258i) q^{74} +(9.08708 + 1.74432i) q^{75} +(0.577195 + 1.08926i) q^{76} +(-1.17432 + 0.571148i) q^{77} +(0.624800 - 2.96319i) q^{78} +(-4.37414 - 7.57623i) q^{79} +(-11.5778 + 5.60632i) q^{80} +(-8.62778 + 2.56151i) q^{81} +(-14.7601 + 8.16798i) q^{82} +(-11.0312 + 6.36888i) q^{83} +(-2.68124 + 8.76419i) q^{84} +(5.84265 + 3.37326i) q^{85} +(9.67767 + 0.175778i) q^{86} +(17.6028 + 3.37895i) q^{87} +(1.24519 - 0.631131i) q^{88} -3.10892 q^{89} +(-10.8640 + 8.25435i) q^{90} +(-2.70974 - 1.83210i) q^{91} +(-0.233845 + 6.43519i) q^{92} +(-5.99068 + 2.07843i) q^{93} +(-0.236929 + 13.0445i) q^{94} +(1.71664 + 0.991101i) q^{95} +(2.71200 - 9.41515i) q^{96} +(5.85807 - 3.38216i) q^{97} +(7.67514 + 6.25237i) q^{98} +(1.16252 - 0.917047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.21170	−	0.729232i	−0.856802	−	0.515645i
$2$	−1.21170	−	0.729232i	−0.856802	−	0.515645i
$3$	1.13327	−	1.30985i	0.654293	−	0.756241i
$3$	1.13327	−	1.30985i	0.654293	−	0.756241i
$4$	0.936442	+	1.76722i	0.468221	+	0.883611i
$5$	2.78508	+	1.60797i	1.24552	+	0.719104i	0.970214	−	0.242251i	$-0.0778858\pi$
$5$	2.78508	+	1.60797i	1.24552	+	0.719104i	0.275311	+	0.961355i	$0.411219\pi$
$6$	−2.32837	+	0.760729i	−0.950552	+	0.310566i
$7$	−0.187474	+	2.63910i	−0.0708584	+	0.997486i
$7$	−0.187474	+	2.63910i	−0.0708584	+	0.997486i
$8$	0.154027	−	2.82423i	0.0544567	−	0.998516i
$9$	−0.431402	−	2.96882i	−0.143801	−	0.989607i
$10$	−2.20210	−	3.97934i	−0.696366	−	1.25838i
$11$	0.246781	+	0.427438i	0.0744074	+	0.128877i	0.900828	−	0.434175i	$-0.142960\pi$
$11$	0.246781	+	0.427438i	0.0744074	+	0.128877i	−0.826421	+	0.563053i	$0.809627\pi$
$12$	3.37603	+	0.776143i	0.974577	+	0.224053i
$13$	−0.618157	+	1.07068i	−0.171446	+	0.296953i	−0.938926	−	0.344120i	$-0.888177\pi$
$13$	−0.618157	+	1.07068i	−0.171446	+	0.296953i	0.767480	+	0.641073i	$0.221511\pi$
$14$	2.15168	−	3.06109i	0.575060	−	0.818111i
$15$	5.26243	−	1.82577i	1.35875	−	0.471412i
$16$	−2.24615	+	3.30980i	−0.561538	+	0.827451i
$17$	2.09784			0.508801			0.254401	−	0.967099i	$-0.418122\pi$
$17$	2.09784			0.508801			0.254401	+	0.967099i	$0.418122\pi$
$18$	−1.64223	+	3.91192i	−0.387077	+	0.922048i
$19$	0.616370			0.141405			0.0707025	−	0.997497i	$-0.477476\pi$
$19$	0.616370			0.141405			0.0707025	+	0.997497i	$0.477476\pi$
$20$	−0.233569	+	6.42762i	−0.0522277	+	1.43726i
$21$	3.24436	+	3.23637i	0.707978	+	0.706235i
$22$	0.0126759	−	0.697888i	0.00270251	−	0.148790i
$23$	2.78836	+	1.60986i	0.581413	+	0.335679i	0.761695	−	0.647936i	$-0.224368\pi$
$23$	2.78836	+	1.60986i	0.581413	+	0.335679i	−0.180282	+	0.983615i	$0.557701\pi$
$24$	−3.52476	−	3.40236i	−0.719488	−	0.694505i
$25$	2.67111	+	4.62649i	0.534221	+	0.925298i
$26$	1.52980	−	0.846565i	0.300018	−	0.166025i
$27$	−4.37760	−	2.79940i	−0.842469	−	0.538745i
$28$	−4.83944	+	2.14006i	−0.914568	+	0.404433i
$29$	5.17425	+	8.96207i	0.960834	+	1.66421i	0.720413	+	0.693545i	$0.243952\pi$
$29$	5.17425	+	8.96207i	0.960834	+	1.66421i	0.240421	+	0.970669i	$0.422715\pi$
$30$	−7.70791	−	1.62524i	−1.40727	−	0.296728i
$31$	−3.17049	−	1.83048i	−0.569437	−	0.328765i	0.187487	−	0.982267i	$-0.439966\pi$
$31$	−3.17049	−	1.83048i	−0.569437	−	0.328765i	−0.756925	+	0.653502i	$0.773299\pi$
$32$	5.13528	−	2.37253i	0.907798	−	0.419408i
$33$	0.839548	+	0.161156i	0.146147	+	0.0280537i
$34$	−2.54196	−	1.52981i	−0.435942	−	0.262361i
$35$	−4.76571	+	7.04865i	−0.805552	+	1.19144i
$36$	4.84258	−	3.54251i	0.807097	−	0.590419i
$37$		−	2.67605i		−	0.439940i	−0.975507	−	0.219970i	$-0.929404\pi$
$37$		−	2.67605i		−	0.439940i	0.975507	−	0.219970i	$-0.0705960\pi$
$38$	−0.746856	−	0.449476i	−0.121156	−	0.0729147i
$39$	0.701889	+	2.02306i	0.112392	+	0.323949i
$40$	4.97024	−	7.61803i	0.785864	−	1.20452i
$41$	5.96422	−	10.3303i	0.931454	−	1.61333i	0.150616	−	0.988592i	$-0.451874\pi$
$41$	5.96422	−	10.3303i	0.931454	−	1.61333i	0.780838	−	0.624734i	$-0.214792\pi$
$42$	−1.57113	−	6.28741i	−0.242431	−	0.970169i
$43$	−5.92731	+	3.42214i	−0.903907	+	0.521871i	−0.878466	−	0.477805i	$-0.841432\pi$
$43$	−5.92731	+	3.42214i	−0.903907	+	0.521871i	−0.0254413	+	0.999676i	$0.508099\pi$
$44$	−0.524282	+	0.836389i	−0.0790384	+	0.126090i
$45$	3.57227	−	8.96207i	0.532523	−	1.33599i
$46$	−2.20470	−	3.98403i	−0.325065	−	0.587413i
$47$	−4.61268	−	7.98939i	−0.672828	−	1.16537i	−0.977099	−	0.212787i	$-0.931746\pi$
$47$	−4.61268	−	7.98939i	−0.672828	−	1.16537i	0.304270	−	0.952586i	$-0.401587\pi$
$48$	1.78984	+	6.69302i	0.258342	+	0.966054i
$49$	−6.92971	−	0.989525i	−0.989958	−	0.141361i
$50$	0.137201	−	7.55378i	0.0194031	−	1.06827i
$51$	2.37742	−	2.74785i	0.332905	−	0.384776i
$52$	−2.47100	−	0.0897922i	−0.342666	−	0.0124519i
$53$	8.87141			1.21858			0.609291	−	0.792947i	$-0.291454\pi$
$53$	8.87141			1.21858			0.609291	+	0.792947i	$0.291454\pi$
$54$	3.26293	+	6.58432i	0.444029	+	0.896013i
$55$			1.58726i			0.214027i
$56$	7.42455	+	0.935962i	0.992148	+	0.125073i
$57$	0.698513	−	0.807351i	0.0925203	−	0.106936i
$58$	0.265775	−	14.6326i	0.0348979	−	1.92135i
$59$	−1.46977	−	0.848571i	−0.191347	−	0.110475i	0.401266	−	0.915962i	$-0.368570\pi$
$59$	−1.46977	−	0.848571i	−0.191347	−	0.110475i	−0.592613	+	0.805487i	$0.701904\pi$
$60$	8.15451	+	7.59016i	1.05274	+	0.979886i
$61$	−3.88555	−	6.72997i	−0.497494	−	0.861685i	0.502502	−	0.864576i	$-0.332413\pi$
$61$	−3.88555	−	6.72997i	−0.497494	−	0.861685i	−0.999996	+	0.00289133i	$0.999080\pi$
$62$	2.50684	+	4.53002i	0.318369	+	0.575314i
$63$	7.91589	−	0.581938i	0.997309	−	0.0733173i
$64$	−7.95255	−	0.870014i	−0.994069	−	0.108752i
$65$	−3.44323	+	1.98795i	−0.427080	+	0.246575i
$66$	−0.899762	−	0.807498i	−0.110753	−	0.0993962i
$67$	4.18454	+	2.41594i	0.511223	+	0.295154i	0.733336	−	0.679866i	$-0.237962\pi$
$67$	4.18454	+	2.41594i	0.511223	+	0.295154i	−0.222114	+	0.975021i	$0.571296\pi$
$68$	1.96451	+	3.70735i	0.238231	+	0.449583i
$69$	5.26863	−	1.82792i	0.634269	−	0.220056i
$70$	10.9147	−	5.06555i	1.30456	−	0.605449i
$71$		−	9.17377i		−	1.08873i	−0.838850	−	0.544363i	$-0.816771\pi$
$71$		−	9.17377i		−	1.08873i	0.838850	−	0.544363i	$-0.183229\pi$
$72$	−8.45108	+	0.761102i	−0.995969	+	0.0896967i
$73$			8.40778i			0.984056i	0.870579	+	0.492028i	$0.163744\pi$
$73$			8.40778i			0.984056i	−0.870579	+	0.492028i	$0.836256\pi$
$74$	−1.95146	+	3.24258i	−0.226853	+	0.376942i
$75$	9.08708	+	1.74432i	1.04929	+	0.201416i
$76$	0.577195	+	1.08926i	0.0662088	+	0.124947i
$77$	−1.17432	+	0.571148i	−0.133826	+	0.0650883i
$78$	0.624800	−	2.96319i	0.0707446	−	0.335515i
$79$	−4.37414	−	7.57623i	−0.492129	−	0.852392i	0.507830	−	0.861457i	$-0.330448\pi$
$79$	−4.37414	−	7.57623i	−0.492129	−	0.852392i	−0.999959	+	0.00906525i	$0.997114\pi$
$80$	−11.5778	+	5.60632i	−1.29443	+	0.626806i
$81$	−8.62778	+	2.56151i	−0.958643	+	0.284612i
$82$	−14.7601	+	8.16798i	−1.62998	+	0.902002i
$83$	−11.0312	+	6.36888i	−1.21083	+	0.699075i	−0.962941	−	0.269712i	$-0.913071\pi$
$83$	−11.0312	+	6.36888i	−1.21083	+	0.699075i	−0.247893	+	0.968788i	$0.579738\pi$
$84$	−2.68124	+	8.76419i	−0.292547	+	0.956251i
$85$	5.84265	+	3.37326i	0.633725	+	0.365881i
$86$	9.67767	+	0.175778i	1.04357	+	0.0189546i
$87$	17.6028	+	3.37895i	1.88721	+	0.362262i
$88$	1.24519	−	0.631131i	0.132738	−	0.0672787i
$89$	−3.10892			−0.329545			−0.164773	−	0.986332i	$-0.552689\pi$
$89$	−3.10892			−0.329545			−0.164773	+	0.986332i	$0.552689\pi$
$90$	−10.8640	+	8.25435i	−1.14516	+	0.870085i
$91$	−2.70974	−	1.83210i	−0.284058	−	0.192057i
$92$	−0.233845	+	6.43519i	−0.0243800	+	0.670915i
$93$	−5.99068	+	2.07843i	−0.621204	+	0.215523i
$94$	−0.236929	+	13.0445i	−0.0244374	+	1.34543i
$95$	1.71664	+	0.991101i	0.176123	+	0.101685i
$96$	2.71200	−	9.41515i	0.276793	−	0.960930i
$97$	5.85807	−	3.38216i	0.594797	−	0.343406i	−0.172195	−	0.985063i	$-0.555086\pi$
$97$	5.85807	−	3.38216i	0.594797	−	0.343406i	0.766992	+	0.641657i	$0.221753\pi$
$98$	7.67514	+	6.25237i	0.775307	+	0.631585i
$99$	1.16252	−	0.917047i	0.116838	−	0.0921667i
$100$	−5.67470	+	9.05288i	−0.567470	+	0.905288i
$101$	7.34635	−	4.24142i	0.730989	−	0.422037i	−0.0877947	−	0.996139i	$-0.527982\pi$
$101$	7.34635	−	4.24142i	0.730989	−	0.422037i	0.818784	+	0.574102i	$0.194649\pi$
$102$	−4.88454	+	1.59589i	−0.483642	+	0.158017i
$103$	−9.23084	−	5.32943i	−0.909542	−	0.525124i	−0.0292582	−	0.999572i	$-0.509314\pi$
$103$	−9.23084	−	5.32943i	−0.909542	−	0.525124i	−0.880284	+	0.474448i	$0.842648\pi$
$104$	2.92863	+	1.91073i	0.287176	+	0.187363i
$105$	3.83182	+	14.2304i	0.373948	+	1.38874i
$106$	−10.7495	−	6.46931i	−1.04408	−	0.628355i
$107$	−3.47521			−0.335962			−0.167981	−	0.985790i	$-0.553725\pi$
$107$	−3.47521			−0.335962			−0.167981	+	0.985790i	$0.553725\pi$
$108$	0.847799	−	10.3577i	0.0815795	−	0.996667i
$109$			18.5481i			1.77658i	0.459281	+	0.888291i	$0.348107\pi$
$109$			18.5481i			1.77658i	−0.459281	+	0.888291i	$0.651893\pi$
$110$	1.15748	−	1.92329i	0.110362	−	0.183379i
$111$	−3.50522	−	3.03269i	−0.332701	−	0.287850i
$112$	−8.31381	−	6.54833i	−0.785581	−	0.618759i
$113$	−15.3081	−	8.83816i	−1.44007	−	0.831424i	−0.442216	−	0.896909i	$-0.645807\pi$
$113$	−15.3081	−	8.83816i	−1.44007	−	0.831424i	−0.997854	+	0.0654845i	$0.979141\pi$
$114$	−1.43513	+	0.468890i	−0.134413	+	0.0439156i
$115$	5.17720	+	8.96717i	0.482776	+	0.836193i
$116$	−10.9926	+	17.5365i	−1.02064	+	1.62822i
$117$	3.44533	+	1.37330i	0.318521	+	0.126962i
$118$	1.16212	+	2.10002i	0.106981	+	0.193322i
$119$	−0.393290	+	5.53642i	−0.0360529	+	0.507522i
$120$	−4.34584	−	15.1435i	−0.396719	−	1.38241i
$121$	5.37820	−	9.31531i	0.488927	−	0.846847i
$122$	−0.199581	+	10.9882i	−0.0180692	+	0.994824i
$123$	−6.77209	−	19.5193i	−0.610619	−	1.75999i
$124$	0.265892	−	7.31711i	0.0238778	−	0.657096i
$125$			1.10053i			0.0984341i
$126$	−10.0161	−	5.06738i	−0.892302	−	0.451438i
$127$	−3.67076			−0.325727			−0.162864	−	0.986649i	$-0.552073\pi$
$127$	−3.67076			−0.325727			−0.162864	+	0.986649i	$0.552073\pi$
$128$	9.00168	+	6.85345i	0.795643	+	0.605765i
$129$	−2.23476	+	11.6421i	−0.196760	+	1.02503i
$130$	5.62185	+	0.102111i	0.493069	+	0.00895571i
$131$	−7.99423	−	4.61547i	−0.698459	−	0.403256i	0.108314	−	0.994117i	$-0.465455\pi$
$131$	−7.99423	−	4.61547i	−0.698459	−	0.403256i	−0.806773	+	0.590861i	$0.798788\pi$
$132$	0.501390	+	1.63458i	0.0436404	+	0.142272i
$133$	−0.115553	+	1.62666i	−0.0100197	+	0.141049i
$134$	−3.30863	−	5.97890i	−0.285822	−	0.516498i
$135$	−7.69061	−	14.8356i	−0.661902	−	1.27684i
$136$	0.323124	−	5.92479i	0.0277076	−	0.508046i
$137$	−8.48252	+	4.89738i	−0.724710	+	0.418412i	−0.816484	−	0.577368i	$-0.804080\pi$
$137$	−8.48252	+	4.89738i	−0.724710	+	0.418412i	0.0917735	+	0.995780i	$0.470746\pi$
$138$	−7.71699	−	1.62716i	−0.656914	−	0.138513i
$139$	4.90709	−	8.49933i	0.416214	−	0.720904i	−0.579341	−	0.815085i	$-0.696690\pi$
$139$	4.90709	−	8.49933i	0.416214	−	0.720904i	0.995555	+	0.0941813i	$0.0300233\pi$
$140$	−16.9193	−	1.82142i	−1.42995	−	0.153938i
$141$	−15.6923	−	3.01223i	−1.32153	−	0.253675i
$142$	−6.68981	+	11.1159i	−0.561396	+	0.932823i
$143$	−0.610199			−0.0510274
$144$	10.7952	+	5.24057i	0.899600	+	0.436714i
$145$			33.2801i			2.76376i
$146$	6.13122	−	10.1877i	0.507423	−	0.843142i
$147$	−9.14935	+	7.95546i	−0.754626	+	0.656156i
$148$	4.72918	−	2.50597i	0.388736	−	0.205989i
$149$	3.97480	−	6.88456i	0.325629	−	0.564005i	−0.656011	−	0.754752i	$-0.727757\pi$
$149$	3.97480	−	6.88456i	0.325629	−	0.564005i	0.981639	+	0.190746i	$0.0610908\pi$
$150$	−9.73882	−	8.74018i	−0.795171	−	0.713633i
$151$	10.2380	+	17.7328i	0.833157	+	1.44307i	0.895522	+	0.445017i	$0.146803\pi$
$151$	10.2380	+	17.7328i	0.833157	+	1.44307i	−0.0623645	+	0.998053i	$0.519864\pi$
$152$	0.0949375	−	1.74077i	0.00770045	−	0.141195i
$153$	−0.905014	−	6.22811i	−0.0731660	−	0.503513i
$154$	1.83942	+	0.164289i	0.148225	+	0.0132388i
$155$	−5.88671	−	10.1961i	−0.472832	−	0.818969i
$156$	−2.91792	+	3.13487i	−0.233621	+	0.250991i
$157$	−9.20218	+	15.9386i	−0.734414	+	1.27204i	0.220566	+	0.975372i	$0.429210\pi$
$157$	−9.20218	+	15.9386i	−0.734414	+	1.27204i	−0.954980	+	0.296670i	$0.904124\pi$
$158$	−0.224677	+	12.3699i	−0.0178743	+	0.984095i
$159$	10.0537	−	11.6202i	0.797310	−	0.921541i
$160$	18.1171	+	1.64968i	1.43228	+	0.130419i
$161$	−4.77133	+	7.05696i	−0.376033	+	0.556166i
$162$	12.3222	+	3.18787i	0.968126	+	0.250462i
$163$		−	9.74409i		−	0.763216i	−0.924324	−	0.381608i	$-0.875370\pi$
$163$		−	9.74409i		−	0.763216i	0.924324	−	0.381608i	$-0.124630\pi$
$164$	23.8411	+	0.866349i	1.86168	+	0.0676505i
$165$	2.07907	+	1.79880i	0.161856	+	0.140036i
$166$	18.0109	+	0.327136i	1.39792	+	0.0253907i
$167$	−7.82471	+	13.5528i	−0.605494	+	1.04875i	0.386479	+	0.922298i	$0.373691\pi$
$167$	−7.82471	+	13.5528i	−0.605494	+	1.04875i	−0.991973	+	0.126449i	$0.959642\pi$
$168$	9.63998	−	8.66434i	0.743741	−	0.668468i
$169$	5.73576	+	9.93463i	0.441213	+	0.764203i
$170$	−4.61966	−	8.34803i	−0.354312	−	0.640265i
$171$	−0.265903	−	1.82989i	−0.0203341	−	0.139935i
$172$	−11.5983	−	7.27025i	−0.884359	−	0.554352i
$173$	−15.1529	+	8.74850i	−1.15205	+	0.665136i	−0.949386	−	0.314112i	$-0.898293\pi$
$173$	−15.1529	+	8.74850i	−1.15205	+	0.665136i	−0.202664	+	0.979248i	$0.564960\pi$
$174$	−18.8653	−	16.9308i	−1.43017	−	1.28352i
$175$	−12.7105	+	6.18197i	−0.960826	+	0.467313i
$176$	−1.96904	−	0.143293i	−0.148422	−	0.0108011i
$177$	−2.77714	+	0.963513i	−0.208743	+	0.0724221i
$178$	3.76709	+	2.26713i	0.282355	+	0.169928i
$179$	22.7135			1.69769			0.848844	−	0.528643i	$-0.177299\pi$
$179$	22.7135			1.69769			0.848844	+	0.528643i	$0.177299\pi$
$180$	19.1832	−	2.07946i	1.42983	−	0.154994i
$181$	13.9170			1.03445			0.517223	−	0.855851i	$-0.326966\pi$
$181$	13.9170			1.03445			0.517223	+	0.855851i	$0.326966\pi$
$182$	1.94737	+	4.19600i	0.144349	+	0.311028i
$183$	−13.2186	−	2.53739i	−0.977148	−	0.187569i
$184$	4.97610	−	7.62701i	0.366843	−	0.562270i
$185$	4.30300	−	7.45301i	0.316363	−	0.547956i
$186$	8.77457	+	1.85015i	0.643383	+	0.135660i
$187$	0.517708	+	0.896697i	0.0378586	+	0.0655730i
$188$	9.79953	−	15.6332i	0.714704	−	1.14017i
$189$	8.20859	−	11.0281i	0.597087	−	0.802177i
$190$	−1.35731	−	2.45275i	−0.0984696	−	0.177941i
$191$	−10.8593	+	6.26965i	−0.785755	+	0.453656i	−0.838466	−	0.544954i	$-0.816547\pi$
$191$	−10.8593	+	6.26965i	−0.785755	+	0.453656i	0.0527111	+	0.998610i	$0.483214\pi$
$192$	−10.1520	+	9.43067i	−0.732655	+	0.680600i
$193$	6.23220	−	10.7945i	0.448604	−	0.777005i	−0.549692	−	0.835368i	$-0.685255\pi$
$193$	6.23220	−	10.7945i	0.448604	−	0.777005i	0.998295	+	0.0583630i	$0.0185881\pi$
$194$	−9.56461	−	0.173724i	−0.686699	−	0.0124727i
$195$	−1.29820	+	6.76299i	−0.0929657	+	0.484308i
$196$	−4.74056	−	13.1730i	−0.338611	−	0.940926i
$197$	−9.30081			−0.662655			−0.331328	−	0.943516i	$-0.607497\pi$
$197$	−9.30081			−0.662655			−0.331328	+	0.943516i	$0.607497\pi$
$198$	−2.07737	+	0.263438i	−0.147632	+	0.0187217i
$199$		−	14.0372i		−	0.995072i	−0.867443	−	0.497536i	$-0.834238\pi$
$199$		−	14.0372i		−	0.995072i	0.867443	−	0.497536i	$-0.165762\pi$
$200$	13.4777	−	6.83121i	0.953017	−	0.483040i
$201$	7.90672	−	2.74319i	0.557697	−	0.193490i
$202$	−11.9946	−	0.217860i	−0.843935	−	0.0153286i
$203$	−24.6218	+	11.9752i	−1.72811	+	0.840495i
$204$	7.08238	+	1.62822i	0.495866	+	0.113998i
$205$	33.2216	−	19.1805i	2.32030	−	1.33962i
$206$	7.29864	+	13.1891i	0.508520	+	0.918928i
$207$	3.57648	−	8.97264i	0.248583	−	0.623641i
$208$	−2.15526	−	4.45089i	−0.149441	−	0.308614i
$209$	0.152109	+	0.263460i	0.0105216	+	0.0182239i
$210$	5.73421	−	20.0373i	0.395698	−	1.38270i
$211$	−9.74449	−	5.62598i	−0.670838	−	0.387309i	0.125556	−	0.992087i	$-0.459929\pi$
$211$	−9.74449	−	5.62598i	−0.670838	−	0.387309i	−0.796394	+	0.604778i	$0.793262\pi$
$212$	8.30756	+	15.6778i	0.570565	+	1.07675i
$213$	−12.0162	−	10.3964i	−0.823339	−	0.712346i
$214$	4.21092	+	2.53424i	0.287853	+	0.173237i
$215$	−22.0107			−1.50112
$216$	−8.58042	+	11.9322i	−0.583824	+	0.811881i
$217$	5.42522	−	8.02408i	0.368288	−	0.544710i
$218$	13.5258	−	22.4747i	0.916085	−	1.52218i
$219$	11.0129	+	9.52828i	0.744184	+	0.643861i
$220$	−2.80505	+	1.48638i	−0.189116	+	0.100212i
$221$	−1.29680	+	2.24612i	−0.0872319	+	0.151090i
$222$	2.03575	+	6.23083i	0.136631	+	0.418186i
$223$	−11.8013	+	6.81349i	−0.790274	+	0.456265i	−0.840059	−	0.542495i	$-0.817480\pi$
$223$	−11.8013	+	6.81349i	−0.790274	+	0.456265i	0.0497851	+	0.998760i	$0.484146\pi$
$224$	5.29861	+	13.9973i	0.354028	+	0.935235i
$225$	12.5829	−	9.92591i	0.838860	−	0.661727i
$226$	12.1038	+	21.8724i	0.805135	+	1.45493i
$227$	11.5976	−	6.69590i	0.769762	−	0.444422i	−0.0630276	−	0.998012i	$-0.520076\pi$
$227$	11.5976	−	6.69590i	0.769762	−	0.444422i	0.832790	+	0.553589i	$0.186742\pi$
$228$	2.08089	+	0.478391i	0.137810	+	0.0316822i
$229$	−6.42378	+	11.1263i	−0.424495	+	0.735247i	−0.996373	−	0.0850915i	$-0.972882\pi$
$229$	−6.42378	+	11.1263i	−0.424495	+	0.735247i	0.571878	+	0.820339i	$0.306215\pi$
$230$	0.265926	−	14.6409i	0.0175346	−	0.965393i
$231$	−0.582701	+	2.18544i	−0.0383389	+	0.143791i
$232$	26.1079	−	13.2329i	1.71407	−	0.868781i
$233$		−	6.05762i		−	0.396848i	−0.980116	−	0.198424i	$-0.936418\pi$
$233$		−	6.05762i		−	0.396848i	0.980116	−	0.198424i	$-0.0635823\pi$
$234$	−3.17326	−	4.17648i	−0.207442	−	0.273025i
$235$		−	29.6681i		−	1.93533i
$236$	0.123262	−	3.39204i	0.00802364	−	0.220803i
$237$	−14.8808	−	2.85645i	−0.966610	−	0.185546i
$238$	4.51388	−	6.42168i	0.292591	−	0.416256i
$239$	23.9135	+	13.8065i	1.54684	+	0.893066i	0.998381	+	0.0568864i	$0.0181173\pi$
$239$	23.9135	+	13.8065i	1.54684	+	0.893066i	0.548455	+	0.836180i	$0.315216\pi$
$240$	−5.77729	+	21.5186i	−0.372922	+	1.38902i
$241$	−7.30945	+	4.22011i	−0.470843	+	0.271841i	−0.716593	−	0.697492i	$-0.754299\pi$
$241$	−7.30945	+	4.22011i	−0.470843	+	0.271841i	0.245749	+	0.969333i	$0.420966\pi$
$242$	−13.3098	+	7.36543i	−0.855586	+	0.473468i
$243$	−6.42241	+	14.2040i	−0.411998	+	0.911185i
$244$	8.25477	−	13.1689i	0.528457	−	0.843050i
$245$	−17.7087	−	13.8986i	−1.13136	−	0.887951i
$246$	−6.02831	+	28.5899i	−0.384351	+	1.82283i
$247$	−0.381014	+	0.659935i	−0.0242433	+	0.0419906i
$248$	−5.65805	+	8.67226i	−0.359287	+	0.550689i
$249$	−4.15908	+	21.6669i	−0.263571	+	1.37308i
$250$	0.802539	−	1.33351i	0.0507570	−	0.0843386i
$251$		−	16.9357i		−	1.06897i	−0.845178	−	0.534485i	$-0.820506\pi$
$251$		−	16.9357i		−	1.06897i	0.845178	−	0.534485i	$-0.179494\pi$
$252$	8.44119	+	13.4442i	0.531745	+	0.846905i
$253$			1.58913i			0.0999080i
$254$	4.44786	+	2.67683i	0.279084	+	0.167960i
$255$	11.0397	−	3.83018i	0.691336	−	0.239855i
$256$	−5.90959	−	14.8686i	−0.369350	−	0.929291i
$257$	12.8304	−	22.2228i	0.800336	−	1.38622i	−0.119060	−	0.992887i	$-0.537988\pi$
$257$	12.8304	−	22.2228i	0.800336	−	1.38622i	0.919395	−	0.393335i	$-0.128679\pi$
$258$	11.1976	−	12.4771i	0.697135	−	0.776788i
$259$	7.06237	+	0.501690i	0.438834	+	0.0311735i
$260$	−6.73754	−	4.22336i	−0.417845	−	0.261922i
$261$	24.3746	−	19.2277i	1.50875	−	1.19016i
$262$	6.32088	+	11.4222i	0.390505	+	0.705668i
$263$	1.27030	−	0.733409i	0.0783301	−	0.0452239i	−0.460323	−	0.887751i	$-0.652267\pi$
$263$	1.27030	−	0.733409i	0.0783301	−	0.0452239i	0.538654	+	0.842527i	$0.318933\pi$
$264$	0.584455	−	2.34626i	0.0359707	−	0.144402i
$265$	24.7076	+	14.2649i	1.51777	+	0.876287i
$266$	1.32623	−	1.88676i	0.0813164	−	0.115685i
$267$	−3.52325	+	4.07222i	−0.215619	+	0.249216i
$268$	−0.350935	+	9.65740i	−0.0214367	+	0.589920i
$269$		−	12.4582i		−	0.759593i	−0.925070	−	0.379796i	$-0.875994\pi$
$269$		−	12.4582i		−	0.759593i	0.925070	−	0.379796i	$-0.124006\pi$
$270$	−1.49985	+	23.5845i	−0.0912778	+	1.43531i
$271$			3.78264i			0.229779i	0.993378	+	0.114889i	$0.0366514\pi$
$271$			3.78264i			0.229779i	−0.993378	+	0.114889i	$0.963349\pi$
$272$	−4.71207	+	6.94344i	−0.285711	+	0.421008i
$273$	−5.47065	+	1.47309i	−0.331099	+	0.0891552i
$274$	13.8496	+	0.251553i	0.836686	+	0.0151969i
$275$	−1.31836	+	2.28346i	−0.0795000	+	0.137698i
$276$	8.16411	+	7.59911i	0.491422	+	0.457412i
$277$	−19.9484	+	11.5172i	−1.19859	+	0.692004i	−0.960240	−	0.279177i	$-0.909939\pi$
$277$	−19.9484	+	11.5172i	−1.19859	+	0.692004i	−0.238346	+	0.971180i	$0.576605\pi$
$278$	−12.1439	+	6.72025i	−0.728344	+	0.403054i
$279$	−4.06662	+	10.2023i	−0.243462	+	0.610795i
$280$	19.1730	+	14.5451i	1.14580	+	0.869239i
$281$	−4.63987	+	2.67883i	−0.276792	+	0.159806i	−0.631970	−	0.774993i	$-0.717753\pi$
$281$	−4.63987	+	2.67883i	−0.276792	+	0.159806i	0.355178	+	0.934799i	$0.384420\pi$
$282$	16.8178	+	15.0932i	1.00148	+	0.898789i
$283$	−8.09427	+	14.0197i	−0.481154	+	0.833384i	−0.999766	−	0.0216260i	$-0.993116\pi$
$283$	−8.09427	+	14.0197i	−0.481154	+	0.833384i	0.518612	+	0.855010i	$0.326449\pi$
$284$	16.2121	−	8.59070i	0.962011	−	0.509764i
$285$	3.24360	−	1.12535i	0.192135	−	0.0666600i
$286$	0.739379	+	0.444976i	0.0437204	+	0.0263120i
$287$	26.1446	+	17.6768i	1.54327	+	1.04343i
$288$	−9.25898	−	14.2222i	−0.545591	−	0.838052i
$289$	−12.5991			−0.741121
$290$	24.2689	−	40.3255i	1.42512	−	2.36800i
$291$	2.20866	−	11.5061i	0.129474	−	0.674498i
$292$	−14.8584	+	7.87340i	−0.869523	+	0.460756i
$293$	22.8325	+	13.1824i	1.33389	+	0.770121i	0.985893	−	0.167375i	$-0.0535290\pi$
$293$	22.8325	+	13.1824i	1.33389	+	0.770121i	0.347996	+	0.937496i	$0.386862\pi$
$294$	16.8877	−	2.96765i	0.984908	−	0.173077i
$295$	−2.72895	−	4.72667i	−0.158885	−	0.275197i
$296$	−7.55779	−	0.412184i	−0.439287	−	0.0239577i
$297$	0.116260	−	2.56199i	0.00674611	−	0.148662i
$298$	−9.83672	+	5.44348i	−0.569826	+	0.315332i
$299$	−3.44729	+	1.99029i	−0.199362	+	0.115102i
$300$	5.42693	+	17.6923i	0.313324	+	1.02147i
$301$	−7.92015	−	16.2843i	−0.456510	−	0.938614i
$302$	0.525874	−	28.9527i	0.0302606	−	1.66604i
$303$	2.76978	−	14.4293i	0.159120	−	0.828940i
$304$	−1.38446	+	2.04006i	−0.0794043	+	0.117006i
$305$		−	24.9913i		−	1.43100i
$306$	−3.44513	+	8.20658i	−0.196945	+	0.469139i
$307$	1.92106			0.109641			0.0548203	−	0.998496i	$-0.482541\pi$
$307$	1.92106			0.109641			0.0548203	+	0.998496i	$0.482541\pi$
$308$	−2.10902	−	1.54043i	−0.120173	−	0.0877743i
$309$	−17.4418	+	6.05132i	−0.992228	+	0.344248i
$310$	−0.302370	+	16.6474i	−0.0171735	+	0.945508i
$311$	6.95419	−	12.0450i	0.394336	−	0.683010i	−0.598680	−	0.800988i	$-0.704308\pi$
$311$	6.95419	−	12.0450i	0.394336	−	0.683010i	0.993016	+	0.117978i	$0.0376414\pi$
$312$	5.82170	−	1.67069i	0.329589	−	0.0945842i
$313$	2.16673	−	1.25096i	0.122471	−	0.0707087i	−0.437513	−	0.899212i	$-0.644141\pi$
$313$	2.16673	−	1.25096i	0.122471	−	0.0707087i	0.559984	+	0.828503i	$0.310807\pi$
$314$	22.7733	−	12.6024i	1.28517	−	0.711192i
$315$	22.9821	+	11.1077i	1.29490	+	0.625850i
$316$	9.29275	−	14.8248i	0.522758	−	0.833958i
$317$	−7.01907	−	12.1574i	−0.394230	−	0.682826i	0.598773	−	0.800919i	$-0.295655\pi$
$317$	−7.01907	−	12.1574i	−0.394230	−	0.682826i	−0.993003	+	0.118093i	$0.962322\pi$
$318$	−20.6559	+	6.74874i	−1.15832	+	0.378450i
$319$	−2.55382	+	4.42334i	−0.142986	+	0.247660i
$320$	−20.7495	−	15.2105i	−1.15993	−	0.850292i
$321$	−3.93835	+	4.55200i	−0.219817	+	0.254068i
$322$	10.9276	−	5.07152i	0.608970	−	0.282625i
$323$	1.29305			0.0719470
$324$	−12.6062	−	12.8485i	−0.700343	−	0.713806i
$325$	−6.60465			−0.366360
$326$	−7.10570	+	11.8069i	−0.393549	+	0.653926i
$327$	24.2951	+	21.0199i	1.34352	+	1.16241i
$328$	−28.2566	−	18.4355i	−1.56021	−	1.01793i
$329$	21.9496	−	10.6755i	1.21012	−	0.588560i
$330$	−1.20748	−	3.69573i	−0.0664694	−	0.203443i
$331$	1.69065	−	0.976098i	0.0929266	−	0.0536512i	−0.452817	−	0.891604i	$-0.649581\pi$
$331$	1.69065	−	0.976098i	0.0929266	−	0.0536512i	0.545743	+	0.837952i	$0.316247\pi$
$332$	−21.5853	−	13.5305i	−1.18465	−	0.742585i
$333$	−7.94472	+	1.15446i	−0.435368	+	0.0632638i
$334$	19.3644	−	10.7159i	1.05957	−	0.586349i
$335$	7.76951	+	13.4572i	0.424493	+	0.735244i
$336$	−17.9991	+	3.46881i	−0.981931	+	0.189239i
$337$	4.87476	−	8.44334i	0.265545	−	0.459938i	−0.702161	−	0.712018i	$-0.747781\pi$
$337$	4.87476	−	8.44334i	0.265545	−	0.459938i	0.967706	+	0.252080i	$0.0811147\pi$
$338$	0.294617	−	16.2205i	0.0160250	−	0.882280i
$339$	−28.9249	+	10.0353i	−1.57098	+	0.545044i
$340$	−0.489992	+	13.4841i	−0.0265735	+	0.731279i
$341$		−	1.80692i		−	0.0978501i
$342$	−1.01222	+	2.41119i	−0.0547345	+	0.130382i
$343$	3.91059	−	18.1027i	0.211152	−	0.977453i
$344$	8.75194	+	17.2672i	0.471873	+	0.930985i
$345$	17.6128	+	3.38088i	0.948241	+	0.182020i
$346$	24.7404	+	0.449366i	1.33005	+	0.0241580i
$347$	−9.23242	+	15.9910i	−0.495622	+	0.858443i	−0.999987	−	0.00504763i	$-0.998393\pi$
$347$	−9.23242	+	15.9910i	−0.495622	+	0.858443i	0.504365	+	0.863491i	$0.331727\pi$
$348$	10.5126	+	34.2722i	0.563535	+	1.83718i
$349$	6.85194	+	11.8679i	0.366776	+	0.635274i	0.989059	−	0.147518i	$-0.0471283\pi$
$349$	6.85194	+	11.8679i	0.366776	+	0.635274i	−0.622284	+	0.782792i	$0.713795\pi$
$350$	19.9095	+	1.77822i	1.06421	+	0.0950500i
$351$	5.70331	−	2.95654i	0.304420	−	0.157808i
$352$	2.28140	+	1.60952i	0.121599	+	0.0857876i
$353$	−10.6263	−	18.4054i	−0.565584	−	0.979619i	−0.996995	−	0.0774642i	$-0.975318\pi$
$353$	−10.6263	−	18.4054i	−0.565584	−	0.979619i	0.431412	−	0.902155i	$-0.358016\pi$
$354$	4.06769	+	0.857689i	0.216195	+	0.0455857i
$355$	14.7511	−	25.5497i	0.782907	−	1.35604i
$356$	−2.91133	−	5.49416i	−0.154300	−	0.291190i
$357$	6.80616	+	6.78940i	0.360220	+	0.359333i
$358$	−27.5220	−	16.5634i	−1.45458	−	0.875404i
$359$		−	15.1208i		−	0.798047i	−0.916941	−	0.399024i	$-0.869349\pi$
$359$		−	15.1208i		−	0.798047i	0.916941	−	0.399024i	$-0.130651\pi$
$360$	−24.7607	−	11.4693i	−1.30501	−	0.604486i
$361$	−18.6201			−0.980005
$362$	−16.8633	−	10.1487i	−0.886315	−	0.533406i
$363$	−6.10670	−	17.6014i	−0.320518	−	0.923833i
$364$	0.700218	−	6.50438i	0.0367014	−	0.340922i
$365$	−13.5194	+	23.4163i	−0.707639	+	1.22567i
$366$	14.1667	+	12.7140i	0.740504	+	0.664571i
$367$	−1.35811	+	0.784105i	−0.0708928	+	0.0409300i	−0.535027	−	0.844835i	$-0.679699\pi$
$367$	−1.35811	+	0.784105i	−0.0708928	+	0.0409300i	0.464135	+	0.885765i	$0.346365\pi$
$368$	−11.5914	+	5.61293i	−0.604244	+	0.292594i
$369$	−33.2419	−	13.2502i	−1.73050	−	0.689776i
$370$	−10.6489	+	5.89295i	−0.553611	+	0.306360i
$371$	−1.66316	+	23.4125i	−0.0863468	+	1.21552i
$372$	−9.28297	−	8.64053i	−0.481300	−	0.447991i
$373$	−9.19088	−	5.30636i	−0.475886	−	0.274753i	0.242814	−	0.970073i	$-0.421929\pi$
$373$	−9.19088	−	5.30636i	−0.475886	−	0.274753i	−0.718700	+	0.695320i	$0.755263\pi$
$374$	0.0265920	−	1.46406i	0.00137504	−	0.0757047i
$375$	1.44152	+	1.24719i	0.0744399	+	0.0644048i
$376$	−23.2744	+	11.7967i	−1.20028	+	0.608367i
$377$	−12.7940			−0.658925
$378$	−17.9884	+	7.37681i	−0.925224	+	0.379422i
$379$			17.0400i			0.875286i	0.899149	+	0.437643i	$0.144187\pi$
$379$			17.0400i			0.875286i	−0.899149	+	0.437643i	$0.855813\pi$
$380$	−0.143965	+	3.96179i	−0.00738526	+	0.203236i
$381$	−4.15996	+	4.80814i	−0.213121	+	0.246328i
$382$	17.7303	+	0.322039i	0.907162	+	0.0164770i
$383$	−17.4046	+	30.1457i	−0.889336	+	1.54037i	−0.0486738	+	0.998815i	$0.515499\pi$
$383$	−17.4046	+	30.1457i	−0.889336	+	1.54037i	−0.840662	+	0.541560i	$0.817834\pi$
$384$	19.1783	−	4.02402i	0.978689	−	0.205350i
$385$	−4.18895	−	0.297570i	−0.213489	−	0.0151656i
$386$	−15.4233	+	8.53498i	−0.785023	+	0.434419i
$387$	12.7168	+	16.1208i	0.646430	+	0.819467i
$388$	11.4628	+	7.18532i	0.581934	+	0.364779i
$389$	−12.3818	−	21.4459i	−0.627781	−	1.08735i	−0.987996	−	0.154479i	$-0.950630\pi$
$389$	−12.3818	−	21.4459i	−0.627781	−	1.08735i	0.360215	−	0.932869i	$-0.382703\pi$
$390$	6.50482	−	7.24805i	0.329384	−	0.367019i
$391$	5.84954	+	3.37723i	0.295824	+	0.170794i
$392$	−3.86201	+	19.4187i	−0.195061	+	0.980791i
$393$	−15.1052	+	5.24066i	−0.761956	+	0.264356i
$394$	11.2698	+	6.78245i	0.567765	+	0.341695i
$395$		−	28.1338i		−	1.41557i
$396$	2.70926	+	1.19568i	0.136146	+	0.0600851i
$397$	−1.44372			−0.0724584			−0.0362292	−	0.999344i	$-0.511535\pi$
$397$	−1.44372			−0.0724584			−0.0362292	+	0.999344i	$0.511535\pi$
$398$	−10.2364	+	17.0089i	−0.513104	+	0.852580i
$399$	1.99973	+	1.99480i	0.100112	+	0.0998651i
$400$	−21.3125	−	1.55097i	−1.06562	−	0.0775486i
$401$	−13.0297	−	7.52271i	−0.650673	−	0.375666i	0.138041	−	0.990427i	$-0.455919\pi$
$401$	−13.0297	−	7.52271i	−0.650673	−	0.375666i	−0.788714	+	0.614760i	$0.789253\pi$
$402$	−11.5810	−	2.44190i	−0.577608	−	0.121791i
$403$	3.91973	−	2.26305i	0.195255	−	0.112731i
$404$	14.3750	+	9.01080i	0.715181	+	0.448304i
$405$	−28.1479	−	6.73917i	−1.39868	−	0.334872i
$406$	38.5670	+	3.44463i	1.91405	+	0.170954i
$407$	1.14385	−	0.660400i	0.0566984	−	0.0327348i
$408$	−7.39438	−	7.13762i	−0.366076	−	0.353365i
$409$	−20.9120	−	12.0736i	−1.03403	−	0.596999i	−0.115895	−	0.993261i	$-0.536974\pi$
$409$	−20.9120	−	12.0736i	−1.03403	−	0.596999i	−0.918137	+	0.396263i	$0.870307\pi$
$410$	−54.2417	−	0.985204i	−2.67881	−	0.0486558i
$411$	−3.19815	+	16.6609i	−0.157753	+	0.821820i
$412$	0.774141	−	21.3037i	0.0381392	−	1.04956i
$413$	2.51501	−	3.71978i	0.123755	−	0.183038i
$414$	−10.8768	+	8.26407i	−0.534563	+	0.406157i
$415$	−40.9637			−2.01083
$416$	−0.634194	+	6.96484i	−0.0310939	+	0.341479i
$417$	−5.57178	−	16.0596i	−0.272851	−	0.786441i
$418$	0.00781304	−	0.430157i	0.000382148	−	0.0210397i
$419$	31.3362	+	18.0920i	1.53088	+	0.883851i	0.999322	+	0.0368263i	$0.0117248\pi$
$419$	31.3362	+	18.0920i	1.53088	+	0.883851i	0.531553	+	0.847025i	$0.321609\pi$
$420$	−21.5600	+	20.0976i	−1.05202	+	0.980663i
$421$	7.12076	−	4.11117i	0.347044	−	0.200366i	−0.316338	−	0.948646i	$-0.602453\pi$
$421$	7.12076	−	4.11117i	0.347044	−	0.200366i	0.663383	+	0.748280i	$0.269120\pi$
$422$	7.70477	+	13.9230i	0.375062	+	0.677761i
$423$	−21.7291	+	17.1409i	−1.05651	+	0.833417i
$424$	1.36643	−	25.0549i	0.0663599	−	1.21677i
$425$	5.60356	+	9.70564i	0.271812	+	0.470793i
$426$	6.97875	+	21.3599i	0.338122	+	1.03489i
$427$	18.4895	−	8.99267i	0.894770	−	0.435186i
$428$	−3.25434	−	6.14148i	−0.157304	−	0.296859i
$429$	−0.691520	+	0.799268i	−0.0333869	+	0.0385890i
$430$	26.6704	+	16.0509i	1.28616	+	0.774044i
$431$			0.873329i			0.0420668i	0.999779	+	0.0210334i	$0.00669563\pi$
$431$			0.873329i			0.0420668i	−0.999779	+	0.0210334i	$0.993304\pi$
$432$	19.0982	−	8.20110i	0.918863	−	0.394576i
$433$		−	15.5486i		−	0.747219i	−0.927586	−	0.373609i	$-0.878120\pi$
$433$		−	15.5486i		−	0.747219i	0.927586	−	0.373609i	$-0.121880\pi$
$434$	−12.4252	+	5.76655i	−0.596427	+	0.276803i
$435$	43.5918	+	37.7153i	2.09007	+	1.80831i
$436$	−32.7786	+	17.3692i	−1.56981	+	0.831833i
$437$	1.71866	+	0.992269i	0.0822147	+	0.0474667i
$438$	−6.39604	−	19.5764i	−0.305615	−	0.935396i
$439$	26.5747	−	15.3429i	1.26834	−	0.732279i	0.293669	−	0.955907i	$-0.405124\pi$
$439$	26.5747	−	15.3429i	1.26834	−	0.732279i	0.974674	+	0.223629i	$0.0717903\pi$
$440$	4.48280	+	0.244481i	0.213709	+	0.0116552i
$441$	0.0517715	+	20.9999i	0.00246531	+	0.999997i
$442$	3.20927	−	1.77596i	0.152649	−	0.0844737i
$443$	2.22951	+	3.86162i	0.105927	+	0.183471i	0.914117	−	0.405451i	$-0.132886\pi$
$443$	2.22951	+	3.86162i	0.105927	+	0.183471i	−0.808190	+	0.588923i	$0.799552\pi$
$444$	2.07700	−	9.03444i	0.0985700	−	0.428756i
$445$	−8.65859	−	4.99904i	−0.410457	−	0.236977i
$446$	19.2683	+	0.349974i	0.912379	+	0.0165717i
$447$	−4.51321	−	13.0085i	−0.213467	−	0.615279i
$448$	3.78695	−	20.8245i	0.178917	−	0.983864i
$449$		−	4.23980i		−	0.200089i	−0.994983	−	0.100044i	$-0.968102\pi$
$449$		−	4.23980i		−	0.200089i	0.994983	−	0.100044i	$-0.0318985\pi$
$450$	−22.4850	+	2.85139i	−1.05995	+	0.134416i
$451$	5.88743			0.277228
$452$	1.28381	−	35.3293i	0.0603854	−	1.66175i
$453$	34.8296	+	6.68575i	1.63644	+	0.314124i
$454$	−18.9357	−	0.343934i	−0.888698	−	0.0161416i
$455$	−4.60089	−	9.45973i	−0.215693	−	0.443479i
$456$	−2.17255	−	2.09711i	−0.101739	−	0.0982064i
$457$	14.9318	+	25.8627i	0.698482	+	1.20981i	0.968993	+	0.247090i	$0.0794743\pi$
$457$	14.9318	+	25.8627i	0.698482	+	1.20981i	−0.270510	+	0.962717i	$0.587192\pi$
$458$	15.8974	−	8.79735i	0.742835	−	0.411073i
$459$	−9.18350	−	5.87270i	−0.428649	−	0.274114i
$460$	−10.9988	+	17.5465i	−0.512824	+	0.818110i
$461$	−6.75128	+	3.89785i	−0.314438	+	0.181541i	−0.648911	−	0.760864i	$-0.724775\pi$
$461$	−6.75128	+	3.89785i	−0.314438	+	0.181541i	0.334473	+	0.942406i	$0.391442\pi$
$462$	2.29975	−	2.22318i	0.106994	−	0.103432i
$463$	0.554768	−	0.960886i	0.0257822	−	0.0446562i	−0.852846	−	0.522162i	$-0.825126\pi$
$463$	0.554768	−	0.960886i	0.0257822	−	0.0446562i	0.878629	+	0.477506i	$0.158459\pi$
$464$	−41.2848	−	3.00442i	−1.91660	−	0.139477i
$465$	−20.0265	−	3.84421i	−0.928709	−	0.178271i
$466$	−4.41741	+	7.34003i	−0.204632	+	0.340020i
$467$		−	10.7643i		−	0.498114i	−0.968489	−	0.249057i	$-0.919879\pi$
$467$		−	10.7643i		−	0.498114i	0.968489	−	0.249057i	$-0.0801206\pi$
$468$	0.799418	+	7.37469i	0.0369531	+	0.340895i
$469$	−7.16041	+	10.5905i	−0.330637	+	0.489023i
$470$	−21.6349	+	35.9489i	−0.997945	+	1.65820i
$471$	10.4487	+	30.1162i	0.481448	+	1.38768i
$472$	−2.62294	+	4.02026i	−0.120731	+	0.185047i
$473$	−2.92550	−	1.68904i	−0.134515	−	0.0776621i
$474$	15.9480	+	14.3127i	0.732518	+	0.657404i
$475$	1.64639	+	2.85163i	0.0755415	+	0.130842i
$476$	−10.1524	+	4.48950i	−0.465333	+	0.205776i
$477$	−3.82715	−	26.3376i	−0.175233	−	1.20592i
$478$	−18.9079	−	34.1678i	−0.864828	−	1.56280i
$479$	9.72434	+	16.8431i	0.444317	+	0.769579i	0.998004	−	0.0631456i	$-0.0201132\pi$
$479$	9.72434	+	16.8431i	0.444317	+	0.769579i	−0.553688	+	0.832724i	$0.686780\pi$
$480$	22.6924	−	21.8611i	1.03576	−	0.997819i
$481$	2.86520	+	1.65422i	0.130642	+	0.0754260i
$482$	11.9343	+	0.216766i	0.543593	+	0.00987340i
$483$	3.83634	+	14.2471i	0.174559	+	0.648267i
$484$	21.4986	+	0.781225i	0.977209	+	0.0355102i
$485$	21.7536			0.987778
$486$	18.1400	−	12.5275i	0.822848	−	0.568261i
$487$	13.8015			0.625406			0.312703	−	0.949851i	$-0.398766\pi$
$487$	13.8015			0.625406			0.312703	+	0.949851i	$0.398766\pi$
$488$	−19.6055	+	9.93710i	−0.887498	+	0.449831i
$489$	−12.7633	−	11.0427i	−0.577175	−	0.499367i
$490$	11.3223	+	29.7547i	0.511488	+	1.34418i
$491$	5.04365	−	8.73586i	0.227617	−	0.394244i	−0.729485	−	0.683997i	$-0.760240\pi$
$491$	5.04365	−	8.73586i	0.227617	−	0.394244i	0.957101	+	0.289754i	$0.0935734\pi$
$492$	28.1532	−	30.2464i	1.26924	−	1.36362i
$493$	10.8548	+	18.8010i	0.488874	+	0.846754i
$494$	0.942920	−	0.521797i	0.0424240	−	0.0234768i
$495$	4.71230	−	0.684749i	0.211802	−	0.0307772i
$496$	13.1800	−	6.38216i	0.591797	−	0.286567i
$497$	24.2105	+	1.71984i	1.08599	+	0.0771455i
$498$	20.8397	−	23.2208i	0.933851	−	1.04055i
$499$	11.1712	+	6.44969i	0.500092	+	0.288728i	0.728751	−	0.684778i	$-0.240101\pi$
$499$	11.1712	+	6.44969i	0.500092	+	0.288728i	−0.228660	+	0.973506i	$0.573434\pi$
$500$	−1.94488	+	1.03058i	−0.0869775	+	0.0460889i
$501$	8.88460	+	25.6082i	0.396935	+	1.14409i
$502$	−12.3500	+	20.5210i	−0.551208	+	0.915896i
$503$	−24.3743			−1.08680			−0.543398	−	0.839476i	$-0.682862\pi$
$503$	−24.3743			−1.08680			−0.543398	+	0.839476i	$0.682862\pi$
$504$	−0.424268	−	22.4459i	−0.0188984	−	0.999821i
$505$	27.2802			1.21395
$506$	1.15885	−	1.92556i	0.0515170	−	0.0856014i
$507$	19.5130	+	3.74564i	0.866604	+	0.166350i
$508$	−3.43745	−	6.48705i	−0.152512	−	0.287816i
$509$	25.9076	+	14.9577i	1.14833	+	0.662990i	0.948480	−	0.316836i	$-0.102620\pi$
$509$	25.9076	+	14.9577i	1.14833	+	0.662990i	0.199853	+	0.979826i	$0.435954\pi$
$510$	−16.1700	−	3.40950i	−0.716018	−	0.150975i
$511$	−22.1890	−	1.57624i	−0.981583	−	0.0697287i
$512$	−3.68203	+	22.3258i	−0.162724	+	0.986672i
$513$	−2.69822	−	1.72547i	−0.119129	−	0.0761812i
$514$	−31.7522	+	17.5711i	−1.40053	+	0.775030i
$515$	−17.1391	−	29.6857i	−0.755238	−	1.30811i
$516$	−22.6669	+	6.95281i	−0.997854	+	0.306080i
$517$	2.27665	−	3.94327i	0.100127	−	0.173425i
$518$	−8.19164	−	5.75800i	−0.359920	−	0.252992i
$519$	−5.71305	+	29.7623i	−0.250775	+	1.30642i
$520$	5.08408	+	10.0307i	0.222952	+	0.439874i
$521$	35.5073			1.55560			0.777801	−	0.628511i	$-0.216335\pi$
$521$	35.5073			1.55560			0.777801	+	0.628511i	$0.216335\pi$
$522$	−43.5561	+	5.52349i	−1.90640	+	0.241757i
$523$	17.1968			0.751964			0.375982	−	0.926627i	$-0.377305\pi$
$523$	17.1968			0.751964			0.375982	+	0.926627i	$0.377305\pi$
$524$	0.670433	−	18.4497i	0.0292880	−	0.805980i
$525$	−6.30702	+	23.6547i	−0.275261	+	1.03238i
$526$	−2.07405	−	0.0376714i	−0.0904329	−	0.00164255i
$527$	−6.65119	−	3.84007i	−0.289730	−	0.167276i
$528$	−2.41915	+	2.41676i	−0.105280	+	0.105176i
$529$	−6.31670	−	10.9408i	−0.274639	−	0.475689i
$530$	−19.5358	−	35.3024i	−0.848579	−	1.53344i
$531$	−1.88519	+	4.72955i	−0.0818104	+	0.205245i
$532$	−2.98288	+	1.31907i	−0.129324	+	0.0571888i
$533$	7.37365	+	12.7715i	0.319388	+	0.553197i
$534$	7.23871	−	2.36505i	0.313250	−	0.102346i
$535$	−9.67874	−	5.58802i	−0.418448	−	0.241591i
$536$	7.46771	−	11.4460i	0.322556	−	0.494391i
$537$	25.7405	−	29.7513i	1.11079	−	1.28386i
$538$	−9.08495	+	15.0957i	−0.391680	+	0.650821i
$539$	−1.28716	−	3.20622i	−0.0554420	−	0.138101i
$540$	19.0160	−	27.4837i	0.818316	−	1.18271i
$541$		−	3.97660i		−	0.170967i	−0.996340	−	0.0854837i	$-0.972756\pi$
$541$		−	3.97660i		−	0.170967i	0.996340	−	0.0854837i	$-0.0272436\pi$
$542$	2.75842	−	4.58343i	0.118484	−	0.196875i
$543$	15.7717	−	18.2292i	0.676830	−	0.782290i
$544$	10.7730	−	4.97719i	0.461889	−	0.213395i
$545$	−29.8246	+	51.6578i	−1.27755	+	2.21278i
$546$	7.70301	+	2.20443i	0.329658	+	0.0943409i
$547$	−32.2039	+	18.5929i	−1.37694	+	0.794975i	−0.991790	−	0.127879i	$-0.959183\pi$
$547$	−32.2039	+	18.5929i	−1.37694	+	0.794975i	−0.385148	+	0.922855i	$0.625850\pi$
$548$	−16.5982	−	10.4044i	−0.709038	−	0.444453i
$549$	−18.3038	+	14.4388i	−0.781189	+	0.616234i
$550$	3.26263	−	1.80549i	0.139119	−	0.0769863i
$551$	3.18925	+	5.52395i	0.135867	+	0.235328i
$552$	−4.35096	−	15.1614i	−0.185189	−	0.645311i
$553$	20.8145	−	10.1234i	0.885121	−	0.430493i
$554$	32.5703	+	0.591581i	1.38378	+	0.0251339i
$555$	−4.88586	−	14.0825i	−0.207393	−	0.597771i
$556$	19.6154	+	0.712793i	0.831879	+	0.0302292i
$557$	14.3781			0.609219			0.304609	−	0.952477i	$-0.401474\pi$
$557$	14.3781			0.609219			0.304609	+	0.952477i	$0.401474\pi$
$558$	12.3674	−	9.39663i	0.523552	−	0.397791i
$559$		−	8.46168i		−	0.357891i
$560$	−12.6251	−	31.6059i	−0.533509	−	1.33559i
$561$	1.76124	+	0.338080i	0.0743596	+	0.0142737i
$562$	7.57563	+	0.137598i	0.319559	+	0.00580421i
$563$	12.3589	+	7.13542i	0.520866	+	0.300722i	0.737289	−	0.675578i	$-0.236106\pi$
$563$	12.3589	+	7.13542i	0.520866	+	0.300722i	−0.216423	+	0.976300i	$0.569439\pi$
$564$	−9.37165	−	30.5526i	−0.394618	−	1.28649i
$565$	−28.4229	−	49.2299i	−1.19576	−	2.07112i
$566$	20.0314	−	11.0851i	0.841984	−	0.465941i
$567$	−5.14261	−	23.2498i	−0.215969	−	0.976400i
$568$	−25.9088	−	1.41301i	−1.08711	−	0.0592884i
$569$	1.46509	−	0.845872i	0.0614199	−	0.0354608i	−0.468976	−	0.883211i	$-0.655377\pi$
$569$	1.46509	−	0.845872i	0.0614199	−	0.0354608i	0.530395	+	0.847750i	$0.322043\pi$
$570$	−4.75092	−	1.00175i	−0.198994	−	0.0419587i
$571$	31.8072	+	18.3639i	1.33109	+	0.768506i	0.985467	−	0.169867i	$-0.0543339\pi$
$571$	31.8072	+	18.3639i	1.33109	+	0.768506i	0.345624	+	0.938373i	$0.387667\pi$
$572$	−0.571416	−	1.07836i	−0.0238921	−	0.0450884i
$573$	−4.09428	+	21.3293i	−0.171041	+	0.891044i
$574$	−18.7890	−	40.4846i	−0.784237	−	1.68979i
$575$			17.2004i			0.717307i
$576$	0.847834	+	23.9850i	0.0353264	+	0.999376i
$577$			12.7862i			0.532296i	0.963932	+	0.266148i	$0.0857509\pi$
$577$			12.7862i			0.532296i	−0.963932	+	0.266148i	$0.914249\pi$
$578$	15.2663	+	9.18764i	0.634995	+	0.382155i
$579$	−7.07638	−	20.3963i	−0.294084	−	0.847641i
$580$	−58.8133	+	31.1648i	−2.44209	+	1.29405i
$581$	−14.7400	−	30.3065i	−0.611520	−	1.25733i
$582$	−11.0668	+	12.3313i	−0.458735	+	0.511149i
$583$	2.18930	+	3.79198i	0.0906715	+	0.157048i
$584$	23.7455	+	1.29502i	0.982596	+	0.0535884i
$585$	7.38729	+	9.36473i	0.305427	+	0.387184i
$586$	−18.0532	−	32.6233i	−0.745771	−	1.34765i
$587$	3.91439	−	2.25997i	0.161564	−	0.0932790i	−0.417038	−	0.908889i	$-0.636932\pi$
$587$	3.91439	−	2.25997i	0.161564	−	0.0932790i	0.578602	+	0.815610i	$0.303598\pi$
$588$	−22.6269	−	8.71911i	−0.933118	−	0.359570i
$589$	−1.95420	−	1.12826i	−0.0805212	−	0.0464889i
$590$	−0.140172	+	7.71735i	−0.00577078	+	0.317718i
$591$	−10.5403	+	12.1826i	−0.433571	+	0.501127i
$592$	8.85721	+	6.01082i	0.364029	+	0.247043i
$593$	10.0420			0.412374			0.206187	−	0.978513i	$-0.433895\pi$
$593$	10.0420			0.412374			0.206187	+	0.978513i	$0.433895\pi$
$594$	−2.00916	+	3.01959i	−0.0824368	+	0.123895i
$595$	−9.99771	+	14.7869i	−0.409866	+	0.606206i
$596$	15.8887	+	0.577371i	0.650828	+	0.0236500i
$597$	−18.3866	−	15.9079i	−0.752514	−	0.651069i
$598$	5.62847	+	0.102231i	0.230165	+	0.00418054i
$599$	9.25533	+	5.34356i	0.378162	+	0.218332i	0.677018	−	0.735966i	$-0.263272\pi$
$599$	9.25533	+	5.34356i	0.378162	+	0.218332i	−0.298856	+	0.954298i	$0.596605\pi$
$600$	6.32601	−	25.3953i	0.258258	−	1.03676i
$601$	23.2117	−	13.4013i	0.946824	−	0.546649i	0.0547314	−	0.998501i	$-0.482570\pi$
$601$	23.2117	−	13.4013i	0.946824	−	0.546649i	0.892093	+	0.451852i	$0.149236\pi$
$602$	−2.27820	+	25.5074i	−0.0928527	+	1.03960i
$603$	5.36728	−	13.4654i	0.218573	−	0.548353i
$604$	−21.7504	+	34.6985i	−0.885012	+	1.41186i
$605$	29.9574	−	17.2959i	1.21794	−	0.703179i
$606$	−13.8784	+	15.4642i	−0.563773	+	0.628188i
$607$	10.1334	+	5.85053i	0.411303	+	0.237466i	0.691349	−	0.722521i	$-0.257017\pi$
$607$	10.1334	+	5.85053i	0.411303	+	0.237466i	−0.280047	+	0.959986i	$0.590350\pi$
$608$	3.16523	−	1.46235i	0.128367	−	0.0593063i
$609$	−12.2174	+	45.8220i	−0.495076	+	1.85680i
$610$	−18.2245	+	30.2820i	−0.737887	+	1.22608i
$611$	11.4054			0.461415
$612$	10.1590	−	7.43163i	0.410652	−	0.300406i
$613$			17.6380i			0.712390i	0.934412	+	0.356195i	$0.115926\pi$
$613$			17.6380i			0.712390i	−0.934412	+	0.356195i	$0.884074\pi$
$614$	−2.32775	−	1.40090i	−0.0939403	−	0.0565356i
$615$	12.5255	−	65.2519i	0.505076	−	2.63121i
$616$	1.43218	+	3.40451i	0.0577040	+	0.137172i
$617$	39.8120	+	22.9855i	1.60277	+	0.925361i	0.990930	+	0.134382i	$0.0429049\pi$
$617$	39.8120	+	22.9855i	1.60277	+	0.925361i	0.611843	+	0.790979i	$0.290428\pi$
$618$	25.5470	+	5.38670i	1.02765	+	0.216685i
$619$	17.6754	+	30.6147i	0.710434	+	1.23051i	0.964694	+	0.263372i	$0.0848347\pi$
$619$	17.6754	+	30.6147i	0.710434	+	1.23051i	−0.254260	+	0.967136i	$0.581832\pi$
$620$	12.5062	−	19.9512i	0.502261	−	0.801258i
$621$	−7.69967	−	14.8531i	−0.308977	−	0.596033i
$622$	−17.2100	+	9.52374i	−0.690058	+	0.381867i
$623$	0.582842	−	8.20476i	0.0233511	−	0.328717i
$624$	−8.27248	−	2.22099i	−0.331164	−	0.0889107i
$625$	11.5859	−	20.0674i	0.463437	−	0.802696i
$626$	−3.53768	−	0.0642556i	−0.141394	−	0.00256817i
$627$	0.517472	+	0.0993318i	0.0206659	+	0.00396693i
$628$	−36.7844	−	1.33669i	−1.46786	−	0.0533397i
$629$		−	5.61393i		−	0.223842i
$630$	−19.7473	−	30.2186i	−0.786753	−	1.20394i
$631$	9.77067			0.388964			0.194482	−	0.980906i	$-0.437697\pi$
$631$	9.77067			0.388964			0.194482	+	0.980906i	$0.437697\pi$
$632$	−22.0707	+	11.1866i	−0.877927	+	0.444980i
$633$	−18.4123	+	6.38805i	−0.731824	+	0.253902i
$634$	−0.360533	+	19.8496i	−0.0143186	+	0.788330i
$635$	−10.2233	−	5.90245i	−0.405701	−	0.234232i
$636$	29.9502	+	6.88548i	1.18760	+	0.273027i
$637$	5.34311	−	6.80782i	0.211702	−	0.269736i
$638$	6.32011	−	3.49745i	0.250215	−	0.138465i
$639$	−27.2353	+	3.95759i	−1.07741	+	0.156560i
$640$	14.0503	+	33.5618i	0.555385	+	1.32665i
$641$	11.2510	−	6.49577i	0.444388	−	0.256568i	−0.261069	−	0.965320i	$-0.584075\pi$
$641$	11.2510	−	6.49577i	0.444388	−	0.256568i	0.705457	+	0.708753i	$0.250742\pi$
$642$	8.09157	−	2.64370i	0.319349	−	0.104338i
$643$	18.4059	−	31.8799i	0.725856	−	1.25722i	−0.232764	−	0.972533i	$-0.574777\pi$
$643$	18.4059	−	31.8799i	0.725856	−	1.25722i	0.958621	−	0.284687i	$-0.0918896\pi$
$644$	−16.9393	−	1.82357i	−0.667501	−	0.0718587i
$645$	−24.9441	+	28.8307i	−0.982171	+	1.13521i
$646$	−1.56679	−	0.942930i	−0.0616444	−	0.0370991i
$647$	−31.4885			−1.23794			−0.618971	−	0.785414i	$-0.712450\pi$
$647$	−31.4885			−1.23794			−0.618971	+	0.785414i	$0.712450\pi$
$648$	5.90539	+	24.7614i	0.231986	+	0.972719i
$649$		−	0.837646i		−	0.0328805i
$650$	8.00287	+	4.81632i	0.313898	+	0.188912i
$651$	−4.36209	−	16.1997i	−0.170964	−	0.634914i
$652$	17.2200	−	9.12478i	0.674387	−	0.357354i
$653$	13.2863	−	23.0125i	0.519932	−	0.900548i	−0.479800	−	0.877378i	$-0.659291\pi$
$653$	13.2863	−	23.0125i	0.519932	−	0.900548i	0.999732	−	0.0231701i	$-0.00737593\pi$
$654$	−14.1100	−	43.1867i	−0.551746	−	1.68873i
$655$	−14.8430	−	25.7089i	−0.579966	−	1.00453i
$656$	20.7948	+	42.9439i	0.811901	+	1.67668i
$657$	24.9612	−	3.62714i	0.973828	−	0.141508i
$658$	−34.3813	−	3.07078i	−1.34032	−	0.119711i
$659$	−6.65804	−	11.5321i	−0.259360	−	0.449225i	0.706710	−	0.707503i	$-0.250178\pi$
$659$	−6.65804	−	11.5321i	−0.259360	−	0.449225i	−0.966071	+	0.258278i	$0.916845\pi$
$660$	−1.23194	+	5.35866i	−0.0479533	+	0.208585i
$661$	−16.1983	+	28.0563i	−0.630041	+	1.09126i	0.357502	+	0.933912i	$0.383628\pi$
$661$	−16.1983	+	28.0563i	−0.630041	+	1.09126i	−0.987543	+	0.157350i	$0.949705\pi$
$662$	−2.76037	−	0.0501371i	−0.107285	−	0.00194864i
$663$	1.47245	+	4.24406i	0.0571853	+	0.164826i
$664$	16.2881	+	32.1357i	0.632100	+	1.24711i
$665$	−2.93744	+	4.34457i	−0.113909	+	0.168475i
$666$	10.4685	+	4.39469i	0.405646	+	0.170291i
$667$			33.3193i			1.29013i
$668$	−31.2782	−	1.13660i	−1.21019	−	0.0439764i
$669$	−4.44942	+	23.1794i	−0.172025	+	0.896168i
$670$	0.399080	−	21.9719i	0.0154178	−	0.848847i
$671$	1.91776	−	3.32166i	0.0740345	−	0.128231i
$672$	24.3391	+	8.92235i	0.938901	+	0.344187i
$673$	−10.2253	−	17.7108i	−0.394157	−	0.682700i	0.598836	−	0.800871i	$-0.295630\pi$
$673$	−10.2253	−	17.7108i	−0.394157	−	0.682700i	−0.992993	+	0.118172i	$0.962297\pi$
$674$	−12.0639	+	6.67597i	−0.464684	+	0.257149i
$675$	1.25838	−	27.7304i	0.0484349	−	1.06734i
$676$	−12.1855	+	19.4396i	−0.468673	+	0.747676i
$677$	−9.29119	+	5.36427i	−0.357090	+	0.206166i	−0.667803	−	0.744338i	$-0.732765\pi$
$677$	−9.29119	+	5.36427i	−0.357090	+	0.206166i	0.310714	+	0.950504i	$0.399432\pi$
$678$	42.3664	+	8.93313i	1.62707	+	0.343075i
$679$	7.82762	+	16.0941i	0.300396	+	0.617635i
$680$	10.4268	−	15.9814i	0.399849	−	0.612860i
$681$	4.37263	−	22.7794i	0.167560	−	0.872908i
$682$	−1.31766	+	2.18945i	−0.0504559	+	0.0838382i
$683$	15.1330			0.579047			0.289524	−	0.957171i	$-0.406503\pi$
$683$	15.1330			0.579047			0.289524	+	0.957171i	$0.406503\pi$
$684$	2.98482	−	2.18350i	0.114128	−	0.0834881i
$685$	−31.4993			−1.20353
$686$	−17.9395	+	19.0833i	−0.684934	+	0.728605i
$687$	7.29390	+	21.0233i	0.278280	+	0.802088i
$688$	1.98706	−	27.3049i	0.0757558	−	1.04099i
$689$	−5.48393	+	9.49844i	−0.208921	+	0.361862i
$690$	−18.8760	−	16.9404i	−0.718597	−	0.644911i
$691$	−18.6437	−	32.2918i	−0.709240	−	1.22844i	−0.965139	−	0.261736i	$-0.915705\pi$
$691$	−18.6437	−	32.2918i	−0.709240	−	1.22844i	0.255899	−	0.966703i	$-0.417628\pi$
$692$	−29.6503	−	18.5860i	−1.12714	−	0.706534i
$693$	2.20224	+	3.23994i	0.0836561	+	0.123075i
$694$	22.8481	−	12.6438i	0.867302	−	0.479951i
$695$	27.3333	−	15.7809i	1.03681	−	0.598602i
$696$	12.2542	−	49.1938i	0.464495	−	1.86469i
$697$	12.5120	−	21.6714i	0.473925	−	0.820862i
$698$	0.351949	−	19.3770i	0.0133215	−	0.733430i
$699$	−7.93456	−	6.86491i	−0.300112	−	0.259655i
$700$	−22.8276	−	16.6733i	−0.862802	−	0.630191i
$701$	13.5709			0.512565			0.256283	−	0.966602i	$-0.417502\pi$
$701$	13.5709			0.512565			0.256283	+	0.966602i	$0.417502\pi$
$702$	−9.06670	−	0.576593i	−0.342201	−	0.0217621i
$703$		−	1.64944i		−	0.0622097i
$704$	−1.59066	−	3.61393i	−0.0599504	−	0.136205i
$705$	−38.8607	−	33.6219i	−1.46358	−	1.26628i
$706$	−0.545821	+	30.0509i	−0.0205422	+	1.13098i
$707$	9.81628	+	20.1829i	0.369179	+	0.759057i
$708$	−4.30337	−	4.00555i	−0.161731	−	0.150538i
$709$	−4.70427	+	2.71601i	−0.176673	+	0.102002i	−0.585728	−	0.810507i	$-0.699191\pi$
$709$	−4.70427	+	2.71601i	−0.176673	+	0.102002i	0.409056	+	0.912509i	$0.365858\pi$
$710$	−36.5056	+	20.2016i	−1.37003	+	0.758152i
$711$	−20.6054	+	16.2544i	−0.772764	+	0.609588i
$712$	−0.478857	+	8.78031i	−0.0179459	+	0.329056i
$713$	−5.89365	−	10.2081i	−0.220719	−	0.382296i
$714$	−3.29599	−	13.1900i	−0.123349	−	0.493623i
$715$	−1.69945	−	0.981179i	−0.0635559	−	0.0366940i
$716$	21.2699	+	40.1399i	0.794894	+	1.50010i
$717$	45.1848	−	15.6766i	1.68746	−	0.585454i
$718$	−11.0266	+	18.3219i	−0.411509	+	0.683769i
$719$	1.65833			0.0618453			0.0309227	−	0.999522i	$-0.490155\pi$
$719$	1.65833			0.0618453			0.0309227	+	0.999522i	$0.490155\pi$
$720$	21.6388	+	31.9537i	0.806432	+	1.19084i
$721$	15.7954	−	23.3620i	0.588253	−	0.870046i
$722$	22.5620	+	13.5784i	0.839670	+	0.505334i
$723$	−2.75587	+	14.3568i	−0.102492	+	0.533935i
$724$	13.0325	+	24.5945i	0.484349	+	0.914047i
$725$	−27.6419	+	47.8772i	−1.02660	+	1.77812i
$726$	−5.43599	+	25.7808i	−0.201749	+	0.956816i
$727$	17.3309	−	10.0060i	0.642768	−	0.371102i	−0.142912	−	0.989735i	$-0.545647\pi$
$727$	17.3309	−	10.0060i	0.642768	−	0.371102i	0.785680	+	0.618633i	$0.212313\pi$
$728$	−5.59166	+	7.37075i	−0.207241	+	0.273178i
$729$	11.3267	+	24.5093i	0.419508	+	0.907752i
$730$	33.4574	−	18.5148i	1.23831	−	0.685264i
$731$	−12.4346	+	7.17910i	−0.459909	+	0.265529i
$732$	−7.89433	−	25.7364i	−0.291783	−	0.951243i
$733$	16.3663	−	28.3472i	0.604502	−	1.04703i	−0.387628	−	0.921816i	$-0.626705\pi$
$733$	16.3663	−	28.3472i	0.604502	−	1.04703i	0.992130	−	0.125213i	$-0.0399613\pi$
$734$	2.21742	+	0.0402755i	0.0818464	+	0.00148659i
$735$	−38.2738	+	7.44475i	−1.41175	+	0.274604i
$736$	18.1384	+	1.65162i	0.668592	+	0.0608797i
$737$			2.38484i			0.0878467i
$738$	30.6168	+	40.2963i	1.12702	+	1.48333i
$739$		−	46.6752i		−	1.71698i	−0.512834	−	0.858488i	$-0.671404\pi$
$739$		−	46.6752i		−	1.71698i	0.512834	−	0.858488i	$-0.328596\pi$
$740$	17.2006	+	0.625044i	0.632308	+	0.0229771i
$741$	0.432623	+	1.24695i	0.0158928	+	0.0458080i
$742$	19.0884	−	27.1562i	0.700758	−	0.996935i
$743$	18.4268	+	10.6387i	0.676015	+	0.390298i	0.798352	−	0.602191i	$-0.205705\pi$
$743$	18.4268	+	10.6387i	0.676015	+	0.390298i	−0.122337	+	0.992489i	$0.539039\pi$
$744$	4.94724	+	17.2392i	0.181375	+	0.632019i
$745$	22.1403	−	12.7827i	0.811157	−	0.468322i
$746$	7.26704	+	13.1320i	0.266065	+	0.480797i
$747$	23.6669	+	30.0022i	0.865928	+	1.09772i
$748$	−1.09986	+	1.75461i	−0.0402149	+	0.0641549i
$749$	0.651512	−	9.17144i	0.0238057	−	0.335117i
$750$	−0.837203	−	2.56243i	−0.0305703	−	0.0935667i
$751$	2.30840	−	3.99826i	0.0842346	−	0.145899i	−0.820830	−	0.571172i	$-0.806489\pi$
$751$	2.30840	−	3.99826i	0.0842346	−	0.145899i	0.905065	+	0.425274i	$0.139822\pi$
$752$	36.8041	+	2.67834i	1.34211	+	0.0976691i
$753$	−22.1831	−	19.1927i	−0.808398	−	0.699419i
$754$	15.5025	+	9.32979i	0.564568	+	0.339771i
$755$			65.8495i			2.39651i
$756$	27.1760	+	4.17922i	0.988381	+	0.151997i
$757$		−	0.841130i		−	0.0305714i	−0.999883	−	0.0152857i	$-0.995134\pi$
$757$		−	0.841130i		−	0.0305714i	0.999883	−	0.0152857i	$-0.00486578\pi$
$758$	12.4261	−	20.6474i	0.451337	−	0.749947i
$759$	2.08152	+	1.80092i	0.0755545	+	0.0653691i
$760$	3.06351	−	4.69552i	0.111125	−	0.170325i
$761$	−0.912813	+	1.58104i	−0.0330895	+	0.0573126i	−0.882096	−	0.471070i	$-0.843868\pi$
$761$	−0.912813	+	1.58104i	−0.0330895	+	0.0573126i	0.849006	+	0.528383i	$0.177201\pi$
$762$	8.54687	−	2.79245i	0.309621	−	0.101160i
$763$	−48.9502	−	3.47728i	−1.77212	−	0.125886i
$764$	−21.2490	−	13.3197i	−0.768762	−	0.481891i
$765$	7.49406	−	18.8010i	0.270948	−	0.679752i
$766$	43.0725	−	23.8356i	1.55627	−	0.861216i
$767$	1.81710	−	1.04910i	0.0656115	−	0.0378808i
$768$	−26.1728	−	9.10951i	−0.944431	−	0.328711i
$769$	14.3832	+	8.30416i	0.518672	+	0.299456i	0.736391	−	0.676556i	$-0.236528\pi$
$769$	14.3832	+	8.30416i	0.518672	+	0.299456i	−0.217719	+	0.976012i	$0.569862\pi$
$770$	4.85876	+	3.41528i	0.175098	+	0.123078i
$771$	−14.5683	−	41.9903i	−0.524664	−	1.51224i
$772$	24.9124	+	0.905276i	0.896616	+	0.0325816i
$773$			22.2490i			0.800242i	0.916462	+	0.400121i	$0.131032\pi$
$773$			22.2490i			0.800242i	−0.916462	+	0.400121i	$0.868968\pi$
$774$	−3.65312	−	28.8071i	−0.131309	−	1.03545i
$775$		−	19.5577i		−	0.702532i
$776$	−8.64969	−	17.0655i	−0.310506	−	0.612615i
$777$	8.66071	−	8.68208i	0.310701	−	0.311468i
$778$	−0.635988	+	35.0152i	−0.0228013	+	1.25535i
$779$	3.67616	−	6.36730i	0.131712	−	0.228132i
$780$	−13.1674	+	4.03895i	−0.471469	+	0.144618i
$781$	3.92122	−	2.26392i	0.140312	−	0.0810093i
$782$	−4.62511	−	8.35786i	−0.165394	−	0.298877i
$783$	2.43762	−	53.7171i	0.0871136	−	1.91969i
$784$	18.8403	−	20.7133i	0.672868	−	0.739762i
$785$	−51.2576	+	29.5936i	−1.82946	+	1.05624i
$786$	22.1246	+	4.66507i	0.789159	+	0.166398i
$787$	−6.09416	+	10.5554i	−0.217233	+	0.376259i	−0.953961	−	0.299930i	$-0.903037\pi$
$787$	−6.09416	+	10.5554i	−0.217233	+	0.376259i	0.736728	+	0.676190i	$0.236370\pi$
$788$	−8.70967	−	16.4366i	−0.310269	−	0.585530i
$789$	0.478939	−	2.49505i	0.0170507	−	0.0888262i
$790$	−20.5161	+	34.0898i	−0.729930	+	1.21286i
$791$	26.1947	−	38.7428i	0.931375	−	1.37754i
$792$	−2.41089	−	3.42449i	−0.0856673	−	0.121684i
$793$	9.60753			0.341173
$794$	1.74936	+	1.05281i	0.0620825	+	0.0373628i
$795$	46.6852	−	16.1972i	1.65575	−	0.574454i
$796$	24.8069	−	13.1450i	0.879257	−	0.465914i
$797$	−4.34529	−	2.50875i	−0.153918	−	0.0888646i	0.421063	−	0.907031i	$-0.361657\pi$
$797$	−4.34529	−	2.50875i	−0.153918	−	0.0888646i	−0.574981	+	0.818167i	$0.694991\pi$
$798$	−0.968399	−	3.87537i	−0.0342809	−	0.137187i
$799$	−9.67667	−	16.7605i	−0.342336	−	0.592943i
$800$	24.6934	+	17.4211i	0.873042	+	0.615927i
$801$	1.34120	+	9.22983i	0.0473889	+	0.326120i
$802$	10.3023	+	18.6170i	0.363788	+	0.657388i
$803$	−3.59380	+	2.07488i	−0.126823	+	0.0732211i
$804$	12.2520	+	11.4041i	0.432095	+	0.402192i
$805$	−24.6359	+	11.9820i	−0.868300	+	0.422311i
$806$	−6.39983	−	0.116241i	−0.225424	−	0.00409443i
$807$	−16.3184	−	14.1185i	−0.574435	−	0.496996i
$808$	−10.8472	−	21.4011i	−0.381603	−	0.752887i
$809$			23.2066i			0.815900i	0.913004	+	0.407950i	$0.133756\pi$
$809$			23.2066i			0.815900i	−0.913004	+	0.407950i	$0.866244\pi$
$810$	29.1924	+	28.6922i	1.02572	+	1.00814i
$811$	−44.8266			−1.57407			−0.787037	−	0.616906i	$-0.788386\pi$
$811$	−44.8266			−1.57407			−0.787037	+	0.616906i	$0.788386\pi$
$812$	−44.2198	−	32.2982i	−1.55181	−	1.13344i
$813$	4.95468	+	4.28674i	0.173768	+	0.150343i
$814$	−1.86759	−	0.0339213i	−0.0654588	−	0.00118894i
$815$	15.6682	−	27.1381i	0.548832	−	0.950605i
$816$	3.75481	+	14.0409i	0.131445	+	0.491529i
$817$	−3.65342	+	2.10930i	−0.127817	+	0.0737951i
$818$	16.5347	+	29.8792i	0.578122	+	1.04470i
$819$	−4.27020	+	8.83512i	−0.149213	+	0.308724i
$820$	65.0063	+	40.7486i	2.27012	+	1.42300i
$821$	5.45960	+	9.45630i	0.190541	+	0.330027i	0.945430	−	0.325826i	$-0.105642\pi$
$821$	5.45960	+	9.45630i	0.190541	+	0.330027i	−0.754888	+	0.655853i	$0.772309\pi$
$822$	16.0248	−	17.8558i	0.558930	−	0.622793i
$823$	−4.82596	+	8.35882i	−0.168223	+	0.291370i	−0.937795	−	0.347190i	$-0.887136\pi$
$823$	−4.82596	+	8.35882i	−0.168223	+	0.291370i	0.769572	+	0.638560i	$0.220469\pi$
$824$	−16.4733	+	25.2491i	−0.573876	+	0.879596i
$825$	1.49693	+	4.31463i	0.0521166	+	0.150216i
$826$	−5.76002	+	2.67324i	−0.200417	+	0.0930140i
$827$	−21.3458			−0.742268			−0.371134	−	0.928579i	$-0.621031\pi$
$827$	−21.3458			−0.742268			−0.371134	+	0.928579i	$0.621031\pi$
$828$	19.2058	−	2.08191i	0.667448	−	0.0723515i
$829$	4.56891			0.158685			0.0793423	−	0.996847i	$-0.474718\pi$
$829$	4.56891			0.158685			0.0793423	+	0.996847i	$0.474718\pi$
$830$	49.6358	+	29.8721i	1.72288	+	1.03687i
$831$	−7.52112	+	39.1816i	−0.260905	+	1.35919i
$832$	5.84743	−	7.97683i	0.202723	−	0.276547i
$833$	−14.5374	−	2.07587i	−0.503692	−	0.0719245i
$834$	−4.95982	+	23.5225i	−0.171745	+	0.814519i
$835$	−43.5849	+	25.1637i	−1.50832	+	0.870827i
$836$	−0.323151	+	0.515525i	−0.0111764	+	0.0178298i
$837$	8.75488	+	16.8886i	0.302613	+	0.583755i
$838$	−24.7769	−	44.7735i	−0.855904	−	1.54667i
$839$	12.0550	+	20.8799i	0.416185	+	0.720854i	0.995552	−	0.0942132i	$-0.0300335\pi$
$839$	12.0550	+	20.8799i	0.416185	+	0.720854i	−0.579367	+	0.815067i	$0.696700\pi$
$840$	40.7801	−	8.63009i	1.40705	−	0.297767i
$841$	−39.0457	+	67.6292i	−1.34640	+	2.33204i
$842$	−11.6262	−	0.211170i	−0.400666	−	0.00727739i
$843$	−1.74936	+	9.11336i	−0.0602512	+	0.313881i
$844$	0.817218	−	22.4891i	0.0281298	−	0.774107i
$845$			36.8916i			1.26911i
$846$	38.8289	−	4.92401i	1.33496	−	0.169291i
$847$	23.5758	+	15.9400i	0.810073	+	0.547704i
$848$	−19.9265	+	29.3626i	−0.684280	+	1.00832i
$849$	9.19067	+	26.4903i	0.315423	+	0.909146i
$850$	0.287826	−	15.8466i	0.00987234	−	0.543535i
$851$	4.30807	−	7.46180i	0.147679	−	0.255787i
$852$	7.12015	−	30.9710i	0.243932	−	1.06105i
$853$	−15.3558	−	26.5970i	−0.525772	−	0.910664i	−0.999549	−	0.0300192i	$-0.990443\pi$
$853$	−15.3558	−	26.5970i	−0.525772	−	0.910664i	0.473777	−	0.880645i	$-0.342890\pi$
$854$	−28.9615	−	2.58671i	−0.991043	−	0.0885154i
$855$	2.20184	−	5.52395i	0.0753013	−	0.188915i
$856$	−0.535276	+	9.81480i	−0.0182954	+	0.335463i
$857$	−2.09337	−	3.62583i	−0.0715082	−	0.123856i	0.828054	−	0.560648i	$-0.189448\pi$
$857$	−2.09337	−	3.62583i	−0.0715082	−	0.123856i	−0.899563	+	0.436792i	$0.856115\pi$
$858$	1.42077	−	0.464196i	0.0485042	−	0.0158474i
$859$	−27.7782	+	48.1133i	−0.947781	+	1.64161i	−0.197696	+	0.980263i	$0.563346\pi$
$859$	−27.7782	+	48.1133i	−0.947781	+	1.64161i	−0.750085	+	0.661342i	$0.769987\pi$
$860$	−20.6118	−	38.8978i	−0.702855	−	1.32640i
$861$	52.7829	−	14.2129i	1.79884	−	0.484374i
$862$	0.636859	−	1.05821i	0.0216915	−	0.0360429i
$863$			22.5233i			0.766703i	0.923603	+	0.383351i	$0.125230\pi$
$863$			22.5233i			0.766703i	−0.923603	+	0.383351i	$0.874770\pi$
$864$	−29.1218	−	3.98974i	−0.990745	−	0.135734i
$865$	−56.2692			−1.91321
$866$	−11.3385	+	18.8403i	−0.385299	+	0.640219i
$867$	−14.2781	+	16.5029i	−0.484911	+	0.560466i
$868$	19.2607	+	2.07348i	0.653752	+	0.0703786i
$869$	2.15891	−	3.73934i	0.0732360	−	0.126849i
$870$	−25.3171	−	77.4882i	−0.858330	−	2.62710i
$871$	−5.17340	+	2.98687i	−0.175294	+	0.101206i
$872$	52.3840	+	2.85690i	1.77395	+	0.0967468i
$873$	−12.5682	−	15.9325i	−0.425369	−	0.539233i
$874$	−1.35891	−	2.45564i	−0.0459658	−	0.0830631i
$875$	−2.90440	−	0.206320i	−0.0981867	−	0.00697489i
$876$	−6.52564	+	28.3849i	−0.220481	+	0.959038i
$877$	−11.4496	−	6.61041i	−0.386624	−	0.223218i	0.294072	−	0.955783i	$-0.404989\pi$
$877$	−11.4496	−	6.61041i	−0.386624	−	0.223218i	−0.680697	+	0.732566i	$0.738323\pi$
$878$	−43.3892	−	0.788088i	−1.46432	−	0.0265967i
$879$	43.1422	−	14.9680i	1.45515	−	0.504856i
$880$	−5.25353	−	3.56524i	−0.177096	−	0.120184i
$881$	−57.9543			−1.95253			−0.976266	−	0.216576i	$-0.930511\pi$
$881$	−57.9543			−1.95253			−0.976266	+	0.216576i	$0.930511\pi$
$882$	15.2511	−	25.4834i	0.513531	−	0.858071i
$883$		−	39.5992i		−	1.33262i	−0.745676	−	0.666309i	$-0.767873\pi$
$883$		−	39.5992i		−	1.33262i	0.745676	−	0.666309i	$-0.232127\pi$
$884$	−5.18376	−	0.188370i	−0.174349	−	0.00633556i
$885$	−9.28385	−	1.78209i	−0.312073	−	0.0599042i
$886$	0.114518	−	6.30496i	0.00384732	−	0.211819i
$887$	−8.36889	+	14.4953i	−0.281000	+	0.486706i	−0.971631	−	0.236501i	$-0.923999\pi$
$887$	−8.36889	+	14.4953i	−0.281000	+	0.486706i	0.690631	+	0.723207i	$0.257333\pi$
$888$	−9.10491	+	9.43244i	−0.305541	+	0.316532i
$889$	0.688171	−	9.68750i	0.0230805	−	0.324908i
$890$	6.84617	+	12.3715i	0.229484	+	0.414692i
$891$	−3.22406	−	3.05571i	−0.108010	−	0.102370i
$892$	−23.0922	−	14.4751i	−0.773184	−	0.484662i
$893$	−2.84312	−	4.92442i	−0.0951412	−	0.164789i
$894$	−4.01752	+	19.0535i	−0.134366	+	0.637246i
$895$	63.2589	+	36.5226i	2.11451	+	1.22081i
$896$	−19.7745	+	22.4715i	−0.660621	+	0.750720i
$897$	−1.29973	+	6.77096i	−0.0433966	+	0.226076i
$898$	−3.09180	+	5.13738i	−0.103175	+	0.171436i
$899$		−	37.8855i		−	1.26355i
$900$	29.3244	+	12.9417i	0.977482	+	0.431391i
$901$	18.6108			0.620016
$902$	−7.13381	−	4.29330i	−0.237530	−	0.142951i
$903$	−30.3057	−	8.08035i	−1.00851	−	0.268897i
$904$	−27.3189	+	41.8724i	−0.908612	+	1.39266i
$905$	38.7600	+	22.3781i	1.28843	+	0.743874i
$906$	−37.3277	−	33.5000i	−1.24013	−	1.11296i
$907$	16.1312	−	9.31334i	0.535627	−	0.309244i	−0.207678	−	0.978197i	$-0.566591\pi$
$907$	16.1312	−	9.31334i	0.535627	−	0.309244i	0.743305	+	0.668953i	$0.233257\pi$
$908$	22.6937	+	14.2253i	0.753115	+	0.472083i
$909$	−15.7612	−	19.9802i	−0.522767	−	0.662703i
$910$	−1.32343	+	14.8175i	−0.0438713	+	0.491195i
$911$	7.45660	−	4.30507i	0.247048	−	0.142633i	−0.371364	−	0.928487i	$-0.621110\pi$
$911$	7.45660	−	4.30507i	0.247048	−	0.142633i	0.618412	+	0.785854i	$0.287776\pi$
$912$	1.10320	+	4.12537i	0.0365308	+	0.136605i
$913$	−5.44460	−	3.14344i	−0.180190	−	0.104033i
$914$	0.766972	−	42.2267i	0.0253692	−	1.39673i
$915$	−32.7348	−	28.3219i	−1.08218	−	0.936293i
$916$	−25.6782	−	0.933104i	−0.848430	−	0.0308306i
$917$	13.6794	−	20.2323i	0.451734	−	0.668130i
$918$	6.84511	+	13.8129i	0.225922	+	0.455892i
$919$	29.5287			0.974063			0.487031	−	0.873384i	$-0.338080\pi$
$919$	29.5287			0.974063			0.487031	+	0.873384i	$0.338080\pi$
$920$	26.1228	−	13.2404i	0.861243	−	0.436524i
$921$	2.17708	−	2.51629i	0.0717371	−	0.0829147i
$922$	11.0230	+	0.200213i	0.363022	+	0.00659365i
$923$	9.82217	+	5.67083i	0.323301	+	0.186658i
$924$	−4.40783	+	1.01678i	−0.145007	+	0.0334495i
$925$	12.3807	−	7.14802i	0.407076	−	0.235025i
$926$	−1.37292	+	0.759753i	−0.0451170	+	0.0249670i
$927$	−11.8399	+	29.7038i	−0.388874	+	0.975602i
$928$	47.8340	+	33.7467i	1.57023	+	1.10779i
$929$	19.8564	+	34.3924i	0.651469	+	1.12838i	0.982767	+	0.184851i	$0.0591803\pi$
$929$	19.8564	+	34.3924i	0.651469	+	1.12838i	−0.331298	+	0.943526i	$0.607486\pi$
$930$	21.4629	+	19.2620i	0.703795	+	0.631627i
$931$	−4.27126	−	0.609913i	−0.139985	−	0.0199891i
$932$	10.7052	−	5.67261i	0.350659	−	0.185812i
$933$	−7.89616	−	22.7592i	−0.258509	−	0.745101i
$934$	−7.84969	+	13.0432i	−0.256850	+	0.426785i
$935$			3.32983i			0.108897i
$936$	4.40920	−	9.51888i	0.144119	−	0.311134i
$937$			11.8678i			0.387703i	0.981031	+	0.193852i	$0.0620981\pi$
$937$			11.8678i			0.387703i	−0.981031	+	0.193852i	$0.937902\pi$
$938$	16.3992	−	7.61091i	0.535453	−	0.248505i
$939$	0.816919	−	4.25577i	0.0266592	−	0.138882i
$940$	52.4301	−	27.7825i	1.71008	−	0.906164i
$941$	−15.6445	−	9.03238i	−0.509997	−	0.294447i	0.222835	−	0.974856i	$-0.428469\pi$
$941$	−15.6445	−	9.03238i	−0.509997	−	0.294447i	−0.732833	+	0.680409i	$0.761802\pi$
$942$	9.30106	−	44.1114i	0.303045	−	1.43723i
$943$	33.2608	−	19.2031i	1.08312	−	0.625339i
$944$	6.10993	−	2.95862i	0.198861	−	0.0962949i
$945$	40.5944	−	17.5150i	1.32053	−	0.569763i
$946$	2.31313	+	4.17998i	0.0752065	+	0.135903i
$947$	11.8357	+	20.5001i	0.384610	+	0.666163i	0.991715	−	0.128458i	$-0.0410027\pi$
$947$	11.8357	+	20.5001i	0.384610	+	0.666163i	−0.607105	+	0.794621i	$0.707669\pi$
$948$	−8.88700	−	28.9725i	−0.288636	−	0.940984i
$949$	−9.00204	−	5.19733i	−0.292219	−	0.168712i
$950$	0.0845665	−	4.65592i	0.00274370	−	0.151058i
$951$	−23.8788	−	4.58367i	−0.774323	−	0.148636i
$952$	15.5755	+	1.96350i	0.504806	+	0.0636374i
$953$		−	33.5962i		−	1.08829i	−0.838992	−	0.544144i	$-0.816855\pi$
$953$		−	33.5962i		−	1.08829i	0.838992	−	0.544144i	$-0.183145\pi$
$954$	−14.5689	+	34.7042i	−0.471684	+	1.12359i
$955$	−40.3255			−1.30490
$956$	−2.00550	+	55.1894i	−0.0648624	+	1.78495i
$957$	2.89974	+	8.35795i	0.0937354	+	0.270174i
$958$	0.499489	−	27.5001i	0.0161378	−	0.888486i
$959$	−11.3344	−	23.3044i	−0.366008	−	0.752537i
$960$	−43.4382	+	9.94114i	−1.40196	+	0.320849i
$961$	−8.79865	−	15.2397i	−0.283828	−	0.491604i
$962$	−2.26545	−	4.09381i	−0.0730411	−	0.131990i
$963$	1.49922	+	10.3173i	0.0483115	+	0.332470i
$964$	−14.3028	−	8.96554i	−0.460661	−	0.288761i
$965$	34.7143	−	20.0423i	1.11749	−	0.645186i
$966$	5.74097	−	20.0609i	0.184713	−	0.645448i
$967$	−18.7566	+	32.4874i	−0.603172	+	1.04473i	0.389165	+	0.921168i	$0.372764\pi$
$967$	−18.7566	+	32.4874i	−0.603172	+	1.04473i	−0.992337	+	0.123557i	$0.960570\pi$
$968$	−25.4802	−	16.6241i	−0.818965	−	0.534318i
$969$	1.46537	−	1.69369i	0.0470744	−	0.0544093i
$970$	−26.3588	−	15.8634i	−0.846331	−	0.509343i
$971$			24.0035i			0.770308i	0.922852	+	0.385154i	$0.125852\pi$
$971$			24.0035i			0.770308i	−0.922852	+	0.385154i	$0.874148\pi$
$972$	−31.1158	+	1.95136i	−0.998039	+	0.0625899i
$973$	21.5106	+	14.5437i	0.689600	+	0.466250i
$974$	−16.7233	−	10.0645i	−0.535850	−	0.322487i
$975$	−7.48485	+	8.65109i	−0.239707	+	0.277057i
$976$	31.0024	+	2.25614i	0.992364	+	0.0722172i
$977$	−3.78977	−	2.18803i	−0.121246	−	0.0700011i	0.438151	−	0.898902i	$-0.355634\pi$
$977$	−3.78977	−	2.18803i	−0.121246	−	0.0700011i	−0.559396	+	0.828900i	$0.688967\pi$
$978$	7.41261	+	22.6878i	0.237029	+	0.725477i
$979$	−0.767224	−	1.32887i	−0.0245206	−	0.0424709i
$980$	7.97886	−	44.3104i	0.254875	−	1.41544i
$981$	55.0658	−	8.00168i	1.75812	−	0.255474i
$982$	−12.4819	+	6.90726i	−0.398312	+	0.220420i
$983$	19.2143	+	33.2801i	0.612841	+	1.06147i	0.990759	+	0.135633i	$0.0433066\pi$
$983$	19.2143	+	33.2801i	0.612841	+	1.06147i	−0.377918	+	0.925839i	$0.623360\pi$
$984$	−56.1700	+	16.1195i	−1.79063	+	0.513870i
$985$	−25.9035	−	14.9554i	−0.825353	−	0.476518i
$986$	0.557553	−	30.6968i	0.0177561	−	0.977586i
$987$	10.8915	−	40.8488i	0.346679	−	1.30023i
$988$	−1.52305	−	0.0553452i	−0.0484546	−	0.00176076i
$989$	−22.0366			−0.700725
$990$	−6.20924	−	2.60665i	−0.197343	−	0.0828447i
$991$	23.7148			0.753324			0.376662	−	0.926351i	$-0.377072\pi$
$991$	23.7148			0.753324			0.376662	+	0.926351i	$0.377072\pi$
$992$	−20.6242	−	1.87797i	−0.654820	−	0.0596256i
$993$	0.637423	−	3.32068i	0.0202280	−	0.105379i
$994$	−28.0817	−	19.7390i	−0.890699	−	0.626083i
$995$	22.5714	−	39.0947i	0.715560	−	1.23939i
$996$	−42.1849	+	12.9397i	−1.33668	+	0.410011i
$997$	−10.2164	−	17.6954i	−0.323558	−	0.560418i	0.657662	−	0.753313i	$-0.271546\pi$
$997$	−10.2164	−	17.6954i	−0.323558	−	0.560418i	−0.981219	+	0.192895i	$0.938212\pi$
$998$	−8.83284	−	15.9615i	−0.279599	−	0.505252i
$999$	−7.49134	+	11.7147i	−0.237016	+	0.370636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.16	yes	168
7.6	odd	2	inner	504.2.cc.b.293.15	✓	168
8.5	even	2	inner	504.2.cc.b.293.43	yes	168
9.2	odd	6	inner	504.2.cc.b.461.44	yes	168
56.13	odd	2	inner	504.2.cc.b.293.44	yes	168
63.20	even	6	inner	504.2.cc.b.461.43	yes	168
72.29	odd	6	inner	504.2.cc.b.461.15	yes	168
504.461	even	6	inner	504.2.cc.b.461.16	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.15	✓	168	7.6	odd	2	inner
504.2.cc.b.293.16	yes	168	1.1	even	1	trivial
504.2.cc.b.293.43	yes	168	8.5	even	2	inner
504.2.cc.b.293.44	yes	168	56.13	odd	2	inner
504.2.cc.b.461.15	yes	168	72.29	odd	6	inner
504.2.cc.b.461.16	yes	168	504.461	even	6	inner
504.2.cc.b.461.43	yes	168	63.20	even	6	inner
504.2.cc.b.461.44	yes	168	9.2	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21170 - 0.729232i) q^{2} +(1.13327 - 1.30985i) q^{3} +(0.936442 + 1.76722i) q^{4} +(2.78508 + 1.60797i) q^{5} +(-2.32837 + 0.760729i) q^{6} +(-0.187474 + 2.63910i) q^{7} +(0.154027 - 2.82423i) q^{8} +(-0.431402 - 2.96882i) q^{9} +O(q^{10})\)	\(q+(-1.21170 - 0.729232i) q^{2} +(1.13327 - 1.30985i) q^{3} +(0.936442 + 1.76722i) q^{4} +(2.78508 + 1.60797i) q^{5} +(-2.32837 + 0.760729i) q^{6} +(-0.187474 + 2.63910i) q^{7} +(0.154027 - 2.82423i) q^{8} +(-0.431402 - 2.96882i) q^{9} +(-2.20210 - 3.97934i) q^{10} +(0.246781 + 0.427438i) q^{11} +(3.37603 + 0.776143i) q^{12} +(-0.618157 + 1.07068i) q^{13} +(2.15168 - 3.06109i) q^{14} +(5.26243 - 1.82577i) q^{15} +(-2.24615 + 3.30980i) q^{16} +2.09784 q^{17} +(-1.64223 + 3.91192i) q^{18} +0.616370 q^{19} +(-0.233569 + 6.42762i) q^{20} +(3.24436 + 3.23637i) q^{21} +(0.0126759 - 0.697888i) q^{22} +(2.78836 + 1.60986i) q^{23} +(-3.52476 - 3.40236i) q^{24} +(2.67111 + 4.62649i) q^{25} +(1.52980 - 0.846565i) q^{26} +(-4.37760 - 2.79940i) q^{27} +(-4.83944 + 2.14006i) q^{28} +(5.17425 + 8.96207i) q^{29} +(-7.70791 - 1.62524i) q^{30} +(-3.17049 - 1.83048i) q^{31} +(5.13528 - 2.37253i) q^{32} +(0.839548 + 0.161156i) q^{33} +(-2.54196 - 1.52981i) q^{34} +(-4.76571 + 7.04865i) q^{35} +(4.84258 - 3.54251i) q^{36} -2.67605i q^{37} +(-0.746856 - 0.449476i) q^{38} +(0.701889 + 2.02306i) q^{39} +(4.97024 - 7.61803i) q^{40} +(5.96422 - 10.3303i) q^{41} +(-1.57113 - 6.28741i) q^{42} +(-5.92731 + 3.42214i) q^{43} +(-0.524282 + 0.836389i) q^{44} +(3.57227 - 8.96207i) q^{45} +(-2.20470 - 3.98403i) q^{46} +(-4.61268 - 7.98939i) q^{47} +(1.78984 + 6.69302i) q^{48} +(-6.92971 - 0.989525i) q^{49} +(0.137201 - 7.55378i) q^{50} +(2.37742 - 2.74785i) q^{51} +(-2.47100 - 0.0897922i) q^{52} +8.87141 q^{53} +(3.26293 + 6.58432i) q^{54} +1.58726i q^{55} +(7.42455 + 0.935962i) q^{56} +(0.698513 - 0.807351i) q^{57} +(0.265775 - 14.6326i) q^{58} +(-1.46977 - 0.848571i) q^{59} +(8.15451 + 7.59016i) q^{60} +(-3.88555 - 6.72997i) q^{61} +(2.50684 + 4.53002i) q^{62} +(7.91589 - 0.581938i) q^{63} +(-7.95255 - 0.870014i) q^{64} +(-3.44323 + 1.98795i) q^{65} +(-0.899762 - 0.807498i) q^{66} +(4.18454 + 2.41594i) q^{67} +(1.96451 + 3.70735i) q^{68} +(5.26863 - 1.82792i) q^{69} +(10.9147 - 5.06555i) q^{70} -9.17377i q^{71} +(-8.45108 + 0.761102i) q^{72} +8.40778i q^{73} +(-1.95146 + 3.24258i) q^{74} +(9.08708 + 1.74432i) q^{75} +(0.577195 + 1.08926i) q^{76} +(-1.17432 + 0.571148i) q^{77} +(0.624800 - 2.96319i) q^{78} +(-4.37414 - 7.57623i) q^{79} +(-11.5778 + 5.60632i) q^{80} +(-8.62778 + 2.56151i) q^{81} +(-14.7601 + 8.16798i) q^{82} +(-11.0312 + 6.36888i) q^{83} +(-2.68124 + 8.76419i) q^{84} +(5.84265 + 3.37326i) q^{85} +(9.67767 + 0.175778i) q^{86} +(17.6028 + 3.37895i) q^{87} +(1.24519 - 0.631131i) q^{88} -3.10892 q^{89} +(-10.8640 + 8.25435i) q^{90} +(-2.70974 - 1.83210i) q^{91} +(-0.233845 + 6.43519i) q^{92} +(-5.99068 + 2.07843i) q^{93} +(-0.236929 + 13.0445i) q^{94} +(1.71664 + 0.991101i) q^{95} +(2.71200 - 9.41515i) q^{96} +(5.85807 - 3.38216i) q^{97} +(7.67514 + 6.25237i) q^{98} +(1.16252 - 0.917047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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