LMFDB - Embedded newform 280.2.s.c.13.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(13,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))

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

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

chi := DirichletCharacter("280.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.19
Character	$\chi$	$=$	280.13
Dual form			280.2.s.c.237.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00402547 - 1.41421i) q^{2} +(-1.09655 - 1.09655i) q^{3} +(-1.99997 - 0.0113857i) q^{4} +(0.721255 - 2.11655i) q^{5} +(-1.55517 + 1.54634i) q^{6} +(-2.63247 + 0.264726i) q^{7} +(-0.0241525 + 2.82832i) q^{8} -0.595144i q^{9} +O(q^{10})$	\(q+(0.00402547 - 1.41421i) q^{2} +(-1.09655 - 1.09655i) q^{3} +(-1.99997 - 0.0113857i) q^{4} +(0.721255 - 2.11655i) q^{5} +(-1.55517 + 1.54634i) q^{6} +(-2.63247 + 0.264726i) q^{7} +(-0.0241525 + 2.82832i) q^{8} -0.595144i q^{9} +(-2.99034 - 1.02852i) q^{10} +2.35868i q^{11} +(2.18059 + 2.20556i) q^{12} +(-1.27672 - 1.27672i) q^{13} +(0.363780 + 3.72393i) q^{14} +(-3.11181 + 1.53002i) q^{15} +(3.99974 + 0.0455420i) q^{16} +(-1.60730 - 1.60730i) q^{17} +(-0.841657 - 0.00239573i) q^{18} +2.48261i q^{19} +(-1.46659 + 4.22482i) q^{20} +(3.17693 + 2.59636i) q^{21} +(3.33567 + 0.00949480i) q^{22} +(0.615870 + 0.615870i) q^{23} +(3.12789 - 3.07492i) q^{24} +(-3.95958 - 3.05315i) q^{25} +(-1.81068 + 1.80041i) q^{26} +(-3.94227 + 3.94227i) q^{27} +(5.26788 - 0.499471i) q^{28} +0.914789 q^{29} +(2.15123 + 4.40690i) q^{30} -5.53513i q^{31} +(0.0805067 - 5.65628i) q^{32} +(2.58642 - 2.58642i) q^{33} +(-2.27952 + 2.26658i) q^{34} +(-1.33838 + 5.76270i) q^{35} +(-0.00677612 + 1.19027i) q^{36} +(-7.02741 - 7.02741i) q^{37} +(3.51093 + 0.00999366i) q^{38} +2.79998i q^{39} +(5.96887 + 2.09106i) q^{40} +5.48122i q^{41} +(3.68458 - 4.48239i) q^{42} +(7.03012 - 7.03012i) q^{43} +(0.0268552 - 4.71729i) q^{44} +(-1.25965 - 0.429250i) q^{45} +(0.873448 - 0.868490i) q^{46} +(-8.82639 - 8.82639i) q^{47} +(-4.33599 - 4.43587i) q^{48} +(6.85984 - 1.39377i) q^{49} +(-4.33372 + 5.58738i) q^{50} +3.52498i q^{51} +(2.53886 + 2.56793i) q^{52} +(4.92582 - 4.92582i) q^{53} +(5.55931 + 5.59105i) q^{54} +(4.99228 + 1.70121i) q^{55} +(-0.685150 - 7.45188i) q^{56} +(2.72231 - 2.72231i) q^{57} +(0.00368245 - 1.29370i) q^{58} -5.85624i q^{59} +(6.24093 - 3.02455i) q^{60} +1.78334 q^{61} +(-7.82783 - 0.0222815i) q^{62} +(0.157550 + 1.56670i) q^{63} +(-7.99883 - 0.136622i) q^{64} +(-3.62308 + 1.78140i) q^{65} +(-3.64733 - 3.66815i) q^{66} +(5.48915 + 5.48915i) q^{67} +(3.19624 + 3.23284i) q^{68} -1.35067i q^{69} +(8.14427 + 1.91594i) q^{70} -10.6024 q^{71} +(1.68326 + 0.0143742i) q^{72} +(2.44585 - 2.44585i) q^{73} +(-9.96651 + 9.90993i) q^{74} +(0.993953 + 7.68983i) q^{75} +(0.0282662 - 4.96514i) q^{76} +(-0.624405 - 6.20917i) q^{77} +(3.95975 + 0.0112712i) q^{78} -8.51575i q^{79} +(2.98123 - 8.43281i) q^{80} +6.86037 q^{81} +(7.75158 + 0.0220645i) q^{82} +(-6.43943 - 6.43943i) q^{83} +(-6.32420 - 5.22881i) q^{84} +(-4.56120 + 2.24266i) q^{85} +(-9.91375 - 9.97034i) q^{86} +(-1.00311 - 1.00311i) q^{87} +(-6.67112 - 0.0569682i) q^{88} -8.47427 q^{89} +(-0.612120 + 1.77968i) q^{90} +(3.69891 + 3.02295i) q^{91} +(-1.22471 - 1.23873i) q^{92} +(-6.06957 + 6.06957i) q^{93} +(-12.5179 + 12.4468i) q^{94} +(5.25457 + 1.79059i) q^{95} +(-6.29069 + 6.11413i) q^{96} +(13.8585 + 13.8585i) q^{97} +(-1.94346 - 9.70685i) q^{98} +1.40376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.00402547	−	1.41421i	0.00284643	−	0.999996i
$2$	0.00402547	−	1.41421i	0.00284643	−	0.999996i
$3$	−1.09655	−	1.09655i	−0.633095	−	0.633095i	0.315748	−	0.948843i	$-0.397745\pi$
$3$	−1.09655	−	1.09655i	−0.633095	−	0.633095i	−0.948843	+	0.315748i	$0.897745\pi$
$4$	−1.99997	−	0.0113857i	−0.999984	−	0.00569284i
$5$	0.721255	−	2.11655i	0.322555	−	0.946551i
$5$	0.721255	−	2.11655i	0.322555	−	0.946551i
$6$	−1.55517	+	1.54634i	−0.634895	+	0.631290i
$7$	−2.63247	+	0.264726i	−0.994982	+	0.100057i
$7$	−2.63247	+	0.264726i	−0.994982	+	0.100057i
$8$	−0.0241525	+	2.82832i	−0.00853921	+	0.999964i
$9$		−	0.595144i		−	0.198381i
$10$	−2.99034	−	1.02852i	−0.945629	−	0.325248i
$11$			2.35868i			0.711170i	0.934644	+	0.355585i	$0.115718\pi$
$11$			2.35868i			0.711170i	−0.934644	+	0.355585i	$0.884282\pi$
$12$	2.18059	+	2.20556i	0.629481	+	0.636689i
$13$	−1.27672	−	1.27672i	−0.354098	−	0.354098i	0.507534	−	0.861632i	$-0.330557\pi$
$13$	−1.27672	−	1.27672i	−0.354098	−	0.354098i	−0.861632	+	0.507534i	$0.830557\pi$
$14$	0.363780	+	3.72393i	0.0972244	+	0.995262i
$15$	−3.11181	+	1.53002i	−0.803465	+	0.395049i
$16$	3.99974	+	0.0455420i	0.999935	+	0.0113855i
$17$	−1.60730	−	1.60730i	−0.389827	−	0.389827i	0.484799	−	0.874626i	$-0.338893\pi$
$17$	−1.60730	−	1.60730i	−0.389827	−	0.389827i	−0.874626	+	0.484799i	$0.838893\pi$
$18$	−0.841657	−	0.00239573i	−0.198380	−	0.000564679i
$19$			2.48261i			0.569550i	0.958594	+	0.284775i	$0.0919188\pi$
$19$			2.48261i			0.569550i	−0.958594	+	0.284775i	$0.908081\pi$
$20$	−1.46659	+	4.22482i	−0.327938	+	0.944699i
$21$	3.17693	+	2.59636i	0.693264	+	0.566572i
$22$	3.33567	+	0.00949480i	0.711167	+	0.00202430i
$23$	0.615870	+	0.615870i	0.128418	+	0.128418i	0.768394	−	0.639977i	$-0.221056\pi$
$23$	0.615870	+	0.615870i	0.128418	+	0.128418i	−0.639977	+	0.768394i	$0.721056\pi$
$24$	3.12789	−	3.07492i	0.638478	−	0.627666i
$25$	−3.95958	−	3.05315i	−0.791916	−	0.610630i
$26$	−1.81068	+	1.80041i	−0.355104	+	0.353088i
$27$	−3.94227	+	3.94227i	−0.758689	+	0.758689i
$28$	5.26788	−	0.499471i	0.995535	−	0.0943911i
$29$	0.914789			0.169872			0.0849360	−	0.996386i	$-0.472931\pi$
$29$	0.914789			0.169872			0.0849360	+	0.996386i	$0.472931\pi$
$30$	2.15123	+	4.40690i	0.392760	+	0.804586i
$31$		−	5.53513i		−	0.994139i	−0.867711	−	0.497070i	$-0.834409\pi$
$31$		−	5.53513i		−	0.994139i	0.867711	−	0.497070i	$-0.165591\pi$
$32$	0.0805067	−	5.65628i	0.0142317	−	0.999899i
$33$	2.58642	−	2.58642i	0.450238	−	0.450238i
$34$	−2.27952	+	2.26658i	−0.390935	+	0.388716i
$35$	−1.33838	+	5.76270i	−0.226227	+	0.974075i
$36$	−0.00677612	+	1.19027i	−0.00112935	+	0.198378i
$37$	−7.02741	−	7.02741i	−1.15530	−	1.15530i	−0.985474	−	0.169825i	$-0.945680\pi$
$37$	−7.02741	−	7.02741i	−1.15530	−	1.15530i	−0.169825	−	0.985474i	$-0.554320\pi$
$38$	3.51093	+	0.00999366i	0.569547	+	0.00162119i
$39$			2.79998i			0.448355i
$40$	5.96887	+	2.09106i	0.943762	+	0.330626i
$41$			5.48122i			0.856022i	0.903773	+	0.428011i	$0.140786\pi$
$41$			5.48122i			0.856022i	−0.903773	+	0.428011i	$0.859214\pi$
$42$	3.68458	−	4.48239i	0.568544	−	0.691648i
$43$	7.03012	−	7.03012i	1.07208	−	1.07208i	0.0748909	−	0.997192i	$-0.476139\pi$
$43$	7.03012	−	7.03012i	1.07208	−	1.07208i	0.997192	−	0.0748909i	$-0.0238609\pi$
$44$	0.0268552	−	4.71729i	0.00404858	−	0.711158i
$45$	−1.25965	−	0.429250i	−0.187778	−	0.0639889i
$46$	0.873448	−	0.868490i	0.128783	−	0.128052i
$47$	−8.82639	−	8.82639i	−1.28746	−	1.28746i	−0.936324	−	0.351138i	$-0.885795\pi$
$47$	−8.82639	−	8.82639i	−1.28746	−	1.28746i	−0.351138	−	0.936324i	$-0.614205\pi$
$48$	−4.33599	−	4.43587i	−0.625846	−	0.640262i
$49$	6.85984	−	1.39377i	0.979977	−	0.199110i
$50$	−4.33372	+	5.58738i	−0.612881	+	0.790175i
$51$			3.52498i			0.493595i
$52$	2.53886	+	2.56793i	0.352076	+	0.356108i
$53$	4.92582	−	4.92582i	0.676613	−	0.676613i	−0.282619	−	0.959232i	$-0.591203\pi$
$53$	4.92582	−	4.92582i	0.676613	−	0.676613i	0.959232	+	0.282619i	$0.0912033\pi$
$54$	5.55931	+	5.59105i	0.756527	+	0.760846i
$55$	4.99228	+	1.70121i	0.673158	+	0.229391i
$56$	−0.685150	−	7.45188i	−0.0915570	−	0.995800i
$57$	2.72231	−	2.72231i	0.360579	−	0.360579i
$58$	0.00368245	−	1.29370i	0.000483529	−	0.169871i
$59$		−	5.85624i		−	0.762417i	−0.924489	−	0.381209i	$-0.875508\pi$
$59$		−	5.85624i		−	0.762417i	0.924489	−	0.381209i	$-0.124492\pi$
$60$	6.24093	−	3.02455i	0.805701	−	0.390468i
$61$	1.78334			0.228334			0.114167	−	0.993462i	$-0.463580\pi$
$61$	1.78334			0.228334			0.114167	+	0.993462i	$0.463580\pi$
$62$	−7.82783	−	0.0222815i	−0.994135	−	0.00282975i
$63$	0.157550	+	1.56670i	0.0198494	+	0.197386i
$64$	−7.99883	−	0.136622i	−0.999854	−	0.0170778i
$65$	−3.62308	+	1.78140i	−0.449388	+	0.220955i
$66$	−3.64733	−	3.66815i	−0.448955	−	0.451518i
$67$	5.48915	+	5.48915i	0.670607	+	0.670607i	0.957856	−	0.287249i	$-0.0927407\pi$
$67$	5.48915	+	5.48915i	0.670607	+	0.670607i	−0.287249	+	0.957856i	$0.592741\pi$
$68$	3.19624	+	3.23284i	0.387602	+	0.392040i
$69$		−	1.35067i		−	0.162601i
$70$	8.14427	+	1.91594i	0.973427	+	0.228999i
$71$	−10.6024			−1.25827			−0.629137	−	0.777295i	$-0.716591\pi$
$71$	−10.6024			−1.25827			−0.629137	+	0.777295i	$0.716591\pi$
$72$	1.68326	+	0.0143742i	0.198374	+	0.00169402i
$73$	2.44585	−	2.44585i	0.286265	−	0.286265i	−0.549336	−	0.835601i	$-0.685119\pi$
$73$	2.44585	−	2.44585i	0.286265	−	0.286265i	0.835601	+	0.549336i	$0.185119\pi$
$74$	−9.96651	+	9.90993i	−1.15858	+	1.15201i
$75$	0.993953	+	7.68983i	0.114772	+	0.887945i
$76$	0.0282662	−	4.96514i	0.00324236	−	0.569540i
$77$	−0.624405	−	6.20917i	−0.0711575	−	0.707601i
$78$	3.95975	+	0.0112712i	0.448353	+	0.00127621i
$79$		−	8.51575i		−	0.958096i	−0.877789	−	0.479048i	$-0.840982\pi$
$79$		−	8.51575i		−	0.958096i	0.877789	−	0.479048i	$-0.159018\pi$
$80$	2.98123	−	8.43281i	0.333311	−	0.942817i
$81$	6.86037			0.762264
$82$	7.75158	+	0.0220645i	0.856019	+	0.00243661i
$83$	−6.43943	−	6.43943i	−0.706819	−	0.706819i	0.259046	−	0.965865i	$-0.416592\pi$
$83$	−6.43943	−	6.43943i	−0.706819	−	0.706819i	−0.965865	+	0.259046i	$0.916592\pi$
$84$	−6.32420	−	5.22881i	−0.690027	−	0.570510i
$85$	−4.56120	+	2.24266i	−0.494732	+	0.243250i
$86$	−9.91375	−	9.97034i	−1.06903	−	1.07513i
$87$	−1.00311	−	1.00311i	−0.107545	−	0.107545i
$88$	−6.67112	−	0.0569682i	−0.711144	−	0.00607283i
$89$	−8.47427			−0.898271			−0.449136	−	0.893464i	$-0.648268\pi$
$89$	−8.47427			−0.898271			−0.449136	+	0.893464i	$0.648268\pi$
$90$	−0.612120	+	1.77968i	−0.0645231	+	0.187595i
$91$	3.69891	+	3.02295i	0.387751	+	0.316891i
$92$	−1.22471	−	1.23873i	−0.127685	−	0.129147i
$93$	−6.06957	+	6.06957i	−0.629385	+	0.629385i
$94$	−12.5179	+	12.4468i	−1.29112	+	1.28379i
$95$	5.25457	+	1.79059i	0.539108	+	0.183711i
$96$	−6.29069	+	6.11413i	−0.642041	+	0.624021i
$97$	13.8585	+	13.8585i	1.40711	+	1.40711i	0.774318	+	0.632796i	$0.218093\pi$
$97$	13.8585	+	13.8585i	1.40711	+	1.40711i	0.632796	+	0.774318i	$0.281907\pi$
$98$	−1.94346	−	9.70685i	−0.196319	−	0.980540i
$99$	1.40376			0.141083
$100$	7.88427	+	6.15128i	0.788427	+	0.615128i
$101$	15.8961			1.58172			0.790859	−	0.611998i	$-0.209634\pi$
$101$	15.8961			1.58172			0.790859	+	0.611998i	$0.209634\pi$
$102$	4.98505	+	0.0141897i	0.493593	+	0.00140499i
$103$	−8.37218	+	8.37218i	−0.824935	+	0.824935i	−0.986811	−	0.161876i	$-0.948246\pi$
$103$	−8.37218	+	8.37218i	−0.824935	+	0.824935i	0.161876	+	0.986811i	$0.448246\pi$
$104$	3.64181	−	3.58014i	0.357109	−	0.351061i
$105$	7.78671	−	4.85150i	0.759905	−	0.473458i
$106$	−6.94630	−	6.98596i	−0.674684	−	0.678536i
$107$	2.68201	+	2.68201i	0.259279	+	0.259279i	0.824761	−	0.565482i	$-0.191310\pi$
$107$	2.68201	+	2.68201i	0.259279	+	0.259279i	−0.565482	+	0.824761i	$0.691310\pi$
$108$	7.92929	−	7.83952i	0.762996	−	0.754358i
$109$	2.50071			0.239525			0.119762	−	0.992803i	$-0.461787\pi$
$109$	2.50071			0.239525			0.119762	+	0.992803i	$0.461787\pi$
$110$	2.42596	−	7.05327i	0.231307	−	0.672503i
$111$			15.4119i			1.46283i
$112$	−10.5413	+	0.938947i	−0.996056	+	0.0887221i
$113$	13.1037	+	13.1037i	1.23269	+	1.23269i	0.962926	+	0.269767i	$0.0869466\pi$
$113$	13.1037	+	13.1037i	1.23269	+	1.23269i	0.269767	+	0.962926i	$0.413053\pi$
$114$	−3.83896	−	3.86087i	−0.359551	−	0.361604i
$115$	1.74772	−	0.859322i	0.162976	−	0.0801322i
$116$	−1.82955	−	0.0104155i	−0.169869	−	0.000967055i
$117$	−0.759830	+	0.759830i	−0.0702464	+	0.0702464i
$118$	−8.28194	−	0.0235741i	−0.762414	−	0.00217017i
$119$	4.65666	+	3.80568i	0.426876	+	0.348866i
$120$	−4.25222	−	8.83815i	−0.388173	−	0.806809i
$121$	5.43661			0.494237
$122$	0.00717878	−	2.52202i	0.000649936	−	0.228333i
$123$	6.01044	−	6.01044i	0.541944	−	0.541944i
$124$	−0.0630213	+	11.0701i	−0.00565948	+	0.994123i
$125$	−9.31801	+	6.17856i	−0.833428	+	0.552627i
$126$	2.21627	−	0.216502i	0.197441	−	0.0192875i
$127$	10.6968	−	10.6968i	0.949187	−	0.949187i	−0.0495825	−	0.998770i	$-0.515789\pi$
$127$	10.6968	−	10.6968i	0.949187	−	0.949187i	0.998770	+	0.0495825i	$0.0157891\pi$
$128$	−0.225411	+	11.3115i	−0.0199237	+	0.999802i
$129$	−15.4178			−1.35746
$130$	2.50469	+	5.13096i	0.219675	+	0.450015i
$131$	−6.66310			−0.582158			−0.291079	−	0.956699i	$-0.594014\pi$
$131$	−6.66310			−0.582158			−0.291079	+	0.956699i	$0.594014\pi$
$132$	−5.20221	+	5.14331i	−0.452794	+	0.447668i
$133$	−0.657211	−	6.53540i	−0.0569874	−	0.566691i
$134$	7.78490	−	7.74071i	0.672513	−	0.668695i
$135$	5.50063	+	11.1874i	0.473419	+	0.962857i
$136$	4.58478	−	4.50714i	0.393142	−	0.386484i
$137$	−3.88185	+	3.88185i	−0.331649	+	0.331649i	−0.853212	−	0.521564i	$-0.825349\pi$
$137$	−3.88185	+	3.88185i	−0.331649	+	0.331649i	0.521564	+	0.853212i	$0.325349\pi$
$138$	−1.91013	−	0.00543707i	−0.162601	−	0.000462834i
$139$		−	2.97870i		−	0.252650i	−0.991989	−	0.126325i	$-0.959682\pi$
$139$		−	2.97870i		−	0.252650i	0.991989	−	0.126325i	$-0.0403182\pi$
$140$	2.74233	−	11.5100i	0.231769	−	0.972771i
$141$			19.3572i			1.63017i
$142$	−0.0426796	+	14.9940i	−0.00358159	+	1.25827i
$143$	3.01137	−	3.01137i	0.251824	−	0.251824i
$144$	0.0271040	−	2.38042i	0.00225867	−	0.198368i
$145$	0.659796	−	1.93620i	0.0547931	−	0.160792i
$146$	−3.44910	−	3.46879i	−0.285449	−	0.287079i
$147$	−9.05052	−	5.99384i	−0.746474	−	0.494363i
$148$	13.9746	+	14.1346i	1.14870	+	1.16186i
$149$	10.6393			0.871607			0.435803	−	0.900042i	$-0.356464\pi$
$149$	10.6393			0.871607			0.435803	+	0.900042i	$0.356464\pi$
$150$	10.8790	−	1.37470i	0.888268	−	0.112244i
$151$	3.51689			0.286201			0.143100	−	0.989708i	$-0.454293\pi$
$151$	3.51689			0.286201			0.143100	+	0.989708i	$0.454293\pi$
$152$	−7.02162	−	0.0599613i	−0.569529	−	0.00486350i
$153$	−0.956573	+	0.956573i	−0.0773344	+	0.0773344i
$154$	−8.78358	+	0.858043i	−0.707801	+	0.0691431i
$155$	−11.7154	−	3.99224i	−0.941003	−	0.320665i
$156$	0.0318797	−	5.59986i	0.00255242	−	0.448348i
$157$	−15.0966	+	15.0966i	−1.20484	+	1.20484i	−0.232160	+	0.972678i	$0.574579\pi$
$157$	−15.0966	+	15.0966i	−1.20484	+	1.20484i	−0.972678	+	0.232160i	$0.925421\pi$
$158$	−12.0430	−	0.0342798i	−0.958093	−	0.00272716i
$159$	−10.8028			−0.856721
$160$	−11.9137	−	4.25002i	−0.941864	−	0.335993i
$161$	−1.78430	−	1.45823i	−0.140623	−	0.114924i
$162$	0.0276162	−	9.70199i	0.00216973	−	0.762261i
$163$	1.01426	−	1.01426i	0.0794429	−	0.0794429i	−0.666269	−	0.745712i	$-0.732110\pi$
$163$	1.01426	−	1.01426i	0.0794429	−	0.0794429i	0.745712	+	0.666269i	$0.232110\pi$
$164$	0.0624074	−	10.9623i	0.00487320	−	0.856008i
$165$	−3.60883	−	7.33976i	−0.280947	−	0.571400i
$166$	−9.13261	+	9.08077i	−0.708828	+	0.704804i
$167$	10.8826	+	10.8826i	0.842124	+	0.842124i	0.989135	−	0.147011i	$-0.0469653\pi$
$167$	10.8826	+	10.8826i	0.842124	+	0.842124i	−0.147011	+	0.989135i	$0.546965\pi$
$168$	−7.42008	+	8.92269i	−0.572472	+	0.688400i
$169$		−	9.73998i		−	0.749229i
$170$	3.15322	+	6.45952i	0.241841	+	0.495422i
$171$	1.47751			0.112988
$172$	−14.1400	+	13.9800i	−1.07817	+	1.06596i
$173$	−11.2808	−	11.2808i	−0.857662	−	0.857662i	0.133400	−	0.991062i	$-0.457410\pi$
$173$	−11.2808	−	11.2808i	−0.857662	−	0.857662i	−0.991062	+	0.133400i	$0.957410\pi$
$174$	−1.42265	+	1.41457i	−0.107851	+	0.107239i
$175$	11.2317	+	6.98913i	0.849040	+	0.528328i
$176$	−0.107419	+	9.43412i	−0.00809703	+	0.711124i
$177$	−6.42168	+	6.42168i	−0.482683	+	0.482683i
$178$	−0.0341129	+	11.9844i	−0.00255687	+	0.898268i
$179$	−12.3821			−0.925479			−0.462739	−	0.886494i	$-0.653133\pi$
$179$	−12.3821			−0.925479			−0.462739	+	0.886494i	$0.653133\pi$
$180$	2.51438	+	0.872829i	0.187411	+	0.0650568i
$181$	5.13021			0.381326			0.190663	−	0.981656i	$-0.438936\pi$
$181$	5.13021			0.381326			0.190663	+	0.981656i	$0.438936\pi$
$182$	4.28996	−	5.21885i	0.317993	−	0.386847i
$183$	−1.95553	−	1.95553i	−0.144557	−	0.144557i
$184$	−1.75676	+	1.72701i	−0.129510	+	0.127317i
$185$	−19.9424	+	9.80532i	−1.46620	+	0.720902i
$186$	8.55920	+	8.60806i	0.627591	+	0.631174i
$187$	3.79111	−	3.79111i	0.277233	−	0.277233i
$188$	17.5520	+	17.7530i	1.28011	+	1.29477i
$189$	9.33429	−	11.4215i	0.678970	−	0.830794i
$190$	2.55343	−	7.42385i	0.185245	−	0.538582i
$191$	−3.71725			−0.268971			−0.134485	−	0.990916i	$-0.542938\pi$
$191$	−3.71725			−0.268971			−0.134485	+	0.990916i	$0.542938\pi$
$192$	8.62133	+	8.92096i	0.622191	+	0.643815i
$193$	−12.7918	−	12.7918i	−0.920774	−	0.920774i	0.0763098	−	0.997084i	$-0.475686\pi$
$193$	−12.7918	−	12.7918i	−0.920774	−	0.920774i	−0.997084	+	0.0763098i	$0.975686\pi$
$194$	19.6545	−	19.5430i	1.41111	−	1.40310i
$195$	5.92630	+	2.01950i	0.424391	+	0.144619i
$196$	−13.7353	+	2.70939i	−0.981095	+	0.193528i
$197$	−9.28519	−	9.28519i	−0.661543	−	0.661543i	0.294201	−	0.955744i	$-0.404946\pi$
$197$	−9.28519	−	9.28519i	−0.661543	−	0.661543i	−0.955744	+	0.294201i	$0.904946\pi$
$198$	0.00565077	−	1.98520i	0.000401583	−	0.141082i
$199$	25.8840			1.83487			0.917435	−	0.397886i	$-0.130256\pi$
$199$	25.8840			1.83487			0.917435	+	0.397886i	$0.130256\pi$
$200$	8.73092	−	11.1252i	0.617370	−	0.786673i
$201$		−	12.0383i		−	0.849116i
$202$	0.0639891	−	22.4804i	0.00450226	−	1.58171i
$203$	−2.40816	+	0.242168i	−0.169020	+	0.0169969i
$204$	0.0401343	−	7.04984i	0.00280996	−	0.493587i
$205$	11.6013	+	3.95336i	0.810269	+	0.276114i
$206$	11.8063	+	11.8737i	0.822584	+	0.827280i
$207$	0.366531	−	0.366531i	0.0254757	−	0.0254757i
$208$	−5.04840	−	5.16468i	−0.350043	−	0.358106i
$209$	−5.85569			−0.405047
$210$	−6.82969	−	11.0316i	−0.471293	−	0.761250i
$211$			2.55282i			0.175743i	0.996132	+	0.0878716i	$0.0280065\pi$
$211$			2.55282i			0.175743i	−0.996132	+	0.0878716i	$0.971993\pi$
$212$	−9.90756	+	9.79539i	−0.680454	+	0.672750i
$213$	11.6261	+	11.6261i	0.796607	+	0.796607i
$214$	3.80371	−	3.78212i	0.260016	−	0.258540i
$215$	−9.80910	−	19.9501i	−0.668975	−	1.36059i
$216$	−11.0548	−	11.2452i	−0.752183	−	0.765140i
$217$	1.46529	+	14.5711i	0.0994706	+	0.989151i
$218$	0.0100665	−	3.53653i	0.000681792	−	0.239524i
$219$	−5.36401			−0.362466
$220$	−9.96502	−	3.45921i	−0.671842	−	0.233220i
$221$			4.10413i			0.276074i
$222$	21.7956	+	0.0620399i	1.46282	+	0.00416384i
$223$	11.5868	−	11.5868i	0.775908	−	0.775908i	−0.203224	−	0.979132i	$-0.565142\pi$
$223$	11.5868	−	11.5868i	0.775908	−	0.775908i	0.979132	+	0.203224i	$0.0651421\pi$
$224$	1.28543	+	14.9113i	0.0858865	+	0.996305i
$225$	−1.81706	+	2.35652i	−0.121137	+	0.157101i
$226$	18.5841	−	18.4786i	1.23620	−	1.22918i
$227$	14.8711	−	14.8711i	0.987032	−	0.987032i	−0.0128847	−	0.999917i	$-0.504101\pi$
$227$	14.8711	−	14.8711i	0.987032	−	0.987032i	0.999917	+	0.0128847i	$0.00410145\pi$
$228$	−5.47553	+	5.41354i	−0.362626	+	0.358520i
$229$		−	9.95151i		−	0.657615i	−0.944397	−	0.328807i	$-0.893353\pi$
$229$		−	9.95151i		−	0.657615i	0.944397	−	0.328807i	$-0.106647\pi$
$230$	−1.20822	−	2.47510i	−0.0796680	−	0.163203i
$231$	−6.12400	+	7.49338i	−0.402929	+	0.493028i
$232$	−0.0220945	+	2.58732i	−0.00145057	+	0.169866i
$233$	2.82674	+	2.82674i	0.185186	+	0.185186i	0.793611	−	0.608425i	$-0.208198\pi$
$233$	2.82674	+	2.82674i	0.185186	+	0.185186i	−0.608425	+	0.793611i	$0.708198\pi$
$234$	1.07150	+	1.07762i	0.0700461	+	0.0704460i
$235$	−25.0476	+	12.3154i	−1.63393	+	0.803371i
$236$	−0.0666773	+	11.7123i	−0.00434032	+	0.762405i
$237$	−9.33797	+	9.33797i	−0.606566	+	0.606566i
$238$	5.40076	−	6.57017i	0.350080	−	0.425881i
$239$			7.84360i			0.507361i	0.967288	+	0.253680i	$0.0816411\pi$
$239$			7.84360i			0.507361i	−0.967288	+	0.253680i	$0.918359\pi$
$240$	−12.5161	+	5.97795i	−0.807910	+	0.385875i
$241$		−	21.6109i		−	1.39208i	−0.718001	−	0.696042i	$-0.754943\pi$
$241$		−	21.6109i		−	1.39208i	0.718001	−	0.696042i	$-0.245057\pi$
$242$	0.0218849	−	7.68850i	0.00140681	−	0.494235i
$243$	4.30403	+	4.30403i	0.276104	+	0.276104i
$244$	−3.56663	−	0.0203046i	−0.228330	−	0.00129987i
$245$	1.99771	−	15.5245i	0.127629	−	0.991822i
$246$	−8.47582	−	8.52421i	−0.540399	−	0.543484i
$247$	3.16959	−	3.16959i	0.201676	−	0.201676i
$248$	15.6552	+	0.133688i	0.994103	+	0.00848917i
$249$			14.1223i			0.894967i
$250$	8.70026	+	13.2025i	0.550253	+	0.834998i
$251$	3.86833			0.244167			0.122083	−	0.992520i	$-0.461042\pi$
$251$	3.86833			0.244167			0.122083	+	0.992520i	$0.461042\pi$
$252$	−0.297257	−	3.13514i	−0.0187254	−	0.197495i
$253$	−1.45264	+	1.45264i	−0.0913269	+	0.0913269i
$254$	−15.0844	−	15.1706i	−0.946482	−	0.951885i
$255$	7.46079	+	2.54241i	0.467213	+	0.159212i
$256$	15.9959	+	0.364313i	0.999741	+	0.0227695i
$257$	−8.27249	−	8.27249i	−0.516024	−	0.516024i	0.400342	−	0.916366i	$-0.368891\pi$
$257$	−8.27249	−	8.27249i	−0.516024	−	0.516024i	−0.916366	+	0.400342i	$0.868891\pi$
$258$	−0.0620638	+	21.8040i	−0.00386392	+	1.35746i
$259$	20.3598	+	16.6391i	1.26510	+	1.03391i
$260$	7.26632	−	3.52149i	0.450638	−	0.218394i
$261$		−	0.544431i		−	0.0336994i
$262$	−0.0268221	+	9.42301i	−0.00165707	+	0.582155i
$263$	−8.10154	−	8.10154i	−0.499562	−	0.499562i	0.411739	−	0.911302i	$-0.364921\pi$
$263$	−8.10154	−	8.10154i	−0.499562	−	0.499562i	−0.911302	+	0.411739i	$0.864921\pi$
$264$	7.25277	+	7.37771i	0.446377	+	0.454066i
$265$	−6.87297	−	13.9785i	−0.422203	−	0.858693i
$266$	−9.24507	+	0.903125i	−0.566851	+	0.0553741i
$267$	9.29249	+	9.29249i	0.568691	+	0.568691i
$268$	−10.9156	−	11.0406i	−0.666778	−	0.674414i
$269$			21.3949i			1.30447i	0.758016	+	0.652236i	$0.226169\pi$
$269$			21.3949i			1.30447i	−0.758016	+	0.652236i	$0.773831\pi$
$270$	15.8434	−	7.73400i	0.964201	−	0.470676i
$271$		−	4.29648i		−	0.260993i	−0.991449	−	0.130496i	$-0.958343\pi$
$271$		−	4.29648i		−	0.260993i	0.991449	−	0.130496i	$-0.0416571\pi$
$272$	−6.35558	−	6.50198i	−0.385363	−	0.394240i
$273$	−0.741226	−	7.37087i	−0.0448611	−	0.446105i
$274$	5.47412	+	5.50537i	0.330704	+	0.332592i
$275$	7.20141	−	9.33940i	0.434261	−	0.563187i
$276$	−0.0153783	+	2.70129i	−0.000925665	+	0.162599i
$277$	7.62870	+	7.62870i	0.458364	+	0.458364i	0.898118	−	0.439754i	$-0.144934\pi$
$277$	7.62870	+	7.62870i	0.458364	+	0.458364i	−0.439754	+	0.898118i	$0.644934\pi$
$278$	−4.21250	−	0.0119907i	−0.252649	−	0.000719152i
$279$	−3.29420			−0.197219
$280$	−16.2665	−	3.92455i	−0.972107	−	0.234537i
$281$	−19.5650			−1.16715			−0.583576	−	0.812059i	$-0.698347\pi$
$281$	−19.5650			−1.16715			−0.583576	+	0.812059i	$0.698347\pi$
$282$	27.3751	+	0.0779218i	1.63016	+	0.00464018i
$283$	−6.26088	−	6.26088i	−0.372170	−	0.372170i	0.496097	−	0.868267i	$-0.334766\pi$
$283$	−6.26088	−	6.26088i	−0.372170	−	0.372170i	−0.868267	+	0.496097i	$0.834766\pi$
$284$	21.2045	+	0.120716i	1.25825	+	0.00716316i
$285$	−3.79843	−	7.72540i	−0.225000	−	0.457613i
$286$	−4.24659	−	4.27083i	−0.251106	−	0.252540i
$287$	−1.45102	−	14.4292i	−0.0856510	−	0.851727i
$288$	−3.36630	−	0.0479130i	−0.198361	−	0.00282330i
$289$		−	11.8332i		−	0.696070i
$290$	−2.73553	−	0.940883i	−0.160636	−	0.0552505i
$291$		−	30.3931i		−	1.78167i
$292$	−4.91947	+	4.86378i	−0.287890	+	0.284631i
$293$	20.2765	+	20.2765i	1.18457	+	1.18457i	0.978548	+	0.206017i	$0.0660502\pi$
$293$	20.2765	+	20.2765i	1.18457	+	1.18457i	0.206017	+	0.978548i	$0.433950\pi$
$294$	−8.51296	+	12.7752i	−0.496486	+	0.745064i
$295$	−12.3950	−	4.22384i	−0.721667	−	0.245922i
$296$	20.0455	−	19.7061i	1.16512	−	1.14539i
$297$	−9.29856	−	9.29856i	−0.539557	−	0.539557i
$298$	0.0428282	−	15.0462i	0.00248097	−	0.871603i
$299$		−	1.57259i		−	0.0909450i
$300$	−1.90032	−	15.3907i	−0.109715	−	0.888584i
$301$	−16.6455	+	20.3677i	−0.959433	+	1.17397i
$302$	0.0141571	−	4.97362i	0.000814652	−	0.286200i
$303$	−17.4309	−	17.4309i	−1.00138	−	1.00138i
$304$	−0.113063	+	9.92979i	−0.00648461	+	0.569513i
$305$	1.28624	−	3.77454i	0.0736502	−	0.216129i
$306$	1.34894	+	1.35664i	0.0771139	+	0.0775542i
$307$	15.6206	−	15.6206i	0.891515	−	0.891515i	−0.103151	−	0.994666i	$-0.532892\pi$
$307$	15.6206	−	15.6206i	0.891515	−	0.891515i	0.994666	+	0.103151i	$0.0328924\pi$
$308$	1.17809	+	12.4253i	0.0671281	+	0.707995i
$309$	18.3611			1.04453
$310$	−5.69302	+	16.5519i	−0.323342	+	0.940087i
$311$		−	2.60168i		−	0.147528i	−0.997276	−	0.0737638i	$-0.976499\pi$
$311$		−	2.60168i		−	0.147528i	0.997276	−	0.0737638i	$-0.0235011\pi$
$312$	−7.91924	−	0.0676265i	−0.448339	−	0.00382860i
$313$	16.5966	−	16.5966i	0.938093	−	0.938093i	−0.0600995	−	0.998192i	$-0.519142\pi$
$313$	16.5966	−	16.5966i	0.938093	−	0.938093i	0.998192	+	0.0600995i	$0.0191418\pi$
$314$	21.2889	+	21.4105i	1.20140	+	1.20826i
$315$	3.42964	+	0.796528i	0.193238	+	0.0448793i
$316$	−0.0969577	+	17.0312i	−0.00545429	+	0.958081i
$317$	5.05882	+	5.05882i	0.284131	+	0.284131i	0.834754	−	0.550623i	$-0.185610\pi$
$317$	5.05882	+	5.05882i	0.284131	+	0.284131i	−0.550623	+	0.834754i	$0.685610\pi$
$318$	−0.0434864	+	15.2775i	−0.00243860	+	0.856717i
$319$			2.15770i			0.120808i
$320$	−6.05837	+	16.8314i	−0.338673	+	0.940904i
$321$		−	5.88192i		−	0.328297i
$322$	−2.06942	+	2.51750i	−0.115324	+	0.140295i
$323$	3.99029	−	3.99029i	0.222026	−	0.222026i
$324$	−13.7205	−	0.0781101i	−0.762251	−	0.00433945i
$325$	1.15726	+	8.95328i	0.0641933	+	0.496638i
$326$	−1.43029	−	1.43846i	−0.0792165	−	0.0796687i
$327$	−2.74216	−	2.74216i	−0.151642	−	0.151642i
$328$	−15.5027	−	0.132385i	−0.855991	−	0.00730975i
$329$	25.5718	+	20.8987i	1.40982	+	1.15218i
$330$	−10.3945	+	5.07408i	−0.572197	+	0.279319i
$331$		−	22.6576i		−	1.24537i	−0.782471	−	0.622687i	$-0.786041\pi$
$331$		−	22.6576i		−	1.24537i	0.782471	−	0.622687i	$-0.213959\pi$
$332$	12.8053	+	12.9520i	0.702784	+	0.710831i
$333$	−4.18232	+	4.18232i	−0.229190	+	0.229190i
$334$	15.4341	−	15.3465i	0.844517	−	0.839723i
$335$	15.5772	−	7.65900i	0.851071	−	0.418456i
$336$	12.5887	+	10.5295i	0.686768	+	0.574429i
$337$	−19.2106	+	19.2106i	−1.04647	+	1.04647i	−0.0476008	+	0.998866i	$0.515158\pi$
$337$	−19.2106	+	19.2106i	−1.04647	+	1.04647i	−0.998866	+	0.0476008i	$0.984842\pi$
$338$	−13.7744	−	0.0392080i	−0.749226	−	0.00213263i
$339$		−	28.7378i		−	1.56082i
$340$	9.14779	−	4.43331i	0.496109	−	0.240430i
$341$	13.0556			0.707002
$342$	0.00594766	−	2.08950i	0.000321613	−	0.112987i
$343$	−17.6894	+	5.48503i	−0.955137	+	0.296164i
$344$	19.7137	+	20.0532i	1.06289	+	1.08120i
$345$	−2.85876	−	0.974177i	−0.153910	−	0.0524479i
$346$	−15.9988	+	15.9080i	−0.860100	+	0.855217i
$347$	12.2233	+	12.2233i	0.656181	+	0.656181i	0.954474	−	0.298293i	$-0.0964174\pi$
$347$	12.2233	+	12.2233i	0.656181	+	0.656181i	−0.298293	+	0.954474i	$0.596417\pi$
$348$	1.99477	+	2.01762i	0.106931	+	0.108156i
$349$		−	13.1133i		−	0.701940i	−0.936387	−	0.350970i	$-0.885852\pi$
$349$		−	13.1133i		−	0.701940i	0.936387	−	0.350970i	$-0.114148\pi$
$350$	9.92929	−	15.8559i	0.530743	−	0.847533i
$351$	10.0663			0.537300
$352$	13.3414	+	0.189890i	0.711098	+	0.0101212i
$353$	−21.3479	+	21.3479i	−1.13624	+	1.13624i	−0.147118	+	0.989119i	$0.547000\pi$
$353$	−21.3479	+	21.3479i	−1.13624	+	1.13624i	−0.989119	+	0.147118i	$0.953000\pi$
$354$	9.05573	+	9.10743i	0.481307	+	0.484055i
$355$	−7.64704	+	22.4405i	−0.405863	+	1.19102i
$356$	16.9483	+	0.0964855i	0.898257	+	0.00511372i
$357$	−0.933152	−	9.27941i	−0.0493876	−	0.491118i
$358$	−0.0498436	+	17.5108i	−0.00263431	+	0.925475i
$359$			9.10567i			0.480579i	0.970701	+	0.240289i	$0.0772424\pi$
$359$			9.10567i			0.480579i	−0.970701	+	0.240289i	$0.922758\pi$
$360$	1.24448	−	3.55234i	0.0655900	−	0.187225i
$361$	12.8367			0.675613
$362$	0.0206515	−	7.25519i	0.00108542	−	0.381324i
$363$	−5.96153	−	5.96153i	−0.312899	−	0.312899i
$364$	−7.36328	−	6.08791i	−0.385941	−	0.319093i
$365$	−3.41269	−	6.94086i	−0.178628	−	0.363301i
$366$	−2.77340	+	2.75765i	−0.144968	+	0.144145i
$367$	6.46101	+	6.46101i	0.337262	+	0.337262i	0.855336	−	0.518074i	$-0.173351\pi$
$367$	6.46101	+	6.46101i	0.337262	+	0.337262i	−0.518074	+	0.855336i	$0.673351\pi$
$368$	2.43527	+	2.49137i	0.126947	+	0.129872i
$369$	3.26211			0.169819
$370$	13.7865	+	28.2422i	0.716725	+	1.46824i
$371$	−11.6631	+	14.2711i	−0.605518	+	0.740917i
$372$	12.2080	−	12.0698i	0.632958	−	0.625792i
$373$	−14.2981	+	14.2981i	−0.740325	+	0.740325i	−0.972640	−	0.232315i	$-0.925370\pi$
$373$	−14.2981	+	14.2981i	−0.740325	+	0.740325i	0.232315	+	0.972640i	$0.425370\pi$
$374$	−5.34615	−	5.37668i	−0.276443	−	0.278021i
$375$	16.9928	+	3.44257i	0.877505	+	0.177774i
$376$	25.1771	−	24.7507i	1.29841	−	1.27642i
$377$	−1.16793	−	1.16793i	−0.0601513	−	0.0601513i
$378$	−16.1148	−	13.2466i	−0.828858	−	0.681332i
$379$	−10.6182			−0.545419			−0.272709	−	0.962096i	$-0.587920\pi$
$379$	−10.6182			−0.545419			−0.272709	+	0.962096i	$0.587920\pi$
$380$	−10.4886	−	3.64096i	−0.538053	−	0.186777i
$381$	−23.4592			−1.20185
$382$	−0.0149637	+	5.25697i	−0.000765608	+	0.268970i
$383$	−16.9945	+	16.9945i	−0.868377	+	0.868377i	−0.992293	−	0.123916i	$-0.960455\pi$
$383$	−16.9945	+	16.9945i	−0.868377	+	0.868377i	0.123916	+	0.992293i	$0.460455\pi$
$384$	12.6508	−	12.1564i	0.645583	−	0.620356i
$385$	−13.5924	−	3.15681i	−0.692733	−	0.160886i
$386$	−18.1418	+	18.0388i	−0.923392	+	0.918150i
$387$	−4.18393	−	4.18393i	−0.212681	−	0.212681i
$388$	−27.5587	−	27.8743i	−1.39908	−	1.41510i
$389$	−29.0527			−1.47303			−0.736515	−	0.676421i	$-0.763530\pi$
$389$	−29.0527			−1.47303			−0.736515	+	0.676421i	$0.763530\pi$
$390$	2.87985	−	8.37289i	0.145827	−	0.423978i
$391$		−	1.97978i		−	0.100122i
$392$	3.77634	+	19.4355i	0.190734	+	0.981642i
$393$	7.30644	+	7.30644i	0.368561	+	0.368561i
$394$	−13.1686	+	13.0938i	−0.663423	+	0.659657i
$395$	−18.0240	−	6.14203i	−0.906887	−	0.309039i
$396$	−2.80747	−	0.0159827i	−0.141080	−	0.000803162i
$397$	−5.74467	+	5.74467i	−0.288317	+	0.288317i	−0.836414	−	0.548098i	$-0.815352\pi$
$397$	−5.74467	+	5.74467i	−0.288317	+	0.288317i	0.548098	+	0.836414i	$0.315352\pi$
$398$	0.104195	−	36.6054i	0.00522283	−	1.83486i
$399$	−6.44575	+	7.88708i	−0.322691	+	0.394848i
$400$	−15.6983	−	12.3921i	−0.784913	−	0.619606i
$401$	29.3864			1.46749			0.733743	−	0.679428i	$-0.237772\pi$
$401$	29.3864			1.46749			0.733743	+	0.679428i	$0.237772\pi$
$402$	−17.0247	−	0.0484597i	−0.849112	−	0.00241695i
$403$	−7.06680	+	7.06680i	−0.352023	+	0.352023i
$404$	−31.7916	−	0.180988i	−1.58169	−	0.00900448i
$405$	4.94808	−	14.5203i	0.245872	−	0.721521i
$406$	0.332782	+	3.40661i	0.0165157	+	0.169067i
$407$	16.5754	−	16.5754i	0.821614	−	0.821614i
$408$	−9.96977	−	0.0851371i	−0.493577	−	0.00421491i
$409$	5.50199			0.272056			0.136028	−	0.990705i	$-0.456566\pi$
$409$	5.50199			0.272056			0.136028	+	0.990705i	$0.456566\pi$
$410$	5.63757	−	16.3907i	0.278420	−	0.809479i
$411$	8.51331			0.419931
$412$	16.8394	−	16.6488i	0.829618	−	0.820226i
$413$	1.55030	+	15.4164i	0.0762852	+	0.758591i
$414$	−0.516876	−	0.519827i	−0.0254031	−	0.0255481i
$415$	−18.2738	+	8.98491i	−0.897028	+	0.441052i
$416$	−7.32426	+	7.11869i	−0.359101	+	0.349023i
$417$	−3.26630	+	3.26630i	−0.159951	+	0.159951i
$418$	−0.0235719	+	8.28116i	−0.00115294	+	0.405045i
$419$			20.2796i			0.990722i	0.868687	+	0.495361i	$0.164964\pi$
$419$			20.2796i			0.990722i	−0.868687	+	0.495361i	$0.835036\pi$
$420$	−15.6284	+	9.61419i	−0.762588	+	0.469125i
$421$		−	33.7978i		−	1.64720i	−0.567169	−	0.823601i	$-0.691961\pi$
$421$		−	33.7978i		−	1.64720i	0.567169	−	0.823601i	$-0.308039\pi$
$422$	3.61021	+	0.0102763i	0.175742	+	0.000500241i
$423$	−5.25297	+	5.25297i	−0.255408	+	0.255408i
$424$	13.8128	+	14.0508i	0.670811	+	0.682366i
$425$	1.45691	+	11.2715i	0.0706706	+	0.546750i
$426$	16.4885	−	16.3949i	0.798871	−	0.794336i
$427$	−4.69460	+	0.472097i	−0.227188	+	0.0228464i
$428$	−5.33339	−	5.39446i	−0.257799	−	0.260751i
$429$	−6.60426			−0.318857
$430$	−28.2531	+	13.7918i	−1.36248	+	0.665099i
$431$	−21.3902			−1.03033			−0.515165	−	0.857091i	$-0.672270\pi$
$431$	−21.3902			−1.03033			−0.515165	+	0.857091i	$0.672270\pi$
$432$	−15.9476	+	15.5885i	−0.767278	+	0.750002i
$433$	−2.93987	+	2.93987i	−0.141281	+	0.141281i	−0.774210	−	0.632929i	$-0.781853\pi$
$433$	−2.93987	+	2.93987i	−0.141281	+	0.141281i	0.632929	+	0.774210i	$0.281853\pi$
$434$	20.6125	−	2.01357i	0.989430	−	0.0966546i
$435$	−2.84664	+	1.39964i	−0.136486	+	0.0671077i
$436$	−5.00134	−	0.0284723i	−0.239521	−	0.00136358i
$437$	−1.52897	+	1.52897i	−0.0731403	+	0.0731403i
$438$	−0.0215926	+	7.58583i	−0.00103174	+	0.362465i
$439$	−10.4865			−0.500495			−0.250248	−	0.968182i	$-0.580512\pi$
$439$	−10.4865			−0.500495			−0.250248	+	0.968182i	$0.580512\pi$
$440$	−4.93216	+	14.0787i	−0.235131	+	0.671175i
$441$	−0.829492	−	4.08259i	−0.0394996	−	0.194409i
$442$	5.80410	+	0.0165210i	0.276073	+	0.000785826i
$443$	−13.0706	+	13.0706i	−0.621003	+	0.621003i	−0.945788	−	0.324785i	$-0.894708\pi$
$443$	−13.0706	+	13.0706i	−0.621003	+	0.621003i	0.324785	+	0.945788i	$0.394708\pi$
$444$	0.175475	−	30.8232i	0.00832766	−	1.46280i
$445$	−6.11211	+	17.9362i	−0.289742	+	0.850259i
$446$	−16.3395	−	16.4328i	−0.773696	−	0.778113i
$447$	−11.6666	−	11.6666i	−0.551810	−	0.551810i
$448$	21.0929	−	1.75784i	0.996545	−	0.0830503i
$449$		−	14.4252i		−	0.680766i	−0.940287	−	0.340383i	$-0.889443\pi$
$449$		−	14.4252i		−	0.680766i	0.940287	−	0.340383i	$-0.110557\pi$
$450$	3.32529	+	2.57919i	0.156756	+	0.121584i
$451$	−12.9285			−0.608777
$452$	−26.0578	−	26.3562i	−1.22565	−	1.23969i
$453$	−3.85646	−	3.85646i	−0.181192	−	0.181192i
$454$	−20.9710	−	21.0907i	−0.984219	−	0.989838i
$455$	9.06608	−	5.64861i	0.425024	−	0.264811i
$456$	7.63383	+	7.76533i	0.357487	+	0.363645i
$457$	−1.20405	+	1.20405i	−0.0563229	+	0.0563229i	−0.734707	−	0.678384i	$-0.762680\pi$
$457$	−1.20405	+	1.20405i	−0.0563229	+	0.0563229i	0.678384	+	0.734707i	$0.262680\pi$
$458$	−14.0735	−	0.0400595i	−0.657612	−	0.00187186i
$459$	12.6728			0.591515
$460$	−3.50517	+	1.69872i	−0.163429	+	0.0792031i
$461$	−7.12260			−0.331733			−0.165866	−	0.986148i	$-0.553042\pi$
$461$	−7.12260			−0.331733			−0.165866	+	0.986148i	$0.553042\pi$
$462$	10.5725	+	8.69077i	0.491879	+	0.404331i
$463$	21.0245	+	21.0245i	0.977090	+	0.977090i	0.999743	−	0.0226530i	$-0.00721129\pi$
$463$	21.0245	+	21.0245i	0.977090	+	0.977090i	−0.0226530	+	0.999743i	$0.507211\pi$
$464$	3.65892	+	0.0416613i	0.169861	+	0.00193408i
$465$	8.46885	+	17.2243i	0.392733	+	0.798756i
$466$	4.00898	−	3.98622i	0.185712	−	0.184658i
$467$	3.16096	−	3.16096i	0.146272	−	0.146272i	−0.630178	−	0.776450i	$-0.717018\pi$
$467$	3.16096	−	3.16096i	0.146272	−	0.146272i	0.776450	+	0.630178i	$0.217018\pi$
$468$	1.52829	−	1.51099i	0.0706451	−	0.0698453i
$469$	−15.9032	−	12.9969i	−0.734341	−	0.600143i
$470$	17.3158	+	35.4721i	0.798716	+	1.63621i
$471$	33.1084			1.52555
$472$	16.5633	+	0.141443i	0.762390	+	0.00651044i
$473$	16.5818	+	16.5818i	0.762433	+	0.762433i
$474$	13.1682	+	13.2434i	0.604837	+	0.608290i
$475$	7.57977	−	9.83009i	0.347784	−	0.451036i
$476$	−9.26985	−	7.66425i	−0.424883	−	0.351290i
$477$	−2.93157	−	2.93157i	−0.134227	−	0.134227i
$478$	11.0925	+	0.0315742i	0.507358	+	0.00144417i
$479$	14.8465			0.678355			0.339178	−	0.940722i	$-0.389851\pi$
$479$	14.8465			0.678355			0.339178	+	0.940722i	$0.389851\pi$
$480$	8.40368	+	17.7244i	0.383574	+	0.809005i
$481$			17.9440i			0.818178i
$482$	−30.5624	−	0.0869941i	−1.39208	−	0.00396247i
$483$	0.357557	+	3.55560i	0.0162694	+	0.161785i
$484$	−10.8730	−	0.0618996i	−0.494229	−	0.00281362i
$485$	39.3277	−	19.3367i	1.78578	−	0.878033i
$486$	6.10412	−	6.06947i	0.276889	−	0.275317i
$487$	−7.09892	+	7.09892i	−0.321683	+	0.321683i	−0.849412	−	0.527730i	$-0.823043\pi$
$487$	−7.09892	+	7.09892i	−0.321683	+	0.321683i	0.527730	+	0.849412i	$0.323043\pi$
$488$	−0.0430722	+	5.04387i	−0.00194979	+	0.228325i
$489$	−2.22438			−0.100590
$490$	−21.9468	−	2.88768i	−0.991455	−	0.130452i
$491$			12.8350i			0.579237i	0.957142	+	0.289618i	$0.0935284\pi$
$491$			12.8350i			0.579237i	−0.957142	+	0.289618i	$0.906472\pi$
$492$	−12.0891	+	11.9523i	−0.545020	+	0.538850i
$493$	−1.47034	−	1.47034i	−0.0662207	−	0.0662207i
$494$	−4.46970	−	4.49522i	−0.201101	−	0.202250i
$495$	1.01247	−	2.97112i	0.0455070	−	0.133542i
$496$	0.252081	−	22.1391i	0.0113188	−	0.994075i
$497$	27.9106	−	2.80673i	1.25196	−	0.125899i
$498$	19.9719	+	0.0568490i	0.894964	+	0.00254747i
$499$	−10.1847			−0.455930			−0.227965	−	0.973669i	$-0.573207\pi$
$499$	−10.1847			−0.455930			−0.227965	+	0.973669i	$0.573207\pi$
$500$	18.7061	−	12.2508i	0.836561	−	0.547874i
$501$		−	23.8668i		−	1.06629i
$502$	0.0155718	−	5.47062i	0.000695005	−	0.244166i
$503$	5.16072	−	5.16072i	0.230105	−	0.230105i	−0.582631	−	0.812737i	$-0.697977\pi$
$503$	5.16072	−	5.16072i	0.230105	−	0.230105i	0.812737	+	0.582631i	$0.197977\pi$
$504$	−4.43494	+	0.407762i	−0.197548	+	0.0181632i
$505$	11.4651	−	33.6449i	0.510191	−	1.49718i
$506$	2.04849	+	2.06019i	0.0910666	+	0.0915865i
$507$	−10.6804	+	10.6804i	−0.474333	+	0.474333i
$508$	−21.5150	+	21.2715i	−0.954576	+	0.943769i
$509$		−	1.65423i		−	0.0733226i	−0.999328	−	0.0366613i	$-0.988328\pi$
$509$		−	1.65423i		−	0.0733226i	0.999328	−	0.0366613i	$-0.0116723\pi$
$510$	3.62552	−	10.5409i	0.160541	−	0.466758i
$511$	−5.79116	+	7.08612i	−0.256186	+	0.313472i
$512$	0.579604	−	22.6200i	0.0256151	−	0.999672i
$513$	−9.78710	−	9.78710i	−0.432111	−	0.432111i
$514$	−11.7323	+	11.6657i	−0.517491	+	0.514553i
$515$	11.6817	+	23.7586i	0.514756	+	1.04693i
$516$	30.8351	+	0.175542i	1.35744	+	0.00772781i
$517$	20.8187	−	20.8187i	0.915604	−	0.915604i
$518$	23.6132	−	28.7260i	1.03750	−	1.26215i
$519$			24.7399i			1.08596i
$520$	−4.95087	−	10.2903i	−0.217110	−	0.451258i
$521$			30.7380i			1.34665i	0.739344	+	0.673327i	$0.235136\pi$
$521$			30.7380i			1.34665i	−0.739344	+	0.673327i	$0.764864\pi$
$522$	−0.769938	−	0.00219159i	−0.0336993	−	9.59232e-5i
$523$	30.0751	+	30.0751i	1.31509	+	1.31509i	0.917608	+	0.397486i	$0.130117\pi$
$523$	30.0751	+	30.0751i	1.31509	+	1.31509i	0.397486	+	0.917608i	$0.369883\pi$
$524$	13.3260	+	0.0758640i	0.582148	+	0.00331413i
$525$	−4.65225	−	19.9802i	−0.203041	−	0.872005i
$526$	−11.4899	+	11.4247i	−0.500982	+	0.498138i
$527$	−8.89661	+	8.89661i	−0.387543	+	0.387543i
$528$	10.4628	−	10.2272i	0.455335	−	0.445083i
$529$		−	22.2414i		−	0.967018i
$530$	−19.7962	+	9.66354i	−0.859892	+	0.419758i
$531$	−3.48530			−0.151249
$532$	1.23999	+	13.0781i	0.0537604	+	0.567007i
$533$	6.99797	−	6.99797i	0.303116	−	0.303116i
$534$	13.1789	−	13.1041i	0.570308	−	0.567070i
$535$	7.61102	−	3.74219i	0.329053	−	0.161789i
$536$	−15.6577	+	15.3925i	−0.676309	+	0.664856i
$537$	13.5776	+	13.5776i	0.585916	+	0.585916i
$538$	30.2569	+	0.0861245i	1.30447	+	0.00371309i
$539$	3.28746	+	16.1802i	0.141601	+	0.696930i
$540$	−10.8737	−	22.4370i	−0.467930	−	0.965536i
$541$			4.43452i			0.190655i	0.995446	+	0.0953275i	$0.0303898\pi$
$541$			4.43452i			0.190655i	−0.995446	+	0.0953275i	$0.969610\pi$
$542$	−6.07612	−	0.0172954i	−0.260992	−	0.000742899i
$543$	−5.62555	−	5.62555i	−0.241415	−	0.241415i
$544$	−9.22073	+	8.96193i	−0.395336	+	0.384240i
$545$	1.80365	−	5.29289i	0.0772600	−	0.226722i
$546$	−10.4269	+	1.01858i	−0.446231	+	0.0435911i
$547$	10.5660	+	10.5660i	0.451771	+	0.451771i	0.895942	−	0.444171i	$-0.146502\pi$
$547$	10.5660	+	10.5660i	0.451771	+	0.451771i	−0.444171	+	0.895942i	$0.646502\pi$
$548$	7.80777	−	7.71938i	0.333532	−	0.329756i
$549$		−	1.06134i		−	0.0452971i
$550$	−13.1789	−	10.2219i	−0.561949	−	0.435863i
$551$			2.27106i			0.0967505i
$552$	3.82013	+	0.0326221i	0.162596	+	0.00138849i
$553$	2.25434	+	22.4175i	0.0958642	+	0.953288i
$554$	10.8193	−	10.7579i	0.459667	−	0.457058i
$555$	32.6200	+	11.1159i	1.38464	+	0.471843i
$556$	−0.0339146	+	5.95730i	−0.00143830	+	0.252646i
$557$	29.7303	+	29.7303i	1.25971	+	1.25971i	0.951230	+	0.308483i	$0.0998212\pi$
$557$	29.7303	+	29.7303i	1.25971	+	1.25971i	0.308483	+	0.951230i	$0.400179\pi$
$558$	−0.0132607	+	4.65868i	−0.000561370	+	0.197218i
$559$	−17.9510			−0.759244
$560$	−5.61562	+	22.9884i	−0.237303	+	0.971436i
$561$	−8.31430			−0.351030
$562$	−0.0787584	+	27.6690i	−0.00332222	+	1.16715i
$563$	−21.5058	−	21.5058i	−0.906362	−	0.906362i	0.0896148	−	0.995976i	$-0.471436\pi$
$563$	−21.5058	−	21.5058i	−0.906362	−	0.906362i	−0.995976	+	0.0896148i	$0.971436\pi$
$564$	0.220395	−	38.7138i	0.00928031	−	1.63015i
$565$	37.1858	−	18.2835i	1.56442	−	0.769195i
$566$	−8.87938	+	8.82898i	−0.373228	+	0.371110i
$567$	−18.0598	+	1.81612i	−0.758438	+	0.0762698i
$568$	0.256075	−	29.9870i	0.0107447	−	1.25823i
$569$		−	21.8433i		−	0.915717i	−0.889025	−	0.457858i	$-0.848617\pi$
$569$		−	21.8433i		−	0.915717i	0.889025	−	0.457858i	$-0.151383\pi$
$570$	−10.9406	+	5.34068i	−0.458252	+	0.223696i
$571$		−	40.7167i		−	1.70394i	−0.523591	−	0.851970i	$-0.675408\pi$
$571$		−	40.7167i		−	1.70394i	0.523591	−	0.851970i	$-0.324592\pi$
$572$	−6.05694	+	5.98836i	−0.253253	+	0.250386i
$573$	4.07616	+	4.07616i	0.170284	+	0.170284i
$574$	−20.4117	+	1.99396i	−0.851967	+	0.0832263i
$575$	−0.558246	−	4.31893i	−0.0232805	−	0.180112i
$576$	−0.0813099	+	4.76045i	−0.00338791	+	0.198352i
$577$	−6.60862	−	6.60862i	−0.275120	−	0.275120i	0.556037	−	0.831157i	$-0.312321\pi$
$577$	−6.60862	−	6.60862i	−0.275120	−	0.275120i	−0.831157	+	0.556037i	$0.812321\pi$
$578$	−16.7346	−	0.0476341i	−0.696067	−	0.00198132i
$579$			28.0538i			1.16588i
$580$	−1.34162	+	3.86482i	−0.0557076	+	0.160478i
$581$	18.6563	+	15.2469i	0.773994	+	0.632550i
$582$	−42.9822	−	0.122346i	−1.78167	−	0.00507142i
$583$	11.6184	+	11.6184i	0.481187	+	0.481187i
$584$	6.85859	+	6.97674i	0.283810	+	0.288699i
$585$	1.06019	+	2.15625i	0.0438334	+	0.0891501i
$586$	28.7568	−	28.5935i	1.18793	−	1.18119i
$587$	−5.86248	+	5.86248i	−0.241971	+	0.241971i	−0.817665	−	0.575694i	$-0.804732\pi$
$587$	−5.86248	+	5.86248i	−0.241971	+	0.241971i	0.575694	+	0.817665i	$0.304732\pi$
$588$	18.0325	+	12.0905i	0.743648	+	0.498605i
$589$	13.7416			0.566212
$590$	−6.02329	+	17.5121i	−0.247975	+	0.720964i
$591$			20.3634i			0.837639i
$592$	−27.7878	−	28.4279i	−1.14207	−	1.16838i
$593$	14.7745	−	14.7745i	0.606717	−	0.606717i	−0.335370	−	0.942087i	$-0.608861\pi$
$593$	14.7745	−	14.7745i	0.606717	−	0.606717i	0.942087	+	0.335370i	$0.108861\pi$
$594$	−13.1875	+	13.1127i	−0.541091	+	0.538019i
$595$	11.4136	−	7.11121i	0.467910	−	0.291531i
$596$	−21.2783	−	0.121136i	−0.871593	−	0.00496192i
$597$	−28.3832	−	28.3832i	−1.16165	−	1.16165i
$598$	−2.22396	−	0.00633039i	−0.0909446	−	0.000258869i
$599$		−	28.1745i		−	1.15118i	−0.817738	−	0.575590i	$-0.804772\pi$
$599$		−	28.1745i		−	1.15118i	0.817738	−	0.575590i	$-0.195228\pi$
$600$	−21.7733	+	2.62549i	−0.888893	+	0.107185i
$601$		−	1.80167i		−	0.0734917i	−0.999325	−	0.0367458i	$-0.988301\pi$
$601$		−	1.80167i		−	0.0734917i	0.999325	−	0.0367458i	$-0.0116992\pi$
$602$	28.7371	+	23.6223i	1.17124	+	0.962771i
$603$	3.26684	−	3.26684i	0.133036	−	0.133036i
$604$	−7.03367	−	0.0400423i	−0.286196	−	0.00162930i
$605$	3.92118	−	11.5069i	0.159419	−	0.467821i
$606$	−24.7211	+	24.5807i	−1.00422	+	0.998524i
$607$	17.2781	+	17.2781i	0.701297	+	0.701297i	0.964689	−	0.263392i	$-0.0848412\pi$
$607$	17.2781	+	17.2781i	0.701297	+	0.701297i	−0.263392	+	0.964689i	$0.584841\pi$
$608$	14.0423	+	0.199867i	0.569492	+	0.00810566i
$609$	2.90622	+	2.37512i	0.117766	+	0.0962448i
$610$	−5.33280	−	1.83421i	−0.215919	−	0.0742651i
$611$			22.5376i			0.911775i
$612$	1.92401	−	1.90222i	0.0777734	−	0.0768929i
$613$	14.6367	−	14.6367i	0.591172	−	0.591172i	−0.346776	−	0.937948i	$-0.612724\pi$
$613$	14.6367	−	14.6367i	0.591172	−	0.591172i	0.937948	+	0.346776i	$0.112724\pi$
$614$	−22.0279	−	22.1537i	−0.888974	−	0.894049i
$615$	−8.38635	−	17.0565i	−0.338170	−	0.687784i
$616$	17.5766	−	1.61605i	0.708183	−	0.0651126i
$617$	8.85764	−	8.85764i	0.356595	−	0.356595i	−0.505961	−	0.862556i	$-0.668862\pi$
$617$	8.85764	−	8.85764i	0.356595	−	0.356595i	0.862556	+	0.505961i	$0.168862\pi$
$618$	0.0739119	−	25.9664i	0.00297317	−	1.04452i
$619$			27.4249i			1.10230i	0.834407	+	0.551149i	$0.185810\pi$
$619$			27.4249i			1.10230i	−0.834407	+	0.551149i	$0.814190\pi$
$620$	23.3850	+	8.11775i	0.939163	+	0.326017i
$621$	−4.85585			−0.194859
$622$	−3.67931	−	0.0104730i	−0.147527	−	0.000419927i
$623$	22.3083	−	2.24336i	0.893764	−	0.0898783i
$624$	−0.127517	+	11.1992i	−0.00510475	+	0.448326i
$625$	6.35658	+	24.1784i	0.254263	+	0.967135i
$626$	−23.4042	−	23.5378i	−0.935419	−	0.940759i
$627$	6.42107	+	6.42107i	0.256433	+	0.256433i
$628$	30.3645	−	30.0208i	1.21168	−	1.19796i
$629$			22.5903i			0.900734i
$630$	1.14026	−	4.84701i	0.0454291	−	0.193110i
$631$	−5.46251			−0.217459			−0.108730	−	0.994071i	$-0.534678\pi$
$631$	−5.46251			−0.217459			−0.108730	+	0.994071i	$0.534678\pi$
$632$	24.0853	+	0.205677i	0.958061	+	0.00818139i
$633$	2.79930	−	2.79930i	0.111262	−	0.111262i
$634$	7.17458	−	7.13385i	0.284939	−	0.283321i
$635$	−14.9252	−	30.3555i	−0.592289	−	1.20462i
$636$	21.6053	+	0.122998i	0.856707	+	0.00487718i
$637$	−10.5375	−	6.97863i	−0.417512	−	0.276503i
$638$	3.05143	+	0.00868574i	0.120807	+	0.000343872i
$639$			6.30995i			0.249618i
$640$	23.7787	+	8.63555i	0.939936	+	0.341350i
$641$	11.8243			0.467033			0.233516	−	0.972353i	$-0.424977\pi$
$641$	11.8243			0.467033			0.233516	+	0.972353i	$0.424977\pi$
$642$	−8.31826	−	0.0236775i	−0.328296	−	0.000934476i
$643$	−1.75785	−	1.75785i	−0.0693227	−	0.0693227i	0.671595	−	0.740918i	$-0.265609\pi$
$643$	−1.75785	−	1.75785i	−0.0693227	−	0.0693227i	−0.740918	+	0.671595i	$0.765609\pi$
$644$	3.55194	+	2.93672i	0.139966	+	0.115723i
$645$	−11.1202	+	32.6325i	−0.437856	+	1.28491i
$646$	−5.62704	−	5.65917i	−0.221393	−	0.222657i
$647$	−3.65322	−	3.65322i	−0.143623	−	0.143623i	0.631639	−	0.775262i	$-0.282382\pi$
$647$	−3.65322	−	3.65322i	−0.143623	−	0.143623i	−0.775262	+	0.631639i	$0.782382\pi$
$648$	−0.165695	+	19.4034i	−0.00650913	+	0.762236i
$649$	13.8130			0.542208
$650$	12.6665	−	1.60057i	0.496819	−	0.0627794i
$651$	14.3712	−	17.5848i	0.563252	−	0.689201i
$652$	−2.04003	+	2.01694i	−0.0798939	+	0.0789894i
$653$	−12.3855	+	12.3855i	−0.484683	+	0.484683i	−0.906624	−	0.421940i	$-0.861349\pi$
$653$	−12.3855	+	12.3855i	−0.484683	+	0.484683i	0.421940	+	0.906624i	$0.361349\pi$
$654$	−3.88903	+	3.86695i	−0.152073	+	0.151210i
$655$	−4.80580	+	14.1028i	−0.187778	+	0.551042i
$656$	−0.249626	+	21.9234i	−0.00974625	+	0.855967i
$657$	−1.45563	−	1.45563i	−0.0567897	−	0.0567897i
$658$	29.6580	−	36.0798i	1.15619	−	1.40654i
$659$	−31.5872			−1.23046			−0.615231	−	0.788347i	$-0.710937\pi$
$659$	−31.5872			−1.23046			−0.615231	+	0.788347i	$0.710937\pi$
$660$	7.13396	+	14.7204i	0.277689	+	0.572990i
$661$	−2.69577			−0.104853			−0.0524267	−	0.998625i	$-0.516696\pi$
$661$	−2.69577			−0.104853			−0.0524267	+	0.998625i	$0.516696\pi$
$662$	−32.0425	−	0.0912073i	−1.24537	−	0.00354487i
$663$	4.50040	−	4.50040i	0.174781	−	0.174781i
$664$	18.3683	−	18.0573i	0.712829	−	0.700757i
$665$	−14.3065	−	3.32267i	−0.554784	−	0.128848i
$666$	5.89783	+	5.93150i	0.228536	+	0.229841i
$667$	0.563391	+	0.563391i	0.0218146	+	0.0218146i
$668$	−21.6410	−	21.8888i	−0.837316	−	0.846904i
$669$	−25.4110			−0.982447
$670$	−10.7687	−	22.0602i	−0.416032	−	0.852259i
$671$			4.20634i			0.162384i
$672$	14.9415	−	17.7606i	0.576381	−	0.685130i
$673$	−2.66949	−	2.66949i	−0.102901	−	0.102901i	0.653782	−	0.756683i	$-0.273181\pi$
$673$	−2.66949	−	2.66949i	−0.102901	−	0.102901i	−0.756683	+	0.653782i	$0.773181\pi$
$674$	27.0904	+	27.2451i	1.04348	+	1.04944i
$675$	27.6460	−	3.57341i	1.06410	−	0.137540i
$676$	−0.110896	+	19.4796i	−0.00426525	+	0.749217i
$677$	3.93572	−	3.93572i	0.151262	−	0.151262i	−0.627419	−	0.778681i	$-0.715889\pi$
$677$	3.93572	−	3.93572i	0.151262	−	0.151262i	0.778681	+	0.627419i	$0.215889\pi$
$678$	−40.6412	−	0.115683i	−1.56082	−	0.00444278i
$679$	−40.1508	−	32.8134i	−1.54084	−	1.25926i
$680$	−6.23280	−	12.9547i	−0.239017	−	0.496791i
$681$	−32.6140			−1.24977
$682$	0.0525550	−	18.4634i	0.00201243	−	0.706999i
$683$	24.0867	−	24.0867i	0.921651	−	0.921651i	−0.0754952	−	0.997146i	$-0.524054\pi$
$683$	24.0867	−	24.0867i	0.921651	−	0.921651i	0.997146	+	0.0754952i	$0.0240538\pi$
$684$	−2.95497	−	0.0168225i	−0.112986	−	0.000643223i
$685$	5.41633	+	11.0159i	0.206947	+	0.420898i
$686$	7.68577	+	25.0385i	0.293444	+	0.955976i
$687$	−10.9124	+	10.9124i	−0.416333	+	0.416333i
$688$	28.4388	−	27.7985i	1.08422	−	1.05981i
$689$	−12.5778			−0.479174
$690$	−1.38920	+	4.03896i	−0.0528858	+	0.153761i
$691$	−32.3478			−1.23057			−0.615284	−	0.788305i	$-0.710959\pi$
$691$	−32.3478			−1.23057			−0.615284	+	0.788305i	$0.710959\pi$
$692$	22.4328	+	22.6896i	0.852766	+	0.862531i
$693$	−3.69535	+	0.371610i	−0.140375	+	0.0141163i
$694$	17.3355	−	17.2371i	0.658046	−	0.654310i
$695$	−6.30457	−	2.14840i	−0.239146	−	0.0814936i
$696$	2.86136	−	2.81290i	0.108460	−	0.106623i
$697$	8.80995	−	8.80995i	0.333701	−	0.333701i
$698$	−18.5450	−	0.0527872i	−0.701937	−	0.00199803i
$699$		−	6.19935i		−	0.234481i
$700$	−22.3835	−	14.1059i	−0.846019	−	0.533153i
$701$		−	16.4563i		−	0.621547i	−0.950484	−	0.310773i	$-0.899412\pi$
$701$		−	16.4563i		−	0.621547i	0.950484	−	0.310773i	$-0.100588\pi$
$702$	0.0405216	−	14.2359i	0.00152939	−	0.537298i
$703$	17.4463	−	17.4463i	0.658000	−	0.658000i
$704$	0.322249	−	18.8667i	0.0121452	−	0.711066i
$705$	40.9705	+	13.9615i	1.54304	+	0.525820i
$706$	30.1045	+	30.2764i	1.13300	+	1.13947i
$707$	−41.8460	+	4.20810i	−1.57378	+	0.158262i
$708$	12.9163	−	12.7700i	0.485423	−	0.479927i
$709$	−19.5504			−0.734232			−0.367116	−	0.930175i	$-0.619655\pi$
$709$	−19.5504			−0.734232			−0.367116	+	0.930175i	$0.619655\pi$
$710$	31.7048	+	10.9048i	1.18986	+	0.409251i
$711$	−5.06809			−0.190068
$712$	0.204675	−	23.9680i	0.00767053	−	0.898239i
$713$	3.40893	−	3.40893i	0.127665	−	0.127665i
$714$	−13.1268	+	1.28232i	−0.491257	+	0.0479895i
$715$	−4.20176	−	8.54570i	−0.157137	−	0.319591i
$716$	24.7637	+	0.140978i	0.925464	+	0.00526861i
$717$	8.60093	−	8.60093i	0.321207	−	0.321207i
$718$	12.8773	+	0.0366546i	0.480577	+	0.00136794i
$719$	26.2406			0.978608			0.489304	−	0.872113i	$-0.337251\pi$
$719$	26.2406			0.978608			0.489304	+	0.872113i	$0.337251\pi$
$720$	−5.01873	−	1.77426i	−0.187037	−	0.0661227i
$721$	19.8232	−	24.2559i	0.738255	−	0.903336i
$722$	0.0516735	−	18.1537i	0.00192309	−	0.675611i
$723$	−23.6975	+	23.6975i	−0.881321	+	0.881321i
$724$	−10.2603	−	0.0584110i	−0.381320	−	0.00217083i
$725$	−3.62218	−	2.79299i	−0.134524	−	0.103729i
$726$	−8.45484	+	8.40685i	−0.313789	+	0.312007i
$727$	−20.3660	−	20.3660i	−0.755332	−	0.755332i	0.220137	−	0.975469i	$-0.429349\pi$
$727$	−20.3660	−	20.3660i	−0.755332	−	0.755332i	−0.975469	+	0.220137i	$0.929349\pi$
$728$	−8.63921	+	10.3887i	−0.320190	+	0.385031i
$729$		−	30.0203i		−	1.11186i
$730$	−9.82955	+	4.79831i	−0.363808	+	0.177593i
$731$	−22.5990			−0.835854
$732$	3.88873	+	3.93326i	0.143732	+	0.145377i
$733$	−13.5866	−	13.5866i	−0.501833	−	0.501833i	0.410174	−	0.912007i	$-0.365468\pi$
$733$	−13.5866	−	13.5866i	−0.501833	−	0.501833i	−0.912007	+	0.410174i	$0.865468\pi$
$734$	9.16322	−	9.11120i	0.338221	−	0.336301i
$735$	−19.2140	+	14.8328i	−0.708719	+	0.547116i
$736$	3.53312	−	3.43395i	0.130232	−	0.126577i
$737$	−12.9472	+	12.9472i	−0.476915	+	0.476915i
$738$	0.0131315	−	4.61330i	0.000483378	−	0.169818i
$739$	26.3183			0.968134			0.484067	−	0.875031i	$-0.339159\pi$
$739$	26.3183			0.968134			0.484067	+	0.875031i	$0.339159\pi$
$740$	39.9959	−	19.3833i	1.47028	−	0.712543i
$741$	−6.95125			−0.255361
$742$	20.1353	+	16.5515i	0.739191	+	0.607624i
$743$	−24.2706	−	24.2706i	−0.890402	−	0.890402i	0.104159	−	0.994561i	$-0.466785\pi$
$743$	−24.2706	−	24.2706i	−0.890402	−	0.890402i	−0.994561	+	0.104159i	$0.966785\pi$
$744$	−17.0201	−	17.3133i	−0.623987	−	0.634736i
$745$	7.67366	−	22.5187i	0.281141	−	0.825020i
$746$	20.1629	+	20.2780i	0.738215	+	0.742429i
$747$	−3.83238	+	3.83238i	−0.140220	+	0.140220i
$748$	−7.62526	+	7.53893i	−0.278807	+	0.275651i
$749$	−7.77031	−	6.35032i	−0.283921	−	0.232036i
$750$	4.93692	−	24.0175i	0.180271	−	0.876996i
$751$	−6.94292			−0.253351			−0.126675	−	0.991944i	$-0.540431\pi$
$751$	−6.94292			−0.253351			−0.126675	+	0.991944i	$0.540431\pi$
$752$	−34.9013	−	35.7053i	−1.27272	−	1.30204i
$753$	−4.24183	−	4.24183i	−0.154581	−	0.154581i
$754$	−1.65639	+	1.64699i	−0.0603223	+	0.0599799i
$755$	2.53658	−	7.44369i	0.0923155	−	0.270904i
$756$	−18.7983	+	22.7364i	−0.683688	+	0.826915i
$757$	−2.73207	−	2.73207i	−0.0992988	−	0.0992988i	0.655712	−	0.755011i	$-0.272368\pi$
$757$	−2.73207	−	2.73207i	−0.0992988	−	0.0992988i	−0.755011	+	0.655712i	$0.772368\pi$
$758$	−0.0427431	+	15.0163i	−0.00155250	+	0.545417i
$759$	3.18580			0.115637
$760$	−5.19129	+	14.8184i	−0.188308	+	0.537519i
$761$			28.2249i			1.02315i	0.859238	+	0.511576i	$0.170938\pi$
$761$			28.2249i			1.02315i	−0.859238	+	0.511576i	$0.829062\pi$
$762$	−0.0944343	+	33.1762i	−0.00342099	+	1.20185i
$763$	−6.58306	+	0.662003i	−0.238323	+	0.0239661i
$764$	7.43438	+	0.0423235i	0.268967	+	0.00153121i
$765$	1.33470	+	2.71457i	0.0482563	+	0.0981455i
$766$	23.9653	+	24.1021i	0.865901	+	0.870845i
$767$	−7.47676	+	7.47676i	−0.269970	+	0.269970i
$768$	−17.1408	−	17.9398i	−0.618516	−	0.647346i
$769$	−18.6596			−0.672883			−0.336442	−	0.941704i	$-0.609223\pi$
$769$	−18.6596			−0.672883			−0.336442	+	0.941704i	$0.609223\pi$
$770$	−4.51911	+	19.2098i	−0.162857	+	0.692272i
$771$			18.1425i			0.653384i
$772$	25.4376	+	25.7288i	0.915518	+	0.926001i
$773$	5.42750	+	5.42750i	0.195214	+	0.195214i	0.797945	−	0.602731i	$-0.205921\pi$
$773$	5.42750	+	5.42750i	0.195214	+	0.195214i	−0.602731	+	0.797945i	$0.705921\pi$
$774$	−5.93379	+	5.90010i	−0.213286	+	0.212075i
$775$	−16.8996	+	21.9168i	−0.607051	+	0.787275i
$776$	−39.5310	+	38.8615i	−1.41908	+	1.39505i
$777$	−4.07992	−	40.5713i	−0.146366	−	1.45549i
$778$	−0.116951	+	41.0865i	−0.00419288	+	1.47302i
$779$	−13.6077			−0.487547
$780$	−11.8294	−	4.10641i	−0.423561	−	0.147033i
$781$		−	25.0077i		−	0.894846i
$782$	−2.79981	−	0.00796952i	−0.100121	−	0.000284989i
$783$	−3.60634	+	3.60634i	−0.128880	+	0.128880i
$784$	27.5011	−	5.26230i	0.982181	−	0.187939i
$785$	21.0642	+	42.8411i	0.751813	+	1.52907i
$786$	10.3622	−	10.3034i	0.369609	−	0.367511i
$787$	36.3797	−	36.3797i	1.29680	−	1.29680i	0.366297	−	0.930498i	$-0.380625\pi$
$787$	36.3797	−	36.3797i	1.29680	−	1.29680i	0.930498	−	0.366297i	$-0.119375\pi$
$788$	18.4644	+	18.6758i	0.657766	+	0.665298i
$789$			17.7675i			0.632541i
$790$	−8.75866	+	25.4650i	−0.311619	+	0.906003i
$791$	−37.9640	−	31.0263i	−1.34985	−	1.10317i
$792$	−0.0339043	+	3.97028i	−0.00120474	+	0.141078i
$793$	−2.27682	−	2.27682i	−0.0808524	−	0.0808524i
$794$	8.10103	+	8.14728i	0.287495	+	0.289136i
$795$	−7.79160	+	22.8648i	−0.276340	+	0.810930i
$796$	−51.7672	−	0.294707i	−1.83484	−	0.0104456i
$797$	−9.35558	+	9.35558i	−0.331392	+	0.331392i	−0.853115	−	0.521723i	$-0.825289\pi$
$797$	−9.35558	+	9.35558i	−0.331392	+	0.331392i	0.521723	+	0.853115i	$0.325289\pi$
$798$	11.1280	+	9.14738i	0.393928	+	0.323814i
$799$			28.3733i			1.00378i
$800$	−17.5882	+	22.1507i	−0.621838	+	0.783146i
$801$			5.04341i			0.178200i
$802$	0.118294	−	41.5584i	0.00417710	−	1.46748i
$803$	5.76899	+	5.76899i	0.203583	+	0.203583i
$804$	−0.137064	+	24.0762i	−0.00483389	+	0.849102i
$805$	−4.37335	+	2.72481i	−0.154140	+	0.0960369i
$806$	9.96548	+	10.0224i	0.351019	+	0.353023i
$807$	23.4607	−	23.4607i	0.825855	−	0.825855i
$808$	−0.383930	+	44.9593i	−0.0135066	+	1.58166i
$809$			42.7708i			1.50374i	0.659310	+	0.751871i	$0.270848\pi$
$809$			42.7708i			1.50374i	−0.659310	+	0.751871i	$0.729152\pi$
$810$	−20.5149	−	7.05606i	−0.720818	−	0.247925i
$811$	−16.5754			−0.582041			−0.291020	−	0.956717i	$-0.593995\pi$
$811$	−16.5754			−0.582041			−0.291020	+	0.956717i	$0.593995\pi$
$812$	4.81899	−	0.456910i	0.169114	−	0.0160344i
$813$	−4.71132	+	4.71132i	−0.165233	+	0.165233i
$814$	−23.3744	−	23.5078i	−0.819272	−	0.823949i
$815$	−1.41519	−	2.87827i	−0.0495720	−	0.100821i
$816$	−0.160535	+	14.0990i	−0.00561983	+	0.493563i
$817$	17.4530	+	17.4530i	0.610604	+	0.610604i
$818$	0.0221481	−	7.78096i	0.000774389	−	0.272055i
$819$	1.79909	−	2.20138i	0.0628652	−	0.0769225i
$820$	−23.1572	−	8.03867i	−0.808684	−	0.280723i
$821$		−	15.5555i		−	0.542890i	−0.962454	−	0.271445i	$-0.912498\pi$
$821$		−	15.5555i		−	0.542890i	0.962454	−	0.271445i	$-0.0875016\pi$
$822$	0.0342700	−	12.0396i	0.00119530	−	0.419929i
$823$	30.7453	+	30.7453i	1.07171	+	1.07171i	0.997222	+	0.0744916i	$0.0237334\pi$
$823$	30.7453	+	30.7453i	1.07171	+	1.07171i	0.0744916	+	0.997222i	$0.476267\pi$
$824$	−23.4770	−	23.8814i	−0.817861	−	0.831950i
$825$	−18.1379	+	2.34442i	−0.631480	+	0.0816223i
$826$	21.8082	−	2.13038i	0.758805	−	0.0741256i
$827$	23.4215	+	23.4215i	0.814445	+	0.814445i	0.985297	−	0.170851i	$-0.0546518\pi$
$827$	23.4215	+	23.4215i	0.814445	+	0.814445i	−0.170851	+	0.985297i	$0.554652\pi$
$828$	−0.737224	+	0.728878i	−0.0256203	+	0.0253302i
$829$			22.4634i			0.780186i	0.920775	+	0.390093i	$0.127557\pi$
$829$			22.4634i			0.780186i	−0.920775	+	0.390093i	$0.872443\pi$
$830$	12.6330	+	25.8792i	0.438497	+	0.898280i
$831$		−	16.7306i		−	0.580377i
$832$	10.0378	+	10.3867i	0.347999	+	0.360093i
$833$	−13.2660	−	8.78561i	−0.459640	−	0.304403i
$834$	4.60608	+	4.63238i	0.159496	+	0.160406i
$835$	30.8828	−	15.1845i	1.06874	−	0.525481i
$836$	11.7112	+	0.0666711i	0.405040	+	0.00230587i
$837$	21.8210	+	21.8210i	0.754243	+	0.754243i
$838$	28.6795	+	0.0816347i	0.990718	+	0.00282003i
$839$	−12.4343			−0.429281			−0.214641	−	0.976693i	$-0.568858\pi$
$839$	−12.4343			−0.429281			−0.214641	+	0.976693i	$0.568858\pi$
$840$	13.5336	+	22.1405i	0.466952	+	0.763921i
$841$	−28.1632			−0.971144
$842$	−47.7971	−	0.136052i	−1.64720	−	0.00468865i
$843$	21.4541	+	21.4541i	0.738918	+	0.738918i
$844$	0.0290656	−	5.10555i	0.00100048	−	0.175740i
$845$	−20.6152	−	7.02501i	−0.709184	−	0.241668i
$846$	7.40765	+	7.44994i	0.254680	+	0.256134i
$847$	−14.3117	+	1.43921i	−0.491757	+	0.0494519i
$848$	19.9263	−	19.4777i	0.684273	−	0.668865i
$849$			13.7308i			0.471239i
$850$	15.9462	−	2.01500i	0.546949	−	0.0691140i
$851$		−	8.65595i		−	0.296722i
$852$	−23.1194	−	23.3842i	−0.792059	−	0.801129i
$853$	−13.4352	−	13.4352i	−0.460014	−	0.460014i	0.438646	−	0.898660i	$-0.355458\pi$
$853$	−13.4352	−	13.4352i	−0.460014	−	0.460014i	−0.898660	+	0.438646i	$0.855458\pi$
$854$	0.648745	+	6.64104i	0.0221996	+	0.227252i
$855$	1.06566	−	3.12722i	0.0364448	−	0.106949i
$856$	−7.65036	+	7.52081i	−0.261484	+	0.257056i
$857$	0.276507	+	0.276507i	0.00944530	+	0.00944530i	0.711814	−	0.702368i	$-0.247874\pi$
$857$	0.276507	+	0.276507i	0.00944530	+	0.00944530i	−0.702368	+	0.711814i	$0.747874\pi$
$858$	−0.0265852	+	9.33980i	−0.000907605	+	0.318855i
$859$		−	46.7422i		−	1.59482i	−0.603435	−	0.797412i	$-0.706202\pi$
$859$		−	46.7422i		−	1.59482i	0.603435	−	0.797412i	$-0.293798\pi$
$860$	19.3907	+	40.0113i	0.661218	+	1.36437i
$861$	−14.2312	+	17.4135i	−0.484999	+	0.593449i
$862$	−0.0861056	+	30.2502i	−0.00293277	+	1.03033i
$863$	−11.1737	−	11.1737i	−0.380359	−	0.380359i	0.490873	−	0.871231i	$-0.336678\pi$
$863$	−11.1737	−	11.1737i	−0.380359	−	0.380359i	−0.871231	+	0.490873i	$0.836678\pi$
$864$	21.9812	+	22.6159i	0.747815	+	0.769410i
$865$	−32.0127	+	15.7400i	−1.08846	+	0.535177i
$866$	4.14575	+	4.16942i	0.140878	+	0.141683i
$867$	−12.9757	+	12.9757i	−0.440678	+	0.440678i
$868$	−2.76464	−	29.1584i	−0.0938379	−	0.989701i
$869$	20.0860			0.681369
$870$	1.96793	+	4.03138i	0.0667189	+	0.136677i
$871$		−	14.0162i		−	0.474921i
$872$	−0.0603985	+	7.07283i	−0.00204535	+	0.239516i
$873$	8.24778	−	8.24778i	0.279145	−	0.279145i
$874$	2.15612	+	2.16843i	0.0729319	+	0.0733482i
$875$	22.8938	−	18.7316i	0.773952	−	0.633244i
$876$	10.7279	+	0.0610730i	0.362461	+	0.00206346i
$877$	1.90129	+	1.90129i	0.0642020	+	0.0642020i	0.738479	−	0.674277i	$-0.235544\pi$
$877$	1.90129	+	1.90129i	0.0642020	+	0.0642020i	−0.674277	+	0.738479i	$0.735544\pi$
$878$	−0.0422132	+	14.8301i	−0.00142463	+	0.500493i
$879$		−	44.4685i		−	1.49988i
$880$	19.8903	+	7.03177i	0.670503	+	0.237041i
$881$		−	32.2820i		−	1.08761i	−0.839213	−	0.543803i	$-0.816984\pi$
$881$		−	32.2820i		−	1.08761i	0.839213	−	0.543803i	$-0.183016\pi$
$882$	−5.77697	+	1.15664i	−0.194521	+	0.0389461i
$883$	5.10115	−	5.10115i	0.171668	−	0.171668i	−0.616044	−	0.787712i	$-0.711266\pi$
$883$	5.10115	−	5.10115i	0.171668	−	0.171668i	0.787712	+	0.616044i	$0.211266\pi$
$884$	0.0467284	−	8.20813i	0.00157165	−	0.276069i
$885$	8.96014	+	18.2235i	0.301192	+	0.612575i
$886$	18.4319	+	18.5372i	0.619233	+	0.622768i
$887$	25.2698	+	25.2698i	0.848478	+	0.848478i	0.989943	−	0.141465i	$-0.0451812\pi$
$887$	25.2698	+	25.2698i	0.848478	+	0.848478i	−0.141465	+	0.989943i	$0.545181\pi$
$888$	−43.5897	−	0.372235i	−1.46278	−	0.0124914i
$889$	−25.3273	+	30.9908i	−0.849451	+	1.03940i
$890$	25.3410	+	8.71600i	0.849431	+	0.292161i
$891$			16.1815i			0.542099i
$892$	−23.3051	+	23.0413i	−0.780312	+	0.771478i
$893$	21.9125	−	21.9125i	0.733273	−	0.733273i
$894$	−16.5459	+	16.4520i	−0.553379	+	0.550237i
$895$	−8.93063	+	26.2073i	−0.298518	+	0.876013i
$896$	−2.40105	−	29.8368i	−0.0802133	−	0.996778i
$897$	−1.72442	+	1.72442i	−0.0575768	+	0.0575768i
$898$	−20.4002	−	0.0580681i	−0.680764	−	0.00193776i
$899$		−	5.06348i		−	0.168876i
$900$	3.66089	−	4.69228i	0.122030	−	0.156409i
$901$	−15.8345			−0.527524
$902$	−0.0520431	+	18.2835i	−0.00173284	+	0.608775i
$903$	40.5869	−	4.08149i	1.35065	−	0.135823i
$904$	−37.3780	+	36.7450i	−1.24317	+	1.22212i
$905$	3.70019	−	10.8584i	0.122999	−	0.360944i
$906$	−5.46936	+	5.43831i	−0.181707	+	0.180676i
$907$	7.46480	+	7.46480i	0.247865	+	0.247865i	0.820094	−	0.572229i	$-0.193921\pi$
$907$	7.46480	+	7.46480i	0.247865	+	0.247865i	−0.572229	+	0.820094i	$0.693921\pi$
$908$	−29.9111	+	29.5725i	−0.992635	+	0.981397i
$909$		−	9.46045i		−	0.313783i
$910$	−7.95182	−	12.8441i	−0.263600	−	0.425776i
$911$	26.3962			0.874545			0.437272	−	0.899329i	$-0.355945\pi$
$911$	26.3962			0.874545			0.437272	+	0.899329i	$0.355945\pi$
$912$	11.0125	−	10.7646i	0.364661	−	0.356450i
$913$	15.1886	−	15.1886i	0.502668	−	0.502668i
$914$	1.69792	+	1.70762i	0.0561623	+	0.0564830i
$915$	−5.54941	+	2.72854i	−0.183458	+	0.0902028i
$916$	−0.113305	+	19.9027i	−0.00374370	+	0.657604i
$917$	17.5404	−	1.76389i	0.579236	−	0.0582489i
$918$	0.0510139	−	17.9220i	0.00168371	−	0.591513i
$919$		−	6.84354i		−	0.225748i	−0.993609	−	0.112874i	$-0.963994\pi$
$919$		−	6.84354i		−	0.225748i	0.993609	−	0.112874i	$-0.0360056\pi$
$920$	2.38823	+	4.96388i	0.0787376	+	0.163654i
$921$	−34.2576			−1.12883
$922$	−0.0286718	+	10.0728i	−0.000944255	+	0.331731i
$923$	13.5363	+	13.5363i	0.445552	+	0.445552i
$924$	12.3331	−	14.9168i	0.405730	−	0.490726i
$925$	6.36989	+	49.2813i	0.209441	+	1.62036i
$926$	29.8176	−	29.6483i	0.979868	−	0.974305i
$927$	4.98265	+	4.98265i	0.163652	+	0.163652i
$928$	0.0736466	−	5.17430i	0.00241757	−	0.169855i
$929$	−12.2665			−0.402452			−0.201226	−	0.979545i	$-0.564493\pi$
$929$	−12.2665			−0.402452			−0.201226	+	0.979545i	$0.564493\pi$
$930$	24.3928	−	11.9074i	0.799871	−	0.390458i
$931$	3.46018	+	17.0303i	0.113403	+	0.558146i
$932$	−5.62121	−	5.68558i	−0.184129	−	0.186237i
$933$	−2.85288	+	2.85288i	−0.0933989	+	0.0933989i
$934$	−4.45753	−	4.48298i	−0.145855	−	0.146688i
$935$	−5.28972	−	10.7584i	−0.172992	−	0.351838i
$936$	−2.13070	−	2.16740i	−0.0696439	−	0.0708436i
$937$	−15.8683	−	15.8683i	−0.518394	−	0.518394i	0.398691	−	0.917085i	$-0.369465\pi$
$937$	−15.8683	−	15.8683i	−0.518394	−	0.518394i	−0.917085	+	0.398691i	$0.869465\pi$
$938$	−18.4444	+	22.4381i	−0.602231	+	0.732629i
$939$	−36.3980			−1.18780
$940$	50.2346	−	24.3453i	1.63847	−	0.794056i
$941$	30.5605			0.996244			0.498122	−	0.867107i	$-0.334023\pi$
$941$	30.5605			0.996244			0.498122	+	0.867107i	$0.334023\pi$
$942$	0.133277	−	46.8221i	0.00434239	−	1.52555i
$943$	−3.37572	+	3.37572i	−0.109929	+	0.109929i
$944$	0.266705	−	23.4234i	0.00868051	−	0.762368i
$945$	−17.4419	−	27.9943i	−0.567384	−	0.910656i
$946$	23.5169	−	23.3834i	0.764600	−	0.760260i
$947$	−29.1784	−	29.1784i	−0.948170	−	0.948170i	0.0505511	−	0.998721i	$-0.483902\pi$
$947$	−29.1784	−	29.1784i	−0.948170	−	0.948170i	−0.998721	+	0.0505511i	$0.983902\pi$
$948$	18.7820	−	18.5693i	0.610009	−	0.603103i
$949$	−6.24533			−0.202732
$950$	−13.8713	−	10.7589i	−0.450044	−	0.349066i
$951$		−	11.0945i		−	0.359764i
$952$	−10.8762	+	13.0786i	−0.352498	+	0.423881i
$953$	−18.6155	−	18.6155i	−0.603014	−	0.603014i	0.338097	−	0.941111i	$-0.390217\pi$
$953$	−18.6155	−	18.6155i	−0.603014	−	0.603014i	−0.941111	+	0.338097i	$0.890217\pi$
$954$	−4.15765	+	4.13405i	−0.134609	+	0.133845i
$955$	−2.68109	+	7.86775i	−0.0867579	+	0.254595i
$956$	0.0893048	−	15.6870i	0.00288832	−	0.507352i
$957$	2.36603	−	2.36603i	0.0764829	−	0.0764829i
$958$	0.0597642	−	20.9961i	0.00193089	−	0.678352i
$959$	9.19125	−	11.2465i	0.296801	−	0.363168i
$960$	25.0998	−	11.8132i	0.810094	−	0.381270i
$961$	0.362289			0.0116868
$962$	25.3766	+	0.0722331i	0.818174	+	0.00232889i
$963$	1.59618	−	1.59618i	0.0514361	−	0.0514361i
$964$	−0.246055	+	43.2212i	−0.00792491	+	1.39206i
$965$	−36.3007	+	17.8484i	−1.16856	+	0.574559i
$966$	5.02980	−	0.491347i	0.161831	−	0.0158088i
$967$	0.812718	−	0.812718i	0.0261352	−	0.0261352i	−0.693918	−	0.720054i	$-0.744117\pi$
$967$	0.812718	−	0.812718i	0.0261352	−	0.0261352i	0.720054	+	0.693918i	$0.244117\pi$
$968$	−0.131308	+	15.3765i	−0.00422040	+	0.494219i
$969$	−8.75114			−0.281127
$970$	−27.1878	−	55.6953i	−0.872947	−	1.78827i
$971$	20.7268			0.665156			0.332578	−	0.943076i	$-0.392082\pi$
$971$	20.7268			0.665156			0.332578	+	0.943076i	$0.392082\pi$
$972$	−8.55892	−	8.65693i	−0.274528	−	0.277671i
$973$	0.788539	+	7.84135i	0.0252794	+	0.251382i
$974$	10.0108	+	10.0679i	0.320766	+	0.322597i
$975$	8.54874	−	11.0867i	0.273779	−	0.355060i
$976$	7.13291	+	0.0812170i	0.228319	+	0.00259969i
$977$	29.8396	−	29.8396i	0.954653	−	0.954653i	−0.0443625	−	0.999016i	$-0.514126\pi$
$977$	29.8396	−	29.8396i	0.954653	−	0.954653i	0.999016	+	0.0443625i	$0.0141256\pi$
$978$	−0.00895416	+	3.14573i	−0.000286322	+	0.100589i
$979$		−	19.9881i		−	0.638824i
$980$	−4.17212	+	31.0257i	−0.133273	+	0.991079i
$981$		−	1.48828i		−	0.0475172i
$982$	18.1514	+	0.0516670i	0.579234	+	0.00164876i
$983$	−4.76417	+	4.76417i	−0.151953	+	0.151953i	−0.778990	−	0.627036i	$-0.784268\pi$
$983$	−4.76417	+	4.76417i	−0.151953	+	0.151953i	0.627036	+	0.778990i	$0.284268\pi$
$984$	16.8543	+	17.1447i	0.537296	+	0.546552i
$985$	−26.3496	+	12.9556i	−0.839568	+	0.412800i
$986$	−2.08528	+	2.07345i	−0.0664089	+	0.0660320i
$987$	−5.12436	−	50.9574i	−0.163110	−	1.62199i
$988$	−6.37517	+	6.30299i	−0.202821	+	0.200525i
$989$	8.65928			0.275349
$990$	−4.19771	−	1.44380i	−0.133412	−	0.0458869i
$991$	8.36065			0.265585			0.132792	−	0.991144i	$-0.457606\pi$
$991$	8.36065			0.265585			0.132792	+	0.991144i	$0.457606\pi$
$992$	−31.3083	−	0.445615i	−0.994039	−	0.0141483i
$993$	−24.8452	+	24.8452i	−0.788440	+	0.788440i
$994$	−3.85695	−	39.4826i	−0.122335	−	1.25231i
$995$	18.6690	−	54.7849i	0.591847	−	1.73680i
$996$	0.160793	−	28.2442i	0.00509491	−	0.894953i
$997$	4.50835	−	4.50835i	0.142781	−	0.142781i	−0.632103	−	0.774884i	$-0.717808\pi$
$997$	4.50835	−	4.50835i	0.142781	−	0.142781i	0.774884	+	0.632103i	$0.217808\pi$
$998$	−0.0409982	+	14.4033i	−0.00129777	+	0.455928i
$999$	55.4078			1.75303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.c.13.19	✓	72
4.3	odd	2		1120.2.w.c.433.28		72
5.2	odd	4	inner	280.2.s.c.237.35	yes	72
7.6	odd	2	inner	280.2.s.c.13.20	yes	72
8.3	odd	2		1120.2.w.c.433.9		72
8.5	even	2	inner	280.2.s.c.13.36	yes	72
20.7	even	4		1120.2.w.c.657.27		72
28.27	even	2		1120.2.w.c.433.10		72
35.27	even	4	inner	280.2.s.c.237.36	yes	72
40.27	even	4		1120.2.w.c.657.10		72
40.37	odd	4	inner	280.2.s.c.237.20	yes	72
56.13	odd	2	inner	280.2.s.c.13.35	yes	72
56.27	even	2		1120.2.w.c.433.27		72
140.27	odd	4		1120.2.w.c.657.9		72
280.27	odd	4		1120.2.w.c.657.28		72
280.237	even	4	inner	280.2.s.c.237.19	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.c.13.19	✓	72	1.1	even	1	trivial
280.2.s.c.13.20	yes	72	7.6	odd	2	inner
280.2.s.c.13.35	yes	72	56.13	odd	2	inner
280.2.s.c.13.36	yes	72	8.5	even	2	inner
280.2.s.c.237.19	yes	72	280.237	even	4	inner
280.2.s.c.237.20	yes	72	40.37	odd	4	inner
280.2.s.c.237.35	yes	72	5.2	odd	4	inner
280.2.s.c.237.36	yes	72	35.27	even	4	inner
1120.2.w.c.433.9		72	8.3	odd	2
1120.2.w.c.433.10		72	28.27	even	2
1120.2.w.c.433.27		72	56.27	even	2
1120.2.w.c.433.28		72	4.3	odd	2
1120.2.w.c.657.9		72	140.27	odd	4
1120.2.w.c.657.10		72	40.27	even	4
1120.2.w.c.657.27		72	20.7	even	4
1120.2.w.c.657.28		72	280.27	odd	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.00402547 - 1.41421i) q^{2} +(-1.09655 - 1.09655i) q^{3} +(-1.99997 - 0.0113857i) q^{4} +(0.721255 - 2.11655i) q^{5} +(-1.55517 + 1.54634i) q^{6} +(-2.63247 + 0.264726i) q^{7} +(-0.0241525 + 2.82832i) q^{8} -0.595144i q^{9} +O(q^{10})\)	\(q+(0.00402547 - 1.41421i) q^{2} +(-1.09655 - 1.09655i) q^{3} +(-1.99997 - 0.0113857i) q^{4} +(0.721255 - 2.11655i) q^{5} +(-1.55517 + 1.54634i) q^{6} +(-2.63247 + 0.264726i) q^{7} +(-0.0241525 + 2.82832i) q^{8} -0.595144i q^{9} +(-2.99034 - 1.02852i) q^{10} +2.35868i q^{11} +(2.18059 + 2.20556i) q^{12} +(-1.27672 - 1.27672i) q^{13} +(0.363780 + 3.72393i) q^{14} +(-3.11181 + 1.53002i) q^{15} +(3.99974 + 0.0455420i) q^{16} +(-1.60730 - 1.60730i) q^{17} +(-0.841657 - 0.00239573i) q^{18} +2.48261i q^{19} +(-1.46659 + 4.22482i) q^{20} +(3.17693 + 2.59636i) q^{21} +(3.33567 + 0.00949480i) q^{22} +(0.615870 + 0.615870i) q^{23} +(3.12789 - 3.07492i) q^{24} +(-3.95958 - 3.05315i) q^{25} +(-1.81068 + 1.80041i) q^{26} +(-3.94227 + 3.94227i) q^{27} +(5.26788 - 0.499471i) q^{28} +0.914789 q^{29} +(2.15123 + 4.40690i) q^{30} -5.53513i q^{31} +(0.0805067 - 5.65628i) q^{32} +(2.58642 - 2.58642i) q^{33} +(-2.27952 + 2.26658i) q^{34} +(-1.33838 + 5.76270i) q^{35} +(-0.00677612 + 1.19027i) q^{36} +(-7.02741 - 7.02741i) q^{37} +(3.51093 + 0.00999366i) q^{38} +2.79998i q^{39} +(5.96887 + 2.09106i) q^{40} +5.48122i q^{41} +(3.68458 - 4.48239i) q^{42} +(7.03012 - 7.03012i) q^{43} +(0.0268552 - 4.71729i) q^{44} +(-1.25965 - 0.429250i) q^{45} +(0.873448 - 0.868490i) q^{46} +(-8.82639 - 8.82639i) q^{47} +(-4.33599 - 4.43587i) q^{48} +(6.85984 - 1.39377i) q^{49} +(-4.33372 + 5.58738i) q^{50} +3.52498i q^{51} +(2.53886 + 2.56793i) q^{52} +(4.92582 - 4.92582i) q^{53} +(5.55931 + 5.59105i) q^{54} +(4.99228 + 1.70121i) q^{55} +(-0.685150 - 7.45188i) q^{56} +(2.72231 - 2.72231i) q^{57} +(0.00368245 - 1.29370i) q^{58} -5.85624i q^{59} +(6.24093 - 3.02455i) q^{60} +1.78334 q^{61} +(-7.82783 - 0.0222815i) q^{62} +(0.157550 + 1.56670i) q^{63} +(-7.99883 - 0.136622i) q^{64} +(-3.62308 + 1.78140i) q^{65} +(-3.64733 - 3.66815i) q^{66} +(5.48915 + 5.48915i) q^{67} +(3.19624 + 3.23284i) q^{68} -1.35067i q^{69} +(8.14427 + 1.91594i) q^{70} -10.6024 q^{71} +(1.68326 + 0.0143742i) q^{72} +(2.44585 - 2.44585i) q^{73} +(-9.96651 + 9.90993i) q^{74} +(0.993953 + 7.68983i) q^{75} +(0.0282662 - 4.96514i) q^{76} +(-0.624405 - 6.20917i) q^{77} +(3.95975 + 0.0112712i) q^{78} -8.51575i q^{79} +(2.98123 - 8.43281i) q^{80} +6.86037 q^{81} +(7.75158 + 0.0220645i) q^{82} +(-6.43943 - 6.43943i) q^{83} +(-6.32420 - 5.22881i) q^{84} +(-4.56120 + 2.24266i) q^{85} +(-9.91375 - 9.97034i) q^{86} +(-1.00311 - 1.00311i) q^{87} +(-6.67112 - 0.0569682i) q^{88} -8.47427 q^{89} +(-0.612120 + 1.77968i) q^{90} +(3.69891 + 3.02295i) q^{91} +(-1.22471 - 1.23873i) q^{92} +(-6.06957 + 6.06957i) q^{93} +(-12.5179 + 12.4468i) q^{94} +(5.25457 + 1.79059i) q^{95} +(-6.29069 + 6.11413i) q^{96} +(13.8585 + 13.8585i) q^{97} +(-1.94346 - 9.70685i) q^{98} +1.40376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

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