LMFDB - Embedded newform 1110.2.o.b.253.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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			253.8
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.b.487.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	0.906760	−	2.04396i	0.405515	−	0.914088i
$5$	0.906760	−	2.04396i	0.405515	−	0.914088i
$6$	−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	$0.160900\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	0.906760	−	2.04396i	0.286743	−	0.646358i
$11$			6.26734i			1.88967i	0.327541	+	0.944837i	$0.393780\pi$
$11$			6.26734i			1.88967i	−0.327541	+	0.944837i	$0.606220\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	0.736934			0.204389			0.102194	−	0.994764i	$-0.467414\pi$
$13$	0.736934			0.204389			0.102194	+	0.994764i	$0.467414\pi$
$14$	1.03373	−	1.03373i	0.276275	−	0.276275i
$15$	0.804124	+	2.08648i	0.207624	+	0.538726i
$16$	1.00000			0.250000
$17$		−	2.79231i		−	0.677235i	−0.940924	−	0.338617i	$-0.890041\pi$
$17$		−	2.79231i		−	0.677235i	0.940924	−	0.338617i	$-0.109959\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.886013	+	0.886013i	0.203265	+	0.203265i	0.801397	−	0.598132i	$-0.204090\pi$
$19$	0.886013	+	0.886013i	0.203265	+	0.203265i	−0.598132	+	0.801397i	$0.704090\pi$
$20$	0.906760	−	2.04396i	0.202758	−	0.457044i
$21$			1.46191i			0.319015i
$22$			6.26734i			1.33620i
$23$	6.92696			1.44437			0.722185	−	0.691700i	$-0.243138\pi$
$23$	6.92696			1.44437			0.722185	+	0.691700i	$0.243138\pi$
$24$	−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	0.0763577	−	0.997080i	$-0.475671\pi$
$29$	5.78064	−	5.78064i	1.07344	−	1.07344i	0.997080	−	0.0763577i	$-0.0243291\pi$
$30$	0.804124	+	2.08648i	0.146812	+	0.380937i
$31$	1.64619	+	1.64619i	0.295664	+	0.295664i	0.839313	−	0.543649i	$-0.182958\pi$
$31$	1.64619	+	1.64619i	0.295664	+	0.295664i	−0.543649	+	0.839313i	$0.682958\pi$
$32$	1.00000			0.176777
$33$	−4.43168	−	4.43168i	−0.771456	−	0.771456i
$34$		−	2.79231i		−	0.478877i
$35$	−1.17556	−	3.05024i	−0.198705	−	0.515585i
$36$		−	1.00000i		−	0.166667i
$37$	4.27248	−	4.32965i	0.702392	−	0.711791i
$37$	4.27248	−	4.32965i	0.702392	−	0.711791i
$38$	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	$-0.978922\pi$
$41$		−	0.847391i		−	0.132340i	0.997808	−	0.0661701i	$-0.0210780\pi$
$42$			1.46191i			0.225578i
$43$	−9.33244			−1.42318			−0.711592	−	0.702593i	$-0.752025\pi$
$43$	−9.33244			−1.42318			−0.711592	+	0.702593i	$0.752025\pi$
$44$			6.26734i			0.944837i
$45$	−2.04396	−	0.906760i	−0.304696	−	0.135172i
$46$	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
$50$	−3.35557	−	3.70677i	−0.474550	−	0.524216i
$51$	1.97446	+	1.97446i	0.276480	+	0.276480i
$52$	0.736934			0.102194
$53$	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
$55$	12.8102	+	5.68297i	1.72733	+	0.766292i
$56$	1.03373	−	1.03373i	0.138137	−	0.138137i
$57$	−1.25301			−0.165965
$58$	5.78064	−	5.78064i	0.759035	−	0.759035i
$59$	−8.40717	−	8.40717i	−1.09452	−	1.09452i	−0.995039	−	0.0994809i	$-0.968282\pi$
$59$	−8.40717	−	8.40717i	−1.09452	−	1.09452i	−0.0994809	−	0.995039i	$-0.531718\pi$
$60$	0.804124	+	2.08648i	0.103812	+	0.269363i
$61$	−5.05111	−	5.05111i	−0.646728	−	0.646728i	0.305472	−	0.952201i	$-0.401186\pi$
$61$	−5.05111	−	5.05111i	−0.646728	−	0.646728i	−0.952201	+	0.305472i	$0.901186\pi$
$62$	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	0.976864	−	0.213860i	$-0.0686035\pi$
$67$	6.24546	+	6.24546i	0.763005	+	0.763005i	−0.213860	+	0.976864i	$0.568604\pi$
$68$		−	2.79231i		−	0.338617i
$69$	−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	$0.518198\pi$
$72$		−	1.00000i		−	0.117851i
$73$	2.59228	−	2.59228i	0.303404	−	0.303404i	−0.538940	−	0.842344i	$-0.681175\pi$
$73$	2.59228	−	2.59228i	0.303404	−	0.303404i	0.842344	+	0.538940i	$0.181175\pi$
$74$	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	0.917424	+	0.397912i	$0.130265\pi$
$79$	11.6910	+	11.6910i	1.31534	+	1.31534i	0.397912	+	0.917424i	$0.369735\pi$
$80$	0.906760	−	2.04396i	0.101379	−	0.228522i
$81$	−1.00000			−0.111111
$82$		−	0.847391i		−	0.0935787i
$83$	−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
$87$			8.17506i			0.876459i
$88$			6.26734i			0.668101i
$89$	−12.7462	+	12.7462i	−1.35109	+	1.35109i	−0.466654	+	0.884440i	$0.654541\pi$
$89$	−12.7462	+	12.7462i	−1.35109	+	1.35109i	−0.884440	+	0.466654i	$0.845459\pi$
$90$	−2.04396	−	0.906760i	−0.215453	−	0.0955809i
$91$	0.761788	−	0.761788i	0.0798571	−	0.0798571i
$92$	6.92696			0.722185
$93$	−2.32806			−0.241409
$94$	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
$97$			18.3296i			1.86109i	0.366174	+	0.930546i	$0.380667\pi$
$97$			18.3296i			1.86109i	−0.366174	+	0.930546i	$0.619333\pi$
$98$			4.86282i			0.491219i
$99$	6.26734			0.629891
$100$	−3.35557	−	3.70677i	−0.335557	−	0.370677i
$101$		−	9.61899i		−	0.957125i	−0.878054	−	0.478562i	$-0.841158\pi$
$101$		−	9.61899i		−	0.957125i	0.878054	−	0.478562i	$-0.158842\pi$
$102$	1.97446	+	1.97446i	0.195501	+	0.195501i
$103$			10.9768i			1.08158i	0.841159	+	0.540788i	$0.181874\pi$
$103$			10.9768i			1.08158i	−0.841159	+	0.540788i	$0.818126\pi$
$104$	0.736934			0.0722623
$105$	2.98809	+	1.32560i	0.291608	+	0.129365i
$106$	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	$-0.345052\pi$
$109$	−4.34378	−	4.34378i	−0.416059	−	0.416059i	−0.883843	+	0.467784i	$0.845052\pi$
$110$	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
$113$			8.66069i			0.814729i	0.913266	+	0.407364i	$0.133552\pi$
$113$			8.66069i			0.814729i	−0.913266	+	0.407364i	$0.866448\pi$
$114$	−1.25301			−0.117355
$115$	6.28109	−	14.1584i	0.585714	−	1.32028i
$116$	5.78064	−	5.78064i	0.536719	−	0.536719i
$117$		−	0.736934i		−	0.0681295i
$118$	−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
$125$	−10.6192	+	3.49752i	−0.949810	+	0.312828i
$126$	−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	$0.904995\pi$
$128$	1.00000			0.0883883
$129$	6.59903	−	6.59903i	0.581012	−	0.581012i
$130$	0.668222	−	1.50627i	0.0586069	−	0.132108i
$131$	−1.76846	−	1.76846i	−0.154511	−	0.154511i	0.625618	−	0.780130i	$-0.284847\pi$
$131$	−1.76846	−	1.76846i	−0.154511	−	0.154511i	−0.780130	+	0.625618i	$0.784847\pi$
$132$	−4.43168	−	4.43168i	−0.385728	−	0.385728i
$133$	1.83179			0.158836
$134$	6.24546	+	6.24546i	0.539526	+	0.539526i
$135$	2.08648	−	0.804124i	0.179575	−	0.0692080i
$136$		−	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	$-0.632885\pi$
$139$	−9.56037			−0.810900			−0.405450	+	0.914117i	$0.632885\pi$
$140$	−1.17556	−	3.05024i	−0.0993527	−	0.257792i
$141$			4.04778i			0.340885i
$142$	−0.962946			−0.0808087
$143$			4.61861i			0.386228i
$144$		−	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
$148$	4.27248	−	4.32965i	0.351196	−	0.355895i
$149$			2.83560i			0.232302i	0.993232	+	0.116151i	$0.0370556\pi$
$149$			2.83560i			0.232302i	−0.993232	+	0.116151i	$0.962944\pi$
$150$	4.99383	+	0.248333i	0.407744	+	0.0202763i
$151$		−	18.3733i		−	1.49520i	−0.664151	−	0.747599i	$-0.731207\pi$
$151$		−	18.3733i		−	1.49520i	0.664151	−	0.747599i	$-0.268793\pi$
$152$	0.886013	+	0.886013i	0.0718651	+	0.0718651i
$153$	−2.79231			−0.225745
$154$	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
$162$	−1.00000			−0.0785674
$163$			1.09629i			0.0858680i	0.999078	+	0.0429340i	$0.0136705\pi$
$163$			1.09629i			0.0858680i	−0.999078	+	0.0429340i	$0.986329\pi$
$164$		−	0.847391i		−	0.0661701i
$165$	−13.0767	+	5.03972i	−1.01802	+	0.392342i
$166$	−7.04605	−	7.04605i	−0.546880	−	0.546880i
$167$		−	17.6829i		−	1.36835i	−0.729319	−	0.684174i	$-0.760163\pi$
$167$		−	17.6829i		−	1.36835i	0.729319	−	0.684174i	$-0.239837\pi$
$168$			1.46191i			0.112789i
$169$	−12.4569			−0.958225
$170$	−5.70738	−	2.53195i	−0.437736	−	0.194192i
$171$	0.886013	−	0.886013i	0.0677551	−	0.0677551i
$172$	−9.33244			−0.711592
$173$	1.52212	−	1.52212i	0.115725	−	0.115725i	−0.646873	−	0.762598i	$-0.723924\pi$
$173$	1.52212	−	1.52212i	0.115725	−	0.115725i	0.762598	+	0.646873i	$0.223924\pi$
$174$			8.17506i			0.619750i
$175$	−7.30053	−	0.363040i	−0.551868	−	0.0274433i
$176$			6.26734i			0.472418i
$177$	11.8895			0.893672
$178$	−12.7462	+	12.7462i	−0.955368	+	0.955368i
$179$	−16.3764	+	16.3764i	−1.22403	+	1.22403i	−0.257844	+	0.966187i	$0.583012\pi$
$179$	−16.3764	+	16.3764i	−1.22403	+	1.22403i	−0.966187	+	0.257844i	$0.916988\pi$
$180$	−2.04396	−	0.906760i	−0.152348	−	0.0675859i
$181$	−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
$183$	7.14335			0.528052
$184$	6.92696			0.510662
$185$	−4.97554	−	12.6588i	−0.365809	−	0.930690i
$186$	−2.32806			−0.170702
$187$	17.5004			1.27975
$188$	2.86222	−	2.86222i	0.208749	−	0.208749i
$189$	1.46191			0.106338
$190$	2.61438	−	1.00758i	0.189667	−	0.0730973i
$191$	6.20872	−	6.20872i	0.449247	−	0.449247i	−0.445857	−	0.895104i	$-0.647101\pi$
$191$	6.20872	−	6.20872i	0.449247	−	0.449247i	0.895104	+	0.445857i	$0.147101\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	0.340975			0.0245439			0.0122720	−	0.999925i	$-0.496094\pi$
$193$	0.340975			0.0245439			0.0122720	+	0.999925i	$0.496094\pi$
$194$			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	$0.279603\pi$
$198$	6.26734			0.445400
$199$	−10.1003	+	10.1003i	−0.715991	+	0.715991i	−0.967782	−	0.251791i	$-0.918981\pi$
$199$	−10.1003	+	10.1003i	−0.715991	+	0.715991i	0.251791	+	0.967782i	$0.418981\pi$
$200$	−3.35557	−	3.70677i	−0.237275	−	0.262108i
$201$	−8.83242			−0.622991
$202$		−	9.61899i		−	0.676789i
$203$		−	11.9512i		−	0.838810i
$204$	1.97446	+	1.97446i	0.138240	+	0.138240i
$205$	−1.73204	−	0.768380i	−0.120971	−	0.0536660i
$206$			10.9768i			0.764790i
$207$		−	6.92696i		−	0.481457i
$208$	0.736934			0.0510972
$209$	−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
$217$	3.40341			0.231039
$218$	−4.34378	−	4.34378i	−0.294198	−	0.294198i
$219$			3.66604i			0.247728i
$220$	12.8102	+	5.68297i	0.863664	+	0.383146i
$221$		−	2.05775i		−	0.138419i
$222$	0.0404257	+	6.08263i	0.00271320	+	0.408239i
$223$	−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
$227$			2.33325i			0.154863i	0.996998	+	0.0774316i	$0.0246719\pi$
$227$			2.33325i			0.154863i	−0.996998	+	0.0774316i	$0.975328\pi$
$228$	−1.25301			−0.0829827
$229$		−	7.41303i		−	0.489867i	−0.969540	−	0.244933i	$-0.921234\pi$
$229$		−	7.41303i		−	0.489867i	0.969540	−	0.244933i	$-0.0787661\pi$
$230$	6.28109	−	14.1584i	0.414163	−	0.933580i
$231$	−9.16228			−0.602834
$232$	5.78064	−	5.78064i	0.379518	−	0.379518i
$233$	10.5495	−	10.5495i	0.691124	−	0.691124i	−0.271356	−	0.962479i	$-0.587472\pi$
$233$	10.5495	−	10.5495i	0.691124	−	0.691124i	0.962479	+	0.271356i	$0.0874719\pi$
$234$		−	0.736934i		−	0.0481749i
$235$	−3.25492	−	8.44561i	−0.212328	−	0.550931i
$236$	−8.40717	−	8.40717i	−0.547260	−	0.547260i
$237$	−16.5335			−1.07397
$238$	−2.88648	−	2.88648i	−0.187103	−	0.187103i
$239$	4.55380	+	4.55380i	0.294561	+	0.294561i	0.838879	−	0.544318i	$-0.183212\pi$
$239$	4.55380	+	4.55380i	0.294561	+	0.294561i	−0.544318	+	0.838879i	$0.683212\pi$
$240$	0.804124	+	2.08648i	0.0519060	+	0.134681i
$241$	−3.48959	+	3.48959i	−0.224784	+	0.224784i	−0.810510	−	0.585725i	$-0.800810\pi$
$241$	−3.48959	+	3.48959i	−0.224784	+	0.224784i	0.585725	+	0.810510i	$0.300810\pi$
$242$	−28.2795			−1.81788
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−5.05111	−	5.05111i	−0.323364	−	0.323364i
$245$	9.93943	+	4.40941i	0.635007	+	0.281707i
$246$	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	−0.999775	−	0.0212296i	$-0.993242\pi$
$251$	−16.1757	−	16.1757i	−1.02100	−	1.02100i	−0.0212296	−	0.999775i	$-0.506758\pi$
$252$	−1.03373	−	1.03373i	−0.0651186	−	0.0651186i
$253$			43.4136i			2.72939i
$254$	−14.0850	+	14.0850i	−0.883773	+	0.883773i
$255$	5.82609	−	2.24536i	0.364844	−	0.140610i
$256$	1.00000			0.0625000
$257$		−	8.10538i		−	0.505600i	−0.967519	−	0.252800i	$-0.918649\pi$
$257$		−	8.10538i		−	0.505600i	0.967519	−	0.252800i	$-0.0813515\pi$
$258$	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	−0.345656	−	0.938361i	$-0.612343\pi$
$263$	9.61207	−	9.61207i	0.592706	−	0.592706i	0.938361	+	0.345656i	$0.112343\pi$
$264$	−4.43168	−	4.43168i	−0.272751	−	0.272751i
$265$	11.7446	−	4.52633i	0.721462	−	0.278050i
$266$	1.83179			0.112314
$267$		−	18.0258i		−	1.10316i
$268$	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	$0.343253\pi$
$272$		−	2.79231i		−	0.169309i
$273$			1.07733i			0.0652030i
$274$	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
$277$	−31.7356			−1.90681			−0.953403	−	0.301701i	$-0.902446\pi$
$277$	−31.7356			−1.90681			−0.953403	+	0.301701i	$0.902446\pi$
$278$	−9.56037			−0.573393
$279$	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	−0.787637	−	0.616139i	$-0.788696\pi$
$281$	−2.87484	+	2.87484i	−0.171498	+	0.171498i	0.616139	+	0.787637i	$0.288696\pi$
$282$			4.04778i			0.241042i
$283$			32.3676i			1.92405i	0.272955	+	0.962027i	$0.411999\pi$
$283$			32.3676i			1.92405i	−0.272955	+	0.962027i	$0.588001\pi$
$284$	−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
$288$		−	1.00000i		−	0.0589256i
$289$	9.20300			0.541353
$290$	−6.57377	−	17.0571i	−0.386025	−	1.00163i
$291$	−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
$298$			2.83560i			0.164262i
$299$	5.10471			0.295213
$300$	4.99383	+	0.248333i	0.288319	+	0.0143375i
$301$	−9.64719	+	9.64719i	−0.556055	+	0.556055i
$302$		−	18.3733i		−	1.05726i
$303$	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	0.867933	−	0.496681i	$-0.165448\pi$
$307$	6.50486	+	6.50486i	0.371252	+	0.371252i	−0.496681	+	0.867933i	$0.665448\pi$
$308$	6.47871	+	6.47871i	0.369159	+	0.369159i
$309$	−7.76177	−	7.76177i	−0.441552	−	0.441552i
$310$	4.85744	−	1.87205i	0.275884	−	0.106325i
$311$	16.8205	+	16.8205i	0.953803	+	0.953803i	0.998979	−	0.0451763i	$-0.0143850\pi$
$311$	16.8205	+	16.8205i	0.953803	+	0.953803i	−0.0451763	+	0.998979i	$0.514385\pi$
$312$	−0.521091	+	0.521091i	−0.0295010	+	0.0295010i
$313$	0.921260			0.0520727			0.0260364	−	0.999661i	$-0.491711\pi$
$313$	0.921260			0.0520727			0.0260364	+	0.999661i	$0.491711\pi$
$314$	−4.70204	+	4.70204i	−0.265352	+	0.265352i
$315$	−3.05024	+	1.17556i	−0.171862	+	0.0662351i
$316$	11.6910	+	11.6910i	0.657668	+	0.657668i
$317$	1.85948	+	1.85948i	0.104439	+	0.104439i	0.757395	−	0.652957i	$-0.226472\pi$
$317$	1.85948	+	1.85948i	0.104439	+	0.104439i	−0.652957	+	0.757395i	$0.726472\pi$
$318$	−5.62889			−0.315653
$319$	36.2292	+	36.2292i	2.02845	+	2.02845i
$320$	0.906760	−	2.04396i	0.0506894	−	0.114261i
$321$			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
$325$	−2.47283	−	2.73164i	−0.137168	−	0.151524i
$326$			1.09629i			0.0607178i
$327$	6.14303			0.339710
$328$		−	0.847391i		−	0.0467893i
$329$		−	5.91750i		−	0.326242i
$330$	−13.0767	+	5.03972i	−0.719846	+	0.277427i
$331$	−8.07530	+	8.07530i	−0.443859	+	0.443859i	−0.893307	−	0.449448i	$-0.851621\pi$
$331$	−8.07530	+	8.07530i	−0.443859	+	0.443859i	0.449448	+	0.893307i	$0.351621\pi$
$332$	−7.04605	−	7.04605i	−0.386702	−	0.386702i
$333$	−4.32965	−	4.27248i	−0.237264	−	0.234131i
$334$		−	17.6829i		−	0.967568i
$335$	18.4286	−	7.10236i	1.00686	−	0.388044i
$336$			1.46191i			0.0797537i
$337$	10.2788	+	10.2788i	0.559924	+	0.559924i	0.929286	−	0.369362i	$-0.120424\pi$
$337$	10.2788	+	10.2788i	0.559924	+	0.559924i	−0.369362	+	0.929286i	$0.620424\pi$
$338$	−12.4569			−0.677568
$339$	−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
$347$	−2.21653			−0.118989			−0.0594947	−	0.998229i	$-0.518949\pi$
$347$	−2.21653			−0.118989			−0.0594947	+	0.998229i	$0.518949\pi$
$348$			8.17506i			0.438229i
$349$			7.91901i			0.423895i	0.977281	+	0.211947i	$0.0679805\pi$
$349$			7.91901i			0.423895i	−0.977281	+	0.211947i	$0.932019\pi$
$350$	−7.30053	−	0.363040i	−0.390230	−	0.0194053i
$351$	0.521091	+	0.521091i	0.0278138	+	0.0278138i
$352$			6.26734i			0.334050i
$353$		−	2.54035i		−	0.135209i	−0.997712	−	0.0676046i	$-0.978464\pi$
$353$		−	2.54035i		−	0.135209i	0.997712	−	0.0676046i	$-0.0215356\pi$
$354$	11.8895			0.631922
$355$	−0.873161	+	1.96823i	−0.0463426	+	0.104463i
$356$	−12.7462	+	12.7462i	−0.675547	+	0.675547i
$357$	4.08211			0.216048
$358$	−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
$362$	−17.7191			−0.931293
$363$	19.9967	−	19.9967i	1.04955	−	1.04955i
$364$	0.761788	−	0.761788i	0.0399285	−	0.0399285i
$365$	−2.94795	−	7.64911i	−0.154303	−	0.400373i
$366$	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	$0.0905500\pi$
$368$	6.92696			0.361093
$369$	−0.847391			−0.0441134
$370$	−4.97554	−	12.6588i	−0.258666	−	0.658097i
$371$	8.22894			0.427225
$372$	−2.32806			−0.120704
$373$	18.1951	−	18.1951i	0.942108	−	0.942108i	−0.0563053	−	0.998414i	$-0.517932\pi$
$373$	18.1951	−	18.1951i	0.942108	−	0.942108i	0.998414	+	0.0563053i	$0.0179320\pi$
$374$	17.5004			0.904922
$375$	5.03579	−	9.98203i	0.260047	−	0.515470i
$376$	2.86222	−	2.86222i	0.147608	−	0.147608i
$377$	4.25995	−	4.25995i	0.219399	−	0.219399i
$378$	1.46191			0.0751925
$379$			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
$383$	4.38944			0.224290			0.112145	−	0.993692i	$-0.464228\pi$
$383$	4.38944			0.224290			0.112145	+	0.993692i	$0.464228\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	19.1169	−	7.36762i	0.974287	−	0.375488i
$386$	0.340975			0.0173552
$387$			9.33244i			0.474395i
$388$			18.3296i			0.930546i
$389$	22.2349	+	22.2349i	1.12736	+	1.12736i	0.990606	+	0.136750i	$0.0436658\pi$
$389$	22.2349	+	22.2349i	1.12736	+	1.12736i	0.136750	+	0.990606i	$0.456334\pi$
$390$	0.592586	+	1.53759i	0.0300068	+	0.0778591i
$391$		−	19.3422i		−	0.978178i
$392$			4.86282i			0.245609i
$393$	2.50099			0.126158
$394$	−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	0.275402	−	0.961329i	$-0.411189\pi$
$397$	−13.6670	−	13.6670i	−0.685927	−	0.685927i	−0.961329	+	0.275402i	$0.911189\pi$
$398$	−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	0.989369	−	0.145426i	$-0.0464551\pi$
$401$	16.9000	+	16.9000i	0.843944	+	0.843944i	−0.145426	+	0.989369i	$0.546455\pi$
$402$	−8.83242			−0.440521
$403$	1.21313	+	1.21313i	0.0604303	+	0.0604303i
$404$		−	9.61899i		−	0.478562i
$405$	−0.906760	+	2.04396i	−0.0450573	+	0.101565i
$406$		−	11.9512i		−	0.593128i
$407$	27.1354	+	26.7771i	1.34505	+	1.32729i
$408$	1.97446	+	1.97446i	0.0977504	+	0.0977504i
$409$	−5.32124	+	5.32124i	−0.263118	+	0.263118i	−0.826320	−	0.563201i	$-0.809570\pi$
$409$	−5.32124	+	5.32124i	−0.263118	+	0.263118i	0.563201	+	0.826320i	$0.309570\pi$
$410$	−1.73204	−	0.768380i	−0.0855392	−	0.0379476i
$411$			8.81845i			0.434982i
$412$			10.9768i			0.540788i
$413$	−17.3814			−0.855284
$414$		−	6.92696i		−	0.340441i
$415$	−20.7910	+	8.01280i	−1.02059	+	0.393333i
$416$	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	$0.907301\pi$
$420$	2.98809	+	1.32560i	0.145804	+	0.0646827i
$421$	−9.16265	−	9.16265i	−0.446560	−	0.446560i	0.447649	−	0.894209i	$-0.352261\pi$
$421$	−9.16265	−	9.16265i	−0.446560	−	0.446560i	−0.894209	+	0.447649i	$0.852261\pi$
$422$	−8.80254			−0.428501
$423$	−2.86222	−	2.86222i	−0.139166	−	0.139166i
$424$	3.98023	+	3.98023i	0.193297	+	0.193297i
$425$	−10.3504	+	9.36980i	−0.502070	+	0.454502i
$426$	0.680906	−	0.680906i	0.0329900	−	0.0329900i
$427$	−10.4429			−0.505369
$428$	9.06848	−	9.06848i	0.438342	−	0.438342i
$429$	−3.26585	−	3.26585i	−0.157677	−	0.157677i
$430$	−8.46228	+	19.0752i	−0.408088	+	0.919886i
$431$	−3.45686	−	3.45686i	−0.166511	−	0.166511i	0.618933	−	0.785444i	$-0.287565\pi$
$431$	−3.45686	−	3.45686i	−0.166511	−	0.166511i	−0.785444	+	0.618933i	$0.787565\pi$
$432$	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
$438$			3.66604i			0.175170i
$439$	24.0778	−	24.0778i	1.14917	−	1.14917i	0.162457	−	0.986716i	$-0.448058\pi$
$439$	24.0778	−	24.0778i	1.14917	−	1.14917i	0.986716	−	0.162457i	$-0.0519420\pi$
$440$	12.8102	+	5.68297i	0.610703	+	0.270925i
$441$	4.86282			0.231563
$442$		−	2.05775i		−	0.0978771i
$443$	−6.83063	+	6.83063i	−0.324533	+	0.324533i	−0.850503	−	0.525970i	$-0.823702\pi$
$443$	−6.83063	+	6.83063i	−0.324533	+	0.324533i	0.525970	+	0.850503i	$0.323702\pi$
$444$	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	−0.999286	−	0.0377790i	$-0.987972\pi$
$449$	−21.9750	−	21.9750i	−1.03707	−	1.03707i	−0.0377790	−	0.999286i	$-0.512028\pi$
$450$	−3.70677	+	3.35557i	−0.174739	+	0.158183i
$451$	5.31089			0.250080
$452$			8.66069i			0.407364i
$453$	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
$457$		−	23.6642i		−	1.10696i	−0.832862	−	0.553481i	$-0.813299\pi$
$457$		−	23.6642i		−	1.10696i	0.832862	−	0.553481i	$-0.186701\pi$
$458$		−	7.41303i		−	0.346388i
$459$	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	−0.967143	−	0.254233i	$-0.918177\pi$
$461$	−15.3068	+	15.3068i	−0.712910	+	0.712910i	0.254233	+	0.967143i	$0.418177\pi$
$462$	−9.16228			−0.426268
$463$	−41.7413			−1.93988			−0.969941	−	0.243341i	$-0.921757\pi$
$463$	−41.7413			−1.93988			−0.969941	+	0.243341i	$0.921757\pi$
$464$	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
$467$		−	18.8139i		−	0.870606i	−0.900284	−	0.435303i	$-0.856641\pi$
$467$		−	18.8139i		−	0.870606i	0.900284	−	0.435303i	$-0.143359\pi$
$468$		−	0.736934i		−	0.0340648i
$469$	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
$473$		−	58.4896i		−	2.68935i
$474$	−16.5335			−0.759409
$475$	0.311164	−	6.25733i	0.0142772	−	0.287106i
$476$	−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	$-0.398776\pi$
$479$	−13.9456	−	13.9456i	−0.637190	−	0.637190i	−0.949861	+	0.312671i	$0.898776\pi$
$480$	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
$483$			10.1266i			0.460776i
$484$	−28.2795			−1.28543
$485$	37.4651	+	16.6206i	1.70120	+	0.754702i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$			2.48057i			0.112405i	0.998419	+	0.0562027i	$0.0178993\pi$
$487$			2.48057i			0.112405i	−0.998419	+	0.0562027i	$0.982101\pi$
$488$	−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
$495$	5.68297	−	12.8102i	0.255431	−	0.575776i
$496$	1.64619	+	1.64619i	0.0739160	+	0.0739160i
$497$	−0.995423	+	0.995423i	−0.0446508	+	0.0446508i
$498$	9.96463			0.446526
$499$	2.96909	−	2.96909i	0.132915	−	0.132915i	−0.637520	−	0.770434i	$-0.720039\pi$
$499$	2.96909	−	2.96909i	0.132915	−	0.132915i	0.770434	+	0.637520i	$0.220039\pi$
$500$	−10.6192	+	3.49752i	−0.474905	+	0.156414i
$501$	12.5037	+	12.5037i	0.558626	+	0.558626i
$502$	−16.1757	−	16.1757i	−0.721959	−	0.721959i
$503$	32.3803			1.44377			0.721883	−	0.692015i	$-0.243277\pi$
$503$	32.3803			1.44377			0.721883	+	0.692015i	$0.243277\pi$
$504$	−1.03373	−	1.03373i	−0.0460458	−	0.0460458i
$505$	−19.6609	−	8.72211i	−0.874897	−	0.388129i
$506$			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	$-0.662812\pi$
$509$	−22.0862			−0.978952			−0.489476	+	0.872017i	$0.662812\pi$
$510$	5.82609	−	2.24536i	0.257984	−	0.0994264i
$511$		−	5.35942i		−	0.237087i
$512$	1.00000			0.0441942
$513$			1.25301i			0.0553218i
$514$		−	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
$518$	−0.0590988	−	8.89225i	−0.00259665	−	0.390703i
$519$			2.15261i			0.0944889i
$520$	0.668222	−	1.50627i	0.0293035	−	0.0660541i
$521$		−	28.8075i		−	1.26208i	−0.775751	−	0.631039i	$-0.782629\pi$
$521$		−	28.8075i		−	1.26208i	0.775751	−	0.631039i	$-0.217371\pi$
$522$	−5.78064	−	5.78064i	−0.253012	−	0.253012i
$523$	−4.73292			−0.206956			−0.103478	−	0.994632i	$-0.532997\pi$
$523$	−4.73292			−0.206956			−0.103478	+	0.994632i	$0.532997\pi$
$524$	−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
$532$	1.83179			0.0794182
$533$		−	0.624471i		−	0.0270488i
$534$		−	18.0258i		−	0.780055i
$535$	−10.3127	−	26.7586i	−0.445857	−	1.15687i
$536$	6.24546	+	6.24546i	0.269763	+	0.269763i
$537$		−	23.1597i		−	0.999417i
$538$		−	7.97934i		−	0.344014i
$539$	−30.4769			−1.31273
$540$	2.08648	−	0.804124i	0.0897877	−	0.0346040i
$541$	−10.7692	+	10.7692i	−0.463003	+	0.463003i	−0.899639	−	0.436635i	$-0.856170\pi$
$541$	−10.7692	+	10.7692i	−0.463003	+	0.463003i	0.436635	+	0.899639i	$0.356170\pi$
$542$	15.5657			0.668603
$543$	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
$547$	21.4263			0.916123			0.458062	−	0.888920i	$-0.348544\pi$
$547$	21.4263			0.916123			0.458062	+	0.888920i	$0.348544\pi$
$548$	6.23559	−	6.23559i	0.266371	−	0.266371i
$549$	−5.05111	+	5.05111i	−0.215576	+	0.215576i
$550$	23.2316	−	21.0305i	0.990598	−	0.896744i
$551$	10.2434			0.436386
$552$	−4.89810	+	4.89810i	−0.208477	+	0.208477i
$553$	24.1705			1.02783
$554$	−31.7356			−1.34831
$555$	12.4693	+	5.43285i	0.529293	+	0.230612i
$556$	−9.56037			−0.405450
$557$	40.6664			1.72309			0.861546	−	0.507680i	$-0.169497\pi$
$557$	40.6664			1.72309			0.861546	+	0.507680i	$0.169497\pi$
$558$	1.64619	−	1.64619i	0.0696887	−	0.0696887i
$559$	−6.87739			−0.290883
$560$	−1.17556	−	3.05024i	−0.0496764	−	0.128896i
$561$	−12.3746	+	12.3746i	−0.522457	+	0.522457i
$562$	−2.87484	+	2.87484i	−0.121268	+	0.121268i
$563$	−2.87035			−0.120971			−0.0604855	−	0.998169i	$-0.519265\pi$
$563$	−2.87035			−0.120971			−0.0604855	+	0.998169i	$0.519265\pi$
$564$			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
$568$	−0.962946			−0.0404043
$569$	−4.67420	+	4.67420i	−0.195953	+	0.195953i	−0.798262	−	0.602310i	$-0.794247\pi$
$569$	−4.67420	+	4.67420i	−0.195953	+	0.195953i	0.602310	+	0.798262i	$0.294247\pi$
$570$	−1.13618	+	2.56111i	−0.0475894	+	0.107273i
$571$	−9.05022			−0.378740			−0.189370	−	0.981906i	$-0.560645\pi$
$571$	−9.05022			−0.378740			−0.189370	+	0.981906i	$0.560645\pi$
$572$			4.61861i			0.193114i
$573$			8.78045i			0.366809i
$574$	−0.875971	−	0.875971i	−0.0365623	−	0.0365623i
$575$	−23.2439	−	25.6766i	−0.969338	−	1.07079i
$576$		−	1.00000i		−	0.0416667i
$577$			43.0099i			1.79052i	0.445539	+	0.895262i	$0.353012\pi$
$577$			43.0099i			1.79052i	−0.445539	+	0.895262i	$0.646988\pi$
$578$	9.20300			0.382795
$579$	−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
$587$	−20.9031			−0.862762			−0.431381	−	0.902170i	$-0.641974\pi$
$587$	−20.9031			−0.862762			−0.431381	+	0.902170i	$0.641974\pi$
$588$	−3.43853	−	3.43853i	−0.141803	−	0.141803i
$589$			2.91709i			0.120196i
$590$	−24.8072	+	9.56066i	−1.02130	+	0.393606i
$591$		−	2.60688i		−	0.107233i
$592$	4.27248	−	4.32965i	0.175598	−	0.177948i
$593$	−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
$597$		−	14.2840i		−	0.584604i
$598$	5.10471			0.208747
$599$		−	8.95384i		−	0.365844i	−0.983127	−	0.182922i	$-0.941444\pi$
$599$		−	8.95384i		−	0.365844i	0.983127	−	0.182922i	$-0.0585556\pi$
$600$	4.99383	+	0.248333i	0.203872	+	0.0101381i
$601$	−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
$605$	−25.6428	+	57.8023i	−1.04253	+	2.35000i
$606$	6.80165	+	6.80165i	0.276298	+	0.276298i
$607$	5.64510			0.229128			0.114564	−	0.993416i	$-0.463453\pi$
$607$	5.64510			0.229128			0.114564	+	0.993416i	$0.463453\pi$
$608$	0.886013	+	0.886013i	0.0359326	+	0.0359326i
$609$	8.45078	+	8.45078i	0.342443	+	0.342443i
$610$	−14.9044	+	5.74414i	−0.603463	+	0.232573i
$611$	2.10926	−	2.10926i	0.0853317	−	0.0853317i
$612$	−2.79231			−0.112872
$613$	−5.16392	+	5.16392i	−0.208569	+	0.208569i	−0.803659	−	0.595090i	$-0.797116\pi$
$613$	−5.16392	+	5.16392i	−0.208569	+	0.208569i	0.595090	+	0.803659i	$0.297116\pi$
$614$	6.50486	+	6.50486i	0.262515	+	0.262515i
$615$	1.76806	−	0.681408i	0.0712951	−	0.0274770i
$616$	6.47871	+	6.47871i	0.261035	+	0.261035i
$617$	27.6646	+	27.6646i	1.11374	+	1.11374i	0.992641	+	0.121094i	$0.0386403\pi$
$617$	27.6646	+	27.6646i	1.11374	+	1.11374i	0.121094	+	0.992641i	$0.461360\pi$
$618$	−7.76177	−	7.76177i	−0.312224	−	0.312224i
$619$	−1.46506			−0.0588858			−0.0294429	−	0.999566i	$-0.509373\pi$
$619$	−1.46506			−0.0588858			−0.0294429	+	0.999566i	$0.509373\pi$
$620$	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
$623$			26.3522i			1.05578i
$624$	−0.521091	+	0.521091i	−0.0208603	+	0.0208603i
$625$	−2.48026	+	24.8767i	−0.0992105	+	0.995066i
$626$	0.921260			0.0368210
$627$		−	7.85305i		−	0.313621i
$628$	−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	0.665308	−	0.746569i	$-0.268300\pi$
$631$	−2.04127	−	2.04127i	−0.0812618	−	0.0812618i	−0.746569	+	0.665308i	$0.768300\pi$
$632$	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
$635$	16.0175	+	41.5610i	0.635636	+	1.64930i
$636$	−5.62889			−0.223200
$637$			3.58358i			0.141986i
$638$	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	$0.661040\pi$
$642$			12.8248i			0.506153i
$643$		−	45.0438i		−	1.77635i	−0.459503	−	0.888176i	$-0.651972\pi$
$643$		−	45.0438i		−	1.77635i	0.459503	−	0.888176i	$-0.348028\pi$
$644$	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
$647$	26.5714			1.04463			0.522316	−	0.852752i	$-0.325068\pi$
$647$	26.5714			1.04463			0.522316	+	0.852752i	$0.325068\pi$
$648$	−1.00000			−0.0392837
$649$	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
$652$			1.09629i			0.0429340i
$653$		−	15.1209i		−	0.591725i	−0.955231	−	0.295862i	$-0.904393\pi$
$653$		−	15.1209i		−	0.591725i	0.955231	−	0.295862i	$-0.0956070\pi$
$654$	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
$658$		−	5.91750i		−	0.230688i
$659$	21.2057			0.826058			0.413029	−	0.910718i	$-0.364471\pi$
$659$	21.2057			0.826058			0.413029	+	0.910718i	$0.364471\pi$
$660$	−13.0767	+	5.03972i	−0.509008	+	0.196171i
$661$	33.2201	+	33.2201i	1.29211	+	1.29211i	0.933478	+	0.358635i	$0.116758\pi$
$661$	33.2201	+	33.2201i	1.29211	+	1.29211i	0.358635	+	0.933478i	$0.383242\pi$
$662$	−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
$668$		−	17.6829i		−	0.684174i
$669$	14.3804			0.555978
$670$	18.4286	−	7.10236i	0.711960	−	0.274388i
$671$	31.6570	−	31.6570i	1.22211	−	1.22211i
$672$			1.46191i			0.0563944i
$673$	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	0.146913	−	0.989149i	$-0.453066\pi$
$677$	−21.9143	−	21.9143i	−0.842236	−	0.842236i	−0.989149	+	0.146913i	$0.953066\pi$
$678$	−6.12403	−	6.12403i	−0.235192	−	0.235192i
$679$	18.9478	+	18.9478i	0.727151	+	0.727151i
$680$	−5.70738	−	2.53195i	−0.218868	−	0.0970960i
$681$	−1.64986	−	1.64986i	−0.0632226	−	0.0632226i
$682$	−10.3172	+	10.3172i	−0.395066	+	0.395066i
$683$	−27.2147			−1.04134			−0.520672	−	0.853757i	$-0.674318\pi$
$683$	−27.2147			−1.04134			−0.520672	+	0.853757i	$0.674318\pi$
$684$	0.886013	−	0.886013i	0.0338776	−	0.0338776i
$685$	−7.09113	−	18.3995i	−0.270938	−	0.703008i
$686$	12.2629	+	12.2629i	0.468200	+	0.468200i
$687$	5.24180	+	5.24180i	0.199987	+	0.199987i
$688$	−9.33244			−0.355796
$689$	2.93317	+	2.93317i	0.111745	+	0.111745i
$690$	5.57013	+	14.4529i	0.212051	+	0.550214i
$691$		−	0.158792i		−	0.00604073i	−0.999995	−	0.00302036i	$-0.999039\pi$
$691$		−	0.158792i		−	0.00604073i	0.999995	−	0.00302036i	$-0.000961413\pi$
$692$	1.52212	−	1.52212i	0.0578624	−	0.0578624i
$693$	6.47871	−	6.47871i	0.246106	−	0.246106i
$694$	−2.21653			−0.0841382
$695$	−8.66896	+	19.5410i	−0.328832	+	0.741234i
$696$			8.17506i			0.309875i
$697$	−2.36618			−0.0896254
$698$			7.91901i			0.299739i
$699$			14.9193i			0.564300i
$700$	−7.30053	−	0.363040i	−0.275934	−	0.0137216i
$701$	−4.97548	+	4.97548i	−0.187921	+	0.187921i	−0.794797	−	0.606876i	$-0.792423\pi$
$701$	−4.97548	+	4.97548i	−0.187921	+	0.187921i	0.606876	+	0.794797i	$0.292423\pi$
$702$	0.521091	+	0.521091i	0.0196673	+	0.0196673i
$703$	7.62160	−	0.0506539i	0.287454	−	0.00191045i
$704$			6.26734i			0.236209i
$705$	8.27352	+	3.67037i	0.311599	+	0.138234i
$706$		−	2.54035i		−	0.0956074i
$707$	−9.94340	−	9.94340i	−0.373960	−	0.373960i
$708$	11.8895			0.446836
$709$	−13.0193	−	13.0193i	−0.488949	−	0.488949i	0.419026	−	0.907974i	$-0.362372\pi$
$709$	−13.0193	−	13.0193i	−0.488949	−	0.488949i	−0.907974	+	0.419026i	$0.862372\pi$
$710$	−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
$717$	−6.44004			−0.240508
$718$			17.2531i			0.643880i
$719$		−	43.2488i		−	1.61291i	−0.591296	−	0.806455i	$-0.701383\pi$
$719$		−	43.2488i		−	1.61291i	0.591296	−	0.806455i	$-0.298617\pi$
$720$	−2.04396	−	0.906760i	−0.0761740	−	0.0337929i
$721$	11.3470	+	11.3470i	0.422585	+	0.422585i
$722$		−	17.4300i		−	0.648676i
$723$		−	4.93503i		−	0.183536i
$724$	−17.7191			−0.658523
$725$	−40.8249	−	2.03014i	−1.51620	−	0.0753973i
$726$	19.9967	−	19.9967i	0.742145	−	0.742145i
$727$	19.1608			0.710634			0.355317	−	0.934746i	$-0.384373\pi$
$727$	19.1608			0.710634			0.355317	+	0.934746i	$0.384373\pi$
$728$	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
$732$	7.14335			0.264026
$733$	32.1045	−	32.1045i	1.18581	−	1.18581i	0.207591	−	0.978216i	$-0.433438\pi$
$733$	32.1045	−	32.1045i	1.18581	−	1.18581i	0.978216	−	0.207591i	$-0.0665624\pi$
$734$	13.0108	−	13.0108i	0.480239	−	0.480239i
$735$	−10.1462	+	3.91031i	−0.374247	+	0.144234i
$736$	6.92696			0.255331
$737$	−39.1424	+	39.1424i	−1.44183	+	1.44183i
$738$	−0.847391			−0.0311929
$739$	8.08459			0.297397			0.148698	−	0.988883i	$-0.452492\pi$
$739$	8.08459			0.297397			0.148698	+	0.988883i	$0.452492\pi$
$740$	−4.97554	−	12.6588i	−0.182904	−	0.465345i
$741$	−0.923386			−0.0339214
$742$	8.22894			0.302094
$743$	−8.70418	+	8.70418i	−0.319326	+	0.319326i	−0.848508	−	0.529182i	$-0.822499\pi$
$743$	−8.70418	+	8.70418i	−0.319326	+	0.319326i	0.529182	+	0.848508i	$0.322499\pi$
$744$	−2.32806			−0.0853508
$745$	5.79587	+	2.57121i	0.212344	+	0.0942020i
$746$	18.1951	−	18.1951i	0.666171	−	0.666171i
$747$	−7.04605	+	7.04605i	−0.257802	+	0.257802i
$748$	17.5004			0.639876
$749$		−	18.7487i		−	0.685061i
$750$	5.03579	−	9.98203i	0.183881	−	0.364492i
$751$		−	19.9209i		−	0.726924i	−0.931609	−	0.363462i	$-0.881595\pi$
$751$		−	19.9209i		−	0.726924i	0.931609	−	0.363462i	$-0.118405\pi$
$752$	2.86222	−	2.86222i	0.104374	−	0.104374i
$753$	22.8760			0.833646
$754$	4.25995	−	4.25995i	0.155138	−	0.155138i
$755$	−37.5543	−	16.6602i	−1.36674	−	0.606326i
$756$	1.46191			0.0531691
$757$		−	33.9202i		−	1.23285i	−0.787413	−	0.616426i	$-0.788580\pi$
$757$		−	33.9202i		−	1.23285i	0.787413	−	0.616426i	$-0.211420\pi$
$758$			26.7132i			0.970269i
$759$	−30.6980	−	30.6980i	−1.11427	−	1.11427i
$760$	2.61438	−	1.00758i	0.0948335	−	0.0365487i
$761$			47.5918i			1.72520i	0.505887	+	0.862600i	$0.331165\pi$
$761$			47.5918i			1.72520i	−0.505887	+	0.862600i	$0.668835\pi$
$762$		−	19.9192i		−	0.721597i
$763$	−8.98056			−0.325118
$764$	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	$-0.747636\pi$
$769$	0.291289	−	0.291289i	0.0105041	−	0.0105041i	0.712339	+	0.701835i	$0.247636\pi$
$770$	19.1169	−	7.36762i	0.688925	−	0.265510i
$771$	5.73137	+	5.73137i	0.206410	+	0.206410i
$772$	0.340975			0.0122720
$773$	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
$775$	0.578134	−	11.6259i	0.0207672	−	0.417616i
$776$			18.3296i			0.657996i
$777$	6.32956	+	6.24598i	0.227072	+	0.224073i
$778$	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
$782$		−	19.3422i		−	0.691676i
$783$	8.17506			0.292153
$784$			4.86282i			0.173672i
$785$	5.34718	+	13.8744i	0.190849	+	0.495200i
$786$	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
$790$	34.4968	−	13.2950i	1.22734	−	0.473015i
$791$	8.95278	+	8.95278i	0.318324	+	0.318324i
$792$	6.26734			0.222700
$793$	−3.72233	−	3.72233i	−0.132184	−	0.132184i
$794$	−13.6670	−	13.6670i	−0.485024	−	0.485024i
$795$	−5.10406	+	11.5053i	−0.181022	+	0.408049i
$796$	−10.1003	+	10.1003i	−0.357996	+	0.357996i
$797$	23.9938			0.849904			0.424952	−	0.905216i	$-0.360291\pi$
$797$	23.9938			0.849904			0.424952	+	0.905216i	$0.360291\pi$
$798$	−1.29527	+	1.29527i	−0.0458521	+	0.0458521i
$799$	−7.99219	−	7.99219i	−0.282744	−	0.282744i
$800$	−3.35557	−	3.70677i	−0.118637	−	0.131054i
$801$	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
$808$		−	9.61899i		−	0.338395i
$809$	10.2600	−	10.2600i	0.360722	−	0.360722i	−0.503357	−	0.864079i	$-0.667902\pi$
$809$	10.2600	−	10.2600i	0.360722	−	0.360722i	0.864079	+	0.503357i	$0.167902\pi$
$810$	−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	$0.475665\pi$
$812$		−	11.9512i		−	0.419405i
$813$	−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
$820$	−1.73204	−	0.768380i	−0.0604853	−	0.0268330i
$821$	8.08918			0.282314			0.141157	−	0.989987i	$-0.454918\pi$
$821$	8.08918			0.282314			0.141157	+	0.989987i	$0.454918\pi$
$822$			8.81845i			0.307579i
$823$	−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
$827$			40.7681i			1.41765i	0.705387	+	0.708823i	$0.250773\pi$
$827$			40.7681i			1.41765i	−0.705387	+	0.708823i	$0.749227\pi$
$828$		−	6.92696i		−	0.240728i
$829$	10.1511	−	10.1511i	0.352562	−	0.352562i	−0.508500	−	0.861062i	$-0.669800\pi$
$829$	10.1511	−	10.1511i	0.352562	−	0.352562i	0.861062	+	0.508500i	$0.169800\pi$
$830$	−20.7910	+	8.01280i	−0.721665	+	0.278128i
$831$	22.4404	−	22.4404i	0.778450	−	0.778450i
$832$	0.736934			0.0255486
$833$	13.5785			0.470467
$834$	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
$837$			2.32806i			0.0804695i
$838$			11.7545i			0.406052i
$839$	29.3925			1.01474			0.507370	−	0.861728i	$-0.330618\pi$
$839$	29.3925			1.01474			0.507370	+	0.861728i	$0.330618\pi$
$840$	2.98809	+	1.32560i	0.103099	+	0.0457376i
$841$		−	37.8316i		−	1.30454i
$842$	−9.16265	−	9.16265i	−0.315766	−	0.315766i
$843$		−	4.06563i		−	0.140028i
$844$	−8.80254			−0.302996
$845$	−11.2954	+	25.4615i	−0.388575	+	0.875902i
$846$	−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
$853$		−	39.8785i		−	1.36541i	−0.730693	−	0.682706i	$-0.760803\pi$
$853$		−	39.8785i		−	1.36541i	0.730693	−	0.682706i	$-0.239197\pi$
$854$	−10.4429			−0.357350
$855$	−1.00758	−	2.61438i	−0.0344584	−	0.0894099i
$856$	9.06848	−	9.06848i	0.309954	−	0.309954i
$857$		−	31.9265i		−	1.09059i	−0.838245	−	0.545294i	$-0.816418\pi$
$857$		−	31.9265i		−	1.09059i	0.838245	−	0.545294i	$-0.183582\pi$
$858$	−3.26585	−	3.26585i	−0.111494	−	0.111494i
$859$	37.9277	+	37.9277i	1.29408	+	1.29408i	0.932242	+	0.361835i	$0.117849\pi$
$859$	37.9277	+	37.9277i	1.29408	+	1.29408i	0.361835	+	0.932242i	$0.382151\pi$
$860$	−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
$865$	−1.73096	−	4.49136i	−0.0588545	−	0.152711i
$866$	−4.11998	−	4.11998i	−0.140003	−	0.140003i
$867$	−6.50751	+	6.50751i	−0.221007	+	0.221007i
$868$	3.40341			0.115519
$869$	−73.2712	+	73.2712i	−2.48555	+	2.48555i
$870$	16.7095	+	7.41282i	0.566506	+	0.251318i
$871$	4.60249	+	4.60249i	0.155950	+	0.155950i
$872$	−4.34378	−	4.34378i	−0.147099	−	0.147099i
$873$	18.3296			0.620364
$874$	6.13737	+	6.13737i	0.207600	+	0.207600i
$875$	−7.36187	+	14.5928i	−0.248877	+	0.493327i
$876$			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
$880$	12.8102	+	5.68297i	0.431832	+	0.191573i
$881$		−	11.2579i		−	0.379287i	−0.981853	−	0.189644i	$-0.939267\pi$
$881$		−	11.2579i		−	0.379287i	0.981853	−	0.189644i	$-0.0607332\pi$
$882$	4.86282			0.163740
$883$			50.7798i			1.70888i	0.519552	+	0.854439i	$0.326099\pi$
$883$			50.7798i			1.70888i	−0.519552	+	0.854439i	$0.673901\pi$
$884$		−	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	0.728916	−	0.684603i	$-0.240024\pi$
$887$	1.31977	+	1.31977i	0.0443134	+	0.0443134i	−0.684603	+	0.728916i	$0.740024\pi$
$888$	0.0404257	+	6.08263i	0.00135660	+	0.204120i
$889$			29.1201i			0.976657i
$890$	14.4950	+	37.6105i	0.485874	+	1.26071i
$891$		−	6.26734i		−	0.209964i
$892$	−10.1685	−	10.1685i	−0.340466	−	0.340466i
$893$	5.07192			0.169725
$894$	−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
$902$	5.31089			0.176833
$903$		−	13.6432i		−	0.454017i
$904$			8.66069i			0.288050i
$905$	−16.0669	+	36.2171i	−0.534083	+	1.20390i
$906$	12.9919	+	12.9919i	0.431626	+	0.431626i
$907$		−	10.6642i		−	0.354097i	−0.984202	−	0.177049i	$-0.943345\pi$
$907$		−	10.6642i		−	0.354097i	0.984202	−	0.177049i	$-0.0566550\pi$
$908$			2.33325i			0.0774316i
$909$	−9.61899			−0.319042
$910$	−0.866308	−	2.24783i	−0.0287178	−	0.0745147i
$911$	−16.4111	+	16.4111i	−0.543725	+	0.543725i	−0.924619	−	0.380894i	$-0.875616\pi$
$911$	−16.4111	+	16.4111i	−0.543725	+	0.543725i	0.380894	+	0.924619i	$0.375616\pi$
$912$	−1.25301			−0.0414914
$913$	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
$917$	−3.65622			−0.120739
$918$	1.97446	−	1.97446i	0.0651669	−	0.0651669i
$919$	−42.0610	+	42.0610i	−1.38746	+	1.38746i	−0.556850	+	0.830613i	$0.687990\pi$
$919$	−42.0610	+	42.0610i	−1.38746	+	1.38746i	−0.830613	+	0.556850i	$0.812010\pi$
$920$	6.28109	−	14.1584i	0.207081	−	0.466790i
$921$	−9.19926			−0.303126
$922$	−15.3068	+	15.3068i	−0.504104	+	0.504104i
$923$	−0.709628			−0.0233577
$924$	−9.16228			−0.301417
$925$	−30.3856	−	1.30864i	−0.999074	−	0.0430277i
$926$	−41.7413			−1.37170
$927$	10.9768			0.360525
$928$	5.78064	−	5.78064i	0.189759	−	0.189759i
$929$	−8.30197			−0.272379			−0.136189	−	0.990683i	$-0.543486\pi$
$929$	−8.30197			−0.272379			−0.136189	+	0.990683i	$0.543486\pi$
$930$	−2.11099	+	4.75847i	−0.0692221	+	0.156036i
$931$	−4.30852	+	4.30852i	−0.141206	+	0.141206i
$932$	10.5495	−	10.5495i	0.345562	−	0.345562i
$933$	−23.7878			−0.778777
$934$		−	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	$0.205194\pi$
$938$	12.9122			0.421598
$939$	−0.651429	+	0.651429i	−0.0212586	+	0.0212586i
$940$	−3.25492	−	8.44561i	−0.106164	−	0.275465i
$941$	−11.0302			−0.359575			−0.179787	−	0.983705i	$-0.557541\pi$
$941$	−11.0302			−0.359575			−0.179787	+	0.983705i	$0.557541\pi$
$942$		−	6.64969i		−	0.216659i
$943$		−	5.86984i		−	0.191148i
$944$	−8.40717	−	8.40717i	−0.273630	−	0.273630i
$945$	1.32560	−	2.98809i	0.0431218	−	0.0972026i
$946$		−	58.4896i		−	1.90166i
$947$			51.2800i			1.66637i	0.552991	+	0.833187i	$0.313487\pi$
$947$			51.2800i			1.66637i	−0.552991	+	0.833187i	$0.686513\pi$
$948$	−16.5335			−0.536983
$949$	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	−0.787890	−	0.615816i	$-0.788826\pi$
$953$	−5.31203	+	5.31203i	−0.172074	+	0.172074i	0.615816	+	0.787890i	$0.288826\pi$
$954$	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
$957$	−51.2359			−1.65622
$958$	−13.9456	−	13.9456i	−0.450561	−	0.450561i
$959$		−	12.8918i		−	0.416297i
$960$	0.804124	+	2.08648i	0.0259530	+	0.0673407i
$961$		−	25.5801i		−	0.825166i
$962$	3.14854	−	3.19067i	0.101513	−	0.102871i
$963$	−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
$967$			15.4122i			0.495623i	0.968808	+	0.247811i	$0.0797113\pi$
$967$			15.4122i			0.495623i	−0.968808	+	0.247811i	$0.920289\pi$
$968$	−28.2795			−0.908939
$969$			3.49880i			0.112398i
$970$	37.4651	+	16.6206i	1.20293	+	0.533655i
$971$	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
$975$	3.68012	+	0.183005i	0.117858	+	0.00586084i
$976$	−5.05111	−	5.05111i	−0.161682	−	0.161682i
$977$	−6.84308			−0.218930			−0.109465	−	0.993991i	$-0.534914\pi$
$977$	−6.84308			−0.218930			−0.109465	+	0.993991i	$0.534914\pi$
$978$	−0.775194	−	0.775194i	−0.0247880	−	0.0247880i
$979$	−79.8847	−	79.8847i	−2.55313	−	2.55313i
$980$	9.93943	+	4.40941i	0.317503	+	0.140853i
$981$	−4.34378	+	4.34378i	−0.138686	+	0.138686i
$982$	−27.0864			−0.864362
$983$	−13.2691	+	13.2691i	−0.423217	+	0.423217i	−0.886310	−	0.463093i	$-0.846740\pi$
$983$	−13.2691	+	13.2691i	−0.423217	+	0.423217i	0.463093	+	0.886310i	$0.346740\pi$
$984$	0.599196	+	0.599196i	0.0191017	+	0.0191017i
$985$	2.09626	+	5.43920i	0.0667924	+	0.173307i
$986$	−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	0.354626	−	0.935008i	$-0.384608\pi$
$991$	−18.2705	−	18.2705i	−0.580382	−	0.580382i	−0.935008	+	0.354626i	$0.884608\pi$
$992$	1.64619	+	1.64619i	0.0522665	+	0.0522665i
$993$		−	11.4202i		−	0.362409i
$994$	−0.995423	+	0.995423i	−0.0315729	+	0.0315729i
$995$	11.4861	+	29.8032i	0.364134	+	0.944825i
$996$	9.96463			0.315741
$997$			8.65428i			0.274084i	0.990565	+	0.137042i	$0.0437595\pi$
$997$			8.65428i			0.274084i	−0.990565	+	0.137042i	$0.956241\pi$
$998$	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.o.b.253.8	yes	40
5.2	odd	4		1110.2.l.b.697.13	yes	40
37.6	odd	4		1110.2.l.b.43.13	✓	40
185.117	even	4	inner	1110.2.o.b.487.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.13	✓	40	37.6	odd	4
1110.2.l.b.697.13	yes	40	5.2	odd	4
1110.2.o.b.253.8	yes	40	1.1	even	1	trivial
1110.2.o.b.487.8	yes	40	185.117	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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