LMFDB - Embedded newform 552.2.j.c.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.1
Character	$\chi$	$=$	552.323
Dual form			552.2.j.c.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39813 - 0.212673i) q^{2} +(1.67830 + 0.428159i) q^{3} +(1.90954 + 0.594688i) q^{4} +1.58050 q^{5} +(-2.25542 - 0.955550i) q^{6} -2.65755i q^{7} +(-2.54331 - 1.23756i) q^{8} +(2.63336 + 1.43716i) q^{9} +O(q^{10})$	\(q+(-1.39813 - 0.212673i) q^{2} +(1.67830 + 0.428159i) q^{3} +(1.90954 + 0.594688i) q^{4} +1.58050 q^{5} +(-2.25542 - 0.955550i) q^{6} -2.65755i q^{7} +(-2.54331 - 1.23756i) q^{8} +(2.63336 + 1.43716i) q^{9} +(-2.20975 - 0.336130i) q^{10} -1.71556i q^{11} +(2.95016 + 1.81565i) q^{12} -4.09435i q^{13} +(-0.565187 + 3.71560i) q^{14} +(2.65255 + 0.676707i) q^{15} +(3.29269 + 2.27116i) q^{16} -5.87903i q^{17} +(-3.37614 - 2.56937i) q^{18} -1.13560 q^{19} +(3.01804 + 0.939907i) q^{20} +(1.13785 - 4.46015i) q^{21} +(-0.364852 + 2.39858i) q^{22} -1.00000 q^{23} +(-3.73856 - 3.16593i) q^{24} -2.50201 q^{25} +(-0.870755 + 5.72443i) q^{26} +(3.80423 + 3.53947i) q^{27} +(1.58041 - 5.07469i) q^{28} +3.33103 q^{29} +(-3.56470 - 1.51025i) q^{30} +9.90325i q^{31} +(-4.12060 - 3.87565i) q^{32} +(0.734531 - 2.87922i) q^{33} +(-1.25031 + 8.21965i) q^{34} -4.20026i q^{35} +(4.17385 + 4.31033i) q^{36} +4.56123i q^{37} +(1.58772 + 0.241511i) q^{38} +(1.75303 - 6.87153i) q^{39} +(-4.01972 - 1.95597i) q^{40} +9.73261i q^{41} +(-2.53942 + 5.99388i) q^{42} -6.27544 q^{43} +(1.02022 - 3.27593i) q^{44} +(4.16204 + 2.27143i) q^{45} +(1.39813 + 0.212673i) q^{46} +2.62297 q^{47} +(4.55370 + 5.22148i) q^{48} -0.0625489 q^{49} +(3.49813 + 0.532108i) q^{50} +(2.51716 - 9.86675i) q^{51} +(2.43486 - 7.81832i) q^{52} +8.73434 q^{53} +(-4.56606 - 5.75770i) q^{54} -2.71145i q^{55} +(-3.28887 + 6.75897i) q^{56} +(-1.90588 - 0.486218i) q^{57} +(-4.65721 - 0.708418i) q^{58} -1.29911i q^{59} +(4.66273 + 2.86964i) q^{60} -1.42025i q^{61} +(2.10615 - 13.8460i) q^{62} +(3.81931 - 6.99827i) q^{63} +(4.93690 + 6.29500i) q^{64} -6.47113i q^{65} +(-1.63930 + 3.86931i) q^{66} -8.90196 q^{67} +(3.49619 - 11.2262i) q^{68} +(-1.67830 - 0.428159i) q^{69} +(-0.893280 + 5.87252i) q^{70} +5.40657 q^{71} +(-4.91890 - 6.91408i) q^{72} +8.08970 q^{73} +(0.970048 - 6.37719i) q^{74} +(-4.19911 - 1.07126i) q^{75} +(-2.16848 - 0.675329i) q^{76} -4.55918 q^{77} +(-3.91235 + 9.23448i) q^{78} -4.26010i q^{79} +(5.20411 + 3.58958i) q^{80} +(4.86917 + 7.56909i) q^{81} +(2.06986 - 13.6075i) q^{82} +16.3027i q^{83} +(4.82517 - 7.84017i) q^{84} -9.29183i q^{85} +(8.77388 + 1.33461i) q^{86} +(5.59045 + 1.42621i) q^{87} +(-2.12310 + 4.36320i) q^{88} -7.01980i q^{89} +(-5.33600 - 4.06091i) q^{90} -10.8809 q^{91} +(-1.90954 - 0.594688i) q^{92} +(-4.24016 + 16.6206i) q^{93} +(-3.66726 - 0.557834i) q^{94} -1.79482 q^{95} +(-5.25620 - 8.26876i) q^{96} +14.3922 q^{97} +(0.0874516 + 0.0133024i) q^{98} +(2.46552 - 4.51768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.39813	−	0.212673i	−0.988628	−	0.150382i
$2$	−1.39813	−	0.212673i	−0.988628	−	0.150382i
$3$	1.67830	+	0.428159i	0.968965	+	0.247198i
$3$	1.67830	+	0.428159i	0.968965	+	0.247198i
$4$	1.90954	+	0.594688i	0.954770	+	0.297344i
$5$	1.58050			0.706823			0.353411	−	0.935468i	$-0.385022\pi$
$5$	1.58050			0.706823			0.353411	+	0.935468i	$0.385022\pi$
$6$	−2.25542	−	0.955550i	−0.920772	−	0.390102i
$7$		−	2.65755i		−	1.00446i	−0.864735	−	0.502229i	$-0.832513\pi$
$7$		−	2.65755i		−	1.00446i	0.864735	−	0.502229i	$-0.167487\pi$
$8$	−2.54331	−	1.23756i	−0.899197	−	0.437543i
$9$	2.63336	+	1.43716i	0.877787	+	0.479052i
$10$	−2.20975	−	0.336130i	−0.698785	−	0.106294i
$11$		−	1.71556i		−	0.517260i	−0.965976	−	0.258630i	$-0.916729\pi$
$11$		−	1.71556i		−	0.517260i	0.965976	−	0.258630i	$-0.0832711\pi$
$12$	2.95016	+	1.81565i	0.851636	+	0.524133i
$13$		−	4.09435i		−	1.13557i	−0.823178	−	0.567784i	$-0.807801\pi$
$13$		−	4.09435i		−	1.13557i	0.823178	−	0.567784i	$-0.192199\pi$
$14$	−0.565187	+	3.71560i	−0.151053	+	0.993035i
$15$	2.65255	+	0.676707i	0.684887	+	0.174725i
$16$	3.29269	+	2.27116i	0.823173	+	0.567791i
$17$		−	5.87903i		−	1.42587i	−0.701228	−	0.712937i	$-0.747365\pi$
$17$		−	5.87903i		−	1.42587i	0.701228	−	0.712937i	$-0.252635\pi$
$18$	−3.37614	−	2.56937i	−0.795764	−	0.605607i
$19$	−1.13560			−0.260525			−0.130262	−	0.991480i	$-0.541582\pi$
$19$	−1.13560			−0.260525			−0.130262	+	0.991480i	$0.541582\pi$
$20$	3.01804	+	0.939907i	0.674854	+	0.210170i
$21$	1.13785	−	4.46015i	0.248300	−	0.973285i
$22$	−0.364852	+	2.39858i	−0.0777868	+	0.511378i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−3.73856	−	3.16593i	−0.763131	−	0.646243i
$25$	−2.50201			−0.500401
$26$	−0.870755	+	5.72443i	−0.170769	+	1.12265i
$27$	3.80423	+	3.53947i	0.732124	+	0.681171i
$28$	1.58041	−	5.07469i	0.298670	−	0.959027i
$29$	3.33103			0.618557			0.309278	−	0.950972i	$-0.399913\pi$
$29$	3.33103			0.618557			0.309278	+	0.950972i	$0.399913\pi$
$30$	−3.56470	−	1.51025i	−0.650823	−	0.275733i
$31$			9.90325i			1.77868i	0.457250	+	0.889338i	$0.348835\pi$
$31$			9.90325i			1.77868i	−0.457250	+	0.889338i	$0.651165\pi$
$32$	−4.12060	−	3.87565i	−0.728426	−	0.685124i
$33$	0.734531	−	2.87922i	0.127866	−	0.501207i
$34$	−1.25031	+	8.21965i	−0.214426	+	1.40966i
$35$		−	4.20026i		−	0.709974i
$36$	4.17385	+	4.31033i	0.695642	+	0.718389i
$37$			4.56123i			0.749861i	0.927053	+	0.374931i	$0.122333\pi$
$37$			4.56123i			0.749861i	−0.927053	+	0.374931i	$0.877667\pi$
$38$	1.58772	+	0.241511i	0.257562	+	0.0391783i
$39$	1.75303	−	6.87153i	0.280710	−	1.10033i
$40$	−4.01972	−	1.95597i	−0.635573	−	0.309266i
$41$			9.73261i			1.51998i	0.649936	+	0.759989i	$0.274796\pi$
$41$			9.73261i			1.51998i	−0.649936	+	0.759989i	$0.725204\pi$
$42$	−2.53942	+	5.99388i	−0.391841	+	0.924876i
$43$	−6.27544			−0.956995			−0.478498	−	0.878089i	$-0.658818\pi$
$43$	−6.27544			−0.956995			−0.478498	+	0.878089i	$0.658818\pi$
$44$	1.02022	−	3.27593i	0.153804	−	0.493865i
$45$	4.16204	+	2.27143i	0.620440	+	0.338605i
$46$	1.39813	+	0.212673i	0.206143	+	0.0313569i
$47$	2.62297			0.382600			0.191300	−	0.981532i	$-0.438730\pi$
$47$	2.62297			0.382600			0.191300	+	0.981532i	$0.438730\pi$
$48$	4.55370	+	5.22148i	0.657269	+	0.753656i
$49$	−0.0625489			−0.00893556
$50$	3.49813	+	0.532108i	0.494711	+	0.0752515i
$51$	2.51716	−	9.86675i	0.352473	−	1.38162i
$52$	2.43486	−	7.81832i	0.337654	−	1.08421i
$53$	8.73434			1.19975			0.599877	−	0.800093i	$-0.295216\pi$
$53$	8.73434			1.19975			0.599877	+	0.800093i	$0.295216\pi$
$54$	−4.56606	−	5.75770i	−0.621362	−	0.783523i
$55$		−	2.71145i		−	0.365611i
$56$	−3.28887	+	6.75897i	−0.439494	+	0.903206i
$57$	−1.90588	−	0.486218i	−0.252440	−	0.0644011i
$58$	−4.65721	−	0.708418i	−0.611522	−	0.0930199i
$59$		−	1.29911i		−	0.169130i	−0.996418	−	0.0845649i	$-0.973050\pi$
$59$		−	1.29911i		−	0.169130i	0.996418	−	0.0845649i	$-0.0269500\pi$
$60$	4.66273	+	2.86964i	0.601956	+	0.370469i
$61$		−	1.42025i		−	0.181845i	−0.995858	−	0.0909224i	$-0.971018\pi$
$61$		−	1.42025i		−	0.181845i	0.995858	−	0.0909224i	$-0.0289815\pi$
$62$	2.10615	−	13.8460i	0.267481	−	1.75845i
$63$	3.81931	−	6.99827i	0.481187	−	0.881700i
$64$	4.93690	+	6.29500i	0.617112	+	0.786875i
$65$		−	6.47113i		−	0.802645i
$66$	−1.63930	+	3.86931i	−0.201784	+	0.476279i
$67$	−8.90196			−1.08755			−0.543774	−	0.839232i	$-0.683005\pi$
$67$	−8.90196			−1.08755			−0.543774	+	0.839232i	$0.683005\pi$
$68$	3.49619	−	11.2262i	0.423975	−	1.36138i
$69$	−1.67830	−	0.428159i	−0.202043	−	0.0515443i
$70$	−0.893280	+	5.87252i	−0.106767	+	0.701900i
$71$	5.40657			0.641642			0.320821	−	0.947140i	$-0.396041\pi$
$71$	5.40657			0.641642			0.320821	+	0.947140i	$0.396041\pi$
$72$	−4.91890	−	6.91408i	−0.579698	−	0.814832i
$73$	8.08970			0.946828			0.473414	−	0.880840i	$-0.343022\pi$
$73$	8.08970			0.946828			0.473414	+	0.880840i	$0.343022\pi$
$74$	0.970048	−	6.37719i	0.112766	−	0.741334i
$75$	−4.19911	−	1.07126i	−0.484871	−	0.123698i
$76$	−2.16848	−	0.675329i	−0.248741	−	0.0774655i
$77$	−4.55918			−0.519566
$78$	−3.91235	+	9.23448i	−0.442987	+	1.04560i
$79$		−	4.26010i		−	0.479298i	−0.970860	−	0.239649i	$-0.922968\pi$
$79$		−	4.26010i		−	0.479298i	0.970860	−	0.239649i	$-0.0770324\pi$
$80$	5.20411	+	3.58958i	0.581838	+	0.401327i
$81$	4.86917	+	7.56909i	0.541019	+	0.841010i
$82$	2.06986	−	13.6075i	0.228578	−	1.50269i
$83$			16.3027i			1.78946i	0.446611	+	0.894728i	$0.352631\pi$
$83$			16.3027i			1.78946i	−0.446611	+	0.894728i	$0.647369\pi$
$84$	4.82517	−	7.84017i	0.526469	−	0.855433i
$85$		−	9.29183i		−	1.00784i
$86$	8.77388	+	1.33461i	0.946112	+	0.143915i
$87$	5.59045	+	1.42621i	0.599360	+	0.152906i
$88$	−2.12310	+	4.36320i	−0.226324	+	0.465119i
$89$		−	7.01980i		−	0.744097i	−0.928213	−	0.372049i	$-0.878655\pi$
$89$		−	7.01980i		−	0.744097i	0.928213	−	0.372049i	$-0.121345\pi$
$90$	−5.33600	−	4.06091i	−0.562464	−	0.428057i
$91$	−10.8809			−1.14063
$92$	−1.90954	−	0.594688i	−0.199083	−	0.0620005i
$93$	−4.24016	+	16.6206i	−0.439685	+	1.72348i
$94$	−3.66726	−	0.557834i	−0.378249	−	0.0575362i
$95$	−1.79482			−0.184145
$96$	−5.25620	−	8.26876i	−0.536458	−	0.843927i
$97$	14.3922			1.46130			0.730652	−	0.682750i	$-0.239216\pi$
$97$	14.3922			1.46130			0.730652	+	0.682750i	$0.239216\pi$
$98$	0.0874516	+	0.0133024i	0.00883394	+	0.00134375i
$99$	2.46552	−	4.51768i	0.247794	−	0.454044i
$100$	−4.77768	−	1.48791i	−0.477768	−	0.148791i
$101$	−9.52905			−0.948176			−0.474088	−	0.880477i	$-0.657222\pi$
$101$	−9.52905			−0.948176			−0.474088	+	0.880477i	$0.657222\pi$
$102$	−5.61770	+	13.2597i	−0.556236	+	1.31290i
$103$			3.33299i			0.328409i	0.986426	+	0.164205i	$0.0525057\pi$
$103$			3.33299i			0.328409i	−0.986426	+	0.164205i	$0.947494\pi$
$104$	−5.06700	+	10.4132i	−0.496860	+	1.02110i
$105$	1.79838	−	7.04929i	0.175504	−	0.687940i
$106$	−12.2117	−	1.85755i	−1.18611	−	0.180422i
$107$		−	0.428651i		−	0.0414393i	−0.999785	−	0.0207196i	$-0.993404\pi$
$107$		−	0.428651i		−	0.0414393i	0.999785	−	0.0207196i	$-0.00659574\pi$
$108$	5.15945	+	9.02109i	0.496468	+	0.868055i
$109$			11.6224i			1.11322i	0.830774	+	0.556610i	$0.187898\pi$
$109$			11.6224i			1.11322i	−0.830774	+	0.556610i	$0.812102\pi$
$110$	−0.576650	+	3.79096i	−0.0549815	+	0.361454i
$111$	−1.95293	+	7.65509i	−0.185364	+	0.726589i
$112$	6.03572	−	8.75048i	0.570322	−	0.826843i
$113$		−	3.34686i		−	0.314846i	−0.987531	−	0.157423i	$-0.949681\pi$
$113$		−	3.34686i		−	0.314846i	0.987531	−	0.157423i	$-0.0503186\pi$
$114$	2.56126	+	1.08512i	0.239884	+	0.101631i
$115$	−1.58050			−0.147383
$116$	6.36074	+	1.98092i	0.590579	+	0.183924i
$117$	5.88421	−	10.7819i	0.543996	−	0.996786i
$118$	−0.276285	+	1.81633i	−0.0254341	+	0.167206i
$119$	−15.6238			−1.43223
$120$	−5.90882	−	5.00377i	−0.539399	−	0.456780i
$121$	8.05686			0.732442
$122$	−0.302049	+	1.98570i	−0.0273462	+	0.179777i
$123$	−4.16710	+	16.3342i	−0.375735	+	1.47281i
$124$	−5.88935	+	18.9107i	−0.528879	+	1.69823i
$125$	−11.8570			−1.06052
$126$	−6.82823	+	8.97224i	−0.608307	+	0.799311i
$127$		−	0.552232i		−	0.0490027i	−0.999700	−	0.0245013i	$-0.992200\pi$
$127$		−	0.552232i		−	0.0490027i	0.999700	−	0.0245013i	$-0.00779980\pi$
$128$	−5.56365	−	9.85118i	−0.491762	−	0.870730i
$129$	−10.5320	−	2.68688i	−0.927295	−	0.236567i
$130$	−1.37623	+	9.04749i	−0.120704	+	0.793518i
$131$			8.06903i			0.704994i	0.935813	+	0.352497i	$0.114667\pi$
$131$			8.06903i			0.704994i	−0.935813	+	0.352497i	$0.885333\pi$
$132$	3.11485	−	5.06116i	0.271113	−	0.440518i
$133$			3.01791i			0.261686i
$134$	12.4461	+	1.89320i	1.07518	+	0.163548i
$135$	6.01260	+	5.59415i	0.517482	+	0.481467i
$136$	−7.27564	+	14.9522i	−0.623881	+	1.28214i
$137$			10.4320i			0.891264i	0.895216	+	0.445632i	$0.147021\pi$
$137$			10.4320i			0.891264i	−0.895216	+	0.445632i	$0.852979\pi$
$138$	2.25542	+	0.955550i	0.191994	+	0.0813418i
$139$	−21.5596			−1.82866			−0.914330	−	0.404970i	$-0.867282\pi$
$139$	−21.5596			−1.82866			−0.914330	+	0.404970i	$0.867282\pi$
$140$	2.49785	−	8.02057i	0.211107	−	0.677862i
$141$	4.40213	+	1.12305i	0.370726	+	0.0945778i
$142$	−7.55909	−	1.14983i	−0.634345	−	0.0964915i
$143$	−7.02409			−0.587384
$144$	5.40683	+	10.7129i	0.450569	+	0.892741i
$145$	5.26470			0.437210
$146$	−11.3105	−	1.72046i	−0.936060	−	0.142386i
$147$	−0.104976	−	0.0267809i	−0.00865824	−	0.00220885i
$148$	−2.71251	+	8.70985i	−0.222967	+	0.715945i
$149$	1.81548			0.148730			0.0743651	−	0.997231i	$-0.476307\pi$
$149$	1.81548			0.148730			0.0743651	+	0.997231i	$0.476307\pi$
$150$	5.64308	+	2.39079i	0.460755	+	0.195207i
$151$			22.0063i			1.79085i	0.445213	+	0.895425i	$0.353128\pi$
$151$			22.0063i			1.79085i	−0.445213	+	0.895425i	$0.646872\pi$
$152$	2.88819	+	1.40537i	0.234263	+	0.113991i
$153$	8.44907	−	15.4816i	0.683067	−	1.25161i
$154$	6.37432	+	0.969611i	0.513658	+	0.0781335i
$155$			15.6521i			1.25721i
$156$	7.43390	−	12.0790i	0.595189	−	0.967091i
$157$		−	18.8420i		−	1.50375i	−0.659304	−	0.751877i	$-0.729149\pi$
$157$		−	18.8420i		−	1.50375i	0.659304	−	0.751877i	$-0.270851\pi$
$158$	−0.906006	+	5.95617i	−0.0720780	+	0.473848i
$159$	14.6588	+	3.73968i	1.16252	+	0.296576i
$160$	−6.51263	−	6.12548i	−0.514868	−	0.484262i
$161$			2.65755i			0.209444i
$162$	−5.19800	−	11.6181i	−0.408393	−	0.912806i
$163$	−21.5250			−1.68597			−0.842986	−	0.537936i	$-0.819204\pi$
$163$	−21.5250			−1.68597			−0.842986	+	0.537936i	$0.819204\pi$
$164$	−5.78787	+	18.5848i	−0.451957	+	1.45123i
$165$	1.16093	−	4.55061i	0.0903783	−	0.354265i
$166$	3.46714	−	22.7933i	0.269102	−	1.76911i
$167$	0.525178			0.0406395			0.0203198	−	0.999794i	$-0.493532\pi$
$167$	0.525178			0.0406395			0.0203198	+	0.999794i	$0.493532\pi$
$168$	−8.41361	+	9.93541i	−0.649124	+	0.766533i
$169$	−3.76368			−0.289514
$170$	−1.97612	+	12.9912i	−0.151561	+	0.996379i
$171$	−2.99045	−	1.63204i	−0.228685	−	0.124805i
$172$	−11.9832	−	3.73193i	−0.913711	−	0.284557i
$173$	−22.1851			−1.68670			−0.843352	−	0.537361i	$-0.819421\pi$
$173$	−22.1851			−1.68670			−0.843352	+	0.537361i	$0.819421\pi$
$174$	−7.51287	−	3.18296i	−0.569549	−	0.241300i
$175$			6.64920i			0.502632i
$176$	3.89631	−	5.64881i	0.293696	−	0.425795i
$177$	0.556226	−	2.18029i	0.0418085	−	0.163881i
$178$	−1.49292	+	9.81460i	−0.111899	+	0.735635i
$179$		−	17.7405i		−	1.32599i	−0.748624	−	0.662995i	$-0.769285\pi$
$179$		−	17.7405i		−	1.32599i	0.748624	−	0.662995i	$-0.230715\pi$
$180$	6.59679	+	6.81250i	0.491695	+	0.507774i
$181$		−	7.72181i		−	0.573958i	−0.957937	−	0.286979i	$-0.907349\pi$
$181$		−	7.72181i		−	0.573958i	0.957937	−	0.286979i	$-0.0926510\pi$
$182$	15.2129	+	2.31407i	1.12766	+	0.171530i
$183$	0.608094	−	2.38361i	0.0449516	−	0.176201i
$184$	2.54331	+	1.23756i	0.187496	+	0.0912341i
$185$			7.20904i			0.530019i
$186$	9.46305	−	22.3360i	0.693865	−	1.63776i
$187$	−10.0858			−0.737548
$188$	5.00867	+	1.55985i	0.365295	+	0.113764i
$189$	9.40630	−	10.1099i	0.684208	−	0.735388i
$190$	2.50940	+	0.381710i	0.182051	+	0.0276921i
$191$	−8.90905			−0.644636			−0.322318	−	0.946631i	$-0.604462\pi$
$191$	−8.90905			−0.644636			−0.322318	+	0.946631i	$0.604462\pi$
$192$	5.59032	+	12.6787i	0.403446	+	0.915003i
$193$	8.47887			0.610322			0.305161	−	0.952301i	$-0.401290\pi$
$193$	8.47887			0.610322			0.305161	+	0.952301i	$0.401290\pi$
$194$	−20.1222	−	3.06082i	−1.44469	−	0.219754i
$195$	2.77067	−	10.8605i	0.198412	−	0.777735i
$196$	−0.119440	−	0.0371971i	−0.00853141	−	0.00265694i
$197$	20.1552			1.43600			0.718000	−	0.696043i	$-0.245058\pi$
$197$	20.1552			1.43600			0.718000	+	0.696043i	$0.245058\pi$
$198$	−4.40791	+	5.79196i	−0.313257	+	0.411617i
$199$		−	19.8749i		−	1.40890i	−0.709756	−	0.704448i	$-0.751195\pi$
$199$		−	19.8749i		−	1.40890i	0.709756	−	0.704448i	$-0.248805\pi$
$200$	6.36339	+	3.09638i	0.449960	+	0.218947i
$201$	−14.9401	−	3.81145i	−1.05380	−	0.268839i
$202$	13.3229	+	2.02657i	0.937393	+	0.142589i
$203$		−	8.85236i		−	0.621314i
$204$	10.6743	−	17.3440i	0.747347	−	1.21433i
$205$			15.3824i			1.07436i
$206$	0.708835	−	4.65996i	0.0493869	−	0.324674i
$207$	−2.63336	−	1.43716i	−0.183031	−	0.0998892i
$208$	9.29893	−	13.4814i	0.644765	−	0.934769i
$209$			1.94819i			0.134759i
$210$	−4.01356	+	9.47336i	−0.276962	+	0.653724i
$211$	8.80678			0.606284			0.303142	−	0.952945i	$-0.401964\pi$
$211$	8.80678			0.606284			0.303142	+	0.952945i	$0.401964\pi$
$212$	16.6786	+	5.19421i	1.14549	+	0.356740i
$213$	9.07383	+	2.31487i	0.621728	+	0.158612i
$214$	−0.0911624	+	0.599311i	−0.00623173	+	0.0409680i
$215$	−9.91836			−0.676426
$216$	−5.29505	−	13.7099i	−0.360282	−	0.932843i
$217$	26.3183			1.78661
$218$	2.47176	−	16.2496i	0.167408	−	1.10056i
$219$	13.5769	+	3.46368i	0.917443	+	0.234054i
$220$	1.61247	−	5.17762i	0.108712	−	0.349075i
$221$	−24.0708			−1.61918
$222$	4.35848	−	10.2875i	0.292522	−	0.690451i
$223$		−	1.51551i		−	0.101486i	−0.998712	−	0.0507429i	$-0.983841\pi$
$223$		−	1.51551i		−	0.101486i	0.998712	−	0.0507429i	$-0.0161589\pi$
$224$	−10.2997	+	10.9507i	−0.688178	+	0.731673i
$225$	−6.58868	−	3.59577i	−0.439246	−	0.239718i
$226$	−0.711785	+	4.67935i	−0.0473472	+	0.311266i
$227$			14.1015i			0.935947i	0.883742	+	0.467974i	$0.155016\pi$
$227$			14.1015i			0.935947i	−0.883742	+	0.467974i	$0.844984\pi$
$228$	−3.35020	−	2.06186i	−0.221872	−	0.136550i
$229$			11.1883i			0.739347i	0.929162	+	0.369673i	$0.120530\pi$
$229$			11.1883i			0.739347i	−0.929162	+	0.369673i	$0.879470\pi$
$230$	2.20975	+	0.336130i	0.145707	+	0.0221637i
$231$	−7.65165	−	1.95205i	−0.503442	−	0.128436i
$232$	−8.47185	−	4.12234i	−0.556204	−	0.270645i
$233$			26.2124i			1.71723i	0.512620	+	0.858616i	$0.328675\pi$
$233$			26.2124i			1.71723i	−0.512620	+	0.858616i	$0.671325\pi$
$234$	−10.5199	+	13.8231i	−0.687708	+	0.903644i
$235$	4.14562			0.270430
$236$	0.772566	−	2.48070i	0.0502897	−	0.161480i
$237$	1.82400	−	7.14971i	0.118481	−	0.464423i
$238$	21.8441	+	3.32275i	1.41594	+	0.215382i
$239$	9.88080			0.639136			0.319568	−	0.947563i	$-0.396462\pi$
$239$	9.88080			0.639136			0.319568	+	0.947563i	$0.396462\pi$
$240$	7.19714	+	8.25257i	0.464573	+	0.532701i
$241$	3.19961			0.206105			0.103053	−	0.994676i	$-0.467139\pi$
$241$	3.19961			0.206105			0.103053	+	0.994676i	$0.467139\pi$
$242$	−11.2645	−	1.71347i	−0.724112	−	0.110146i
$243$	4.93114	+	14.7880i	0.316333	+	0.948648i
$244$	0.844608	−	2.71203i	0.0540705	−	0.173620i
$245$	−0.0988588			−0.00631586
$246$	9.29999	−	21.9511i	0.592946	−	1.39955i
$247$			4.64955i			0.295844i
$248$	12.2559	−	25.1871i	0.778248	−	1.59938i
$249$	−6.98015	+	27.3608i	−0.442349	+	1.73392i
$250$	16.5776	+	2.52165i	1.04846	+	0.159483i
$251$		−	7.35322i		−	0.464131i	−0.972700	−	0.232066i	$-0.925452\pi$
$251$		−	7.35322i		−	0.464131i	0.972700	−	0.232066i	$-0.0745484\pi$
$252$	11.4549	−	11.0922i	0.721592	−	0.698743i
$253$			1.71556i			0.107856i
$254$	−0.117445	+	0.772093i	−0.00736913	+	0.0484454i
$255$	3.97838	−	15.5944i	0.249136	−	0.976562i
$256$	5.68364	+	14.9565i	0.355228	+	0.934780i
$257$		−	16.9673i		−	1.05839i	−0.848499	−	0.529197i	$-0.822493\pi$
$257$		−	16.9673i		−	1.05839i	0.848499	−	0.529197i	$-0.177507\pi$
$258$	14.1538	+	5.99649i	0.881174	+	0.373325i
$259$	12.1217			0.753204
$260$	3.84831	−	12.3569i	0.238662	−	0.766342i
$261$	8.77180	+	4.78720i	0.542961	+	0.296321i
$262$	1.71606	−	11.2816i	0.106019	−	0.696977i
$263$	−30.6514			−1.89005			−0.945025	−	0.326999i	$-0.893963\pi$
$263$	−30.6514			−1.89005			−0.945025	+	0.326999i	$0.893963\pi$
$264$	−5.43134	+	6.41373i	−0.334276	+	0.394738i
$265$	13.8047			0.848013
$266$	0.641827	−	4.21944i	0.0393530	−	0.258710i
$267$	3.00559	−	11.7813i	0.183939	−	0.721004i
$268$	−16.9987	−	5.29389i	−1.03836	−	0.323376i
$269$	−8.58138			−0.523216			−0.261608	−	0.965174i	$-0.584253\pi$
$269$	−8.58138			−0.523216			−0.261608	+	0.965174i	$0.584253\pi$
$270$	−7.21668	−	9.10006i	−0.439193	−	0.553812i
$271$		−	20.8419i		−	1.26605i	−0.774130	−	0.633026i	$-0.781812\pi$
$271$		−	20.8419i		−	1.26605i	0.774130	−	0.633026i	$-0.218188\pi$
$272$	13.3522	−	19.3578i	0.809598	−	1.17374i
$273$	−18.2614	−	4.65876i	−1.10523	−	0.281961i
$274$	2.21860	−	14.5853i	0.134030	−	0.881128i
$275$			4.29234i			0.258838i
$276$	−2.95016	−	1.81565i	−0.177578	−	0.109289i
$277$		−	6.26968i		−	0.376709i	−0.982101	−	0.188354i	$-0.939685\pi$
$277$		−	6.26968i		−	0.376709i	0.982101	−	0.188354i	$-0.0603153\pi$
$278$	30.1431	+	4.58513i	1.80786	+	0.274998i
$279$	−14.2325	+	26.0788i	−0.852078	+	1.56130i
$280$	−5.19807	+	10.6826i	−0.310644	+	0.638407i
$281$		−	27.4596i		−	1.63810i	−0.573720	−	0.819052i	$-0.694500\pi$
$281$		−	27.4596i		−	1.63810i	0.573720	−	0.819052i	$-0.305500\pi$
$282$	−5.91591	−	2.50638i	−0.352287	−	0.149253i
$283$	18.7691			1.11571			0.557854	−	0.829939i	$-0.311625\pi$
$283$	18.7691			1.11571			0.557854	+	0.829939i	$0.311625\pi$
$284$	10.3241	+	3.21522i	0.612621	+	0.190788i
$285$	−3.01225	−	0.768469i	−0.178430	−	0.0455202i
$286$	9.82060	+	1.49383i	0.580704	+	0.0883321i
$287$	25.8649			1.52675
$288$	−5.28112	−	16.1279i	−0.311193	−	0.950347i
$289$	−17.5630			−1.03312
$290$	−7.36075	−	1.11966i	−0.432238	−	0.0657486i
$291$	24.1543	+	6.16214i	1.41595	+	0.361231i
$292$	15.4476	+	4.81085i	0.904003	+	0.281534i
$293$	−13.1444			−0.767903			−0.383951	−	0.923353i	$-0.625437\pi$
$293$	−13.1444			−0.767903			−0.383951	+	0.923353i	$0.625437\pi$
$294$	0.141074	+	0.0597686i	0.00822761	+	0.00348577i
$295$		−	2.05325i		−	0.119545i
$296$	5.64479	−	11.6006i	0.328097	−	0.674273i
$297$	6.07217	−	6.52638i	0.352343	−	0.378699i
$298$	−2.53828	−	0.386103i	−0.147039	−	0.0223664i
$299$			4.09435i			0.236782i
$300$	−7.38131	−	4.54277i	−0.426160	−	0.262277i
$301$			16.6773i			0.961261i
$302$	4.68014	−	30.7677i	0.269312	−	1.77048i
$303$	−15.9926	−	4.07995i	−0.918749	−	0.234387i
$304$	−3.73919	−	2.57914i	−0.214457	−	0.147924i
$305$		−	2.24472i		−	0.128532i
$306$	−15.1054	+	19.8484i	−0.863520	+	1.13466i
$307$	−9.63342			−0.549808			−0.274904	−	0.961472i	$-0.588646\pi$
$307$	−9.63342			−0.549808			−0.274904	+	0.961472i	$0.588646\pi$
$308$	−8.70593	−	2.71129i	−0.496066	−	0.154490i
$309$	−1.42705	+	5.59374i	−0.0811820	+	0.318217i
$310$	3.32878	−	21.8837i	0.189062	−	1.24291i
$311$	−9.61534			−0.545236			−0.272618	−	0.962122i	$-0.587890\pi$
$311$	−9.61534			−0.545236			−0.272618	+	0.962122i	$0.587890\pi$
$312$	−12.9624	+	15.3070i	−0.733853	+	0.866587i
$313$	−3.43956			−0.194416			−0.0972078	−	0.995264i	$-0.530991\pi$
$313$	−3.43956			−0.194416			−0.0972078	+	0.995264i	$0.530991\pi$
$314$	−4.00717	+	26.3436i	−0.226138	+	1.48665i
$315$	6.03643	−	11.0608i	0.340114	−	0.623206i
$316$	2.53343	−	8.13483i	0.142517	−	0.457620i
$317$	−0.105229			−0.00591025			−0.00295512	−	0.999996i	$-0.500941\pi$
$317$	−0.105229			−0.00591025			−0.00295512	+	0.999996i	$0.500941\pi$
$318$	−19.6996	−	8.34609i	−1.10470	−	0.468026i
$319$		−	5.71457i		−	0.319955i
$320$	7.80278	+	9.94928i	0.436189	+	0.556182i
$321$	0.183531	−	0.719404i	0.0102437	−	0.0401532i
$322$	0.565187	−	3.71560i	0.0314966	−	0.207062i
$323$			6.67623i			0.371476i
$324$	4.79663	+	17.3491i	0.266479	+	0.963841i
$325$			10.2441i			0.568240i
$326$	30.0948	+	4.57778i	1.66680	+	0.253540i
$327$	−4.97621	+	19.5058i	−0.275185	+	1.07867i
$328$	12.0447	−	24.7531i	0.665056	−	1.36676i
$329$		−	6.97067i		−	0.384305i
$330$	−2.59092	+	6.11546i	−0.142626	+	0.336645i
$331$	7.72836			0.424789			0.212395	−	0.977184i	$-0.431874\pi$
$331$	7.72836			0.424789			0.212395	+	0.977184i	$0.431874\pi$
$332$	−9.69504	+	31.1307i	−0.532084	+	1.70852i
$333$	−6.55519	+	12.0114i	−0.359222	+	0.658218i
$334$	−0.734268	−	0.111691i	−0.0401774	−	0.00611146i
$335$	−14.0696			−0.768703
$336$	13.8763	−	12.1017i	0.757015	−	0.660199i
$337$	27.9018			1.51991			0.759955	−	0.649976i	$-0.225221\pi$
$337$	27.9018			1.51991			0.759955	+	0.649976i	$0.225221\pi$
$338$	5.26212	+	0.800432i	0.286222	+	0.0435378i
$339$	1.43299	−	5.61702i	0.0778292	−	0.305075i
$340$	5.52574	−	17.7431i	0.299675	−	0.962256i
$341$	16.9896			0.920039
$342$	3.83395	+	2.91779i	0.207316	+	0.157776i
$343$		−	18.4366i		−	0.995482i
$344$	15.9604	+	7.76622i	0.860528	+	0.418727i
$345$	−2.65255	−	0.676707i	−0.142809	−	0.0364327i
$346$	31.0177	+	4.71817i	1.66752	+	0.253650i
$347$		−	15.3950i		−	0.826446i	−0.910630	−	0.413223i	$-0.864403\pi$
$347$		−	15.3950i		−	0.826446i	0.910630	−	0.413223i	$-0.135597\pi$
$348$	9.82705	+	6.04798i	0.526785	+	0.324206i
$349$		−	5.76352i		−	0.308514i	−0.988031	−	0.154257i	$-0.950702\pi$
$349$		−	5.76352i		−	0.308514i	0.988031	−	0.154257i	$-0.0492984\pi$
$350$	1.41410	−	9.29645i	0.0755869	−	0.496916i
$351$	14.4918	−	15.5758i	0.773516	−	0.831377i
$352$	−6.64890	+	7.06913i	−0.354388	+	0.376786i
$353$			13.3325i			0.709616i	0.934939	+	0.354808i	$0.115454\pi$
$353$			13.3325i			0.709616i	−0.934939	+	0.354808i	$0.884546\pi$
$354$	−1.24136	+	2.93004i	−0.0659778	+	0.155730i
$355$	8.54511			0.453527
$356$	4.17459	−	13.4046i	0.221253	−	0.710442i
$357$	−26.2213	−	6.68946i	−1.38778	−	0.354044i
$358$	−3.77292	+	24.8036i	−0.199405	+	1.31091i
$359$	−5.89980			−0.311380			−0.155690	−	0.987806i	$-0.549760\pi$
$359$	−5.89980			−0.311380			−0.155690	+	0.987806i	$0.549760\pi$
$360$	−7.77434	−	10.9277i	−0.409744	−	0.575942i
$361$	−17.7104			−0.932127
$362$	−1.64222	+	10.7961i	−0.0863130	+	0.567431i
$363$	13.5218	+	3.44961i	0.709710	+	0.181058i
$364$	−20.7776	−	6.47075i	−1.08904	−	0.339160i
$365$	12.7858			0.669240
$366$	−1.35712	+	3.20327i	−0.0709380	+	0.167438i
$367$		−	0.544516i		−	0.0284235i	−0.999899	−	0.0142118i	$-0.995476\pi$
$367$		−	0.544516i		−	0.0284235i	0.999899	−	0.0142118i	$-0.00452390\pi$
$368$	−3.29269	−	2.27116i	−0.171643	−	0.118393i
$369$	−13.9873	+	25.6295i	−0.728148	+	1.33422i
$370$	1.53316	−	10.0792i	0.0797054	−	0.523992i
$371$		−	23.2119i		−	1.20510i
$372$	−17.9808	+	29.2161i	−0.932263	+	1.51479i
$373$		−	12.5530i		−	0.649968i	−0.945719	−	0.324984i	$-0.894641\pi$
$373$		−	12.5530i		−	0.649968i	0.945719	−	0.324984i	$-0.105359\pi$
$374$	14.1013	+	2.14498i	0.729161	+	0.110914i
$375$	−19.8995	−	5.07666i	−1.02760	−	0.262158i
$376$	−6.67104	−	3.24608i	−0.344033	−	0.167404i
$377$		−	13.6384i		−	0.702413i
$378$	−15.3013	+	12.1345i	−0.787016	+	0.624132i
$379$	−3.98612			−0.204753			−0.102377	−	0.994746i	$-0.532645\pi$
$379$	−3.98612			−0.204753			−0.102377	+	0.994746i	$0.532645\pi$
$380$	−3.42729	−	1.06736i	−0.175816	−	0.0547544i
$381$	0.236443	−	0.926810i	0.0121133	−	0.0474819i
$382$	12.4560	+	1.89471i	0.637306	+	0.0969418i
$383$	36.5538			1.86781			0.933906	−	0.357520i	$-0.116378\pi$
$383$	36.5538			1.86781			0.933906	+	0.357520i	$0.116378\pi$
$384$	−5.11959	−	18.9153i	−0.261258	−	0.965269i
$385$	−7.20580			−0.367241
$386$	−11.8546	−	1.80322i	−0.603382	−	0.0917816i
$387$	−16.5255	−	9.01878i	−0.840038	−	0.458450i
$388$	27.4825	+	8.55886i	1.39521	+	0.434510i
$389$	−20.0043			−1.01426			−0.507130	−	0.861870i	$-0.669294\pi$
$389$	−20.0043			−1.01426			−0.507130	+	0.861870i	$0.669294\pi$
$390$	−6.18349	+	14.5951i	−0.313113	+	0.739053i
$391$			5.87903i			0.297315i
$392$	0.159082	+	0.0774079i	0.00803483	+	0.00390969i
$393$	−3.45483	+	13.5422i	−0.174273	+	0.683115i
$394$	−28.1796	−	4.28646i	−1.41967	−	0.215949i
$395$		−	6.73310i		−	0.338779i
$396$	7.39463	−	7.16048i	0.371594	−	0.359828i
$397$		−	6.38757i		−	0.320583i	−0.987070	−	0.160292i	$-0.948757\pi$
$397$		−	6.38757i		−	0.320583i	0.987070	−	0.160292i	$-0.0512434\pi$
$398$	−4.22685	+	27.7877i	−0.211873	+	1.39287i
$399$	−1.29215	+	5.06495i	−0.0646882	+	0.253565i
$400$	−8.23834	−	5.68246i	−0.411917	−	0.284123i
$401$			34.2445i			1.71009i	0.518555	+	0.855044i	$0.326470\pi$
$401$			34.2445i			1.71009i	−0.518555	+	0.855044i	$0.673530\pi$
$402$	20.0777	+	8.50626i	1.00138	+	0.424254i
$403$	40.5474			2.01981
$404$	−18.1961	−	5.66681i	−0.905290	−	0.281935i
$405$	7.69574	+	11.9630i	0.382405	+	0.594445i
$406$	−1.88265	+	12.3768i	−0.0934346	+	0.614248i
$407$	7.82505			0.387874
$408$	−18.6126	+	21.9791i	−0.921462	+	1.08813i
$409$	−20.3476			−1.00612			−0.503062	−	0.864250i	$-0.667793\pi$
$409$	−20.3476			−1.00612			−0.503062	+	0.864250i	$0.667793\pi$
$410$	3.27142	−	21.5067i	0.161564	−	1.06214i
$411$	−4.46654	+	17.5080i	−0.220318	+	0.863604i
$412$	−1.98209	+	6.36448i	−0.0976505	+	0.313555i
$413$	−3.45245			−0.169884
$414$	3.37614	+	2.56937i	0.165928	+	0.126278i
$415$			25.7665i			1.26483i
$416$	−15.8683	+	16.8712i	−0.778005	+	0.827177i
$417$	−36.1834	−	9.23092i	−1.77191	−	0.452040i
$418$	0.414327	−	2.72383i	0.0202654	−	0.133227i
$419$			31.2544i			1.52688i	0.645881	+	0.763438i	$0.276490\pi$
$419$			31.2544i			1.52688i	−0.645881	+	0.763438i	$0.723510\pi$
$420$	7.62621	−	12.3914i	0.372121	−	0.604640i
$421$		−	31.1878i		−	1.52000i	−0.649922	−	0.760001i	$-0.725199\pi$
$421$		−	31.1878i		−	1.52000i	0.649922	−	0.760001i	$-0.274801\pi$
$422$	−12.3130	−	1.87296i	−0.599389	−	0.0911743i
$423$	6.90723	+	3.76962i	0.335841	+	0.183285i
$424$	−22.2142	−	10.8093i	−1.07882	−	0.524944i
$425$			14.7094i			0.713509i
$426$	−12.1941	−	5.16625i	−0.590806	−	0.250305i
$427$	−3.77439			−0.182655
$428$	0.254914	−	0.818527i	0.0123217	−	0.0395650i
$429$	−11.7885	−	3.00743i	−0.569155	−	0.145200i
$430$	13.8672	+	2.10936i	0.668734	+	0.101722i
$431$	5.05847			0.243658			0.121829	−	0.992551i	$-0.461124\pi$
$431$	5.05847			0.243658			0.121829	+	0.992551i	$0.461124\pi$
$432$	4.48745	+	20.2944i	0.215902	+	0.976415i
$433$	7.13071			0.342680			0.171340	−	0.985212i	$-0.445190\pi$
$433$	7.13071			0.342680			0.171340	+	0.985212i	$0.445190\pi$
$434$	−36.7965	−	5.59719i	−1.76629	−	0.268674i
$435$	8.83574	+	2.25413i	0.423641	+	0.108077i
$436$	−6.91168	+	22.1934i	−0.331009	+	1.06287i
$437$	1.13560			0.0543232
$438$	−18.2457	−	7.73011i	−0.871812	−	0.369359i
$439$			30.9199i			1.47573i	0.674950	+	0.737863i	$0.264165\pi$
$439$			30.9199i			1.47573i	−0.674950	+	0.737863i	$0.735835\pi$
$440$	−3.35558	+	6.89606i	−0.159971	+	0.328757i
$441$	−0.164714	−	0.0898925i	−0.00784351	−	0.00428059i
$442$	33.6541	+	5.11920i	1.60076	+	0.243495i
$443$		−	13.4987i		−	0.641342i	−0.947191	−	0.320671i	$-0.896092\pi$
$443$		−	13.4987i		−	0.641342i	0.947191	−	0.320671i	$-0.103908\pi$
$444$	−8.28159	+	13.4563i	−0.393027	+	0.638609i
$445$		−	11.0948i		−	0.525945i
$446$	−0.322306	+	2.11888i	−0.0152617	+	0.100332i
$447$	3.04692	+	0.777315i	0.144114	+	0.0367657i
$448$	16.7293	−	13.1200i	0.790383	−	0.619863i
$449$			7.00334i			0.330508i	0.986251	+	0.165254i	$0.0528444\pi$
$449$			7.00334i			0.330508i	−0.986251	+	0.165254i	$0.947156\pi$
$450$	8.44712	+	6.42859i	0.398201	+	0.303047i
$451$	16.6969			0.786224
$452$	1.99034	−	6.39096i	0.0936176	−	0.300606i
$453$	−9.42220	+	36.9331i	−0.442694	+	1.73527i
$454$	2.99899	−	19.7157i	0.140750	−	0.925304i
$455$	−17.1973			−0.806223
$456$	4.24552	+	3.59524i	0.198815	+	0.168363i
$457$	−36.8926			−1.72576			−0.862881	−	0.505406i	$-0.831343\pi$
$457$	−36.8926			−1.72576			−0.862881	+	0.505406i	$0.831343\pi$
$458$	2.37945	−	15.6428i	0.111185	−	0.730939i
$459$	20.8086	−	22.3652i	0.971264	−	1.04392i
$460$	−3.01804	−	0.939907i	−0.140717	−	0.0438234i
$461$	−28.8877			−1.34543			−0.672716	−	0.739900i	$-0.734873\pi$
$461$	−28.8877			−1.34543			−0.672716	+	0.739900i	$0.734873\pi$
$462$	10.2829	+	4.35652i	0.478402	+	0.202684i
$463$		−	10.4162i		−	0.484081i	−0.970266	−	0.242041i	$-0.922183\pi$
$463$		−	10.4162i		−	0.484081i	0.970266	−	0.242041i	$-0.0778167\pi$
$464$	10.9681	+	7.56531i	0.509179	+	0.351211i
$465$	−6.70160	+	26.2689i	−0.310779	+	1.21819i
$466$	5.57466	−	36.6484i	0.258241	−	1.69770i
$467$		−	1.37694i		−	0.0637171i	−0.999492	−	0.0318586i	$-0.989857\pi$
$467$		−	1.37694i		−	0.0637171i	0.999492	−	0.0318586i	$-0.0101426\pi$
$468$	17.6480	−	17.0892i	0.815779	−	0.789948i
$469$			23.6574i			1.09240i
$470$	−5.79612	−	0.881659i	−0.267355	−	0.0406679i
$471$	8.06736	−	31.6224i	0.371724	−	1.45708i
$472$	−1.60773	+	3.30405i	−0.0740016	+	0.152081i
$473$			10.7659i			0.495016i
$474$	−4.07074	+	9.60831i	−0.186975	+	0.441325i
$475$	2.84128			0.130367
$476$	−29.8343	−	9.29128i	−1.36745	−	0.425865i
$477$	23.0007	+	12.5526i	1.05313	+	0.574744i
$478$	−13.8147	−	2.10138i	−0.631868	−	0.0961147i
$479$	37.5098			1.71387			0.856933	−	0.515427i	$-0.172367\pi$
$479$	37.5098			1.71387			0.856933	+	0.515427i	$0.172367\pi$
$480$	−8.30744	−	13.0688i	−0.379181	−	0.596507i
$481$	18.6753			0.851518
$482$	−4.47348	−	0.680470i	−0.203761	−	0.0309946i
$483$	−1.13785	+	4.46015i	−0.0517740	+	0.202944i
$484$	15.3849	+	4.79132i	0.699314	+	0.217787i
$485$	22.7469			1.03288
$486$	−3.74939	−	21.7242i	−0.170076	−	0.985431i
$487$			17.9232i			0.812178i	0.913834	+	0.406089i	$0.133108\pi$
$487$			17.9232i			0.812178i	−0.913834	+	0.406089i	$0.866892\pi$
$488$	−1.75765	+	3.61215i	−0.0795650	+	0.163514i
$489$	−36.1254	−	9.21613i	−1.63365	−	0.416768i
$490$	0.138218	+	0.0210246i	0.00624403	+	0.000949792i
$491$			0.0223256i			0.00100754i	1.00000		0.000503770i	$0.000160355\pi$
$491$			0.0223256i			0.00100754i	−1.00000		0.000503770i	$0.999840\pi$
$492$	−17.6710	+	28.7127i	−0.796671	+	1.29447i
$493$		−	19.5832i		−	0.881984i
$494$	0.988831	−	6.50068i	0.0444896	−	0.292479i
$495$	3.89677	−	7.14022i	0.175147	−	0.320929i
$496$	−22.4919	+	32.6084i	−1.00992	+	1.46416i
$497$		−	14.3682i		−	0.644502i
$498$	15.5781	−	36.7695i	0.698070	−	1.64768i
$499$	−15.7199			−0.703721			−0.351860	−	0.936053i	$-0.614451\pi$
$499$	−15.7199			−0.703721			−0.351860	+	0.936053i	$0.614451\pi$
$500$	−22.6413	−	7.05119i	−1.01255	−	0.315339i
$501$	0.881405	+	0.224860i	0.0393783	+	0.0100460i
$502$	−1.56383	+	10.2808i	−0.0697971	+	0.458853i
$503$	−8.39386			−0.374264			−0.187132	−	0.982335i	$-0.559919\pi$
$503$	−8.39386			−0.374264			−0.187132	+	0.982335i	$0.559919\pi$
$504$	−18.3745	+	13.0722i	−0.818464	+	0.582282i
$505$	−15.0607			−0.670193
$506$	0.364852	−	2.39858i	0.0162197	−	0.106630i
$507$	−6.31658	−	1.61145i	−0.280529	−	0.0715672i
$508$	0.328406	−	1.05451i	0.0145707	−	0.0467863i
$509$	25.3442			1.12336			0.561680	−	0.827354i	$-0.310155\pi$
$509$	25.3442			1.12336			0.561680	+	0.827354i	$0.310155\pi$
$510$	−8.87880	+	20.9570i	−0.393160	+	0.927991i
$511$		−	21.4987i		−	0.951048i
$512$	−4.76564	−	22.1199i	−0.210614	−	0.977569i
$513$	−4.32009	−	4.01943i	−0.190737	−	0.177462i
$514$	−3.60849	+	23.7226i	−0.159163	+	1.04636i
$515$			5.26780i			0.232127i
$516$	−18.5135	−	11.3940i	−0.815012	−	0.501593i
$517$		−	4.49986i		−	0.197904i
$518$	−16.9477	−	2.57795i	−0.744639	−	0.113268i
$519$	−37.2332	−	9.49876i	−1.63436	−	0.416949i
$520$	−8.00841	+	16.4581i	−0.351192	+	0.721737i
$521$		−	30.8556i		−	1.35181i	−0.736989	−	0.675904i	$-0.763753\pi$
$521$		−	30.8556i		−	1.35181i	0.736989	−	0.675904i	$-0.236247\pi$
$522$	−11.2460	−	8.55866i	−0.492225	−	0.374602i
$523$	−13.1621			−0.575538			−0.287769	−	0.957700i	$-0.592914\pi$
$523$	−13.1621			−0.575538			−0.287769	+	0.957700i	$0.592914\pi$
$524$	−4.79856	+	15.4081i	−0.209626	+	0.673108i
$525$	−2.84691	+	11.1593i	−0.124249	+	0.487033i
$526$	42.8547	+	6.51872i	1.86856	+	0.284230i
$527$	58.2215			2.53617
$528$	8.95775	−	7.81213i	0.389836	−	0.339979i
$529$	1.00000			0.0434783
$530$	−19.3007	−	2.93587i	−0.838369	−	0.127526i
$531$	1.86702	−	3.42103i	0.0810219	−	0.148460i
$532$	−1.79472	+	5.76283i	−0.0778109	+	0.249850i
$533$	39.8487			1.72604
$534$	−6.70777	+	15.8326i	−0.290273	+	0.685144i
$535$		−	0.677485i		−	0.0292902i
$536$	22.6405	+	11.0167i	0.977920	+	0.475849i
$537$	7.59576	−	29.7739i	0.327781	−	1.28484i
$538$	11.9979	+	1.82502i	0.517266	+	0.0786824i
$539$			0.107306i			0.00462201i
$540$	8.15453	+	14.2579i	0.350915	+	0.613561i
$541$			27.6105i			1.18707i	0.804809	+	0.593534i	$0.202268\pi$
$541$			27.6105i			1.18707i	−0.804809	+	0.593534i	$0.797732\pi$
$542$	−4.43249	+	29.1397i	−0.190392	+	1.25166i
$543$	3.30616	−	12.9595i	0.141881	−	0.556145i
$544$	−22.7850	+	24.2251i	−0.976901	+	1.03864i
$545$			18.3692i			0.786849i
$546$	24.5410	+	10.3973i	1.05026	+	0.444962i
$547$	−12.0996			−0.517341			−0.258671	−	0.965966i	$-0.583284\pi$
$547$	−12.0996			−0.517341			−0.258671	+	0.965966i	$0.583284\pi$
$548$	−6.20377	+	19.9203i	−0.265012	+	0.850952i
$549$	2.04112	−	3.74004i	0.0871131	−	0.159621i
$550$	0.912863	−	6.00125i	0.0389246	−	0.255894i
$551$	−3.78272			−0.161149
$552$	3.73856	+	3.16593i	0.159124	+	0.134751i
$553$	−11.3214			−0.481435
$554$	−1.33339	+	8.76584i	−0.0566503	+	0.372425i
$555$	−3.08661	+	12.0989i	−0.131019	+	0.513570i
$556$	−41.1689	−	12.8212i	−1.74595	−	0.543741i
$557$	43.4053			1.83914			0.919571	−	0.392924i	$-0.128537\pi$
$557$	43.4053			1.83914			0.919571	+	0.392924i	$0.128537\pi$
$558$	25.4452	−	33.4348i	1.07718	−	1.41541i
$559$			25.6938i			1.08673i
$560$	9.53948	−	13.8302i	0.403117	−	0.584431i
$561$	−16.9270	−	4.31833i	−0.714658	−	0.182320i
$562$	−5.83991	+	38.3921i	−0.246342	+	1.61948i
$563$		−	32.9021i		−	1.38666i	−0.720622	−	0.693328i	$-0.756144\pi$
$563$		−	32.9021i		−	1.38666i	0.720622	−	0.693328i	$-0.243856\pi$
$564$	7.73817	+	4.76240i	0.325836	+	0.200533i
$565$		−	5.28973i		−	0.222540i
$566$	−26.2417	−	3.99168i	−1.10302	−	0.167783i
$567$	20.1152	−	12.9400i	0.844759	−	0.543431i
$568$	−13.7506	−	6.69095i	−0.576963	−	0.280746i
$569$			20.0307i			0.839732i	0.907586	+	0.419866i	$0.137923\pi$
$569$			20.0307i			0.839732i	−0.907586	+	0.419866i	$0.862077\pi$
$570$	4.04808	+	1.71504i	0.169556	+	0.0718352i
$571$	37.6801			1.57686			0.788432	−	0.615122i	$-0.210893\pi$
$571$	37.6801			1.57686			0.788432	+	0.615122i	$0.210893\pi$
$572$	−13.4128	−	4.17715i	−0.560817	−	0.174655i
$573$	−14.9520	−	3.81449i	−0.624630	−	0.159353i
$574$	−36.1625	−	5.50074i	−1.50939	−	0.229597i
$575$	2.50201			0.104341
$576$	3.95373	+	23.6721i	0.164739	+	0.986337i
$577$	−15.9202			−0.662769			−0.331384	−	0.943496i	$-0.607516\pi$
$577$	−15.9202			−0.662769			−0.331384	+	0.943496i	$0.607516\pi$
$578$	24.5553	+	3.73516i	1.02137	+	0.155362i
$579$	14.2301	+	3.63030i	0.591381	+	0.150870i
$580$	10.0532	+	3.13086i	0.417435	+	0.130002i
$581$	43.3252			1.79743
$582$	−32.4604	−	13.7524i	−1.34553	−	0.570057i
$583$		−	14.9843i		−	0.620585i
$584$	−20.5746	−	10.0115i	−0.851385	−	0.414278i
$585$	9.30002	−	17.0408i	0.384509	−	0.704551i
$586$	18.3776	+	2.79545i	0.759170	+	0.115479i
$587$		−	15.2726i		−	0.630368i	−0.949031	−	0.315184i	$-0.897934\pi$
$587$		−	15.2726i		−	0.630368i	0.949031	−	0.315184i	$-0.102066\pi$
$588$	−0.184529	−	0.113567i	−0.00760985	−	0.00468342i
$589$		−	11.2462i		−	0.463390i
$590$	−0.436670	+	2.87071i	−0.0179774	+	0.118185i
$591$	33.8265	+	8.62964i	1.39143	+	0.354976i
$592$	−10.3593	+	15.0187i	−0.425764	+	0.617266i
$593$		−	6.88254i		−	0.282632i	−0.989965	−	0.141316i	$-0.954867\pi$
$593$		−	6.88254i		−	0.282632i	0.989965	−	0.141316i	$-0.0451334\pi$
$594$	−9.87767	+	7.83335i	−0.405286	+	0.321406i
$595$	−24.6935			−1.01233
$596$	3.46674	+	1.07965i	0.142003	+	0.0442240i
$597$	8.50962	−	33.3560i	0.348276	−	1.36517i
$598$	0.870755	−	5.72443i	0.0356078	−	0.234090i
$599$	1.65952			0.0678061			0.0339031	−	0.999425i	$-0.489206\pi$
$599$	1.65952			0.0678061			0.0339031	+	0.999425i	$0.489206\pi$
$600$	9.35391	+	7.92119i	0.381872	+	0.323381i
$601$	−15.8394			−0.646102			−0.323051	−	0.946381i	$-0.604709\pi$
$601$	−15.8394			−0.646102			−0.323051	+	0.946381i	$0.604709\pi$
$602$	3.54680	−	23.3170i	0.144557	−	0.950330i
$603$	−23.4421	−	12.7935i	−0.954635	−	0.520991i
$604$	−13.0869	+	42.0220i	−0.532498	+	1.70985i
$605$	12.7339			0.517707
$606$	21.4920	+	9.10548i	0.873054	+	0.369885i
$607$		−	33.5670i		−	1.36244i	−0.732078	−	0.681221i	$-0.761449\pi$
$607$		−	33.5670i		−	1.36244i	0.732078	−	0.681221i	$-0.238551\pi$
$608$	4.67936	+	4.40119i	0.189773	+	0.178492i
$609$	3.79022	−	14.8569i	0.153587	−	0.602032i
$610$	−0.477390	+	3.13841i	−0.0193289	+	0.127070i
$611$		−	10.7394i		−	0.434468i
$612$	25.3406	−	24.5382i	1.02433	−	0.991897i
$613$		−	33.7909i		−	1.36480i	−0.730979	−	0.682400i	$-0.760936\pi$
$613$		−	33.7909i		−	1.36480i	0.730979	−	0.682400i	$-0.239064\pi$
$614$	13.4688	+	2.04876i	0.543556	+	0.0826814i
$615$	−6.58612	+	25.8163i	−0.265578	+	1.04101i
$616$	11.5954	+	5.64225i	0.467193	+	0.227333i
$617$		−	40.0855i		−	1.61378i	−0.590701	−	0.806890i	$-0.701149\pi$
$617$		−	40.0855i		−	1.61378i	0.590701	−	0.806890i	$-0.298851\pi$
$618$	3.18484	−	7.51729i	0.128113	−	0.302390i
$619$	4.18748			0.168309			0.0841545	−	0.996453i	$-0.473181\pi$
$619$	4.18748			0.168309			0.0841545	+	0.996453i	$0.473181\pi$
$620$	−9.30814	+	29.8884i	−0.373824	+	1.20035i
$621$	−3.80423	−	3.53947i	−0.152658	−	0.142034i
$622$	13.4435	+	2.04492i	0.539036	+	0.0819938i
$623$	−18.6554			−0.747414
$624$	21.3786	−	18.6444i	0.855827	−	0.746374i
$625$	−6.22993			−0.249197
$626$	4.80896	+	0.731501i	0.192205	+	0.0292366i
$627$	−0.834135	+	3.26964i	−0.0333121	+	0.130577i
$628$	11.2051	−	35.9795i	0.447132	−	1.43574i
$629$	26.8156			1.06921
$630$	−10.7920	+	14.1807i	−0.429965	+	0.564971i
$631$			20.2955i			0.807949i	0.914770	+	0.403975i	$0.132372\pi$
$631$			20.2955i			0.807949i	−0.914770	+	0.403975i	$0.867628\pi$
$632$	−5.27212	+	10.8348i	−0.209714	+	0.430984i
$633$	14.7804	+	3.77070i	0.587468	+	0.149872i
$634$	0.147124	+	0.0223793i	0.00584304	+	0.000888796i
$635$		−	0.872805i		−	0.0346362i
$636$	25.7676	+	15.8585i	1.02175	+	0.628830i
$637$			0.256097i			0.0101469i
$638$	−1.21533	+	7.98972i	−0.0481155	+	0.316316i
$639$	14.2374	+	7.77008i	0.563225	+	0.307380i
$640$	−8.79338	−	15.5698i	−0.347589	−	0.615452i
$641$			17.7145i			0.699681i	0.936809	+	0.349840i	$0.113764\pi$
$641$			17.7145i			0.699681i	−0.936809	+	0.349840i	$0.886236\pi$
$642$	−0.409598	+	0.966789i	−0.0161655	+	0.0381561i
$643$	8.88047			0.350212			0.175106	−	0.984550i	$-0.443973\pi$
$643$	8.88047			0.350212			0.175106	+	0.984550i	$0.443973\pi$
$644$	−1.58041	+	5.07469i	−0.0622769	+	0.199971i
$645$	−16.6459	−	4.24663i	−0.655433	−	0.167211i
$646$	1.41985	−	9.33425i	0.0558633	−	0.367251i
$647$	47.2599			1.85798			0.928989	−	0.370107i	$-0.120679\pi$
$647$	47.2599			1.85798			0.928989	+	0.370107i	$0.120679\pi$
$648$	−3.01663	−	25.2765i	−0.118505	−	0.992954i
$649$	−2.22870			−0.0874841
$650$	2.17864	−	14.3226i	0.0854531	−	0.561778i
$651$	44.1700	+	11.2684i	1.73116	+	0.441645i
$652$	−41.1029	−	12.8007i	−1.60972	−	0.501314i
$653$	−42.0378			−1.64507			−0.822533	−	0.568718i	$-0.807440\pi$
$653$	−42.0378			−1.64507			−0.822533	+	0.568718i	$0.807440\pi$
$654$	11.1057	−	26.2133i	0.434269	−	1.02502i
$655$			12.7531i			0.498306i
$656$	−22.1043	+	32.0465i	−0.863029	+	1.25120i
$657$	21.3031	+	11.6262i	0.831113	+	0.453579i
$658$	−1.48247	+	9.74591i	−0.0577927	+	0.379935i
$659$		−	32.4847i		−	1.26543i	−0.774387	−	0.632713i	$-0.781941\pi$
$659$		−	32.4847i		−	1.26543i	0.774387	−	0.632713i	$-0.218059\pi$
$660$	4.92304	−	7.99919i	0.191629	−	0.311368i
$661$		−	12.0307i		−	0.467940i	−0.972244	−	0.233970i	$-0.924828\pi$
$661$		−	12.0307i		−	0.467940i	0.972244	−	0.233970i	$-0.0751717\pi$
$662$	−10.8053	−	1.64361i	−0.419958	−	0.0638807i
$663$	−40.3979	−	10.3061i	−1.56893	−	0.400256i
$664$	20.1756	−	41.4630i	0.782964	−	1.60907i
$665$			4.76982i			0.184966i
$666$	11.7195	−	15.3993i	0.454122	−	0.596712i
$667$	−3.33103			−0.128978
$668$	1.00285	+	0.312317i	0.0388014	+	0.0120839i
$669$	0.648877	−	2.54347i	0.0250870	−	0.0983362i
$670$	19.6711	+	2.99221i	0.759962	+	0.115599i
$671$	−2.43653			−0.0940611
$672$	−21.9746	+	13.9686i	−0.847689	+	0.538850i
$673$	15.4793			0.596682			0.298341	−	0.954459i	$-0.403567\pi$
$673$	15.4793			0.596682			0.298341	+	0.954459i	$0.403567\pi$
$674$	−39.0104	−	5.93395i	−1.50263	−	0.228567i
$675$	−9.51821	−	8.85577i	−0.366356	−	0.340859i
$676$	−7.18691	−	2.23822i	−0.276420	−	0.0860853i
$677$	−0.369726			−0.0142097			−0.00710485	−	0.999975i	$-0.502262\pi$
$677$	−0.369726			−0.0142097			−0.00710485	+	0.999975i	$0.502262\pi$
$678$	−3.19809	+	7.54858i	−0.122822	+	0.289901i
$679$		−	38.2479i		−	1.46782i
$680$	−11.4992	+	23.6320i	−0.440974	+	0.906247i
$681$	−6.03767	+	23.6664i	−0.231364	+	0.906900i
$682$	−23.7537	−	3.61322i	−0.909576	−	0.138357i
$683$		−	11.7324i		−	0.448928i	−0.974482	−	0.224464i	$-0.927937\pi$
$683$		−	11.7324i		−	0.448928i	0.974482	−	0.224464i	$-0.0720631\pi$
$684$	−4.73983	−	4.89482i	−0.181232	−	0.187158i
$685$			16.4878i			0.629966i
$686$	−3.92096	+	25.7768i	−0.149703	+	0.984162i
$687$	−4.79039	+	18.7774i	−0.182765	+	0.716401i
$688$	−20.6631	−	14.2525i	−0.787773	−	0.543373i
$689$		−	35.7614i		−	1.36240i
$690$	3.56470	+	1.51025i	0.135706	+	0.0574942i
$691$	−39.5562			−1.50479			−0.752395	−	0.658713i	$-0.771101\pi$
$691$	−39.5562			−1.50479			−0.752395	+	0.658713i	$0.771101\pi$
$692$	−42.3634	−	13.1932i	−1.61042	−	0.501532i
$693$	−12.0059	−	6.55224i	−0.456068	−	0.248899i
$694$	−3.27409	+	21.5242i	−0.124283	+	0.817048i
$695$	−34.0750			−1.29254
$696$	−12.4533	−	10.5458i	−0.472040	−	0.399738i
$697$	57.2183			2.16730
$698$	−1.22574	+	8.05816i	−0.0463950	+	0.305006i
$699$	−11.2231	+	43.9922i	−0.424496	+	1.66394i
$700$	−3.95420	+	12.6969i	−0.149455	+	0.479898i
$701$	17.3202			0.654175			0.327087	−	0.944994i	$-0.393933\pi$
$701$	17.3202			0.654175			0.327087	+	0.944994i	$0.393933\pi$
$702$	−23.5740	+	18.6951i	−0.889744	+	0.705599i
$703$		−	5.17974i		−	0.195358i
$704$	10.7994	−	8.46953i	0.407019	−	0.319208i
$705$	6.95758	+	1.77498i	0.262038	+	0.0668497i
$706$	2.83545	−	18.6405i	0.106714	−	0.701546i
$707$			25.3239i			0.952403i
$708$	2.35873	−	3.83258i	0.0886465	−	0.144037i
$709$			38.2307i			1.43578i	0.696154	+	0.717892i	$0.254893\pi$
$709$			38.2307i			1.43578i	−0.696154	+	0.717892i	$0.745107\pi$
$710$	−11.9472	−	1.81731i	−0.448370	−	0.0682024i
$711$	6.12242	−	11.2184i	0.229609	−	0.420722i
$712$	−8.68741	+	17.8536i	−0.325575	+	0.669090i
$713$		−	9.90325i		−	0.370880i
$714$	35.2382	+	14.9293i	1.31876	+	0.558715i
$715$	−11.1016			−0.415177
$716$	10.5501	−	33.8763i	0.394275	−	1.26602i
$717$	16.5829	+	4.23055i	0.619300	+	0.157993i
$718$	8.24870	+	1.25473i	0.307839	+	0.0468260i
$719$	−1.68530			−0.0628510			−0.0314255	−	0.999506i	$-0.510005\pi$
$719$	−1.68530			−0.0628510			−0.0314255	+	0.999506i	$0.510005\pi$
$720$	8.54552	+	16.9318i	0.318473	+	0.631010i
$721$	8.85757			0.329873
$722$	24.7615	+	3.76652i	0.921527	+	0.140175i
$723$	5.36990	+	1.36994i	0.199709	+	0.0509487i
$724$	4.59207	−	14.7451i	0.170663	−	0.547998i
$725$	−8.33426			−0.309527
$726$	−18.1716	−	7.69873i	−0.674412	−	0.285727i
$727$		−	8.87197i		−	0.329043i	−0.986373	−	0.164522i	$-0.947392\pi$
$727$		−	8.87197i		−	0.329043i	0.986373	−	0.164522i	$-0.0526080\pi$
$728$	27.6736	+	13.4658i	1.02565	+	0.499075i
$729$	1.94432	+	26.9299i	0.0720118	+	0.997404i
$730$	−17.8762	−	2.71919i	−0.661629	−	0.100642i
$731$			36.8935i			1.36455i
$732$	2.57868	−	4.18997i	0.0953109	−	0.154866i
$733$			45.4660i			1.67932i	0.543109	+	0.839662i	$0.317247\pi$
$733$			45.4660i			1.67932i	−0.543109	+	0.839662i	$0.682753\pi$
$734$	−0.115804	+	0.761305i	−0.00427439	+	0.0281003i
$735$	−0.165914	−	0.0423273i	−0.00611984	−	0.00156126i
$736$	4.12060	+	3.87565i	0.151887	+	0.142858i
$737$			15.2718i			0.562545i
$738$	25.0067	−	32.8586i	0.920510	−	1.20954i
$739$	−10.3971			−0.382464			−0.191232	−	0.981545i	$-0.561248\pi$
$739$	−10.3971			−0.382464			−0.191232	+	0.981545i	$0.561248\pi$
$740$	−4.28713	+	13.7660i	−0.157598	+	0.506047i
$741$	−1.99074	+	7.80332i	−0.0731318	+	0.286662i
$742$	−4.93653	+	32.4533i	−0.181226	+	1.19140i
$743$	−23.5924			−0.865522			−0.432761	−	0.901509i	$-0.642461\pi$
$743$	−23.5924			−0.865522			−0.432761	+	0.901509i	$0.642461\pi$
$744$	31.3530	−	37.0240i	1.14946	−	1.35736i
$745$	2.86938			0.105126
$746$	−2.66967	+	17.5507i	−0.0977437	+	0.642577i
$747$	−23.4295	+	42.9309i	−0.857242	+	1.57076i
$748$	−19.2593	−	5.99792i	−0.704189	−	0.219306i
$749$	−1.13916			−0.0416240
$750$	26.7424	+	11.3299i	0.976495	+	0.413710i
$751$			25.5463i			0.932197i	0.884733	+	0.466098i	$0.154341\pi$
$751$			25.5463i			0.932197i	−0.884733	+	0.466098i	$0.845659\pi$
$752$	8.63664	+	5.95720i	0.314946	+	0.217237i
$753$	3.14835	−	12.3409i	0.114732	−	0.449727i
$754$	−2.90051	+	19.0683i	−0.105630	+	0.694425i
$755$			34.7811i			1.26581i
$756$	23.9740	−	13.7115i	0.871924	−	0.498682i
$757$			13.7350i			0.499206i	0.968348	+	0.249603i	$0.0803002\pi$
$757$			13.7350i			0.499206i	−0.968348	+	0.249603i	$0.919700\pi$
$758$	5.57311	+	0.847738i	0.202425	+	0.0307912i
$759$	−0.734531	+	2.87922i	−0.0266618	+	0.104509i
$760$	4.56480	+	2.22120i	0.165583	+	0.0805714i
$761$		−	12.2173i		−	0.442877i	−0.975174	−	0.221438i	$-0.928925\pi$
$761$		−	12.2173i		−	0.442877i	0.975174	−	0.221438i	$-0.0710751\pi$
$762$	−0.527685	+	1.24552i	−0.0191160	+	0.0451203i
$763$	30.8869			1.11818
$764$	−17.0122	−	5.29811i	−0.615480	−	0.191679i
$765$	13.3538	−	24.4687i	0.482808	−	0.884669i
$766$	−51.1070	−	7.77399i	−1.84657	−	0.280886i
$767$	−5.31901			−0.192058
$768$	3.13509	+	27.5349i	0.113128	+	0.993580i
$769$	12.4868			0.450286			0.225143	−	0.974326i	$-0.427715\pi$
$769$	12.4868			0.450286			0.225143	+	0.974326i	$0.427715\pi$
$770$	10.0746	+	1.53247i	0.363065	+	0.0552266i
$771$	7.26471	−	28.4762i	0.261632	−	1.02555i
$772$	16.1907	+	5.04228i	0.582718	+	0.181476i
$773$	−19.3853			−0.697240			−0.348620	−	0.937264i	$-0.613350\pi$
$773$	−19.3853			−0.697240			−0.348620	+	0.937264i	$0.613350\pi$
$774$	21.1868	+	16.1239i	0.761542	+	0.579563i
$775$		−	24.7780i		−	0.890052i
$776$	−36.6038	−	17.8112i	−1.31400	−	0.639384i
$777$	20.3438	+	5.19000i	0.729828	+	0.186190i
$778$	27.9687	+	4.25437i	1.00273	+	0.152527i
$779$		−	11.0524i		−	0.395992i
$780$	11.7493	−	19.0908i	0.420693	−	0.683562i
$781$		−	9.27529i		−	0.331896i
$782$	1.25031	−	8.21965i	0.0447109	−	0.293934i
$783$	12.6720	+	11.7901i	0.452860	+	0.421343i
$784$	−0.205954	−	0.142059i	−0.00735551	−	0.00507353i
$785$		−	29.7798i		−	1.06289i
$786$	7.71036	−	18.1991i	0.275019	−	0.649139i
$787$	−27.5269			−0.981228			−0.490614	−	0.871377i	$-0.663227\pi$
$787$	−27.5269			−0.981228			−0.490614	+	0.871377i	$0.663227\pi$
$788$	38.4872	+	11.9861i	1.37105	+	0.426986i
$789$	−51.4422	−	13.1237i	−1.83139	−	0.467216i
$790$	−1.43195	+	9.41376i	−0.0509464	+	0.334927i
$791$	−8.89443			−0.316250
$792$	−11.8615	+	8.43866i	−0.421480	+	0.299855i
$793$	−5.81501			−0.206497
$794$	−1.35846	+	8.93066i	−0.0482100	+	0.316937i
$795$	23.1683	+	5.91058i	0.821695	+	0.209627i
$796$	11.8194	−	37.9520i	0.418927	−	1.34517i
$797$	−3.73818			−0.132413			−0.0662065	−	0.997806i	$-0.521090\pi$
$797$	−3.73818			−0.132413			−0.0662065	+	0.997806i	$0.521090\pi$
$798$	2.88377	−	6.80667i	0.102084	−	0.240953i
$799$		−	15.4205i		−	0.545539i
$800$	10.3098	+	9.69690i	0.364505	+	0.342837i
$801$	10.0885	−	18.4857i	0.356461	−	0.653159i
$802$	7.28286	−	47.8783i	0.257167	−	1.69064i
$803$		−	13.8784i		−	0.489756i
$804$	−26.2622	−	16.1628i	−0.926195	−	0.570019i
$805$			4.20026i			0.148040i
$806$	−56.6905	−	8.62331i	−1.99684	−	0.303743i
$807$	−14.4021	−	3.67419i	−0.506978	−	0.129338i
$808$	24.2354	+	11.7928i	0.852597	+	0.414868i
$809$		−	16.6870i		−	0.586685i	−0.956007	−	0.293343i	$-0.905232\pi$
$809$		−	16.6870i		−	0.586685i	0.956007	−	0.293343i	$-0.0947677\pi$
$810$	−8.21546	−	18.3625i	−0.288662	−	0.645192i
$811$	10.5706			0.371185			0.185592	−	0.982627i	$-0.440580\pi$
$811$	10.5706			0.371185			0.185592	+	0.982627i	$0.440580\pi$
$812$	5.26439	−	16.9039i	0.184744	−	0.593212i
$813$	8.92363	−	34.9788i	0.312965	−	1.22676i
$814$	−10.9405	−	1.66417i	−0.383463	−	0.0583293i
$815$	−34.0204			−1.19168
$816$	30.6972	−	26.7713i	1.07462	−	0.937183i
$817$	7.12640			0.249321
$818$	28.4486	+	4.32737i	0.994682	+	0.151303i
$819$	−28.6534	−	15.6376i	−1.00123	−	0.546421i
$820$	−9.14775	+	29.3734i	−0.319453	+	1.02576i
$821$	−16.1254			−0.562781			−0.281390	−	0.959593i	$-0.590796\pi$
$821$	−16.1254			−0.562781			−0.281390	+	0.959593i	$0.590796\pi$
$822$	9.96827	−	23.5285i	0.347683	−	0.820651i
$823$			49.1513i			1.71331i	0.515894	+	0.856653i	$0.327460\pi$
$823$			49.1513i			1.71331i	−0.515894	+	0.856653i	$0.672540\pi$
$824$	4.12477	−	8.47684i	0.143693	−	0.295305i
$825$	−1.83780	+	7.20382i	−0.0639841	+	0.250805i
$826$	4.82697	+	0.734240i	0.167952	+	0.0255475i
$827$			33.2552i			1.15640i	0.815897	+	0.578198i	$0.196244\pi$
$827$			33.2552i			1.15640i	−0.815897	+	0.578198i	$0.803756\pi$
$828$	−4.17385	−	4.31033i	−0.145051	−	0.149794i
$829$			17.9299i			0.622731i	0.950290	+	0.311365i	$0.100786\pi$
$829$			17.9299i			0.622731i	−0.950290	+	0.311365i	$0.899214\pi$
$830$	5.47983	−	36.0250i	0.190208	−	1.25045i
$831$	2.68442	−	10.5224i	0.0931215	−	0.365018i
$832$	25.7739	−	20.2134i	0.893550	−	0.700772i
$833$			0.367727i			0.0127410i
$834$	48.6259	+	20.6012i	1.68378	+	0.713363i
$835$	0.830047			0.0287249
$836$	−1.15857	+	3.72015i	−0.0400699	+	0.128664i
$837$	−35.0523	+	37.6742i	−1.21158	+	1.30221i
$838$	6.64695	−	43.6977i	0.229615	−	1.50951i
$839$	23.2392			0.802305			0.401152	−	0.916011i	$-0.368610\pi$
$839$	23.2392			0.802305			0.401152	+	0.916011i	$0.368610\pi$
$840$	−13.2977	+	15.7030i	−0.458816	+	0.541803i
$841$	−17.9042			−0.617388
$842$	−6.63279	+	43.6047i	−0.228581	+	1.50272i
$843$	11.7571	−	46.0854i	0.404935	−	1.58727i
$844$	16.8169	+	5.23729i	0.578862	+	0.180275i
$845$	−5.94852			−0.204635
$846$	−8.85552	−	6.73940i	−0.304459	−	0.231705i
$847$		−	21.4115i		−	0.735707i
$848$	28.7595	+	19.8371i	0.987604	+	0.681209i
$849$	31.5001	+	8.03616i	1.08108	+	0.275800i
$850$	3.12828	−	20.5656i	0.107299	−	0.705395i
$851$		−	4.56123i		−	0.156357i
$852$	15.9502	+	9.81644i	0.546445	+	0.336306i
$853$			29.6157i			1.01402i	0.861939	+	0.507011i	$0.169250\pi$
$853$			29.6157i			1.01402i	−0.861939	+	0.507011i	$0.830750\pi$
$854$	5.27709	+	0.802709i	0.180578	+	0.0274681i
$855$	−4.72642	−	2.57944i	−0.161640	−	0.0882150i
$856$	−0.530481	+	1.09020i	−0.0181315	+	0.0372621i
$857$			32.9449i			1.12538i	0.826669	+	0.562688i	$0.190233\pi$
$857$			32.9449i			1.12538i	−0.826669	+	0.562688i	$0.809767\pi$
$858$	15.8423	+	6.71187i	0.540847	+	0.229139i
$859$	−1.05368			−0.0359510			−0.0179755	−	0.999838i	$-0.505722\pi$
$859$	−1.05368			−0.0359510			−0.0179755	+	0.999838i	$0.505722\pi$
$860$	−18.9395	−	5.89833i	−0.645832	−	0.201131i
$861$	43.4089	+	11.0743i	1.47937	+	0.377410i
$862$	−7.07240	−	1.07580i	−0.240887	−	0.0366418i
$863$	23.4719			0.798994			0.399497	−	0.916735i	$-0.369185\pi$
$863$	23.4719			0.798994			0.399497	+	0.916735i	$0.369185\pi$
$864$	−1.95797	−	29.3286i	−0.0666116	−	0.997779i
$865$	−35.0637			−1.19220
$866$	−9.96967	−	1.51651i	−0.338783	−	0.0515330i
$867$	−29.4759	−	7.51974i	−1.00105	−	0.255384i
$868$	50.2560	+	15.6512i	1.70580	+	0.531237i
$869$	−7.30845			−0.247922
$870$	−11.8741	−	5.03069i	−0.402571	−	0.170556i
$871$			36.4477i			1.23498i
$872$	14.3834	−	29.5593i	0.487082	−	1.00100i
$873$	37.8998	+	20.6838i	1.28271	+	0.700040i
$874$	−1.58772	−	0.241511i	−0.0537054	−	0.00816924i
$875$			31.5104i			1.06525i
$876$	23.8659	+	14.6881i	0.806353	+	0.496264i
$877$		−	39.3118i		−	1.32747i	−0.747969	−	0.663733i	$-0.768971\pi$
$877$		−	39.3118i		−	1.32747i	0.747969	−	0.663733i	$-0.231029\pi$
$878$	6.57582	−	43.2301i	0.221923	−	1.45894i
$879$	−22.0602	−	5.62788i	−0.744071	−	0.189824i
$880$	6.15814	−	8.92796i	0.207591	−	0.300961i
$881$			22.4841i			0.757509i	0.925497	+	0.378755i	$0.123648\pi$
$881$			22.4841i			0.757509i	−0.925497	+	0.378755i	$0.876352\pi$
$882$	0.211174	+	0.160712i	0.00711059	+	0.00541144i
$883$	28.9937			0.975717			0.487858	−	0.872923i	$-0.337778\pi$
$883$	28.9937			0.975717			0.487858	+	0.872923i	$0.337778\pi$
$884$	−45.9641	−	14.3146i	−1.54594	−	0.481453i
$885$	0.879117	−	3.44596i	0.0295512	−	0.115835i
$886$	−2.87080	+	18.8729i	−0.0964464	+	0.634049i
$887$	−27.5965			−0.926601			−0.463301	−	0.886201i	$-0.653335\pi$
$887$	−27.5965			−0.926601			−0.463301	+	0.886201i	$0.653335\pi$
$888$	14.4405	−	17.0524i	0.484593	−	0.572243i
$889$	−1.46758			−0.0492211
$890$	−2.35956	+	15.5120i	−0.0790928	+	0.519964i
$891$	12.9852	−	8.35335i	0.435021	−	0.279848i
$892$	0.901253	−	2.89392i	0.0301762	−	0.0968956i
$893$	−2.97865			−0.0996768
$894$	−4.09468	−	1.73478i	−0.136947	−	0.0580199i
$895$		−	28.0390i		−	0.937240i
$896$	−26.1800	+	14.7857i	−0.874611	+	0.493954i
$897$	−1.75303	+	6.87153i	−0.0585320	+	0.229434i
$898$	1.48942	−	9.79158i	0.0497025	−	0.326749i
$899$			32.9880i			1.10021i
$900$	−10.4430	−	10.7845i	−0.348100	−	0.359483i
$901$		−	51.3494i		−	1.71070i
$902$	−23.3444	−	3.55096i	−0.777283	−	0.118234i
$903$	−7.14052	+	27.9894i	−0.237622	+	0.931429i
$904$	−4.14194	+	8.51212i	−0.137759	+	0.283109i
$905$		−	12.2044i		−	0.405687i
$906$	21.0281	−	49.6335i	0.698613	−	1.64896i
$907$	5.61089			0.186306			0.0931532	−	0.995652i	$-0.470305\pi$
$907$	5.61089			0.186306			0.0931532	+	0.995652i	$0.470305\pi$
$908$	−8.38598	+	26.9273i	−0.278298	+	0.893615i
$909$	−25.0934	−	13.6947i	−0.832296	−	0.454225i
$910$	24.0441	+	3.65740i	0.797055	+	0.121242i
$911$	34.3641			1.13853			0.569266	−	0.822153i	$-0.307227\pi$
$911$	34.3641			1.13853			0.569266	+	0.822153i	$0.307227\pi$
$912$	−5.17118	−	5.92952i	−0.171235	−	0.196346i
$913$	27.9683			0.925615
$914$	51.5807	+	7.84604i	1.70614	+	0.259524i
$915$	0.961095	−	3.76730i	0.0317728	−	0.124543i
$916$	−6.65358	+	21.3646i	−0.219840	+	0.705906i
$917$	21.4438			0.708137
$918$	−33.8497	+	26.8440i	−1.11721	+	0.885984i
$919$			26.5388i			0.875433i	0.899113	+	0.437716i	$0.144213\pi$
$919$			26.5388i			0.875433i	−0.899113	+	0.437716i	$0.855787\pi$
$920$	4.01972	+	1.95597i	0.132526	+	0.0644863i
$921$	−16.1677	−	4.12463i	−0.532745	−	0.135911i
$922$	40.3887	+	6.14361i	1.33013	+	0.202329i
$923$		−	22.1364i		−	0.728628i
$924$	−13.4503	−	8.27787i	−0.442482	−	0.272322i
$925$		−	11.4122i		−	0.375232i
$926$	−2.21524	+	14.5632i	−0.0727972	+	0.478576i
$927$	−4.79002	+	8.77696i	−0.157325	+	0.288273i
$928$	−13.7258	−	12.9099i	−0.450573	−	0.423788i
$929$			49.7280i			1.63152i	0.578389	+	0.815761i	$0.303682\pi$
$929$			49.7280i			1.63152i	−0.578389	+	0.815761i	$0.696318\pi$
$930$	14.9564	−	35.3022i	0.490439	−	1.15760i
$931$	0.0710306			0.00232794
$932$	−15.5882	+	50.0537i	−0.510609	+	1.63956i
$933$	−16.1374	−	4.11689i	−0.528315	−	0.134781i
$934$	−0.292837	+	1.92514i	−0.00958192	+	0.0629926i
$935$	−15.9407			−0.521316
$936$	−28.3086	+	20.1397i	−0.925296	+	0.658286i
$937$	35.3645			1.15531			0.577653	−	0.816282i	$-0.303969\pi$
$937$	35.3645			1.15531			0.577653	+	0.816282i	$0.303969\pi$
$938$	5.03127	−	33.0761i	0.164277	−	1.07997i
$939$	−5.77261	−	1.47268i	−0.188382	−	0.0480591i
$940$	7.91623	+	2.46535i	0.258199	+	0.0804109i
$941$	−60.0713			−1.95827			−0.979135	−	0.203211i	$-0.934862\pi$
$941$	−60.0713			−1.95827			−0.979135	+	0.203211i	$0.934862\pi$
$942$	−18.0044	+	42.4966i	−0.586617	+	1.38461i
$943$		−	9.73261i		−	0.316937i
$944$	2.95049	−	4.27757i	0.0960303	−	0.139223i
$945$	14.8667	−	15.9788i	0.483614	−	0.519789i
$946$	2.28961	−	15.0521i	0.0744416	−	0.489386i
$947$			12.0937i			0.392992i	0.980505	+	0.196496i	$0.0629562\pi$
$947$			12.0937i			0.392992i	−0.980505	+	0.196496i	$0.937044\pi$
$948$	7.73485	−	12.5679i	0.251216	−	0.408188i
$949$		−	33.1220i		−	1.07519i
$950$	−3.97249	−	0.604263i	−0.128884	−	0.0196049i
$951$	−0.176605	−	0.0450547i	−0.00572683	−	0.00146100i
$952$	39.7362	+	19.3354i	1.28786	+	0.626662i
$953$		−	28.2785i		−	0.916030i	−0.888944	−	0.458015i	$-0.848561\pi$
$953$		−	28.2785i		−	0.916030i	0.888944	−	0.458015i	$-0.151439\pi$
$954$	−29.4883	−	22.4418i	−0.954720	−	0.726579i
$955$	−14.0808			−0.455644
$956$	18.8678	+	5.87600i	0.610228	+	0.190043i
$957$	2.44675	−	9.59075i	0.0790920	−	0.310025i
$958$	−52.4436	−	7.97731i	−1.69438	−	0.257735i
$959$	27.7235			0.895237
$960$	8.83552	+	20.0387i	0.285165	+	0.646745i
$961$	−67.0744			−2.16369
$962$	−26.1105	−	3.97171i	−0.841835	−	0.128053i
$963$	0.616038	−	1.12879i	0.0198516	−	0.0363749i
$964$	6.10979	+	1.90277i	0.196783	+	0.0612842i
$965$	13.4009			0.431390
$966$	2.53942	−	5.99388i	0.0817044	−	0.192850i
$967$		−	28.9790i		−	0.931901i	−0.884811	−	0.465950i	$-0.845713\pi$
$967$		−	28.9790i		−	0.931901i	0.884811	−	0.465950i	$-0.154287\pi$
$968$	−20.4911	−	9.97084i	−0.658610	−	0.320475i
$969$	−2.85849	+	11.2047i	−0.0918279	+	0.359947i
$970$	−31.8031	−	4.83764i	−1.02114	−	0.155327i
$971$		−	15.2294i		−	0.488735i	−0.969683	−	0.244367i	$-0.921420\pi$
$971$		−	15.2294i		−	0.488735i	0.969683	−	0.244367i	$-0.0785803\pi$
$972$	0.621986	+	31.1707i	0.0199502	+	0.999801i
$973$			57.2956i			1.83681i
$974$	3.81177	−	25.0590i	0.122137	−	0.802942i
$975$	−4.38610	+	17.1926i	−0.140467	+	0.550604i
$976$	3.22563	−	4.67646i	0.103250	−	0.149690i
$977$		−	30.6879i		−	0.981792i	−0.871218	−	0.490896i	$-0.836669\pi$
$977$		−	30.6879i		−	0.981792i	0.871218	−	0.490896i	$-0.163331\pi$
$978$	48.5480	+	20.5682i	1.55239	+	0.657700i
$979$	−12.0429			−0.384892
$980$	−0.188775	−	0.0587902i	−0.00603019	−	0.00187798i
$981$	−16.7031	+	30.6059i	−0.533290	+	0.977170i
$982$	0.00474804	−	0.0312141i	0.000151516	−	0.000996083i
$983$	−56.6470			−1.80676			−0.903379	−	0.428843i	$-0.858921\pi$
$983$	−56.6470			−1.80676			−0.903379	+	0.428843i	$0.858921\pi$
$984$	30.8128	−	36.3860i	0.982276	−	1.15994i
$985$	31.8554			1.01500
$986$	−4.16481	+	27.3799i	−0.132635	+	0.871954i
$987$	2.98455	−	11.6988i	0.0949994	−	0.372378i
$988$	−2.76503	+	8.87850i	−0.0879674	+	0.282463i
$989$	6.27544			0.199547
$990$	−6.96672	+	9.15422i	−0.221417	+	0.290940i
$991$		−	6.91764i		−	0.219746i	−0.993946	−	0.109873i	$-0.964956\pi$
$991$		−	6.91764i		−	0.219746i	0.993946	−	0.109873i	$-0.0350444\pi$
$992$	38.3815	−	40.8074i	1.21861	−	1.29563i
$993$	12.9705	+	3.30896i	0.411606	+	0.105007i
$994$	−3.05572	+	20.0886i	−0.0969216	+	0.637173i
$995$		−	31.4124i		−	0.995840i
$996$	−29.6000	+	48.0956i	−0.937913	+	1.52397i
$997$			31.7349i			1.00505i	0.864561	+	0.502527i	$0.167596\pi$
$997$			31.7349i			1.00505i	−0.864561	+	0.502527i	$0.832404\pi$
$998$	21.9785	+	3.34320i	0.695718	+	0.105827i
$999$	−16.1443	+	17.3520i	−0.510784	+	0.548992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.c.323.1	✓	42
3.2	odd	2		552.2.j.d.323.42	yes	42
4.3	odd	2		2208.2.j.c.47.5		42
8.3	odd	2		552.2.j.d.323.41	yes	42
8.5	even	2		2208.2.j.d.47.5		42
12.11	even	2		2208.2.j.d.47.6		42
24.5	odd	2		2208.2.j.c.47.6		42
24.11	even	2	inner	552.2.j.c.323.2	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.1	✓	42	1.1	even	1	trivial
552.2.j.c.323.2	yes	42	24.11	even	2	inner
552.2.j.d.323.41	yes	42	8.3	odd	2
552.2.j.d.323.42	yes	42	3.2	odd	2
2208.2.j.c.47.5		42	4.3	odd	2
2208.2.j.c.47.6		42	24.5	odd	2
2208.2.j.d.47.5		42	8.5	even	2
2208.2.j.d.47.6		42	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39813 - 0.212673i) q^{2} +(1.67830 + 0.428159i) q^{3} +(1.90954 + 0.594688i) q^{4} +1.58050 q^{5} +(-2.25542 - 0.955550i) q^{6} -2.65755i q^{7} +(-2.54331 - 1.23756i) q^{8} +(2.63336 + 1.43716i) q^{9} +O(q^{10})\)	\(q+(-1.39813 - 0.212673i) q^{2} +(1.67830 + 0.428159i) q^{3} +(1.90954 + 0.594688i) q^{4} +1.58050 q^{5} +(-2.25542 - 0.955550i) q^{6} -2.65755i q^{7} +(-2.54331 - 1.23756i) q^{8} +(2.63336 + 1.43716i) q^{9} +(-2.20975 - 0.336130i) q^{10} -1.71556i q^{11} +(2.95016 + 1.81565i) q^{12} -4.09435i q^{13} +(-0.565187 + 3.71560i) q^{14} +(2.65255 + 0.676707i) q^{15} +(3.29269 + 2.27116i) q^{16} -5.87903i q^{17} +(-3.37614 - 2.56937i) q^{18} -1.13560 q^{19} +(3.01804 + 0.939907i) q^{20} +(1.13785 - 4.46015i) q^{21} +(-0.364852 + 2.39858i) q^{22} -1.00000 q^{23} +(-3.73856 - 3.16593i) q^{24} -2.50201 q^{25} +(-0.870755 + 5.72443i) q^{26} +(3.80423 + 3.53947i) q^{27} +(1.58041 - 5.07469i) q^{28} +3.33103 q^{29} +(-3.56470 - 1.51025i) q^{30} +9.90325i q^{31} +(-4.12060 - 3.87565i) q^{32} +(0.734531 - 2.87922i) q^{33} +(-1.25031 + 8.21965i) q^{34} -4.20026i q^{35} +(4.17385 + 4.31033i) q^{36} +4.56123i q^{37} +(1.58772 + 0.241511i) q^{38} +(1.75303 - 6.87153i) q^{39} +(-4.01972 - 1.95597i) q^{40} +9.73261i q^{41} +(-2.53942 + 5.99388i) q^{42} -6.27544 q^{43} +(1.02022 - 3.27593i) q^{44} +(4.16204 + 2.27143i) q^{45} +(1.39813 + 0.212673i) q^{46} +2.62297 q^{47} +(4.55370 + 5.22148i) q^{48} -0.0625489 q^{49} +(3.49813 + 0.532108i) q^{50} +(2.51716 - 9.86675i) q^{51} +(2.43486 - 7.81832i) q^{52} +8.73434 q^{53} +(-4.56606 - 5.75770i) q^{54} -2.71145i q^{55} +(-3.28887 + 6.75897i) q^{56} +(-1.90588 - 0.486218i) q^{57} +(-4.65721 - 0.708418i) q^{58} -1.29911i q^{59} +(4.66273 + 2.86964i) q^{60} -1.42025i q^{61} +(2.10615 - 13.8460i) q^{62} +(3.81931 - 6.99827i) q^{63} +(4.93690 + 6.29500i) q^{64} -6.47113i q^{65} +(-1.63930 + 3.86931i) q^{66} -8.90196 q^{67} +(3.49619 - 11.2262i) q^{68} +(-1.67830 - 0.428159i) q^{69} +(-0.893280 + 5.87252i) q^{70} +5.40657 q^{71} +(-4.91890 - 6.91408i) q^{72} +8.08970 q^{73} +(0.970048 - 6.37719i) q^{74} +(-4.19911 - 1.07126i) q^{75} +(-2.16848 - 0.675329i) q^{76} -4.55918 q^{77} +(-3.91235 + 9.23448i) q^{78} -4.26010i q^{79} +(5.20411 + 3.58958i) q^{80} +(4.86917 + 7.56909i) q^{81} +(2.06986 - 13.6075i) q^{82} +16.3027i q^{83} +(4.82517 - 7.84017i) q^{84} -9.29183i q^{85} +(8.77388 + 1.33461i) q^{86} +(5.59045 + 1.42621i) q^{87} +(-2.12310 + 4.36320i) q^{88} -7.01980i q^{89} +(-5.33600 - 4.06091i) q^{90} -10.8809 q^{91} +(-1.90954 - 0.594688i) q^{92} +(-4.24016 + 16.6206i) q^{93} +(-3.66726 - 0.557834i) q^{94} -1.79482 q^{95} +(-5.25620 - 8.26876i) q^{96} +14.3922 q^{97} +(0.0874516 + 0.0133024i) q^{98} +(2.46552 - 4.51768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more