LMFDB - Embedded newform 1110.2.l.b.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.13
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.04396 + 0.906760i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.03373 - 1.03373i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.04396 + 0.906760i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.03373 - 1.03373i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.906760 - 2.04396i) q^{10} -6.26734i q^{11} +(-0.707107 + 0.707107i) q^{12} +0.736934i q^{13} +(-1.03373 - 1.03373i) q^{14} +(2.08648 - 0.804124i) q^{15} +1.00000 q^{16} +2.79231 q^{17} -1.00000 q^{18} +(-0.886013 + 0.886013i) q^{19} +(-2.04396 - 0.906760i) q^{20} -1.46191i q^{21} -6.26734 q^{22} +6.92696i q^{23} +(0.707107 + 0.707107i) q^{24} +(3.35557 + 3.70677i) q^{25} +0.736934 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.03373 + 1.03373i) q^{28} +(-5.78064 - 5.78064i) q^{29} +(-0.804124 - 2.08648i) q^{30} +(1.64619 - 1.64619i) q^{31} -1.00000i q^{32} +(-4.43168 - 4.43168i) q^{33} -2.79231i q^{34} +(3.05024 - 1.17556i) q^{35} +1.00000i q^{36} +(4.32965 - 4.27248i) q^{37} +(0.886013 + 0.886013i) q^{38} +(0.521091 + 0.521091i) q^{39} +(-0.906760 + 2.04396i) q^{40} +0.847391i q^{41} -1.46191 q^{42} -9.33244i q^{43} +6.26734i q^{44} +(0.906760 - 2.04396i) q^{45} +6.92696 q^{46} +(2.86222 - 2.86222i) q^{47} +(0.707107 - 0.707107i) q^{48} +4.86282i q^{49} +(3.70677 - 3.35557i) q^{50} +(1.97446 - 1.97446i) q^{51} -0.736934i q^{52} +(3.98023 + 3.98023i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(5.68297 - 12.8102i) q^{55} +(1.03373 + 1.03373i) q^{56} +1.25301i q^{57} +(-5.78064 + 5.78064i) q^{58} +(8.40717 - 8.40717i) q^{59} +(-2.08648 + 0.804124i) q^{60} +(-5.05111 + 5.05111i) q^{61} +(-1.64619 - 1.64619i) q^{62} +(-1.03373 - 1.03373i) q^{63} -1.00000 q^{64} +(-0.668222 + 1.50627i) q^{65} +(-4.43168 + 4.43168i) q^{66} +(-6.24546 - 6.24546i) q^{67} -2.79231 q^{68} +(4.89810 + 4.89810i) q^{69} +(-1.17556 - 3.05024i) q^{70} -0.962946 q^{71} +1.00000 q^{72} +(-2.59228 + 2.59228i) q^{73} +(-4.27248 - 4.32965i) q^{74} +(4.99383 + 0.248333i) q^{75} +(0.886013 - 0.886013i) q^{76} +(-6.47871 - 6.47871i) q^{77} +(0.521091 - 0.521091i) q^{78} +(-11.6910 + 11.6910i) q^{79} +(2.04396 + 0.906760i) q^{80} -1.00000 q^{81} +0.847391 q^{82} +(-7.04605 - 7.04605i) q^{83} +1.46191i q^{84} +(5.70738 + 2.53195i) q^{85} -9.33244 q^{86} -8.17506 q^{87} +6.26734 q^{88} +(12.7462 + 12.7462i) q^{89} +(-2.04396 - 0.906760i) q^{90} +(0.761788 + 0.761788i) q^{91} -6.92696i q^{92} -2.32806i q^{93} +(-2.86222 - 2.86222i) q^{94} +(-2.61438 + 1.00758i) q^{95} +(-0.707107 - 0.707107i) q^{96} -18.3296 q^{97} +4.86282 q^{98} -6.26734 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	2.04396	+	0.906760i	0.914088	+	0.405515i
$5$	2.04396	+	0.906760i	0.914088	+	0.405515i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	1.03373	−	1.03373i	0.390712	−	0.390712i	−0.484229	−	0.874941i	$-0.660900\pi$
$7$	1.03373	−	1.03373i	0.390712	−	0.390712i	0.874941	+	0.484229i	$0.160900\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	0.906760	−	2.04396i	0.286743	−	0.646358i
$11$		−	6.26734i		−	1.88967i	−0.327541	−	0.944837i	$-0.606220\pi$
$11$		−	6.26734i		−	1.88967i	0.327541	−	0.944837i	$-0.393780\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$			0.736934i			0.204389i	0.994764	+	0.102194i	$0.0325864\pi$
$13$			0.736934i			0.204389i	−0.994764	+	0.102194i	$0.967414\pi$
$14$	−1.03373	−	1.03373i	−0.276275	−	0.276275i
$15$	2.08648	−	0.804124i	0.538726	−	0.207624i
$16$	1.00000			0.250000
$17$	2.79231			0.677235			0.338617	−	0.940924i	$-0.390041\pi$
$17$	2.79231			0.677235			0.338617	+	0.940924i	$0.390041\pi$
$18$	−1.00000			−0.235702
$19$	−0.886013	+	0.886013i	−0.203265	+	0.203265i	−0.801397	−	0.598132i	$-0.795910\pi$
$19$	−0.886013	+	0.886013i	−0.203265	+	0.203265i	0.598132	+	0.801397i	$0.295910\pi$
$20$	−2.04396	−	0.906760i	−0.457044	−	0.202758i
$21$		−	1.46191i		−	0.319015i
$22$	−6.26734			−1.33620
$23$			6.92696i			1.44437i	0.691700	+	0.722185i	$0.256862\pi$
$23$			6.92696i			1.44437i	−0.691700	+	0.722185i	$0.743138\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	3.35557	+	3.70677i	0.671115	+	0.741354i
$26$	0.736934			0.144525
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.03373	+	1.03373i	−0.195356	+	0.195356i
$29$	−5.78064	−	5.78064i	−1.07344	−	1.07344i	−0.997080	−	0.0763577i	$-0.975671\pi$
$29$	−5.78064	−	5.78064i	−1.07344	−	1.07344i	−0.0763577	−	0.997080i	$-0.524329\pi$
$30$	−0.804124	−	2.08648i	−0.146812	−	0.380937i
$31$	1.64619	−	1.64619i	0.295664	−	0.295664i	−0.543649	−	0.839313i	$-0.682958\pi$
$31$	1.64619	−	1.64619i	0.295664	−	0.295664i	0.839313	+	0.543649i	$0.182958\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.43168	−	4.43168i	−0.771456	−	0.771456i
$34$		−	2.79231i		−	0.478877i
$35$	3.05024	−	1.17556i	0.515585	−	0.198705i
$36$			1.00000i			0.166667i
$37$	4.32965	−	4.27248i	0.711791	−	0.702392i
$37$	4.32965	−	4.27248i	0.711791	−	0.702392i
$38$	0.886013	+	0.886013i	0.143730	+	0.143730i
$39$	0.521091	+	0.521091i	0.0834413	+	0.0834413i
$40$	−0.906760	+	2.04396i	−0.143371	+	0.323179i
$41$			0.847391i			0.132340i	0.997808	+	0.0661701i	$0.0210780\pi$
$41$			0.847391i			0.132340i	−0.997808	+	0.0661701i	$0.978922\pi$
$42$	−1.46191			−0.225578
$43$		−	9.33244i		−	1.42318i	−0.702593	−	0.711592i	$-0.747975\pi$
$43$		−	9.33244i		−	1.42318i	0.702593	−	0.711592i	$-0.252025\pi$
$44$			6.26734i			0.944837i
$45$	0.906760	−	2.04396i	0.135172	−	0.304696i
$46$	6.92696			1.02132
$47$	2.86222	−	2.86222i	0.417497	−	0.417497i	−0.466843	−	0.884340i	$-0.654609\pi$
$47$	2.86222	−	2.86222i	0.417497	−	0.417497i	0.884340	+	0.466843i	$0.154609\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			4.86282i			0.694689i
$50$	3.70677	−	3.35557i	0.524216	−	0.474550i
$51$	1.97446	−	1.97446i	0.276480	−	0.276480i
$52$		−	0.736934i		−	0.102194i
$53$	3.98023	+	3.98023i	0.546727	+	0.546727i	0.925493	−	0.378766i	$-0.123651\pi$
$53$	3.98023	+	3.98023i	0.546727	+	0.546727i	−0.378766	+	0.925493i	$0.623651\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	5.68297	−	12.8102i	0.766292	−	1.72733i
$56$	1.03373	+	1.03373i	0.138137	+	0.138137i
$57$			1.25301i			0.165965i
$58$	−5.78064	+	5.78064i	−0.759035	+	0.759035i
$59$	8.40717	−	8.40717i	1.09452	−	1.09452i	0.0994809	−	0.995039i	$-0.468282\pi$
$59$	8.40717	−	8.40717i	1.09452	−	1.09452i	0.995039	−	0.0994809i	$-0.0317182\pi$
$60$	−2.08648	+	0.804124i	−0.269363	+	0.103812i
$61$	−5.05111	+	5.05111i	−0.646728	+	0.646728i	−0.952201	−	0.305472i	$-0.901186\pi$
$61$	−5.05111	+	5.05111i	−0.646728	+	0.646728i	0.305472	+	0.952201i	$0.401186\pi$
$62$	−1.64619	−	1.64619i	−0.209066	−	0.209066i
$63$	−1.03373	−	1.03373i	−0.130237	−	0.130237i
$64$	−1.00000			−0.125000
$65$	−0.668222	+	1.50627i	−0.0828827	+	0.186829i
$66$	−4.43168	+	4.43168i	−0.545502	+	0.545502i
$67$	−6.24546	−	6.24546i	−0.763005	−	0.763005i	0.213860	−	0.976864i	$-0.431396\pi$
$67$	−6.24546	−	6.24546i	−0.763005	−	0.763005i	−0.976864	+	0.213860i	$0.931396\pi$
$68$	−2.79231			−0.338617
$69$	4.89810	+	4.89810i	0.589662	+	0.589662i
$70$	−1.17556	−	3.05024i	−0.140506	−	0.364573i
$71$	−0.962946			−0.114281			−0.0571404	−	0.998366i	$-0.518198\pi$
$71$	−0.962946			−0.114281			−0.0571404	+	0.998366i	$0.518198\pi$
$72$	1.00000			0.117851
$73$	−2.59228	+	2.59228i	−0.303404	+	0.303404i	−0.842344	−	0.538940i	$-0.818825\pi$
$73$	−2.59228	+	2.59228i	−0.303404	+	0.303404i	0.538940	+	0.842344i	$0.318825\pi$
$74$	−4.27248	−	4.32965i	−0.496666	−	0.503312i
$75$	4.99383	+	0.248333i	0.576638	+	0.0286750i
$76$	0.886013	−	0.886013i	0.101633	−	0.101633i
$77$	−6.47871	−	6.47871i	−0.738318	−	0.738318i
$78$	0.521091	−	0.521091i	0.0590019	−	0.0590019i
$79$	−11.6910	+	11.6910i	−1.31534	+	1.31534i	−0.397912	+	0.917424i	$0.630265\pi$
$79$	−11.6910	+	11.6910i	−1.31534	+	1.31534i	−0.917424	+	0.397912i	$0.869735\pi$
$80$	2.04396	+	0.906760i	0.228522	+	0.101379i
$81$	−1.00000			−0.111111
$82$	0.847391			0.0935787
$83$	−7.04605	−	7.04605i	−0.773405	−	0.773405i	0.205295	−	0.978700i	$-0.434185\pi$
$83$	−7.04605	−	7.04605i	−0.773405	−	0.773405i	−0.978700	+	0.205295i	$0.934185\pi$
$84$			1.46191i			0.159507i
$85$	5.70738	+	2.53195i	0.619052	+	0.274629i
$86$	−9.33244			−1.00634
$87$	−8.17506			−0.876459
$88$	6.26734			0.668101
$89$	12.7462	+	12.7462i	1.35109	+	1.35109i	0.884440	+	0.466654i	$0.154541\pi$
$89$	12.7462	+	12.7462i	1.35109	+	1.35109i	0.466654	+	0.884440i	$0.345459\pi$
$90$	−2.04396	−	0.906760i	−0.215453	−	0.0955809i
$91$	0.761788	+	0.761788i	0.0798571	+	0.0798571i
$92$		−	6.92696i		−	0.722185i
$93$		−	2.32806i		−	0.241409i
$94$	−2.86222	−	2.86222i	−0.295215	−	0.295215i
$95$	−2.61438	+	1.00758i	−0.268230	+	0.103375i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−18.3296			−1.86109			−0.930546	−	0.366174i	$-0.880667\pi$
$97$	−18.3296			−1.86109			−0.930546	+	0.366174i	$0.880667\pi$
$98$	4.86282			0.491219
$99$	−6.26734			−0.629891
$100$	−3.35557	−	3.70677i	−0.335557	−	0.370677i
$101$			9.61899i			0.957125i	0.878054	+	0.478562i	$0.158842\pi$
$101$			9.61899i			0.957125i	−0.878054	+	0.478562i	$0.841158\pi$
$102$	−1.97446	−	1.97446i	−0.195501	−	0.195501i
$103$	10.9768			1.08158			0.540788	−	0.841159i	$-0.318126\pi$
$103$	10.9768			1.08158			0.540788	+	0.841159i	$0.318126\pi$
$104$	−0.736934			−0.0722623
$105$	1.32560	−	2.98809i	0.129365	−	0.291608i
$106$	3.98023	−	3.98023i	0.386594	−	0.386594i
$107$	9.06848	−	9.06848i	0.876683	−	0.876683i	−0.116507	−	0.993190i	$-0.537170\pi$
$107$	9.06848	−	9.06848i	0.876683	−	0.876683i	0.993190	+	0.116507i	$0.0371697\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	4.34378	−	4.34378i	0.416059	−	0.416059i	−0.467784	−	0.883843i	$-0.654948\pi$
$109$	4.34378	−	4.34378i	0.416059	−	0.416059i	0.883843	+	0.467784i	$0.154948\pi$
$110$	−12.8102	−	5.68297i	−1.22141	−	0.541850i
$111$	0.0404257	−	6.08263i	0.00383704	−	0.577338i
$112$	1.03373	−	1.03373i	0.0976780	−	0.0976780i
$113$	8.66069			0.814729			0.407364	−	0.913266i	$-0.366448\pi$
$113$	8.66069			0.814729			0.407364	+	0.913266i	$0.366448\pi$
$114$	1.25301			0.117355
$115$	−6.28109	+	14.1584i	−0.585714	+	1.32028i
$116$	5.78064	+	5.78064i	0.536719	+	0.536719i
$117$	0.736934			0.0681295
$118$	−8.40717	−	8.40717i	−0.773943	−	0.773943i
$119$	2.88648	−	2.88648i	0.264604	−	0.264604i
$120$	0.804124	+	2.08648i	0.0734062	+	0.190468i
$121$	−28.2795			−2.57087
$122$	5.05111	+	5.05111i	0.457306	+	0.457306i
$123$	0.599196	+	0.599196i	0.0540277	+	0.0540277i
$124$	−1.64619	+	1.64619i	−0.147832	+	0.147832i
$125$	3.49752	+	10.6192i	0.312828	+	0.949810i
$126$	−1.03373	+	1.03373i	−0.0920917	+	0.0920917i
$127$	−14.0850	+	14.0850i	−1.24984	+	1.24984i	−0.294054	+	0.955789i	$0.595005\pi$
$127$	−14.0850	+	14.0850i	−1.24984	+	1.24984i	−0.955789	+	0.294054i	$0.904995\pi$
$128$			1.00000i			0.0883883i
$129$	−6.59903	−	6.59903i	−0.581012	−	0.581012i
$130$	1.50627	+	0.668222i	0.132108	+	0.0586069i
$131$	−1.76846	+	1.76846i	−0.154511	+	0.154511i	−0.780130	−	0.625618i	$-0.784847\pi$
$131$	−1.76846	+	1.76846i	−0.154511	+	0.154511i	0.625618	+	0.780130i	$0.284847\pi$
$132$	4.43168	+	4.43168i	0.385728	+	0.385728i
$133$			1.83179i			0.158836i
$134$	−6.24546	+	6.24546i	−0.539526	+	0.539526i
$135$	−0.804124	−	2.08648i	−0.0692080	−	0.179575i
$136$			2.79231i			0.239439i
$137$	6.23559	−	6.23559i	0.532742	−	0.532742i	−0.388645	−	0.921387i	$-0.627057\pi$
$137$	6.23559	−	6.23559i	0.532742	−	0.532742i	0.921387	+	0.388645i	$0.127057\pi$
$138$	4.89810	−	4.89810i	0.416954	−	0.416954i
$139$	9.56037			0.810900			0.405450	−	0.914117i	$-0.367115\pi$
$139$	9.56037			0.810900			0.405450	+	0.914117i	$0.367115\pi$
$140$	−3.05024	+	1.17556i	−0.257792	+	0.0993527i
$141$		−	4.04778i		−	0.340885i
$142$			0.962946i			0.0808087i
$143$	4.61861			0.386228
$144$		−	1.00000i		−	0.0833333i
$145$	−6.57377	−	17.0571i	−0.545922	−	1.41651i
$146$	2.59228	+	2.59228i	0.214539	+	0.214539i
$147$	3.43853	+	3.43853i	0.283605	+	0.283605i
$148$	−4.32965	+	4.27248i	−0.355895	+	0.351196i
$149$			2.83560i			0.232302i	0.993232	+	0.116151i	$0.0370556\pi$
$149$			2.83560i			0.232302i	−0.993232	+	0.116151i	$0.962944\pi$
$150$	0.248333	−	4.99383i	0.0202763	−	0.407744i
$151$			18.3733i			1.49520i	0.664151	+	0.747599i	$0.268793\pi$
$151$			18.3733i			1.49520i	−0.664151	+	0.747599i	$0.731207\pi$
$152$	−0.886013	−	0.886013i	−0.0718651	−	0.0718651i
$153$		−	2.79231i		−	0.225745i
$154$	−6.47871	+	6.47871i	−0.522070	+	0.522070i
$155$	4.85744	−	1.87205i	0.390159	−	0.150367i
$156$	−0.521091	−	0.521091i	−0.0417207	−	0.0417207i
$157$	−4.70204	+	4.70204i	−0.375264	+	0.375264i	−0.869390	−	0.494126i	$-0.835488\pi$
$157$	−4.70204	+	4.70204i	−0.375264	+	0.375264i	0.494126	+	0.869390i	$0.335488\pi$
$158$	11.6910	+	11.6910i	0.930083	+	0.930083i
$159$	5.62889			0.446400
$160$	0.906760	−	2.04396i	0.0716857	−	0.161589i
$161$	7.16058	+	7.16058i	0.564332	+	0.564332i
$162$			1.00000i			0.0785674i
$163$	1.09629			0.0858680			0.0429340	−	0.999078i	$-0.486329\pi$
$163$	1.09629			0.0858680			0.0429340	+	0.999078i	$0.486329\pi$
$164$		−	0.847391i		−	0.0661701i
$165$	−5.03972	−	13.0767i	−0.392342	−	1.01802i
$166$	−7.04605	+	7.04605i	−0.546880	+	0.546880i
$167$	17.6829			1.36835			0.684174	−	0.729319i	$-0.260163\pi$
$167$	17.6829			1.36835			0.684174	+	0.729319i	$0.260163\pi$
$168$	1.46191			0.112789
$169$	12.4569			0.958225
$170$	2.53195	−	5.70738i	0.194192	−	0.437736i
$171$	0.886013	+	0.886013i	0.0677551	+	0.0677551i
$172$			9.33244i			0.711592i
$173$	−1.52212	+	1.52212i	−0.115725	+	0.115725i	−0.762598	−	0.646873i	$-0.776076\pi$
$173$	−1.52212	+	1.52212i	−0.115725	+	0.115725i	0.646873	+	0.762598i	$0.276076\pi$
$174$			8.17506i			0.619750i
$175$	7.30053	+	0.363040i	0.551868	+	0.0274433i
$176$		−	6.26734i		−	0.472418i
$177$		−	11.8895i		−	0.893672i
$178$	12.7462	−	12.7462i	0.955368	−	0.955368i
$179$	16.3764	+	16.3764i	1.22403	+	1.22403i	0.966187	+	0.257844i	$0.0830121\pi$
$179$	16.3764	+	16.3764i	1.22403	+	1.22403i	0.257844	+	0.966187i	$0.416988\pi$
$180$	−0.906760	+	2.04396i	−0.0675859	+	0.152348i
$181$	−17.7191			−1.31705			−0.658523	−	0.752560i	$-0.728819\pi$
$181$	−17.7191			−1.31705			−0.658523	+	0.752560i	$0.728819\pi$
$182$	0.761788	−	0.761788i	0.0564675	−	0.0564675i
$183$			7.14335i			0.528052i
$184$	−6.92696			−0.510662
$185$	12.7238	−	4.80684i	0.935470	−	0.353406i
$186$	−2.32806			−0.170702
$187$		−	17.5004i		−	1.27975i
$188$	−2.86222	+	2.86222i	−0.208749	+	0.208749i
$189$	−1.46191			−0.106338
$190$	1.00758	+	2.61438i	0.0730973	+	0.189667i
$191$	6.20872	+	6.20872i	0.449247	+	0.449247i	0.895104	−	0.445857i	$-0.147101\pi$
$191$	6.20872	+	6.20872i	0.449247	+	0.449247i	−0.445857	+	0.895104i	$0.647101\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$			0.340975i			0.0245439i	0.999925	+	0.0122720i	$0.00390639\pi$
$193$			0.340975i			0.0245439i	−0.999925	+	0.0122720i	$0.996094\pi$
$194$			18.3296i			1.31599i
$195$	0.592586	+	1.53759i	0.0424360	+	0.110109i
$196$		−	4.86282i		−	0.347344i
$197$	−1.84335	+	1.84335i	−0.131333	+	0.131333i	−0.769718	−	0.638385i	$-0.779603\pi$
$197$	−1.84335	+	1.84335i	−0.131333	+	0.131333i	0.638385	+	0.769718i	$0.279603\pi$
$198$			6.26734i			0.445400i
$199$	10.1003	+	10.1003i	0.715991	+	0.715991i	0.967782	−	0.251791i	$-0.0810194\pi$
$199$	10.1003	+	10.1003i	0.715991	+	0.715991i	−0.251791	+	0.967782i	$0.581019\pi$
$200$	−3.70677	+	3.35557i	−0.262108	+	0.237275i
$201$	−8.83242			−0.622991
$202$	9.61899			0.676789
$203$	−11.9512			−0.838810
$204$	−1.97446	+	1.97446i	−0.138240	+	0.138240i
$205$	−0.768380	+	1.73204i	−0.0536660	+	0.120971i
$206$		−	10.9768i		−	0.764790i
$207$	6.92696			0.481457
$208$			0.736934i			0.0510972i
$209$	5.55294	+	5.55294i	0.384105	+	0.384105i
$210$	−2.98809	−	1.32560i	−0.206198	−	0.0914752i
$211$	−8.80254			−0.605992			−0.302996	−	0.952992i	$-0.597987\pi$
$211$	−8.80254			−0.605992			−0.302996	+	0.952992i	$0.597987\pi$
$212$	−3.98023	−	3.98023i	−0.273363	−	0.273363i
$213$	−0.680906	+	0.680906i	−0.0466549	+	0.0466549i
$214$	−9.06848	−	9.06848i	−0.619909	−	0.619909i
$215$	8.46228	−	19.0752i	0.577123	−	1.30092i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$		−	3.40341i		−	0.231039i
$218$	−4.34378	−	4.34378i	−0.294198	−	0.294198i
$219$			3.66604i			0.247728i
$220$	−5.68297	+	12.8102i	−0.383146	+	0.863664i
$221$			2.05775i			0.138419i
$222$	−6.08263	−	0.0404257i	−0.408239	−	0.00271320i
$223$	−10.1685	−	10.1685i	−0.680931	−	0.680931i	0.279279	−	0.960210i	$-0.409905\pi$
$223$	−10.1685	−	10.1685i	−0.680931	−	0.680931i	−0.960210	+	0.279279i	$0.909905\pi$
$224$	−1.03373	−	1.03373i	−0.0690687	−	0.0690687i
$225$	3.70677	−	3.35557i	0.247118	−	0.223705i
$226$		−	8.66069i		−	0.576100i
$227$	−2.33325			−0.154863			−0.0774316	−	0.996998i	$-0.524672\pi$
$227$	−2.33325			−0.154863			−0.0774316	+	0.996998i	$0.524672\pi$
$228$		−	1.25301i		−	0.0829827i
$229$		−	7.41303i		−	0.489867i	−0.969540	−	0.244933i	$-0.921234\pi$
$229$		−	7.41303i		−	0.489867i	0.969540	−	0.244933i	$-0.0787661\pi$
$230$	14.1584	+	6.28109i	0.933580	+	0.414163i
$231$	−9.16228			−0.602834
$232$	5.78064	−	5.78064i	0.379518	−	0.379518i
$233$	−10.5495	+	10.5495i	−0.691124	+	0.691124i	−0.962479	−	0.271356i	$-0.912528\pi$
$233$	−10.5495	+	10.5495i	−0.691124	+	0.691124i	0.271356	+	0.962479i	$0.412528\pi$
$234$		−	0.736934i		−	0.0481749i
$235$	8.44561	−	3.25492i	0.550931	−	0.212328i
$236$	−8.40717	+	8.40717i	−0.547260	+	0.547260i
$237$			16.5335i			1.07397i
$238$	−2.88648	−	2.88648i	−0.187103	−	0.187103i
$239$	−4.55380	+	4.55380i	−0.294561	+	0.294561i	−0.838879	−	0.544318i	$-0.816788\pi$
$239$	−4.55380	+	4.55380i	−0.294561	+	0.294561i	0.544318	+	0.838879i	$0.316788\pi$
$240$	2.08648	−	0.804124i	0.134681	−	0.0519060i
$241$	−3.48959	−	3.48959i	−0.224784	−	0.224784i	0.585725	−	0.810510i	$-0.300810\pi$
$241$	−3.48959	−	3.48959i	−0.224784	−	0.224784i	−0.810510	+	0.585725i	$0.800810\pi$
$242$			28.2795i			1.81788i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	5.05111	−	5.05111i	0.323364	−	0.323364i
$245$	−4.40941	+	9.93943i	−0.281707	+	0.635007i
$246$	0.599196	−	0.599196i	0.0382033	−	0.0382033i
$247$	−0.652933	−	0.652933i	−0.0415451	−	0.0415451i
$248$	1.64619	+	1.64619i	0.104533	+	0.104533i
$249$	−9.96463			−0.631483
$250$	10.6192	−	3.49752i	0.671617	−	0.221203i
$251$	−16.1757	+	16.1757i	−1.02100	+	1.02100i	−0.0212296	+	0.999775i	$0.506758\pi$
$251$	−16.1757	+	16.1757i	−1.02100	+	1.02100i	−0.999775	+	0.0212296i	$0.993242\pi$
$252$	1.03373	+	1.03373i	0.0651186	+	0.0651186i
$253$	43.4136			2.72939
$254$	14.0850	+	14.0850i	0.883773	+	0.883773i
$255$	5.82609	−	2.24536i	0.364844	−	0.140610i
$256$	1.00000			0.0625000
$257$	8.10538			0.505600			0.252800	−	0.967519i	$-0.418649\pi$
$257$	8.10538			0.505600			0.252800	+	0.967519i	$0.418649\pi$
$258$	−6.59903	+	6.59903i	−0.410838	+	0.410838i
$259$	0.0590988	−	8.89225i	0.00367222	−	0.552538i
$260$	0.668222	−	1.50627i	0.0414414	−	0.0934146i
$261$	−5.78064	+	5.78064i	−0.357813	+	0.357813i
$262$	1.76846	+	1.76846i	0.109256	+	0.109256i
$263$	−9.61207	+	9.61207i	−0.592706	+	0.592706i	−0.938361	−	0.345656i	$-0.887657\pi$
$263$	−9.61207	+	9.61207i	−0.592706	+	0.592706i	0.345656	+	0.938361i	$0.387657\pi$
$264$	4.43168	−	4.43168i	0.272751	−	0.272751i
$265$	4.52633	+	11.7446i	0.278050	+	0.721462i
$266$	1.83179			0.112314
$267$	18.0258			1.10316
$268$	6.24546	+	6.24546i	0.381502	+	0.381502i
$269$		−	7.97934i		−	0.486509i	−0.969962	−	0.243255i	$-0.921785\pi$
$269$		−	7.97934i		−	0.486509i	0.969962	−	0.243255i	$-0.0782150\pi$
$270$	−2.08648	+	0.804124i	−0.126979	+	0.0489374i
$271$	15.5657			0.945548			0.472774	−	0.881184i	$-0.343253\pi$
$271$	15.5657			0.945548			0.472774	+	0.881184i	$0.343253\pi$
$272$	2.79231			0.169309
$273$	1.07733			0.0652030
$274$	−6.23559	−	6.23559i	−0.376706	−	0.376706i
$275$	23.2316	−	21.0305i	1.40092	−	1.26819i
$276$	−4.89810	−	4.89810i	−0.294831	−	0.294831i
$277$			31.7356i			1.90681i	0.301701	+	0.953403i	$0.402446\pi$
$277$			31.7356i			1.90681i	−0.301701	+	0.953403i	$0.597554\pi$
$278$		−	9.56037i		−	0.573393i
$279$	−1.64619	−	1.64619i	−0.0985546	−	0.0985546i
$280$	1.17556	+	3.05024i	0.0702530	+	0.182287i
$281$	−2.87484	−	2.87484i	−0.171498	−	0.171498i	0.616139	−	0.787637i	$-0.288696\pi$
$281$	−2.87484	−	2.87484i	−0.171498	−	0.171498i	−0.787637	+	0.616139i	$0.788696\pi$
$282$	−4.04778			−0.241042
$283$	32.3676			1.92405			0.962027	−	0.272955i	$-0.0880009\pi$
$283$	32.3676			1.92405			0.962027	+	0.272955i	$0.0880009\pi$
$284$	0.962946			0.0571404
$285$	−1.13618	+	2.56111i	−0.0673015	+	0.151707i
$286$		−	4.61861i		−	0.273104i
$287$	0.875971	+	0.875971i	0.0517069	+	0.0517069i
$288$	−1.00000			−0.0589256
$289$	−9.20300			−0.541353
$290$	−17.0571	+	6.57377i	−1.00163	+	0.386025i
$291$	−12.9610	+	12.9610i	−0.759788	+	0.759788i
$292$	2.59228	−	2.59228i	0.151702	−	0.151702i
$293$	3.87790	+	3.87790i	0.226550	+	0.226550i	0.811250	−	0.584700i	$-0.198788\pi$
$293$	3.87790	+	3.87790i	0.226550	+	0.226550i	−0.584700	+	0.811250i	$0.698788\pi$
$294$	3.43853	−	3.43853i	0.200539	−	0.200539i
$295$	24.8072	−	9.56066i	1.44433	−	0.556643i
$296$	4.27248	+	4.32965i	0.248333	+	0.251656i
$297$	−4.43168	+	4.43168i	−0.257152	+	0.257152i
$298$	2.83560			0.164262
$299$	−5.10471			−0.295213
$300$	−4.99383	−	0.248333i	−0.288319	−	0.0143375i
$301$	−9.64719	−	9.64719i	−0.556055	−	0.556055i
$302$	18.3733			1.05726
$303$	6.80165	+	6.80165i	0.390745	+	0.390745i
$304$	−0.886013	+	0.886013i	−0.0508163	+	0.0508163i
$305$	−14.9044	+	5.74414i	−0.853425	+	0.328909i
$306$	−2.79231			−0.159626
$307$	−6.50486	−	6.50486i	−0.371252	−	0.371252i	0.496681	−	0.867933i	$-0.334552\pi$
$307$	−6.50486	−	6.50486i	−0.371252	−	0.371252i	−0.867933	+	0.496681i	$0.834552\pi$
$308$	6.47871	+	6.47871i	0.369159	+	0.369159i
$309$	7.76177	−	7.76177i	0.441552	−	0.441552i
$310$	−1.87205	−	4.85744i	−0.106325	−	0.275884i
$311$	16.8205	−	16.8205i	0.953803	−	0.953803i	−0.0451763	−	0.998979i	$-0.514385\pi$
$311$	16.8205	−	16.8205i	0.953803	−	0.953803i	0.998979	+	0.0451763i	$0.0143850\pi$
$312$	−0.521091	+	0.521091i	−0.0295010	+	0.0295010i
$313$			0.921260i			0.0520727i	0.999661	+	0.0260364i	$0.00828857\pi$
$313$			0.921260i			0.0520727i	−0.999661	+	0.0260364i	$0.991711\pi$
$314$	4.70204	+	4.70204i	0.265352	+	0.265352i
$315$	−1.17556	−	3.05024i	−0.0662351	−	0.171862i
$316$	11.6910	−	11.6910i	0.657668	−	0.657668i
$317$	−1.85948	−	1.85948i	−0.104439	−	0.104439i	0.652957	−	0.757395i	$-0.273528\pi$
$317$	−1.85948	−	1.85948i	−0.104439	−	0.104439i	−0.757395	+	0.652957i	$0.773528\pi$
$318$		−	5.62889i		−	0.315653i
$319$	−36.2292	+	36.2292i	−2.02845	+	2.02845i
$320$	−2.04396	−	0.906760i	−0.114261	−	0.0506894i
$321$		−	12.8248i		−	0.715809i
$322$	7.16058	−	7.16058i	0.399043	−	0.399043i
$323$	−2.47402	+	2.47402i	−0.137658	+	0.137658i
$324$	1.00000			0.0555556
$325$	−2.73164	+	2.47283i	−0.151524	+	0.137168i
$326$		−	1.09629i		−	0.0607178i
$327$		−	6.14303i		−	0.339710i
$328$	−0.847391			−0.0467893
$329$		−	5.91750i		−	0.326242i
$330$	−13.0767	+	5.03972i	−0.719846	+	0.277427i
$331$	−8.07530	−	8.07530i	−0.443859	−	0.443859i	0.449448	−	0.893307i	$-0.351621\pi$
$331$	−8.07530	−	8.07530i	−0.443859	−	0.443859i	−0.893307	+	0.449448i	$0.851621\pi$
$332$	7.04605	+	7.04605i	0.386702	+	0.386702i
$333$	−4.27248	−	4.32965i	−0.234131	−	0.237264i
$334$		−	17.6829i		−	0.967568i
$335$	−7.10236	−	18.4286i	−0.388044	−	1.00686i
$336$		−	1.46191i		−	0.0797537i
$337$	−10.2788	−	10.2788i	−0.559924	−	0.559924i	0.369362	−	0.929286i	$-0.379576\pi$
$337$	−10.2788	−	10.2788i	−0.559924	−	0.559924i	−0.929286	+	0.369362i	$0.879576\pi$
$338$		−	12.4569i		−	0.677568i
$339$	6.12403	−	6.12403i	0.332612	−	0.332612i
$340$	−5.70738	−	2.53195i	−0.309526	−	0.137315i
$341$	−10.3172	−	10.3172i	−0.558708	−	0.558708i
$342$	0.886013	−	0.886013i	0.0479101	−	0.0479101i
$343$	12.2629	+	12.2629i	0.662135	+	0.662135i
$344$	9.33244			0.503171
$345$	5.57013	+	14.4529i	0.299886	+	0.778120i
$346$	1.52212	+	1.52212i	0.0818298	+	0.0818298i
$347$			2.21653i			0.118989i	0.998229	+	0.0594947i	$0.0189489\pi$
$347$			2.21653i			0.118989i	−0.998229	+	0.0594947i	$0.981051\pi$
$348$	8.17506			0.438229
$349$			7.91901i			0.423895i	0.977281	+	0.211947i	$0.0679805\pi$
$349$			7.91901i			0.423895i	−0.977281	+	0.211947i	$0.932019\pi$
$350$	0.363040	−	7.30053i	0.0194053	−	0.390230i
$351$	0.521091	−	0.521091i	0.0278138	−	0.0278138i
$352$	−6.26734			−0.334050
$353$	−2.54035			−0.135209			−0.0676046	−	0.997712i	$-0.521536\pi$
$353$	−2.54035			−0.135209			−0.0676046	+	0.997712i	$0.521536\pi$
$354$	−11.8895			−0.631922
$355$	−1.96823	−	0.873161i	−0.104463	−	0.0463426i
$356$	−12.7462	−	12.7462i	−0.675547	−	0.675547i
$357$		−	4.08211i		−	0.216048i
$358$	16.3764	−	16.3764i	0.865520	−	0.865520i
$359$			17.2531i			0.910584i	0.890342	+	0.455292i	$0.150465\pi$
$359$			17.2531i			0.910584i	−0.890342	+	0.455292i	$0.849535\pi$
$360$	2.04396	+	0.906760i	0.107726	+	0.0477904i
$361$			17.4300i			0.917366i
$362$			17.7191i			0.931293i
$363$	−19.9967	+	19.9967i	−1.04955	+	1.04955i
$364$	−0.761788	−	0.761788i	−0.0399285	−	0.0399285i
$365$	−7.64911	+	2.94795i	−0.400373	+	0.154303i
$366$	7.14335			0.373389
$367$	13.0108	−	13.0108i	0.679160	−	0.679160i	−0.280650	−	0.959810i	$-0.590550\pi$
$367$	13.0108	−	13.0108i	0.679160	−	0.679160i	0.959810	+	0.280650i	$0.0905500\pi$
$368$			6.92696i			0.361093i
$369$	0.847391			0.0441134
$370$	−4.80684	−	12.7238i	−0.249896	−	0.661477i
$371$	8.22894			0.427225
$372$			2.32806i			0.120704i
$373$	−18.1951	+	18.1951i	−0.942108	+	0.942108i	−0.998414	−	0.0563053i	$-0.982068\pi$
$373$	−18.1951	+	18.1951i	−0.942108	+	0.942108i	0.0563053	+	0.998414i	$0.482068\pi$
$374$	−17.5004			−0.904922
$375$	9.98203	+	5.03579i	0.515470	+	0.260047i
$376$	2.86222	+	2.86222i	0.147608	+	0.147608i
$377$	4.25995	−	4.25995i	0.219399	−	0.219399i
$378$			1.46191i			0.0751925i
$379$			26.7132i			1.37217i	0.727523	+	0.686084i	$0.240672\pi$
$379$			26.7132i			1.37217i	−0.727523	+	0.686084i	$0.759328\pi$
$380$	2.61438	−	1.00758i	0.134115	−	0.0516876i
$381$			19.9192i			1.02049i
$382$	6.20872	−	6.20872i	0.317666	−	0.317666i
$383$			4.38944i			0.224290i	0.993692	+	0.112145i	$0.0357721\pi$
$383$			4.38944i			0.224290i	−0.993692	+	0.112145i	$0.964228\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−7.36762	−	19.1169i	−0.375488	−	0.974287i
$386$	0.340975			0.0173552
$387$	−9.33244			−0.474395
$388$	18.3296			0.930546
$389$	−22.2349	+	22.2349i	−1.12736	+	1.12736i	−0.136750	+	0.990606i	$0.543666\pi$
$389$	−22.2349	+	22.2349i	−1.12736	+	1.12736i	−0.990606	+	0.136750i	$0.956334\pi$
$390$	1.53759	−	0.592586i	0.0778591	−	0.0300068i
$391$			19.3422i			0.978178i
$392$	−4.86282			−0.245609
$393$			2.50099i			0.126158i
$394$	1.84335	+	1.84335i	0.0928664	+	0.0928664i
$395$	−34.4968	+	13.2950i	−1.73572	+	0.668944i
$396$	6.26734			0.314946
$397$	13.6670	+	13.6670i	0.685927	+	0.685927i	0.961329	−	0.275402i	$-0.0888109\pi$
$397$	13.6670	+	13.6670i	0.685927	+	0.685927i	−0.275402	+	0.961329i	$0.588811\pi$
$398$	10.1003	−	10.1003i	0.506282	−	0.506282i
$399$	1.29527	+	1.29527i	0.0648447	+	0.0648447i
$400$	3.35557	+	3.70677i	0.167779	+	0.185338i
$401$	16.9000	−	16.9000i	0.843944	−	0.843944i	−0.145426	−	0.989369i	$-0.546455\pi$
$401$	16.9000	−	16.9000i	0.843944	−	0.843944i	0.989369	+	0.145426i	$0.0464551\pi$
$402$			8.83242i			0.440521i
$403$	1.21313	+	1.21313i	0.0604303	+	0.0604303i
$404$		−	9.61899i		−	0.478562i
$405$	−2.04396	−	0.906760i	−0.101565	−	0.0450573i
$406$			11.9512i			0.593128i
$407$	−26.7771	−	27.1354i	−1.32729	−	1.34505i
$408$	1.97446	+	1.97446i	0.0977504	+	0.0977504i
$409$	5.32124	+	5.32124i	0.263118	+	0.263118i	0.826320	−	0.563201i	$-0.190430\pi$
$409$	5.32124	+	5.32124i	0.263118	+	0.263118i	−0.563201	+	0.826320i	$0.690430\pi$
$410$	1.73204	+	0.768380i	0.0855392	+	0.0379476i
$411$		−	8.81845i		−	0.434982i
$412$	−10.9768			−0.540788
$413$		−	17.3814i		−	0.855284i
$414$		−	6.92696i		−	0.340441i
$415$	−8.01280	−	20.7910i	−0.393333	−	1.02059i
$416$	0.736934			0.0361311
$417$	6.76020	−	6.76020i	0.331048	−	0.331048i
$418$	5.55294	−	5.55294i	0.271603	−	0.271603i
$419$			11.7545i			0.574245i	0.957894	+	0.287122i	$0.0926986\pi$
$419$			11.7545i			0.574245i	−0.957894	+	0.287122i	$0.907301\pi$
$420$	−1.32560	+	2.98809i	−0.0646827	+	0.145804i
$421$	−9.16265	+	9.16265i	−0.446560	+	0.446560i	−0.894209	−	0.447649i	$-0.852261\pi$
$421$	−9.16265	+	9.16265i	−0.446560	+	0.446560i	0.447649	+	0.894209i	$0.352261\pi$
$422$			8.80254i			0.428501i
$423$	−2.86222	−	2.86222i	−0.139166	−	0.139166i
$424$	−3.98023	+	3.98023i	−0.193297	+	0.193297i
$425$	9.36980	+	10.3504i	0.454502	+	0.502070i
$426$	0.680906	+	0.680906i	0.0329900	+	0.0329900i
$427$			10.4429i			0.505369i
$428$	−9.06848	+	9.06848i	−0.438342	+	0.438342i
$429$	3.26585	−	3.26585i	0.157677	−	0.157677i
$430$	−19.0752	−	8.46228i	−0.919886	−	0.408088i
$431$	−3.45686	+	3.45686i	−0.166511	+	0.166511i	−0.785444	−	0.618933i	$-0.787565\pi$
$431$	−3.45686	+	3.45686i	−0.166511	+	0.166511i	0.618933	+	0.785444i	$0.287565\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−4.11998	−	4.11998i	−0.197994	−	0.197994i	0.601146	−	0.799139i	$-0.294711\pi$
$433$	−4.11998	−	4.11998i	−0.197994	−	0.197994i	−0.799139	+	0.601146i	$0.794711\pi$
$434$	−3.40341			−0.163369
$435$	−16.7095	−	7.41282i	−0.801160	−	0.355417i
$436$	−4.34378	+	4.34378i	−0.208029	+	0.208029i
$437$	−6.13737	−	6.13737i	−0.293590	−	0.293590i
$438$	3.66604			0.175170
$439$	−24.0778	−	24.0778i	−1.14917	−	1.14917i	−0.986716	−	0.162457i	$-0.948058\pi$
$439$	−24.0778	−	24.0778i	−1.14917	−	1.14917i	−0.162457	−	0.986716i	$-0.551942\pi$
$440$	12.8102	+	5.68297i	0.610703	+	0.270925i
$441$	4.86282			0.231563
$442$	2.05775			0.0978771
$443$	6.83063	−	6.83063i	0.324533	−	0.324533i	−0.525970	−	0.850503i	$-0.676298\pi$
$443$	6.83063	−	6.83063i	0.324533	−	0.324533i	0.850503	+	0.525970i	$0.176298\pi$
$444$	−0.0404257	+	6.08263i	−0.00191852	+	0.288669i
$445$	14.4950	+	37.6105i	0.687130	+	1.78291i
$446$	−10.1685	+	10.1685i	−0.481491	+	0.481491i
$447$	2.00508	+	2.00508i	0.0948368	+	0.0948368i
$448$	−1.03373	+	1.03373i	−0.0488390	+	0.0488390i
$449$	21.9750	−	21.9750i	1.03707	−	1.03707i	0.0377790	−	0.999286i	$-0.487972\pi$
$449$	21.9750	−	21.9750i	1.03707	−	1.03707i	0.999286	−	0.0377790i	$-0.0120283\pi$
$450$	−3.35557	−	3.70677i	−0.158183	−	0.174739i
$451$	5.31089			0.250080
$452$	−8.66069			−0.407364
$453$	12.9919	+	12.9919i	0.610412	+	0.610412i
$454$			2.33325i			0.109505i
$455$	0.866308	+	2.24783i	0.0406131	+	0.105380i
$456$	−1.25301			−0.0586776
$457$	23.6642			1.10696			0.553481	−	0.832862i	$-0.313299\pi$
$457$	23.6642			1.10696			0.553481	+	0.832862i	$0.313299\pi$
$458$	−7.41303			−0.346388
$459$	−1.97446	−	1.97446i	−0.0921600	−	0.0921600i
$460$	6.28109	−	14.1584i	0.292857	−	0.660141i
$461$	−15.3068	−	15.3068i	−0.712910	−	0.712910i	0.254233	−	0.967143i	$-0.418177\pi$
$461$	−15.3068	−	15.3068i	−0.712910	−	0.712910i	−0.967143	+	0.254233i	$0.918177\pi$
$462$			9.16228i			0.426268i
$463$		−	41.7413i		−	1.93988i	−0.243341	−	0.969941i	$-0.578243\pi$
$463$		−	41.7413i		−	1.93988i	0.243341	−	0.969941i	$-0.421757\pi$
$464$	−5.78064	−	5.78064i	−0.268360	−	0.268360i
$465$	2.11099	−	4.75847i	0.0978949	−	0.220669i
$466$	10.5495	+	10.5495i	0.488698	+	0.488698i
$467$	18.8139			0.870606			0.435303	−	0.900284i	$-0.356641\pi$
$467$	18.8139			0.870606			0.435303	+	0.900284i	$0.356641\pi$
$468$	−0.736934			−0.0340648
$469$	−12.9122			−0.596230
$470$	−3.25492	−	8.44561i	−0.150138	−	0.389567i
$471$			6.64969i			0.306402i
$472$	8.40717	+	8.40717i	0.386971	+	0.386971i
$473$	−58.4896			−2.68935
$474$	16.5335			0.759409
$475$	−6.25733	−	0.311164i	−0.287106	−	0.0142772i
$476$	−2.88648	+	2.88648i	−0.132302	+	0.132302i
$477$	3.98023	−	3.98023i	0.182242	−	0.182242i
$478$	4.55380	+	4.55380i	0.208286	+	0.208286i
$479$	13.9456	−	13.9456i	0.637190	−	0.637190i	−0.312671	−	0.949861i	$-0.601224\pi$
$479$	13.9456	−	13.9456i	0.637190	−	0.637190i	0.949861	+	0.312671i	$0.101224\pi$
$480$	−0.804124	−	2.08648i	−0.0367031	−	0.0952342i
$481$	3.14854	+	3.19067i	0.143561	+	0.145482i
$482$	−3.48959	+	3.48959i	−0.158947	+	0.158947i
$483$	10.1266			0.460776
$484$	28.2795			1.28543
$485$	−37.4651	−	16.6206i	−1.70120	−	0.754702i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−2.48057			−0.112405			−0.0562027	−	0.998419i	$-0.517899\pi$
$487$	−2.48057			−0.112405			−0.0562027	+	0.998419i	$0.517899\pi$
$488$	−5.05111	−	5.05111i	−0.228653	−	0.228653i
$489$	0.775194	−	0.775194i	0.0350555	−	0.0350555i
$490$	9.93943	+	4.40941i	0.449017	+	0.199197i
$491$	−27.0864			−1.22239			−0.611196	−	0.791479i	$-0.709311\pi$
$491$	−27.0864			−1.22239			−0.611196	+	0.791479i	$0.709311\pi$
$492$	−0.599196	−	0.599196i	−0.0270138	−	0.0270138i
$493$	−16.1413	−	16.1413i	−0.726970	−	0.726970i
$494$	−0.652933	+	0.652933i	−0.0293768	+	0.0293768i
$495$	−12.8102	−	5.68297i	−0.575776	−	0.255431i
$496$	1.64619	−	1.64619i	0.0739160	−	0.0739160i
$497$	−0.995423	+	0.995423i	−0.0446508	+	0.0446508i
$498$			9.96463i			0.446526i
$499$	−2.96909	−	2.96909i	−0.132915	−	0.132915i	0.637520	−	0.770434i	$-0.279961\pi$
$499$	−2.96909	−	2.96909i	−0.132915	−	0.132915i	−0.770434	+	0.637520i	$0.779961\pi$
$500$	−3.49752	−	10.6192i	−0.156414	−	0.474905i
$501$	12.5037	−	12.5037i	0.558626	−	0.558626i
$502$	16.1757	+	16.1757i	0.721959	+	0.721959i
$503$			32.3803i			1.44377i	0.692015	+	0.721883i	$0.256723\pi$
$503$			32.3803i			1.44377i	−0.692015	+	0.721883i	$0.743277\pi$
$504$	1.03373	−	1.03373i	0.0460458	−	0.0460458i
$505$	−8.72211	+	19.6609i	−0.388129	+	0.874897i
$506$		−	43.4136i		−	1.92997i
$507$	8.80838	−	8.80838i	0.391194	−	0.391194i
$508$	14.0850	−	14.0850i	0.624922	−	0.624922i
$509$	22.0862			0.978952			0.489476	−	0.872017i	$-0.337188\pi$
$509$	22.0862			0.978952			0.489476	+	0.872017i	$0.337188\pi$
$510$	−2.24536	−	5.82609i	−0.0994264	−	0.257984i
$511$			5.35942i			0.237087i
$512$		−	1.00000i		−	0.0441942i
$513$	1.25301			0.0553218
$514$		−	8.10538i		−	0.357513i
$515$	22.4362	+	9.95332i	0.988656	+	0.438596i
$516$	6.59903	+	6.59903i	0.290506	+	0.290506i
$517$	−17.9385	−	17.9385i	−0.788933	−	0.788933i
$518$	−8.89225	−	0.0590988i	−0.390703	−	0.00259665i
$519$			2.15261i			0.0944889i
$520$	−1.50627	−	0.668222i	−0.0660541	−	0.0293035i
$521$			28.8075i			1.26208i	0.775751	+	0.631039i	$0.217371\pi$
$521$			28.8075i			1.26208i	−0.775751	+	0.631039i	$0.782629\pi$
$522$	5.78064	+	5.78064i	0.253012	+	0.253012i
$523$		−	4.73292i		−	0.206956i	−0.994632	−	0.103478i	$-0.967003\pi$
$523$		−	4.73292i		−	0.206956i	0.994632	−	0.103478i	$-0.0329972\pi$
$524$	1.76846	−	1.76846i	0.0772557	−	0.0772557i
$525$	5.41896	−	4.90554i	0.236503	−	0.214096i
$526$	9.61207	+	9.61207i	0.419106	+	0.419106i
$527$	4.59666	−	4.59666i	0.200234	−	0.200234i
$528$	−4.43168	−	4.43168i	−0.192864	−	0.192864i
$529$	−24.9827			−1.08620
$530$	11.7446	−	4.52633i	0.510151	−	0.196611i
$531$	−8.40717	−	8.40717i	−0.364840	−	0.364840i
$532$		−	1.83179i		−	0.0794182i
$533$	−0.624471			−0.0270488
$534$		−	18.0258i		−	0.780055i
$535$	26.7586	−	10.3127i	1.15687	−	0.445857i
$536$	6.24546	−	6.24546i	0.269763	−	0.269763i
$537$	23.1597			0.999417
$538$	−7.97934			−0.344014
$539$	30.4769			1.31273
$540$	0.804124	+	2.08648i	0.0346040	+	0.0897877i
$541$	−10.7692	−	10.7692i	−0.463003	−	0.463003i	0.436635	−	0.899639i	$-0.356170\pi$
$541$	−10.7692	−	10.7692i	−0.463003	−	0.463003i	−0.899639	+	0.436635i	$0.856170\pi$
$542$		−	15.5657i		−	0.668603i
$543$	−12.5293	+	12.5293i	−0.537682	+	0.537682i
$544$		−	2.79231i		−	0.119719i
$545$	12.8173	−	4.93976i	0.549032	−	0.211596i
$546$		−	1.07733i		−	0.0461055i
$547$		−	21.4263i		−	0.916123i	−0.888920	−	0.458062i	$-0.848544\pi$
$547$		−	21.4263i		−	0.916123i	0.888920	−	0.458062i	$-0.151456\pi$
$548$	−6.23559	+	6.23559i	−0.266371	+	0.266371i
$549$	5.05111	+	5.05111i	0.215576	+	0.215576i
$550$	−21.0305	−	23.2316i	−0.896744	−	0.990598i
$551$	10.2434			0.436386
$552$	−4.89810	+	4.89810i	−0.208477	+	0.208477i
$553$			24.1705i			1.02783i
$554$	31.7356			1.34831
$555$	5.59811	−	12.3960i	0.237627	−	0.526181i
$556$	−9.56037			−0.405450
$557$		−	40.6664i		−	1.72309i	−0.507680	−	0.861546i	$-0.669497\pi$
$557$		−	40.6664i		−	1.72309i	0.507680	−	0.861546i	$-0.330503\pi$
$558$	−1.64619	+	1.64619i	−0.0696887	+	0.0696887i
$559$	6.87739			0.290883
$560$	3.05024	−	1.17556i	0.128896	−	0.0496764i
$561$	−12.3746	−	12.3746i	−0.522457	−	0.522457i
$562$	−2.87484	+	2.87484i	−0.121268	+	0.121268i
$563$		−	2.87035i		−	0.120971i	−0.998169	−	0.0604855i	$-0.980735\pi$
$563$		−	2.87035i		−	0.120971i	0.998169	−	0.0604855i	$-0.0192649\pi$
$564$			4.04778i			0.170442i
$565$	17.7021	+	7.85316i	0.744734	+	0.330385i
$566$		−	32.3676i		−	1.36051i
$567$	−1.03373	+	1.03373i	−0.0434124	+	0.0434124i
$568$		−	0.962946i		−	0.0404043i
$569$	4.67420	+	4.67420i	0.195953	+	0.195953i	0.798262	−	0.602310i	$-0.205753\pi$
$569$	4.67420	+	4.67420i	0.195953	+	0.195953i	−0.602310	+	0.798262i	$0.705753\pi$
$570$	2.56111	+	1.13618i	0.107273	+	0.0475894i
$571$	−9.05022			−0.378740			−0.189370	−	0.981906i	$-0.560645\pi$
$571$	−9.05022			−0.378740			−0.189370	+	0.981906i	$0.560645\pi$
$572$	−4.61861			−0.193114
$573$	8.78045			0.366809
$574$	0.875971	−	0.875971i	0.0365623	−	0.0365623i
$575$	−25.6766	+	23.2439i	−1.07079	+	0.969338i
$576$			1.00000i			0.0416667i
$577$	−43.0099			−1.79052			−0.895262	−	0.445539i	$-0.853012\pi$
$577$	−43.0099			−1.79052			−0.895262	+	0.445539i	$0.853012\pi$
$578$			9.20300i			0.382795i
$579$	0.241106	+	0.241106i	0.0100200	+	0.0100200i
$580$	6.57377	+	17.0571i	0.272961	+	0.708256i
$581$	−14.5674			−0.604357
$582$	12.9610	+	12.9610i	0.537251	+	0.537251i
$583$	24.9454	−	24.9454i	1.03313	−	1.03313i
$584$	−2.59228	−	2.59228i	−0.107269	−	0.107269i
$585$	1.50627	+	0.668222i	0.0622764	+	0.0276276i
$586$	3.87790	−	3.87790i	0.160195	−	0.160195i
$587$			20.9031i			0.862762i	0.902170	+	0.431381i	$0.141974\pi$
$587$			20.9031i			0.862762i	−0.902170	+	0.431381i	$0.858026\pi$
$588$	−3.43853	−	3.43853i	−0.141803	−	0.141803i
$589$			2.91709i			0.120196i
$590$	−9.56066	−	24.8072i	−0.393606	−	1.02130i
$591$			2.60688i			0.107233i
$592$	4.32965	−	4.27248i	0.177948	−	0.175598i
$593$	−5.48408	−	5.48408i	−0.225204	−	0.225204i	0.585482	−	0.810686i	$-0.300905\pi$
$593$	−5.48408	−	5.48408i	−0.225204	−	0.225204i	−0.810686	+	0.585482i	$0.800905\pi$
$594$	4.43168	+	4.43168i	0.181834	+	0.181834i
$595$	8.51722	−	3.28252i	0.349172	−	0.134570i
$596$		−	2.83560i		−	0.116151i
$597$	14.2840			0.584604
$598$			5.10471i			0.208747i
$599$		−	8.95384i		−	0.365844i	−0.983127	−	0.182922i	$-0.941444\pi$
$599$		−	8.95384i		−	0.365844i	0.983127	−	0.182922i	$-0.0585556\pi$
$600$	−0.248333	+	4.99383i	−0.0101381	+	0.203872i
$601$	−23.2252			−0.947374			−0.473687	−	0.880693i	$-0.657077\pi$
$601$	−23.2252			−0.947374			−0.473687	+	0.880693i	$0.657077\pi$
$602$	−9.64719	+	9.64719i	−0.393190	+	0.393190i
$603$	−6.24546	+	6.24546i	−0.254335	+	0.254335i
$604$		−	18.3733i		−	0.747599i
$605$	−57.8023	−	25.6428i	−2.35000	−	1.04253i
$606$	6.80165	−	6.80165i	0.276298	−	0.276298i
$607$		−	5.64510i		−	0.229128i	−0.993416	−	0.114564i	$-0.963453\pi$
$607$		−	5.64510i		−	0.229128i	0.993416	−	0.114564i	$-0.0365471\pi$
$608$	0.886013	+	0.886013i	0.0359326	+	0.0359326i
$609$	−8.45078	+	8.45078i	−0.342443	+	0.342443i
$610$	5.74414	+	14.9044i	0.232573	+	0.603463i
$611$	2.10926	+	2.10926i	0.0853317	+	0.0853317i
$612$			2.79231i			0.112872i
$613$	5.16392	−	5.16392i	0.208569	−	0.208569i	−0.595090	−	0.803659i	$-0.702884\pi$
$613$	5.16392	−	5.16392i	0.208569	−	0.208569i	0.803659	+	0.595090i	$0.202884\pi$
$614$	−6.50486	+	6.50486i	−0.262515	+	0.262515i
$615$	0.681408	+	1.76806i	0.0274770	+	0.0712951i
$616$	6.47871	−	6.47871i	0.261035	−	0.261035i
$617$	−27.6646	−	27.6646i	−1.11374	−	1.11374i	−0.992641	−	0.121094i	$-0.961360\pi$
$617$	−27.6646	−	27.6646i	−1.11374	−	1.11374i	−0.121094	−	0.992641i	$-0.538640\pi$
$618$	−7.76177	−	7.76177i	−0.312224	−	0.312224i
$619$	1.46506			0.0588858			0.0294429	−	0.999566i	$-0.490627\pi$
$619$	1.46506			0.0588858			0.0294429	+	0.999566i	$0.490627\pi$
$620$	−4.85744	+	1.87205i	−0.195080	+	0.0751833i
$621$	4.89810	−	4.89810i	0.196554	−	0.196554i
$622$	−16.8205	−	16.8205i	−0.674440	−	0.674440i
$623$	26.3522			1.05578
$624$	0.521091	+	0.521091i	0.0208603	+	0.0208603i
$625$	−2.48026	+	24.8767i	−0.0992105	+	0.995066i
$626$	0.921260			0.0368210
$627$	7.85305			0.313621
$628$	4.70204	−	4.70204i	0.187632	−	0.187632i
$629$	12.0897	−	11.9301i	0.482049	−	0.475684i
$630$	−3.05024	+	1.17556i	−0.121524	+	0.0468353i
$631$	−2.04127	+	2.04127i	−0.0812618	+	0.0812618i	−0.746569	−	0.665308i	$-0.768300\pi$
$631$	−2.04127	+	2.04127i	−0.0812618	+	0.0812618i	0.665308	+	0.746569i	$0.268300\pi$
$632$	−11.6910	−	11.6910i	−0.465041	−	0.465041i
$633$	−6.22433	+	6.22433i	−0.247395	+	0.247395i
$634$	−1.85948	+	1.85948i	−0.0738494	+	0.0738494i
$635$	−41.5610	+	16.0175i	−1.64930	+	0.635636i
$636$	−5.62889			−0.223200
$637$	−3.58358			−0.141986
$638$	36.2292	+	36.2292i	1.43433	+	1.43433i
$639$			0.962946i			0.0380936i
$640$	−0.906760	+	2.04396i	−0.0358428	+	0.0807947i
$641$	−24.5390			−0.969231			−0.484615	−	0.874727i	$-0.661040\pi$
$641$	−24.5390			−0.969231			−0.484615	+	0.874727i	$0.661040\pi$
$642$	−12.8248			−0.506153
$643$	−45.0438			−1.77635			−0.888176	−	0.459503i	$-0.848028\pi$
$643$	−45.0438			−1.77635			−0.888176	+	0.459503i	$0.848028\pi$
$644$	−7.16058	−	7.16058i	−0.282166	−	0.282166i
$645$	−7.50444	−	19.4719i	−0.295487	−	0.766706i
$646$	2.47402	+	2.47402i	0.0973391	+	0.0973391i
$647$		−	26.5714i		−	1.04463i	−0.852752	−	0.522316i	$-0.825068\pi$
$647$		−	26.5714i		−	1.04463i	0.852752	−	0.522316i	$-0.174932\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−52.6906	−	52.6906i	−2.06829	−	2.06829i
$650$	2.47283	+	2.73164i	0.0969926	+	0.107144i
$651$	−2.40658	−	2.40658i	−0.0943212	−	0.0943212i
$652$	−1.09629			−0.0429340
$653$	−15.1209			−0.591725			−0.295862	−	0.955231i	$-0.595607\pi$
$653$	−15.1209			−0.591725			−0.295862	+	0.955231i	$0.595607\pi$
$654$	−6.14303			−0.240212
$655$	−5.21825	+	2.01110i	−0.203894	+	0.0785803i
$656$			0.847391i			0.0330851i
$657$	2.59228	+	2.59228i	0.101135	+	0.101135i
$658$	−5.91750			−0.230688
$659$	−21.2057			−0.826058			−0.413029	−	0.910718i	$-0.635529\pi$
$659$	−21.2057			−0.826058			−0.413029	+	0.910718i	$0.635529\pi$
$660$	5.03972	+	13.0767i	0.196171	+	0.509008i
$661$	33.2201	−	33.2201i	1.29211	−	1.29211i	0.358635	−	0.933478i	$-0.383242\pi$
$661$	33.2201	−	33.2201i	1.29211	−	1.29211i	0.933478	−	0.358635i	$-0.116758\pi$
$662$	−8.07530	+	8.07530i	−0.313856	+	0.313856i
$663$	1.45505	+	1.45505i	0.0565094	+	0.0565094i
$664$	7.04605	−	7.04605i	0.273440	−	0.273440i
$665$	−1.66099	+	3.74411i	−0.0644106	+	0.145190i
$666$	−4.32965	+	4.27248i	−0.167771	+	0.165555i
$667$	40.0422	−	40.0422i	1.55044	−	1.55044i
$668$	−17.6829			−0.684174
$669$	−14.3804			−0.555978
$670$	−18.4286	+	7.10236i	−0.711960	+	0.274388i
$671$	31.6570	+	31.6570i	1.22211	+	1.22211i
$672$	−1.46191			−0.0563944
$673$	15.9591	+	15.9591i	0.615179	+	0.615179i	0.944291	−	0.329112i	$-0.106749\pi$
$673$	15.9591	+	15.9591i	0.615179	+	0.615179i	−0.329112	+	0.944291i	$0.606749\pi$
$674$	−10.2788	+	10.2788i	−0.395926	+	0.395926i
$675$	0.248333	−	4.99383i	0.00955833	−	0.192213i
$676$	−12.4569			−0.479113
$677$	21.9143	+	21.9143i	0.842236	+	0.842236i	0.989149	−	0.146913i	$-0.0469338\pi$
$677$	21.9143	+	21.9143i	0.842236	+	0.842236i	−0.146913	+	0.989149i	$0.546934\pi$
$678$	−6.12403	−	6.12403i	−0.235192	−	0.235192i
$679$	−18.9478	+	18.9478i	−0.727151	+	0.727151i
$680$	−2.53195	+	5.70738i	−0.0970960	+	0.218868i
$681$	−1.64986	+	1.64986i	−0.0632226	+	0.0632226i
$682$	−10.3172	+	10.3172i	−0.395066	+	0.395066i
$683$		−	27.2147i		−	1.04134i	−0.853757	−	0.520672i	$-0.825682\pi$
$683$		−	27.2147i		−	1.04134i	0.853757	−	0.520672i	$-0.174318\pi$
$684$	−0.886013	−	0.886013i	−0.0338776	−	0.0338776i
$685$	18.3995	−	7.09113i	0.703008	−	0.270938i
$686$	12.2629	−	12.2629i	0.468200	−	0.468200i
$687$	−5.24180	−	5.24180i	−0.199987	−	0.199987i
$688$		−	9.33244i		−	0.355796i
$689$	−2.93317	+	2.93317i	−0.111745	+	0.111745i
$690$	14.4529	−	5.57013i	0.550214	−	0.212051i
$691$			0.158792i			0.00604073i	0.999995	+	0.00302036i	$0.000961413\pi$
$691$			0.158792i			0.00604073i	−0.999995	+	0.00302036i	$0.999039\pi$
$692$	1.52212	−	1.52212i	0.0578624	−	0.0578624i
$693$	−6.47871	+	6.47871i	−0.246106	+	0.246106i
$694$	2.21653			0.0841382
$695$	19.5410	+	8.66896i	0.741234	+	0.328832i
$696$		−	8.17506i		−	0.309875i
$697$			2.36618i			0.0896254i
$698$	7.91901			0.299739
$699$			14.9193i			0.564300i
$700$	−7.30053	−	0.363040i	−0.275934	−	0.0137216i
$701$	−4.97548	−	4.97548i	−0.187921	−	0.187921i	0.606876	−	0.794797i	$-0.292423\pi$
$701$	−4.97548	−	4.97548i	−0.187921	−	0.187921i	−0.794797	+	0.606876i	$0.792423\pi$
$702$	−0.521091	−	0.521091i	−0.0196673	−	0.0196673i
$703$	−0.0506539	+	7.62160i	−0.00191045	+	0.287454i
$704$			6.26734i			0.236209i
$705$	3.67037	−	8.27352i	0.138234	−	0.311599i
$706$			2.54035i			0.0956074i
$707$	9.94340	+	9.94340i	0.373960	+	0.373960i
$708$			11.8895i			0.446836i
$709$	13.0193	−	13.0193i	0.488949	−	0.488949i	−0.419026	−	0.907974i	$-0.637628\pi$
$709$	13.0193	−	13.0193i	0.488949	−	0.488949i	0.907974	+	0.419026i	$0.137628\pi$
$710$	−0.873161	+	1.96823i	−0.0327692	+	0.0738663i
$711$	11.6910	+	11.6910i	0.438445	+	0.438445i
$712$	−12.7462	+	12.7462i	−0.477684	+	0.477684i
$713$	11.4031	+	11.4031i	0.427048	+	0.427048i
$714$	−4.08211			−0.152769
$715$	9.44028	+	4.18797i	0.353046	+	0.156621i
$716$	−16.3764	−	16.3764i	−0.612015	−	0.612015i
$717$			6.44004i			0.240508i
$718$	17.2531			0.643880
$719$		−	43.2488i		−	1.61291i	−0.591296	−	0.806455i	$-0.701383\pi$
$719$		−	43.2488i		−	1.61291i	0.591296	−	0.806455i	$-0.298617\pi$
$720$	0.906760	−	2.04396i	0.0337929	−	0.0761740i
$721$	11.3470	−	11.3470i	0.422585	−	0.422585i
$722$	17.4300			0.648676
$723$	−4.93503			−0.183536
$724$	17.7191			0.658523
$725$	2.03014	−	40.8249i	0.0753973	−	1.51620i
$726$	19.9967	+	19.9967i	0.742145	+	0.742145i
$727$		−	19.1608i		−	0.710634i	−0.934746	−	0.355317i	$-0.884373\pi$
$727$		−	19.1608i		−	0.710634i	0.934746	−	0.355317i	$-0.115627\pi$
$728$	−0.761788	+	0.761788i	−0.0282337	+	0.0282337i
$729$			1.00000i			0.0370370i
$730$	2.94795	+	7.64911i	0.109109	+	0.283106i
$731$		−	26.0591i		−	0.963829i
$732$		−	7.14335i		−	0.264026i
$733$	−32.1045	+	32.1045i	−1.18581	+	1.18581i	−0.207591	+	0.978216i	$0.566562\pi$
$733$	−32.1045	+	32.1045i	−1.18581	+	1.18581i	−0.978216	+	0.207591i	$0.933438\pi$
$734$	−13.0108	−	13.0108i	−0.480239	−	0.480239i
$735$	3.91031	+	10.1462i	0.144234	+	0.374247i
$736$	6.92696			0.255331
$737$	−39.1424	+	39.1424i	−1.44183	+	1.44183i
$738$		−	0.847391i		−	0.0311929i
$739$	−8.08459			−0.297397			−0.148698	−	0.988883i	$-0.547508\pi$
$739$	−8.08459			−0.297397			−0.148698	+	0.988883i	$0.547508\pi$
$740$	−12.7238	+	4.80684i	−0.467735	+	0.176703i
$741$	−0.923386			−0.0339214
$742$		−	8.22894i		−	0.302094i
$743$	8.70418	−	8.70418i	0.319326	−	0.319326i	−0.529182	−	0.848508i	$-0.677501\pi$
$743$	8.70418	−	8.70418i	0.319326	−	0.319326i	0.848508	+	0.529182i	$0.177501\pi$
$744$	2.32806			0.0853508
$745$	−2.57121	+	5.79587i	−0.0942020	+	0.212344i
$746$	18.1951	+	18.1951i	0.666171	+	0.666171i
$747$	−7.04605	+	7.04605i	−0.257802	+	0.257802i
$748$			17.5004i			0.639876i
$749$		−	18.7487i		−	0.685061i
$750$	5.03579	−	9.98203i	0.183881	−	0.364492i
$751$			19.9209i			0.726924i	0.931609	+	0.363462i	$0.118405\pi$
$751$			19.9209i			0.726924i	−0.931609	+	0.363462i	$0.881595\pi$
$752$	2.86222	−	2.86222i	0.104374	−	0.104374i
$753$			22.8760i			0.833646i
$754$	−4.25995	−	4.25995i	−0.155138	−	0.155138i
$755$	−16.6602	+	37.5543i	−0.606326	+	1.36674i
$756$	1.46191			0.0531691
$757$	33.9202			1.23285			0.616426	−	0.787413i	$-0.288580\pi$
$757$	33.9202			1.23285			0.616426	+	0.787413i	$0.288580\pi$
$758$	26.7132			0.970269
$759$	30.6980	−	30.6980i	1.11427	−	1.11427i
$760$	−1.00758	−	2.61438i	−0.0365487	−	0.0948335i
$761$		−	47.5918i		−	1.72520i	−0.505887	−	0.862600i	$-0.668835\pi$
$761$		−	47.5918i		−	1.72520i	0.505887	−	0.862600i	$-0.331165\pi$
$762$	19.9192			0.721597
$763$		−	8.98056i		−	0.325118i
$764$	−6.20872	−	6.20872i	−0.224624	−	0.224624i
$765$	2.53195	−	5.70738i	0.0915430	−	0.206351i
$766$	4.38944			0.158597
$767$	6.19553	+	6.19553i	0.223708	+	0.223708i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−0.291289	−	0.291289i	−0.0105041	−	0.0105041i	0.701835	−	0.712339i	$-0.252364\pi$
$769$	−0.291289	−	0.291289i	−0.0105041	−	0.0105041i	−0.712339	+	0.701835i	$0.752364\pi$
$770$	−19.1169	+	7.36762i	−0.688925	+	0.265510i
$771$	5.73137	−	5.73137i	0.206410	−	0.206410i
$772$		−	0.340975i		−	0.0122720i
$773$	3.56144	+	3.56144i	0.128096	+	0.128096i	0.768248	−	0.640152i	$-0.221129\pi$
$773$	3.56144	+	3.56144i	0.128096	+	0.128096i	−0.640152	+	0.768248i	$0.721129\pi$
$774$			9.33244i			0.335448i
$775$	11.6259	+	0.578134i	0.417616	+	0.0207672i
$776$		−	18.3296i		−	0.657996i
$777$	−6.24598	−	6.32956i	−0.224073	−	0.227072i
$778$	22.2349	+	22.2349i	0.797161	+	0.797161i
$779$	−0.750800	−	0.750800i	−0.0269002	−	0.0269002i
$780$	−0.592586	−	1.53759i	−0.0212180	−	0.0550547i
$781$			6.03511i			0.215953i
$782$	19.3422			0.691676
$783$			8.17506i			0.292153i
$784$			4.86282i			0.173672i
$785$	−13.8744	+	5.34718i	−0.495200	+	0.190849i
$786$	2.50099			0.0892072
$787$	21.0765	−	21.0765i	0.751297	−	0.751297i	−0.223424	−	0.974721i	$-0.571724\pi$
$787$	21.0765	−	21.0765i	0.751297	−	0.751297i	0.974721	+	0.223424i	$0.0717235\pi$
$788$	1.84335	−	1.84335i	0.0656665	−	0.0656665i
$789$			13.5935i			0.483942i
$790$	13.2950	+	34.4968i	0.473015	+	1.22734i
$791$	8.95278	−	8.95278i	0.318324	−	0.318324i
$792$		−	6.26734i		−	0.222700i
$793$	−3.72233	−	3.72233i	−0.132184	−	0.132184i
$794$	13.6670	−	13.6670i	0.485024	−	0.485024i
$795$	11.5053	+	5.10406i	0.408049	+	0.181022i
$796$	−10.1003	−	10.1003i	−0.357996	−	0.357996i
$797$		−	23.9938i		−	0.849904i	−0.905216	−	0.424952i	$-0.860291\pi$
$797$		−	23.9938i		−	0.849904i	0.905216	−	0.424952i	$-0.139709\pi$
$798$	1.29527	−	1.29527i	0.0458521	−	0.0458521i
$799$	7.99219	−	7.99219i	0.282744	−	0.282744i
$800$	3.70677	−	3.35557i	0.131054	−	0.118637i
$801$	12.7462	−	12.7462i	0.450365	−	0.450365i
$802$	−16.9000	−	16.9000i	−0.596758	−	0.596758i
$803$	16.2467	+	16.2467i	0.573334	+	0.573334i
$804$	8.83242			0.311495
$805$	8.14303	+	21.1289i	0.287004	+	0.744695i
$806$	1.21313	−	1.21313i	0.0427307	−	0.0427307i
$807$	−5.64225	−	5.64225i	−0.198617	−	0.198617i
$808$	−9.61899			−0.338395
$809$	−10.2600	−	10.2600i	−0.360722	−	0.360722i	0.503357	−	0.864079i	$-0.332098\pi$
$809$	−10.2600	−	10.2600i	−0.360722	−	0.360722i	−0.864079	+	0.503357i	$0.832098\pi$
$810$	−0.906760	+	2.04396i	−0.0318603	+	0.0718176i
$811$	4.35007			0.152752			0.0763758	−	0.997079i	$-0.475665\pi$
$811$	4.35007			0.152752			0.0763758	+	0.997079i	$0.475665\pi$
$812$	11.9512			0.419405
$813$	11.0066	−	11.0066i	0.386018	−	0.386018i
$814$	−27.1354	+	26.7771i	−0.951095	+	0.938537i
$815$	2.24078	+	0.994071i	0.0784909	+	0.0348208i
$816$	1.97446	−	1.97446i	0.0691200	−	0.0691200i
$817$	8.26866	+	8.26866i	0.289284	+	0.289284i
$818$	5.32124	−	5.32124i	0.186053	−	0.186053i
$819$	0.761788	−	0.761788i	0.0266190	−	0.0266190i
$820$	0.768380	−	1.73204i	0.0268330	−	0.0604853i
$821$	8.08918			0.282314			0.141157	−	0.989987i	$-0.454918\pi$
$821$	8.08918			0.282314			0.141157	+	0.989987i	$0.454918\pi$
$822$	−8.81845			−0.307579
$823$	−6.98877	−	6.98877i	−0.243613	−	0.243613i	0.574730	−	0.818343i	$-0.305107\pi$
$823$	−6.98877	−	6.98877i	−0.243613	−	0.243613i	−0.818343	+	0.574730i	$0.805107\pi$
$824$			10.9768i			0.382395i
$825$	1.55639	−	31.2980i	0.0541864	−	1.08966i
$826$	−17.3814			−0.604777
$827$	−40.7681			−1.41765			−0.708823	−	0.705387i	$-0.750773\pi$
$827$	−40.7681			−1.41765			−0.708823	+	0.705387i	$0.750773\pi$
$828$	−6.92696			−0.240728
$829$	−10.1511	−	10.1511i	−0.352562	−	0.352562i	0.508500	−	0.861062i	$-0.330200\pi$
$829$	−10.1511	−	10.1511i	−0.352562	−	0.352562i	−0.861062	+	0.508500i	$0.830200\pi$
$830$	−20.7910	+	8.01280i	−0.721665	+	0.278128i
$831$	22.4404	+	22.4404i	0.778450	+	0.778450i
$832$		−	0.736934i		−	0.0255486i
$833$			13.5785i			0.470467i
$834$	−6.76020	−	6.76020i	−0.234087	−	0.234087i
$835$	36.1433	+	16.0342i	1.25079	+	0.554886i
$836$	−5.55294	−	5.55294i	−0.192053	−	0.192053i
$837$	−2.32806			−0.0804695
$838$	11.7545			0.406052
$839$	−29.3925			−1.01474			−0.507370	−	0.861728i	$-0.669382\pi$
$839$	−29.3925			−1.01474			−0.507370	+	0.861728i	$0.669382\pi$
$840$	2.98809	+	1.32560i	0.103099	+	0.0457376i
$841$			37.8316i			1.30454i
$842$	9.16265	+	9.16265i	0.315766	+	0.315766i
$843$	−4.06563			−0.140028
$844$	8.80254			0.302996
$845$	25.4615	+	11.2954i	0.875902	+	0.388575i
$846$	−2.86222	+	2.86222i	−0.0984050	+	0.0984050i
$847$	−29.2333	+	29.2333i	−1.00447	+	1.00447i
$848$	3.98023	+	3.98023i	0.136682	+	0.136682i
$849$	22.8873	−	22.8873i	0.785492	−	0.785492i
$850$	10.3504	−	9.36980i	0.355017	−	0.321381i
$851$	29.5953	+	29.9913i	1.01451	+	1.02809i
$852$	0.680906	−	0.680906i	0.0233275	−	0.0233275i
$853$	−39.8785			−1.36541			−0.682706	−	0.730693i	$-0.739197\pi$
$853$	−39.8785			−1.36541			−0.682706	+	0.730693i	$0.739197\pi$
$854$	10.4429			0.357350
$855$	1.00758	+	2.61438i	0.0344584	+	0.0894099i
$856$	9.06848	+	9.06848i	0.309954	+	0.309954i
$857$	31.9265			1.09059			0.545294	−	0.838245i	$-0.316418\pi$
$857$	31.9265			1.09059			0.545294	+	0.838245i	$0.316418\pi$
$858$	−3.26585	−	3.26585i	−0.111494	−	0.111494i
$859$	−37.9277	+	37.9277i	−1.29408	+	1.29408i	−0.361835	+	0.932242i	$0.617849\pi$
$859$	−37.9277	+	37.9277i	−1.29408	+	1.29408i	−0.932242	+	0.361835i	$0.882151\pi$
$860$	−8.46228	+	19.0752i	−0.288561	+	0.650458i
$861$	1.23881			0.0422185
$862$	3.45686	+	3.45686i	0.117741	+	0.117741i
$863$	−23.7541	−	23.7541i	−0.808600	−	0.808600i	0.175822	−	0.984422i	$-0.443742\pi$
$863$	−23.7541	−	23.7541i	−0.808600	−	0.808600i	−0.984422	+	0.175822i	$0.943742\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	−4.49136	+	1.73096i	−0.152711	+	0.0588545i
$866$	−4.11998	+	4.11998i	−0.140003	+	0.140003i
$867$	−6.50751	+	6.50751i	−0.221007	+	0.221007i
$868$			3.40341i			0.115519i
$869$	73.2712	+	73.2712i	2.48555	+	2.48555i
$870$	−7.41282	+	16.7095i	−0.251318	+	0.566506i
$871$	4.60249	−	4.60249i	0.155950	−	0.155950i
$872$	4.34378	+	4.34378i	0.147099	+	0.147099i
$873$			18.3296i			0.620364i
$874$	−6.13737	+	6.13737i	−0.207600	+	0.207600i
$875$	14.5928	+	7.36187i	0.493327	+	0.248877i
$876$		−	3.66604i		−	0.123864i
$877$	4.98747	−	4.98747i	0.168415	−	0.168415i	−0.617867	−	0.786282i	$-0.712003\pi$
$877$	4.98747	−	4.98747i	0.168415	−	0.168415i	0.786282	+	0.617867i	$0.212003\pi$
$878$	−24.0778	+	24.0778i	−0.812588	+	0.812588i
$879$	5.48418			0.184977
$880$	5.68297	−	12.8102i	0.191573	−	0.431832i
$881$			11.2579i			0.379287i	0.981853	+	0.189644i	$0.0607332\pi$
$881$			11.2579i			0.379287i	−0.981853	+	0.189644i	$0.939267\pi$
$882$		−	4.86282i		−	0.163740i
$883$	50.7798			1.70888			0.854439	−	0.519552i	$-0.173901\pi$
$883$	50.7798			1.70888			0.854439	+	0.519552i	$0.173901\pi$
$884$		−	2.05775i		−	0.0692095i
$885$	10.7810	−	24.3018i	0.362398	−	0.816895i
$886$	−6.83063	−	6.83063i	−0.229480	−	0.229480i
$887$	−1.31977	−	1.31977i	−0.0443134	−	0.0443134i	0.684603	−	0.728916i	$-0.259976\pi$
$887$	−1.31977	−	1.31977i	−0.0443134	−	0.0443134i	−0.728916	+	0.684603i	$0.759976\pi$
$888$	6.08263	+	0.0404257i	0.204120	+	0.00135660i
$889$			29.1201i			0.976657i
$890$	37.6105	−	14.4950i	1.26071	−	0.485874i
$891$			6.26734i			0.209964i
$892$	10.1685	+	10.1685i	0.340466	+	0.340466i
$893$			5.07192i			0.169725i
$894$	2.00508	−	2.00508i	0.0670598	−	0.0670598i
$895$	18.6233	+	48.3223i	0.622509	+	1.61524i
$896$	1.03373	+	1.03373i	0.0345344	+	0.0345344i
$897$	−3.60957	+	3.60957i	−0.120520	+	0.120520i
$898$	−21.9750	−	21.9750i	−0.733316	−	0.733316i
$899$	−19.0320			−0.634754
$900$	−3.70677	+	3.35557i	−0.123559	+	0.111852i
$901$	11.1140	+	11.1140i	0.370262	+	0.370262i
$902$		−	5.31089i		−	0.176833i
$903$	−13.6432			−0.454017
$904$			8.66069i			0.288050i
$905$	−36.2171	−	16.0669i	−1.20390	−	0.534083i
$906$	12.9919	−	12.9919i	0.431626	−	0.431626i
$907$	10.6642			0.354097			0.177049	−	0.984202i	$-0.443345\pi$
$907$	10.6642			0.354097			0.177049	+	0.984202i	$0.443345\pi$
$908$	2.33325			0.0774316
$909$	9.61899			0.319042
$910$	2.24783	−	0.866308i	0.0745147	−	0.0287178i
$911$	−16.4111	−	16.4111i	−0.543725	−	0.543725i	0.380894	−	0.924619i	$-0.375616\pi$
$911$	−16.4111	−	16.4111i	−0.543725	−	0.543725i	−0.924619	+	0.380894i	$0.875616\pi$
$912$			1.25301i			0.0414914i
$913$	−44.1600	+	44.1600i	−1.46148	+	1.46148i
$914$		−	23.6642i		−	0.782741i
$915$	−6.47730	+	14.6007i	−0.214133	+	0.482686i
$916$			7.41303i			0.244933i
$917$			3.65622i			0.120739i
$918$	−1.97446	+	1.97446i	−0.0651669	+	0.0651669i
$919$	42.0610	+	42.0610i	1.38746	+	1.38746i	0.830613	+	0.556850i	$0.187990\pi$
$919$	42.0610	+	42.0610i	1.38746	+	1.38746i	0.556850	+	0.830613i	$0.312010\pi$
$920$	−14.1584	−	6.28109i	−0.466790	−	0.207081i
$921$	−9.19926			−0.303126
$922$	−15.3068	+	15.3068i	−0.504104	+	0.504104i
$923$		−	0.709628i		−	0.0233577i
$924$	9.16228			0.301417
$925$	30.3656	+	1.71239i	0.998414	+	0.0563032i
$926$	−41.7413			−1.37170
$927$		−	10.9768i		−	0.360525i
$928$	−5.78064	+	5.78064i	−0.189759	+	0.189759i
$929$	8.30197			0.272379			0.136189	−	0.990683i	$-0.456514\pi$
$929$	8.30197			0.272379			0.136189	+	0.990683i	$0.456514\pi$
$930$	−4.75847	−	2.11099i	−0.156036	−	0.0692221i
$931$	−4.30852	−	4.30852i	−0.141206	−	0.141206i
$932$	10.5495	−	10.5495i	0.345562	−	0.345562i
$933$		−	23.7878i		−	0.778777i
$934$		−	18.8139i		−	0.615611i
$935$	15.8686	−	35.7701i	0.518959	−	1.16981i
$936$			0.736934i			0.0240874i
$937$	6.07351	−	6.07351i	0.198413	−	0.198413i	−0.600906	−	0.799319i	$-0.705194\pi$
$937$	6.07351	−	6.07351i	0.198413	−	0.198413i	0.799319	+	0.600906i	$0.205194\pi$
$938$			12.9122i			0.421598i
$939$	0.651429	+	0.651429i	0.0212586	+	0.0212586i
$940$	−8.44561	+	3.25492i	−0.275465	+	0.106164i
$941$	−11.0302			−0.359575			−0.179787	−	0.983705i	$-0.557541\pi$
$941$	−11.0302			−0.359575			−0.179787	+	0.983705i	$0.557541\pi$
$942$	6.64969			0.216659
$943$	−5.86984			−0.191148
$944$	8.40717	−	8.40717i	0.273630	−	0.273630i
$945$	−2.98809	−	1.32560i	−0.0972026	−	0.0431218i
$946$			58.4896i			1.90166i
$947$	−51.2800			−1.66637			−0.833187	−	0.552991i	$-0.813487\pi$
$947$	−51.2800			−1.66637			−0.833187	+	0.552991i	$0.813487\pi$
$948$		−	16.5335i		−	0.536983i
$949$	−1.91034	−	1.91034i	−0.0620123	−	0.0620123i
$950$	−0.311164	+	6.25733i	−0.0100955	+	0.203014i
$951$	−2.62970			−0.0852739
$952$	2.88648	+	2.88648i	0.0935515	+	0.0935515i
$953$	5.31203	−	5.31203i	0.172074	−	0.172074i	−0.615816	−	0.787890i	$-0.711174\pi$
$953$	5.31203	−	5.31203i	0.172074	−	0.172074i	0.787890	+	0.615816i	$0.211174\pi$
$954$	−3.98023	−	3.98023i	−0.128865	−	0.128865i
$955$	7.06058	+	18.3202i	0.228475	+	0.592828i
$956$	4.55380	−	4.55380i	0.147280	−	0.147280i
$957$			51.2359i			1.65622i
$958$	−13.9456	−	13.9456i	−0.450561	−	0.450561i
$959$		−	12.8918i		−	0.416297i
$960$	−2.08648	+	0.804124i	−0.0673407	+	0.0259530i
$961$			25.5801i			0.825166i
$962$	3.19067	−	3.14854i	0.102871	−	0.101513i
$963$	−9.06848	−	9.06848i	−0.292228	−	0.292228i
$964$	3.48959	+	3.48959i	0.112392	+	0.112392i
$965$	−0.309183	+	0.696941i	−0.00995294	+	0.0224353i
$966$		−	10.1266i		−	0.325818i
$967$	−15.4122			−0.495623			−0.247811	−	0.968808i	$-0.579711\pi$
$967$	−15.4122			−0.495623			−0.247811	+	0.968808i	$0.579711\pi$
$968$		−	28.2795i		−	0.908939i
$969$			3.49880i			0.112398i
$970$	−16.6206	+	37.4651i	−0.533655	+	1.20293i
$971$	25.1115			0.805868			0.402934	−	0.915229i	$-0.367990\pi$
$971$	25.1115			0.805868			0.402934	+	0.915229i	$0.367990\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	9.88280	−	9.88280i	0.316828	−	0.316828i
$974$			2.48057i			0.0794826i
$975$	−0.183005	+	3.68012i	−0.00586084	+	0.117858i
$976$	−5.05111	+	5.05111i	−0.161682	+	0.161682i
$977$			6.84308i			0.218930i	0.993991	+	0.109465i	$0.0349137\pi$
$977$			6.84308i			0.218930i	−0.993991	+	0.109465i	$0.965086\pi$
$978$	−0.775194	−	0.775194i	−0.0247880	−	0.0247880i
$979$	79.8847	−	79.8847i	2.55313	−	2.55313i
$980$	4.40941	−	9.93943i	0.140853	−	0.317503i
$981$	−4.34378	−	4.34378i	−0.138686	−	0.138686i
$982$			27.0864i			0.864362i
$983$	13.2691	−	13.2691i	0.423217	−	0.423217i	−0.463093	−	0.886310i	$-0.653260\pi$
$983$	13.2691	−	13.2691i	0.423217	−	0.423217i	0.886310	+	0.463093i	$0.153260\pi$
$984$	−0.599196	+	0.599196i	−0.0191017	+	0.0191017i
$985$	−5.43920	+	2.09626i	−0.173307	+	0.0667924i
$986$	−16.1413	+	16.1413i	−0.514045	+	0.514045i
$987$	−4.18430	−	4.18430i	−0.133188	−	0.133188i
$988$	0.652933	+	0.652933i	0.0207726	+	0.0207726i
$989$	64.6454			2.05560
$990$	−5.68297	+	12.8102i	−0.180617	+	0.407135i
$991$	−18.2705	+	18.2705i	−0.580382	+	0.580382i	−0.935008	−	0.354626i	$-0.884608\pi$
$991$	−18.2705	+	18.2705i	−0.580382	+	0.580382i	0.354626	+	0.935008i	$0.384608\pi$
$992$	−1.64619	−	1.64619i	−0.0522665	−	0.0522665i
$993$	−11.4202			−0.362409
$994$	0.995423	+	0.995423i	0.0315729	+	0.0315729i
$995$	11.4861	+	29.8032i	0.364134	+	0.944825i
$996$	9.96463			0.315741
$997$	−8.65428			−0.274084			−0.137042	−	0.990565i	$-0.543759\pi$
$997$	−8.65428			−0.274084			−0.137042	+	0.990565i	$0.543759\pi$
$998$	−2.96909	+	2.96909i	−0.0939848	+	0.0939848i
$999$	−6.08263	−	0.0404257i	−0.192446	−	0.00127901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.43.13	✓	40
5.2	odd	4		1110.2.o.b.487.8	yes	40
37.31	odd	4		1110.2.o.b.253.8	yes	40
185.142	even	4	inner	1110.2.l.b.697.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.13	✓	40	1.1	even	1	trivial
1110.2.l.b.697.13	yes	40	185.142	even	4	inner
1110.2.o.b.253.8	yes	40	37.31	odd	4
1110.2.o.b.487.8	yes	40	5.2	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.04396 + 0.906760i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.03373 - 1.03373i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.04396 + 0.906760i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.03373 - 1.03373i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.906760 - 2.04396i) q^{10} -6.26734i q^{11} +(-0.707107 + 0.707107i) q^{12} +0.736934i q^{13} +(-1.03373 - 1.03373i) q^{14} +(2.08648 - 0.804124i) q^{15} +1.00000 q^{16} +2.79231 q^{17} -1.00000 q^{18} +(-0.886013 + 0.886013i) q^{19} +(-2.04396 - 0.906760i) q^{20} -1.46191i q^{21} -6.26734 q^{22} +6.92696i q^{23} +(0.707107 + 0.707107i) q^{24} +(3.35557 + 3.70677i) q^{25} +0.736934 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.03373 + 1.03373i) q^{28} +(-5.78064 - 5.78064i) q^{29} +(-0.804124 - 2.08648i) q^{30} +(1.64619 - 1.64619i) q^{31} -1.00000i q^{32} +(-4.43168 - 4.43168i) q^{33} -2.79231i q^{34} +(3.05024 - 1.17556i) q^{35} +1.00000i q^{36} +(4.32965 - 4.27248i) q^{37} +(0.886013 + 0.886013i) q^{38} +(0.521091 + 0.521091i) q^{39} +(-0.906760 + 2.04396i) q^{40} +0.847391i q^{41} -1.46191 q^{42} -9.33244i q^{43} +6.26734i q^{44} +(0.906760 - 2.04396i) q^{45} +6.92696 q^{46} +(2.86222 - 2.86222i) q^{47} +(0.707107 - 0.707107i) q^{48} +4.86282i q^{49} +(3.70677 - 3.35557i) q^{50} +(1.97446 - 1.97446i) q^{51} -0.736934i q^{52} +(3.98023 + 3.98023i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(5.68297 - 12.8102i) q^{55} +(1.03373 + 1.03373i) q^{56} +1.25301i q^{57} +(-5.78064 + 5.78064i) q^{58} +(8.40717 - 8.40717i) q^{59} +(-2.08648 + 0.804124i) q^{60} +(-5.05111 + 5.05111i) q^{61} +(-1.64619 - 1.64619i) q^{62} +(-1.03373 - 1.03373i) q^{63} -1.00000 q^{64} +(-0.668222 + 1.50627i) q^{65} +(-4.43168 + 4.43168i) q^{66} +(-6.24546 - 6.24546i) q^{67} -2.79231 q^{68} +(4.89810 + 4.89810i) q^{69} +(-1.17556 - 3.05024i) q^{70} -0.962946 q^{71} +1.00000 q^{72} +(-2.59228 + 2.59228i) q^{73} +(-4.27248 - 4.32965i) q^{74} +(4.99383 + 0.248333i) q^{75} +(0.886013 - 0.886013i) q^{76} +(-6.47871 - 6.47871i) q^{77} +(0.521091 - 0.521091i) q^{78} +(-11.6910 + 11.6910i) q^{79} +(2.04396 + 0.906760i) q^{80} -1.00000 q^{81} +0.847391 q^{82} +(-7.04605 - 7.04605i) q^{83} +1.46191i q^{84} +(5.70738 + 2.53195i) q^{85} -9.33244 q^{86} -8.17506 q^{87} +6.26734 q^{88} +(12.7462 + 12.7462i) q^{89} +(-2.04396 - 0.906760i) q^{90} +(0.761788 + 0.761788i) q^{91} -6.92696i q^{92} -2.32806i q^{93} +(-2.86222 - 2.86222i) q^{94} +(-2.61438 + 1.00758i) q^{95} +(-0.707107 - 0.707107i) q^{96} -18.3296 q^{97} +4.86282 q^{98} -6.26734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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