LMFDB - Embedded newform 1110.2.l.b.43.6

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			43.6
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.21384 - 0.314477i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.376687 + 0.376687i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.21384 - 0.314477i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.376687 + 0.376687i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-0.314477 - 2.21384i) q^{10} +1.28566i q^{11} +(0.707107 - 0.707107i) q^{12} +5.12767i q^{13} +(0.376687 + 0.376687i) q^{14} +(-1.34306 + 1.78779i) q^{15} +1.00000 q^{16} -2.31038 q^{17} -1.00000 q^{18} +(3.87466 - 3.87466i) q^{19} +(-2.21384 + 0.314477i) q^{20} -0.532716i q^{21} +1.28566 q^{22} +6.29757i q^{23} +(-0.707107 - 0.707107i) q^{24} +(4.80221 - 1.39241i) q^{25} +5.12767 q^{26} +(0.707107 + 0.707107i) q^{27} +(0.376687 - 0.376687i) q^{28} +(-1.15504 - 1.15504i) q^{29} +(1.78779 + 1.34306i) q^{30} +(-7.11133 + 7.11133i) q^{31} -1.00000i q^{32} +(-0.909099 - 0.909099i) q^{33} +2.31038i q^{34} +(-0.715467 + 0.952386i) q^{35} +1.00000i q^{36} +(5.17182 + 3.20192i) q^{37} +(-3.87466 - 3.87466i) q^{38} +(-3.62581 - 3.62581i) q^{39} +(0.314477 + 2.21384i) q^{40} -2.12896i q^{41} -0.532716 q^{42} +2.56124i q^{43} -1.28566i q^{44} +(-0.314477 - 2.21384i) q^{45} +6.29757 q^{46} +(2.64523 - 2.64523i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.71621i q^{49} +(-1.39241 - 4.80221i) q^{50} +(1.63368 - 1.63368i) q^{51} -5.12767i q^{52} +(0.572887 + 0.572887i) q^{53} +(0.707107 - 0.707107i) q^{54} +(0.404311 + 2.84625i) q^{55} +(-0.376687 - 0.376687i) q^{56} +5.47960i q^{57} +(-1.15504 + 1.15504i) q^{58} +(-1.04438 + 1.04438i) q^{59} +(1.34306 - 1.78779i) q^{60} +(3.44882 - 3.44882i) q^{61} +(7.11133 + 7.11133i) q^{62} +(0.376687 + 0.376687i) q^{63} -1.00000 q^{64} +(1.61253 + 11.3519i) q^{65} +(-0.909099 + 0.909099i) q^{66} +(5.32260 + 5.32260i) q^{67} +2.31038 q^{68} +(-4.45305 - 4.45305i) q^{69} +(0.952386 + 0.715467i) q^{70} +4.38568 q^{71} +1.00000 q^{72} +(9.81049 - 9.81049i) q^{73} +(3.20192 - 5.17182i) q^{74} +(-2.41109 + 4.38025i) q^{75} +(-3.87466 + 3.87466i) q^{76} +(-0.484292 - 0.484292i) q^{77} +(-3.62581 + 3.62581i) q^{78} +(-11.4000 + 11.4000i) q^{79} +(2.21384 - 0.314477i) q^{80} -1.00000 q^{81} -2.12896 q^{82} +(11.5202 + 11.5202i) q^{83} +0.532716i q^{84} +(-5.11482 + 0.726561i) q^{85} +2.56124 q^{86} +1.63348 q^{87} -1.28566 q^{88} +(8.09354 + 8.09354i) q^{89} +(-2.21384 + 0.314477i) q^{90} +(-1.93153 - 1.93153i) q^{91} -6.29757i q^{92} -10.0569i q^{93} +(-2.64523 - 2.64523i) q^{94} +(7.35940 - 9.79638i) q^{95} +(0.707107 + 0.707107i) q^{96} +8.07546 q^{97} +6.71621 q^{98} +1.28566 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
$5$	2.21384	−	0.314477i	0.990061	−	0.140638i
$5$	2.21384	−	0.314477i	0.990061	−	0.140638i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−0.376687	+	0.376687i	−0.142374	+	0.142374i	−0.774702	−	0.632327i	$-0.782100\pi$
$7$	−0.376687	+	0.376687i	−0.142374	+	0.142374i	0.632327	+	0.774702i	$0.282100\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−0.314477	−	2.21384i	−0.0994464	−	0.700079i
$11$			1.28566i			0.387641i	0.981037	+	0.193821i	$0.0620880\pi$
$11$			1.28566i			0.387641i	−0.981037	+	0.193821i	$0.937912\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$			5.12767i			1.42216i	0.703112	+	0.711080i	$0.251793\pi$
$13$			5.12767i			1.42216i	−0.703112	+	0.711080i	$0.748207\pi$
$14$	0.376687	+	0.376687i	0.100674	+	0.100674i
$15$	−1.34306	+	1.78779i	−0.346775	+	0.461606i
$16$	1.00000			0.250000
$17$	−2.31038			−0.560349			−0.280175	−	0.959949i	$-0.590392\pi$
$17$	−2.31038			−0.560349			−0.280175	+	0.959949i	$0.590392\pi$
$18$	−1.00000			−0.235702
$19$	3.87466	−	3.87466i	0.888908	−	0.888908i	−0.105510	−	0.994418i	$-0.533648\pi$
$19$	3.87466	−	3.87466i	0.888908	−	0.888908i	0.994418	+	0.105510i	$0.0336476\pi$
$20$	−2.21384	+	0.314477i	−0.495031	+	0.0703192i
$21$		−	0.532716i		−	0.116248i
$22$	1.28566			0.274104
$23$			6.29757i			1.31313i	0.754268	+	0.656567i	$0.227992\pi$
$23$			6.29757i			1.31313i	−0.754268	+	0.656567i	$0.772008\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	4.80221	−	1.39241i	0.960442	−	0.278481i
$26$	5.12767			1.00562
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.376687	−	0.376687i	0.0711872	−	0.0711872i
$29$	−1.15504	−	1.15504i	−0.214486	−	0.214486i	0.591684	−	0.806170i	$-0.298463\pi$
$29$	−1.15504	−	1.15504i	−0.214486	−	0.214486i	−0.806170	+	0.591684i	$0.798463\pi$
$30$	1.78779	+	1.34306i	0.326405	+	0.245207i
$31$	−7.11133	+	7.11133i	−1.27723	+	1.27723i	−0.335023	+	0.942210i	$0.608744\pi$
$31$	−7.11133	+	7.11133i	−1.27723	+	1.27723i	−0.942210	+	0.335023i	$0.891256\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.909099	−	0.909099i	−0.158254	−	0.158254i
$34$			2.31038i			0.396227i
$35$	−0.715467	+	0.952386i	−0.120936	+	0.160983i
$36$			1.00000i			0.166667i
$37$	5.17182	+	3.20192i	0.850242	+	0.526392i
$37$	5.17182	+	3.20192i	0.850242	+	0.526392i
$38$	−3.87466	−	3.87466i	−0.628553	−	0.628553i
$39$	−3.62581	−	3.62581i	−0.580594	−	0.580594i
$40$	0.314477	+	2.21384i	0.0497232	+	0.350039i
$41$		−	2.12896i		−	0.332487i	−0.986085	−	0.166244i	$-0.946836\pi$
$41$		−	2.12896i		−	0.332487i	0.986085	−	0.166244i	$-0.0531638\pi$
$42$	−0.532716			−0.0821999
$43$			2.56124i			0.390585i	0.980745	+	0.195292i	$0.0625656\pi$
$43$			2.56124i			0.390585i	−0.980745	+	0.195292i	$0.937434\pi$
$44$		−	1.28566i		−	0.193821i
$45$	−0.314477	−	2.21384i	−0.0468795	−	0.330020i
$46$	6.29757			0.928526
$47$	2.64523	−	2.64523i	0.385847	−	0.385847i	−0.487356	−	0.873203i	$-0.662039\pi$
$47$	2.64523	−	2.64523i	0.385847	−	0.385847i	0.873203	+	0.487356i	$0.162039\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			6.71621i			0.959459i
$50$	−1.39241	−	4.80221i	−0.196916	−	0.679135i
$51$	1.63368	−	1.63368i	0.228762	−	0.228762i
$52$		−	5.12767i		−	0.711080i
$53$	0.572887	+	0.572887i	0.0786920	+	0.0786920i	0.745357	−	0.666665i	$-0.232279\pi$
$53$	0.572887	+	0.572887i	0.0786920	+	0.0786920i	−0.666665	+	0.745357i	$0.732279\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	0.404311	+	2.84625i	0.0545172	+	0.383788i
$56$	−0.376687	−	0.376687i	−0.0503369	−	0.0503369i
$57$			5.47960i			0.725790i
$58$	−1.15504	+	1.15504i	−0.151664	+	0.151664i
$59$	−1.04438	+	1.04438i	−0.135966	+	0.135966i	−0.771814	−	0.635848i	$-0.780651\pi$
$59$	−1.04438	+	1.04438i	−0.135966	+	0.135966i	0.635848	+	0.771814i	$0.280651\pi$
$60$	1.34306	−	1.78779i	0.173388	−	0.230803i
$61$	3.44882	−	3.44882i	0.441576	−	0.441576i	−0.450965	−	0.892542i	$-0.648920\pi$
$61$	3.44882	−	3.44882i	0.441576	−	0.441576i	0.892542	+	0.450965i	$0.148920\pi$
$62$	7.11133	+	7.11133i	0.903140	+	0.903140i
$63$	0.376687	+	0.376687i	0.0474581	+	0.0474581i
$64$	−1.00000			−0.125000
$65$	1.61253	+	11.3519i	0.200010	+	1.40802i
$66$	−0.909099	+	0.909099i	−0.111902	+	0.111902i
$67$	5.32260	+	5.32260i	0.650259	+	0.650259i	0.953055	−	0.302797i	$-0.0979203\pi$
$67$	5.32260	+	5.32260i	0.650259	+	0.650259i	−0.302797	+	0.953055i	$0.597920\pi$
$68$	2.31038			0.280175
$69$	−4.45305	−	4.45305i	−0.536085	−	0.536085i
$70$	0.952386	+	0.715467i	0.113832	+	0.0855147i
$71$	4.38568			0.520484			0.260242	−	0.965543i	$-0.416198\pi$
$71$	4.38568			0.520484			0.260242	+	0.965543i	$0.416198\pi$
$72$	1.00000			0.117851
$73$	9.81049	−	9.81049i	1.14823	−	1.14823i	0.161330	−	0.986901i	$-0.448422\pi$
$73$	9.81049	−	9.81049i	1.14823	−	1.14823i	0.986901	−	0.161330i	$-0.0515783\pi$
$74$	3.20192	−	5.17182i	0.372215	−	0.601212i
$75$	−2.41109	+	4.38025i	−0.278409	+	0.505788i
$76$	−3.87466	+	3.87466i	−0.444454	+	0.444454i
$77$	−0.484292	−	0.484292i	−0.0551902	−	0.0551902i
$78$	−3.62581	+	3.62581i	−0.410542	+	0.410542i
$79$	−11.4000	+	11.4000i	−1.28259	+	1.28259i	−0.343409	+	0.939186i	$0.611582\pi$
$79$	−11.4000	+	11.4000i	−1.28259	+	1.28259i	−0.939186	+	0.343409i	$0.888418\pi$
$80$	2.21384	−	0.314477i	0.247515	−	0.0351596i
$81$	−1.00000			−0.111111
$82$	−2.12896			−0.235104
$83$	11.5202	+	11.5202i	1.26450	+	1.26450i	0.948887	+	0.315617i	$0.102212\pi$
$83$	11.5202	+	11.5202i	1.26450	+	1.26450i	0.315617	+	0.948887i	$0.397788\pi$
$84$			0.532716i			0.0581241i
$85$	−5.11482	+	0.726561i	−0.554780	+	0.0788066i
$86$	2.56124			0.276185
$87$	1.63348			0.175127
$88$	−1.28566			−0.137052
$89$	8.09354	+	8.09354i	0.857914	+	0.857914i	0.991092	−	0.133179i	$-0.0425184\pi$
$89$	8.09354	+	8.09354i	0.857914	+	0.857914i	−0.133179	+	0.991092i	$0.542518\pi$
$90$	−2.21384	+	0.314477i	−0.233360	+	0.0331488i
$91$	−1.93153	−	1.93153i	−0.202479	−	0.202479i
$92$		−	6.29757i		−	0.656567i
$93$		−	10.0569i		−	1.04286i
$94$	−2.64523	−	2.64523i	−0.272835	−	0.272835i
$95$	7.35940	−	9.79638i	0.755059	−	1.00509i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	8.07546			0.819939			0.409969	−	0.912099i	$-0.365539\pi$
$97$	8.07546			0.819939			0.409969	+	0.912099i	$0.365539\pi$
$98$	6.71621			0.678440
$99$	1.28566			0.129214
$100$	−4.80221	+	1.39241i	−0.480221	+	0.139241i
$101$		−	15.8768i		−	1.57980i	−0.613233	−	0.789902i	$-0.710131\pi$
$101$		−	15.8768i		−	1.57980i	0.613233	−	0.789902i	$-0.289869\pi$
$102$	−1.63368	−	1.63368i	−0.161759	−	0.161759i
$103$	−9.00947			−0.887729			−0.443865	−	0.896094i	$-0.646393\pi$
$103$	−9.00947			−0.887729			−0.443865	+	0.896094i	$0.646393\pi$
$104$	−5.12767			−0.502809
$105$	−0.167527	−	1.17935i	−0.0163490	−	0.115093i
$106$	0.572887	−	0.572887i	0.0556437	−	0.0556437i
$107$	1.41163	−	1.41163i	0.136468	−	0.136468i	−0.635573	−	0.772041i	$-0.719236\pi$
$107$	1.41163	−	1.41163i	0.136468	−	0.136468i	0.772041	+	0.635573i	$0.219236\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−1.15892	+	1.15892i	−0.111004	+	0.111004i	−0.760427	−	0.649423i	$-0.775010\pi$
$109$	−1.15892	+	1.15892i	−0.111004	+	0.111004i	0.649423	+	0.760427i	$0.275010\pi$
$110$	2.84625	−	0.404311i	0.271379	−	0.0385495i
$111$	−5.92113	+	1.39293i	−0.562009	+	0.132211i
$112$	−0.376687	+	0.376687i	−0.0355936	+	0.0355936i
$113$	2.77598			0.261142			0.130571	−	0.991439i	$-0.458319\pi$
$113$	2.77598			0.261142			0.130571	+	0.991439i	$0.458319\pi$
$114$	5.47960			0.513211
$115$	1.98044	+	13.9418i	0.184677	+	1.30008i
$116$	1.15504	+	1.15504i	0.107243	+	0.107243i
$117$	5.12767			0.474053
$118$	1.04438	+	1.04438i	0.0961427	+	0.0961427i
$119$	0.870290	−	0.870290i	0.0797794	−	0.0797794i
$120$	−1.78779	−	1.34306i	−0.163202	−	0.122604i
$121$	9.34708			0.849734
$122$	−3.44882	−	3.44882i	−0.312242	−	0.312242i
$123$	1.50540	+	1.50540i	0.135737	+	0.135737i
$124$	7.11133	−	7.11133i	0.638616	−	0.638616i
$125$	10.1935	−	4.59275i	0.911731	−	0.410788i
$126$	0.376687	−	0.376687i	0.0335580	−	0.0335580i
$127$	−10.6282	+	10.6282i	−0.943105	+	0.943105i	−0.998466	−	0.0553618i	$-0.982369\pi$
$127$	−10.6282	+	10.6282i	−0.943105	+	0.943105i	0.0553618	+	0.998466i	$0.482369\pi$
$128$			1.00000i			0.0883883i
$129$	−1.81107	−	1.81107i	−0.159456	−	0.159456i
$130$	11.3519	−	1.61253i	0.995623	−	0.141429i
$131$	10.6555	−	10.6555i	0.930972	−	0.930972i	−0.0667945	−	0.997767i	$-0.521277\pi$
$131$	10.6555	−	10.6555i	0.930972	−	0.930972i	0.997767	+	0.0667945i	$0.0212772\pi$
$132$	0.909099	+	0.909099i	0.0791269	+	0.0791269i
$133$			2.91907i			0.253115i
$134$	5.32260	−	5.32260i	0.459802	−	0.459802i
$135$	1.78779	+	1.34306i	0.153869	+	0.115592i
$136$		−	2.31038i		−	0.198113i
$137$	8.98795	−	8.98795i	0.767892	−	0.767892i	−0.209843	−	0.977735i	$-0.567295\pi$
$137$	8.98795	−	8.98795i	0.767892	−	0.767892i	0.977735	+	0.209843i	$0.0672953\pi$
$138$	−4.45305	+	4.45305i	−0.379069	+	0.379069i
$139$	−19.4517			−1.64987			−0.824937	−	0.565225i	$-0.808789\pi$
$139$	−19.4517			−1.64987			−0.824937	+	0.565225i	$0.808789\pi$
$140$	0.715467	−	0.952386i	0.0604680	−	0.0804913i
$141$			3.74092i			0.315042i
$142$		−	4.38568i		−	0.368038i
$143$	−6.59244			−0.551287
$144$		−	1.00000i		−	0.0833333i
$145$	−2.92032	−	2.19385i	−0.242519	−	0.182189i
$146$	−9.81049	−	9.81049i	−0.811922	−	0.811922i
$147$	−4.74908	−	4.74908i	−0.391698	−	0.391698i
$148$	−5.17182	−	3.20192i	−0.425121	−	0.263196i
$149$		−	15.6534i		−	1.28238i	−0.767382	−	0.641190i	$-0.778441\pi$
$149$		−	15.6534i		−	1.28238i	0.767382	−	0.641190i	$-0.221559\pi$
$150$	4.38025	+	2.41109i	0.357646	+	0.196865i
$151$		−	3.10992i		−	0.253082i	−0.991961	−	0.126541i	$-0.959612\pi$
$151$		−	3.10992i		−	0.253082i	0.991961	−	0.126541i	$-0.0403875\pi$
$152$	3.87466	+	3.87466i	0.314276	+	0.314276i
$153$			2.31038i			0.186783i
$154$	−0.484292	+	0.484292i	−0.0390253	+	0.0390253i
$155$	−13.5070	+	17.9797i	−1.08491	+	1.44417i
$156$	3.62581	+	3.62581i	0.290297	+	0.290297i
$157$	−12.5025	+	12.5025i	−0.997805	+	0.997805i	−0.999998	−	0.00219308i	$-0.999302\pi$
$157$	−12.5025	+	12.5025i	−0.997805	+	0.997805i	0.00219308	+	0.999998i	$0.499302\pi$
$158$	11.4000	+	11.4000i	0.906931	+	0.906931i
$159$	−0.810184			−0.0642518
$160$	−0.314477	−	2.21384i	−0.0248616	−	0.175020i
$161$	−2.37221	−	2.37221i	−0.186957	−	0.186957i
$162$			1.00000i			0.0785674i
$163$	−8.61293			−0.674617			−0.337308	−	0.941394i	$-0.609517\pi$
$163$	−8.61293			−0.674617			−0.337308	+	0.941394i	$0.609517\pi$
$164$			2.12896i			0.166244i
$165$	−2.29849	−	1.72671i	−0.178938	−	0.134424i
$166$	11.5202	−	11.5202i	0.894139	−	0.894139i
$167$	−21.8398			−1.69001			−0.845007	−	0.534755i	$-0.820404\pi$
$167$	−21.8398			−1.69001			−0.845007	+	0.534755i	$0.820404\pi$
$168$	0.532716			0.0410999
$169$	−13.2930			−1.02254
$170$	0.726561	+	5.11482i	0.0557247	+	0.392289i
$171$	−3.87466	−	3.87466i	−0.296303	−	0.296303i
$172$		−	2.56124i		−	0.195292i
$173$	1.32378	−	1.32378i	0.100645	−	0.100645i	−0.654991	−	0.755636i	$-0.727328\pi$
$173$	1.32378	−	1.32378i	0.100645	−	0.100645i	0.755636	+	0.654991i	$0.227328\pi$
$174$		−	1.63348i		−	0.123833i
$175$	−1.28443	+	2.33343i	−0.0970937	+	0.176391i
$176$			1.28566i			0.0969103i
$177$		−	1.47697i		−	0.111016i
$178$	8.09354	−	8.09354i	0.606636	−	0.606636i
$179$	−17.8003	−	17.8003i	−1.33046	−	1.33046i	−0.904958	−	0.425501i	$-0.860098\pi$
$179$	−17.8003	−	17.8003i	−1.33046	−	1.33046i	−0.425501	−	0.904958i	$-0.639902\pi$
$180$	0.314477	+	2.21384i	0.0234397	+	0.165010i
$181$	−1.98719			−0.147707			−0.0738533	−	0.997269i	$-0.523530\pi$
$181$	−1.98719			−0.147707			−0.0738533	+	0.997269i	$0.523530\pi$
$182$	−1.93153	+	1.93153i	−0.143174	+	0.143174i
$183$			4.87737i			0.360546i
$184$	−6.29757			−0.464263
$185$	12.4565	+	5.46213i	0.915822	+	0.401584i
$186$	−10.0569			−0.737411
$187$		−	2.97036i		−	0.217214i
$188$	−2.64523	+	2.64523i	−0.192923	+	0.192923i
$189$	−0.532716			−0.0387494
$190$	−9.79638	−	7.35940i	−0.710704	−	0.533907i
$191$	−4.41456	−	4.41456i	−0.319426	−	0.319426i	0.529120	−	0.848547i	$-0.322522\pi$
$191$	−4.41456	−	4.41456i	−0.319426	−	0.319426i	−0.848547	+	0.529120i	$0.822522\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$		−	2.09366i		−	0.150705i	−0.997157	−	0.0753524i	$-0.975992\pi$
$193$		−	2.09366i		−	0.150705i	0.997157	−	0.0753524i	$-0.0240082\pi$
$194$		−	8.07546i		−	0.579784i
$195$	−9.16721	−	6.88674i	−0.656477	−	0.493170i
$196$		−	6.71621i		−	0.479730i
$197$	−4.75052	+	4.75052i	−0.338460	+	0.338460i	−0.855788	−	0.517327i	$-0.826927\pi$
$197$	−4.75052	+	4.75052i	−0.338460	+	0.338460i	0.517327	+	0.855788i	$0.326927\pi$
$198$		−	1.28566i		−	0.0913679i
$199$	4.93690	+	4.93690i	0.349968	+	0.349968i	0.860097	−	0.510130i	$-0.170403\pi$
$199$	4.93690	+	4.93690i	0.349968	+	0.349968i	−0.510130	+	0.860097i	$0.670403\pi$
$200$	1.39241	+	4.80221i	0.0984580	+	0.339567i
$201$	−7.52729			−0.530934
$202$	−15.8768			−1.11709
$203$	0.870179			0.0610746
$204$	−1.63368	+	1.63368i	−0.114381	+	0.114381i
$205$	−0.669508	−	4.71318i	−0.0467605	−	0.329183i
$206$			9.00947i			0.627719i
$207$	6.29757			0.437711
$208$			5.12767i			0.355540i
$209$	4.98150	+	4.98150i	0.344577	+	0.344577i
$210$	−1.17935	+	0.167527i	−0.0813829	+	0.0115605i
$211$	−13.1658			−0.906374			−0.453187	−	0.891416i	$-0.649713\pi$
$211$	−13.1658			−0.906374			−0.453187	+	0.891416i	$0.649713\pi$
$212$	−0.572887	−	0.572887i	−0.0393460	−	0.0393460i
$213$	−3.10114	+	3.10114i	−0.212487	+	0.212487i
$214$	−1.41163	−	1.41163i	−0.0964974	−	0.0964974i
$215$	0.805450	+	5.67018i	0.0549312	+	0.386703i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$		−	5.35750i		−	0.363690i
$218$	1.15892	+	1.15892i	0.0784919	+	0.0784919i
$219$			13.8741i			0.937526i
$220$	−0.404311	−	2.84625i	−0.0272586	−	0.191894i
$221$		−	11.8469i		−	0.796906i
$222$	1.39293	+	5.92113i	0.0934874	+	0.397400i
$223$	−13.0670	−	13.0670i	−0.875031	−	0.875031i	0.117984	−	0.993015i	$-0.462357\pi$
$223$	−13.0670	−	13.0670i	−0.875031	−	0.875031i	−0.993015	+	0.117984i	$0.962357\pi$
$224$	0.376687	+	0.376687i	0.0251685	+	0.0251685i
$225$	−1.39241	−	4.80221i	−0.0928271	−	0.320147i
$226$		−	2.77598i		−	0.184655i
$227$	16.0865			1.06770			0.533848	−	0.845580i	$-0.320745\pi$
$227$	16.0865			1.06770			0.533848	+	0.845580i	$0.320745\pi$
$228$		−	5.47960i		−	0.362895i
$229$		−	6.71533i		−	0.443762i	−0.975074	−	0.221881i	$-0.928780\pi$
$229$		−	6.71533i		−	0.443762i	0.975074	−	0.221881i	$-0.0712196\pi$
$230$	13.9418	−	1.98044i	0.919297	−	0.130586i
$231$	0.684892			0.0450626
$232$	1.15504	−	1.15504i	0.0758322	−	0.0758322i
$233$	4.61749	−	4.61749i	0.302502	−	0.302502i	−0.539490	−	0.841992i	$-0.681383\pi$
$233$	4.61749	−	4.61749i	0.302502	−	0.302502i	0.841992	+	0.539490i	$0.181383\pi$
$234$		−	5.12767i		−	0.335206i
$235$	5.02426	−	6.68799i	0.327747	−	0.436277i
$236$	1.04438	−	1.04438i	0.0679832	−	0.0679832i
$237$		−	16.1220i		−	1.04723i
$238$	−0.870290	−	0.870290i	−0.0564125	−	0.0564125i
$239$	13.1078	−	13.1078i	0.847873	−	0.847873i	−0.141995	−	0.989867i	$-0.545352\pi$
$239$	13.1078	−	13.1078i	0.847873	−	0.847873i	0.989867	+	0.141995i	$0.0453516\pi$
$240$	−1.34306	+	1.78779i	−0.0866938	+	0.115402i
$241$	−12.6538	−	12.6538i	−0.815103	−	0.815103i	0.170291	−	0.985394i	$-0.445529\pi$
$241$	−12.6538	−	12.6538i	−0.815103	−	0.815103i	−0.985394	+	0.170291i	$0.945529\pi$
$242$		−	9.34708i		−	0.600853i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−3.44882	+	3.44882i	−0.220788	+	0.220788i
$245$	2.11209	+	14.8686i	0.134937	+	0.949923i
$246$	1.50540	−	1.50540i	0.0959808	−	0.0959808i
$247$	19.8680	+	19.8680i	1.26417	+	1.26417i
$248$	−7.11133	−	7.11133i	−0.451570	−	0.451570i
$249$	−16.2920			−1.03246
$250$	−4.59275	−	10.1935i	−0.290471	−	0.644691i
$251$	−0.829972	+	0.829972i	−0.0523874	+	0.0523874i	−0.732815	−	0.680428i	$-0.761794\pi$
$251$	−0.829972	+	0.829972i	−0.0523874	+	0.0523874i	0.680428	+	0.732815i	$0.261794\pi$
$252$	−0.376687	−	0.376687i	−0.0237291	−	0.0237291i
$253$	−8.09653			−0.509025
$254$	10.6282	+	10.6282i	0.666876	+	0.666876i
$255$	3.10297	−	4.13048i	0.194315	−	0.258661i
$256$	1.00000			0.0625000
$257$	−9.61238			−0.599604			−0.299802	−	0.954001i	$-0.596921\pi$
$257$	−9.61238			−0.599604			−0.299802	+	0.954001i	$0.596921\pi$
$258$	−1.81107	+	1.81107i	−0.112752	+	0.112752i
$259$	−3.15428	+	0.742037i	−0.195997	+	0.0461079i
$260$	−1.61253	−	11.3519i	−0.100005	−	0.704012i
$261$	−1.15504	+	1.15504i	−0.0714953	+	0.0714953i
$262$	−10.6555	−	10.6555i	−0.658297	−	0.658297i
$263$	11.2512	−	11.2512i	0.693779	−	0.693779i	−0.269283	−	0.963061i	$-0.586787\pi$
$263$	11.2512	−	11.2512i	0.693779	−	0.693779i	0.963061	+	0.269283i	$0.0867866\pi$
$264$	0.909099	−	0.909099i	0.0559512	−	0.0559512i
$265$	1.44844	+	1.08812i	0.0889770	+	0.0668428i
$266$	2.91907			0.178980
$267$	−11.4460			−0.700483
$268$	−5.32260	−	5.32260i	−0.325129	−	0.325129i
$269$			23.2912i			1.42009i	0.704158	+	0.710043i	$0.251325\pi$
$269$			23.2912i			1.42009i	−0.704158	+	0.710043i	$0.748675\pi$
$270$	1.34306	−	1.78779i	0.0817357	−	0.108802i
$271$	13.8775			0.842996			0.421498	−	0.906829i	$-0.361504\pi$
$271$	13.8775			0.842996			0.421498	+	0.906829i	$0.361504\pi$
$272$	−2.31038			−0.140087
$273$	2.73159			0.165323
$274$	−8.98795	−	8.98795i	−0.542982	−	0.542982i
$275$	1.79016	+	6.17401i	0.107951	+	0.372307i
$276$	4.45305	+	4.45305i	0.268042	+	0.268042i
$277$			6.57502i			0.395055i	0.980297	+	0.197527i	$0.0632912\pi$
$277$			6.57502i			0.395055i	−0.980297	+	0.197527i	$0.936709\pi$
$278$			19.4517i			1.16664i
$279$	7.11133	+	7.11133i	0.425744	+	0.425744i
$280$	−0.952386	−	0.715467i	−0.0569160	−	0.0427573i
$281$	−13.5903	−	13.5903i	−0.810729	−	0.810729i	0.174015	−	0.984743i	$-0.444326\pi$
$281$	−13.5903	−	13.5903i	−0.810729	−	0.810729i	−0.984743	+	0.174015i	$0.944326\pi$
$282$	3.74092			0.222769
$283$	8.54984			0.508235			0.254118	−	0.967173i	$-0.418215\pi$
$283$	8.54984			0.508235			0.254118	+	0.967173i	$0.418215\pi$
$284$	−4.38568			−0.260242
$285$	1.72321	+	12.1310i	0.102074	+	0.718577i
$286$			6.59244i			0.389819i
$287$	0.801951	+	0.801951i	0.0473377	+	0.0473377i
$288$	−1.00000			−0.0589256
$289$	−11.6621			−0.686009
$290$	−2.19385	+	2.92032i	−0.128827	+	0.171487i
$291$	−5.71021	+	5.71021i	−0.334739	+	0.334739i
$292$	−9.81049	+	9.81049i	−0.574115	+	0.574115i
$293$	7.61554	+	7.61554i	0.444905	+	0.444905i	0.893656	−	0.448752i	$-0.148131\pi$
$293$	7.61554	+	7.61554i	0.444905	+	0.444905i	−0.448752	+	0.893656i	$0.648131\pi$
$294$	−4.74908	+	4.74908i	−0.276972	+	0.276972i
$295$	−1.98366	+	2.64052i	−0.115493	+	0.153737i
$296$	−3.20192	+	5.17182i	−0.186108	+	0.300606i
$297$	−0.909099	+	0.909099i	−0.0527513	+	0.0527513i
$298$	−15.6534			−0.906779
$299$	−32.2918			−1.86749
$300$	2.41109	−	4.38025i	0.139205	−	0.252894i
$301$	−0.964785	−	0.964785i	−0.0556093	−	0.0556093i
$302$	−3.10992			−0.178956
$303$	11.2266	+	11.2266i	0.644952	+	0.644952i
$304$	3.87466	−	3.87466i	0.222227	−	0.222227i
$305$	6.55058	−	8.71973i	0.375085	−	0.499290i
$306$	2.31038			0.132076
$307$	19.6731	+	19.6731i	1.12280	+	1.12280i	0.991319	+	0.131482i	$0.0419736\pi$
$307$	19.6731	+	19.6731i	1.12280	+	1.12280i	0.131482	+	0.991319i	$0.458026\pi$
$308$	0.484292	+	0.484292i	0.0275951	+	0.0275951i
$309$	6.37065	−	6.37065i	0.362414	−	0.362414i
$310$	17.9797	+	13.5070i	1.02118	+	0.767147i
$311$	−3.86047	+	3.86047i	−0.218907	+	0.218907i	−0.808038	−	0.589131i	$-0.799470\pi$
$311$	−3.86047	+	3.86047i	−0.218907	+	0.218907i	0.589131	+	0.808038i	$0.299470\pi$
$312$	3.62581	−	3.62581i	0.205271	−	0.205271i
$313$			18.9968i			1.07376i	0.843659	+	0.536880i	$0.180397\pi$
$313$			18.9968i			1.07376i	−0.843659	+	0.536880i	$0.819603\pi$
$314$	12.5025	+	12.5025i	0.705554	+	0.705554i
$315$	0.952386	+	0.715467i	0.0536609	+	0.0403120i
$316$	11.4000	−	11.4000i	0.641297	−	0.641297i
$317$	−17.8153	−	17.8153i	−1.00061	−	1.00061i	−1.00000		0.000608272i	$-0.999806\pi$
$317$	−17.8153	−	17.8153i	−1.00061	−	1.00061i	−0.000608272	−	1.00000i	$-0.500194\pi$
$318$			0.810184i			0.0454329i
$319$	1.48499	−	1.48499i	0.0831435	−	0.0831435i
$320$	−2.21384	+	0.314477i	−0.123758	+	0.0175798i
$321$			1.99635i			0.111426i
$322$	−2.37221	+	2.37221i	−0.132198	+	0.132198i
$323$	−8.95194	+	8.95194i	−0.498099	+	0.498099i
$324$	1.00000			0.0555556
$325$	7.13980	+	24.6241i	0.396045	+	1.36590i
$326$			8.61293i			0.477026i
$327$		−	1.63896i		−	0.0906347i
$328$	2.12896			0.117552
$329$			1.99285i			0.109869i
$330$	−1.72671	+	2.29849i	−0.0950524	+	0.126528i
$331$	−1.11563	−	1.11563i	−0.0613208	−	0.0613208i	0.675781	−	0.737102i	$-0.263806\pi$
$331$	−1.11563	−	1.11563i	−0.0613208	−	0.0613208i	−0.737102	+	0.675781i	$0.763806\pi$
$332$	−11.5202	−	11.5202i	−0.632252	−	0.632252i
$333$	3.20192	−	5.17182i	0.175464	−	0.283414i
$334$			21.8398i			1.19502i
$335$	13.4572	+	10.1096i	0.735247	+	0.552344i
$336$		−	0.532716i		−	0.0290621i
$337$	19.6821	+	19.6821i	1.07215	+	1.07215i	0.997186	+	0.0749653i	$0.0238846\pi$
$337$	19.6821	+	19.6821i	1.07215	+	1.07215i	0.0749653	+	0.997186i	$0.476115\pi$
$338$			13.2930i			0.723042i
$339$	−1.96291	+	1.96291i	−0.106611	+	0.106611i
$340$	5.11482	−	0.726561i	0.277390	−	0.0394033i
$341$	−9.14275	−	9.14275i	−0.495108	−	0.495108i
$342$	−3.87466	+	3.87466i	−0.209518	+	0.209518i
$343$	−5.16672	−	5.16672i	−0.278977	−	0.278977i
$344$	−2.56124			−0.138093
$345$	−11.2587	−	8.45798i	−0.606151	−	0.455362i
$346$	−1.32378	−	1.32378i	−0.0711669	−	0.0711669i
$347$			3.98304i			0.213821i	0.994269	+	0.106910i	$0.0340958\pi$
$347$			3.98304i			0.213821i	−0.994269	+	0.106910i	$0.965904\pi$
$348$	−1.63348			−0.0875635
$349$		−	7.69090i		−	0.411684i	−0.978585	−	0.205842i	$-0.934007\pi$
$349$		−	7.69090i		−	0.411684i	0.978585	−	0.205842i	$-0.0659934\pi$
$350$	2.33343	+	1.28443i	0.124727	+	0.0686556i
$351$	−3.62581	+	3.62581i	−0.193531	+	0.193531i
$352$	1.28566			0.0685259
$353$	−21.0577			−1.12079			−0.560395	−	0.828226i	$-0.689351\pi$
$353$	−21.0577			−1.12079			−0.560395	+	0.828226i	$0.689351\pi$
$354$	−1.47697			−0.0785002
$355$	9.70920	−	1.37919i	0.515311	−	0.0732000i
$356$	−8.09354	−	8.09354i	−0.428957	−	0.428957i
$357$			1.23078i			0.0651396i
$358$	−17.8003	+	17.8003i	−0.940777	+	0.940777i
$359$		−	19.0802i		−	1.00701i	−0.863992	−	0.503506i	$-0.832043\pi$
$359$		−	19.0802i		−	1.00701i	0.863992	−	0.503506i	$-0.167957\pi$
$360$	2.21384	−	0.314477i	0.116680	−	0.0165744i
$361$		−	11.0260i		−	0.580315i
$362$			1.98719i			0.104444i
$363$	−6.60938	+	6.60938i	−0.346903	+	0.346903i
$364$	1.93153	+	1.93153i	0.101240	+	0.101240i
$365$	18.6337	−	24.8041i	0.975333	−	1.29830i
$366$	4.87737			0.254944
$367$	13.0910	−	13.0910i	0.683346	−	0.683346i	−0.277407	−	0.960753i	$-0.589475\pi$
$367$	13.0910	−	13.0910i	0.683346	−	0.683346i	0.960753	+	0.277407i	$0.0894750\pi$
$368$			6.29757i			0.328283i
$369$	−2.12896			−0.110829
$370$	5.46213	−	12.4565i	0.283963	−	0.647584i
$371$	−0.431598			−0.0224075
$372$			10.0569i			0.521428i
$373$	17.5157	−	17.5157i	0.906927	−	0.906927i	−0.0890959	−	0.996023i	$-0.528398\pi$
$373$	17.5157	−	17.5157i	0.906927	−	0.906927i	0.996023	+	0.0890959i	$0.0283978\pi$
$374$	−2.97036			−0.153594
$375$	−3.96030	+	10.4554i	−0.204509	+	0.539916i
$376$	2.64523	+	2.64523i	0.136417	+	0.136417i
$377$	5.92267	−	5.92267i	0.305033	−	0.305033i
$378$			0.532716i			0.0274000i
$379$		−	21.8739i		−	1.12358i	−0.827278	−	0.561792i	$-0.810112\pi$
$379$		−	21.8739i		−	1.12358i	0.827278	−	0.561792i	$-0.189888\pi$
$380$	−7.35940	+	9.79638i	−0.377529	+	0.502544i
$381$		−	15.0306i		−	0.770042i
$382$	−4.41456	+	4.41456i	−0.225868	+	0.225868i
$383$		−	5.61751i		−	0.287042i	−0.989647	−	0.143521i	$-0.954158\pi$
$383$		−	5.61751i		−	0.287042i	0.989647	−	0.143521i	$-0.0458424\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−1.22444	−	0.919848i	−0.0624035	−	0.0468798i
$386$	−2.09366			−0.106564
$387$	2.56124			0.130195
$388$	−8.07546			−0.409969
$389$	−5.37334	+	5.37334i	−0.272439	+	0.272439i	−0.830081	−	0.557642i	$-0.811706\pi$
$389$	−5.37334	+	5.37334i	−0.272439	+	0.272439i	0.557642	+	0.830081i	$0.311706\pi$
$390$	−6.88674	+	9.16721i	−0.348724	+	0.464200i
$391$		−	14.5498i		−	0.735814i
$392$	−6.71621			−0.339220
$393$			15.0691i			0.760136i
$394$	4.75052	+	4.75052i	0.239328	+	0.239328i
$395$	−21.6527	+	28.8227i	−1.08946	+	1.45023i
$396$	−1.28566			−0.0646069
$397$	−17.9874	−	17.9874i	−0.902761	−	0.902761i	0.0929128	−	0.995674i	$-0.470382\pi$
$397$	−17.9874	−	17.9874i	−0.902761	−	0.902761i	−0.995674	+	0.0929128i	$0.970382\pi$
$398$	4.93690	−	4.93690i	0.247465	−	0.247465i
$399$	−2.06409	−	2.06409i	−0.103334	−	0.103334i
$400$	4.80221	−	1.39241i	0.240110	−	0.0696203i
$401$	15.1996	−	15.1996i	0.759033	−	0.759033i	−0.217113	−	0.976146i	$-0.569664\pi$
$401$	15.1996	−	15.1996i	0.759033	−	0.759033i	0.976146	+	0.217113i	$0.0696641\pi$
$402$			7.52729i			0.375427i
$403$	−36.4645	−	36.4645i	−1.81643	−	1.81643i
$404$			15.8768i			0.789902i
$405$	−2.21384	+	0.314477i	−0.110007	+	0.0156265i
$406$		−	0.870179i		−	0.0431863i
$407$	−4.11658	+	6.64920i	−0.204051	+	0.329589i
$408$	1.63368	+	1.63368i	0.0808795	+	0.0808795i
$409$	27.1312	+	27.1312i	1.34155	+	1.34155i	0.894517	+	0.447033i	$0.147519\pi$
$409$	27.1312	+	27.1312i	1.34155	+	1.34155i	0.447033	+	0.894517i	$0.352481\pi$
$410$	−4.71318	+	0.669508i	−0.232767	+	0.0330646i
$411$			12.7109i			0.626981i
$412$	9.00947			0.443865
$413$		−	0.786807i		−	0.0387163i
$414$		−	6.29757i		−	0.309509i
$415$	29.1267	+	21.8810i	1.42977	+	1.07410i
$416$	5.12767			0.251405
$417$	13.7544	−	13.7544i	0.673558	−	0.673558i
$418$	4.98150	−	4.98150i	0.243653	−	0.243653i
$419$		−	7.19965i		−	0.351726i	−0.984415	−	0.175863i	$-0.943728\pi$
$419$		−	7.19965i		−	0.351726i	0.984415	−	0.175863i	$-0.0562716\pi$
$420$	0.167527	+	1.17935i	0.00817448	+	0.0575464i
$421$	6.17926	−	6.17926i	0.301159	−	0.301159i	−0.540308	−	0.841467i	$-0.681692\pi$
$421$	6.17926	−	6.17926i	0.301159	−	0.301159i	0.841467	+	0.540308i	$0.181692\pi$
$422$			13.1658i			0.640903i
$423$	−2.64523	−	2.64523i	−0.128616	−	0.128616i
$424$	−0.572887	+	0.572887i	−0.0278218	+	0.0278218i
$425$	−11.0949	+	3.21699i	−0.538183	+	0.156047i
$426$	3.10114	+	3.10114i	0.150251	+	0.150251i
$427$			2.59825i			0.125738i
$428$	−1.41163	+	1.41163i	−0.0682340	+	0.0682340i
$429$	4.66156	−	4.66156i	0.225062	−	0.225062i
$430$	5.67018	−	0.805450i	0.273440	−	0.0388423i
$431$	19.0871	−	19.0871i	0.919394	−	0.919394i	−0.0775910	−	0.996985i	$-0.524723\pi$
$431$	19.0871	−	19.0871i	0.919394	−	0.919394i	0.996985	+	0.0775910i	$0.0247228\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−27.0193	−	27.0193i	−1.29847	−	1.29847i	−0.929405	−	0.369061i	$-0.879679\pi$
$433$	−27.0193	−	27.0193i	−1.29847	−	1.29847i	−0.369061	−	0.929405i	$-0.620321\pi$
$434$	−5.35750			−0.257168
$435$	3.61626	−	0.513691i	0.173386	−	0.0246296i
$436$	1.15892	−	1.15892i	0.0555022	−	0.0555022i
$437$	24.4009	+	24.4009i	1.16726	+	1.16726i
$438$	13.8741			0.662931
$439$	8.21948	+	8.21948i	0.392294	+	0.392294i	0.875504	−	0.483210i	$-0.160529\pi$
$439$	8.21948	+	8.21948i	0.392294	+	0.392294i	−0.483210	+	0.875504i	$0.660529\pi$
$440$	−2.84625	+	0.404311i	−0.135690	+	0.0192748i
$441$	6.71621			0.319820
$442$	−11.8469			−0.563497
$443$	−7.35664	+	7.35664i	−0.349525	+	0.349525i	−0.859932	−	0.510408i	$-0.829494\pi$
$443$	−7.35664	+	7.35664i	−0.349525	+	0.349525i	0.510408	+	0.859932i	$0.329494\pi$
$444$	5.92113	−	1.39293i	0.281004	−	0.0661055i
$445$	20.4631	+	15.3726i	0.970042	+	0.728731i
$446$	−13.0670	+	13.0670i	−0.618740	+	0.618740i
$447$	11.0687	+	11.0687i	0.523529	+	0.523529i
$448$	0.376687	−	0.376687i	0.0177968	−	0.0177968i
$449$	15.3192	−	15.3192i	0.722956	−	0.722956i	−0.246250	−	0.969206i	$-0.579199\pi$
$449$	15.3192	−	15.3192i	0.722956	−	0.722956i	0.969206	+	0.246250i	$0.0791986\pi$
$450$	−4.80221	+	1.39241i	−0.226378	+	0.0656387i
$451$	2.73711			0.128886
$452$	−2.77598			−0.130571
$453$	2.19905	+	2.19905i	0.103320	+	0.103320i
$454$		−	16.0865i		−	0.754975i
$455$	−4.88352	−	3.66868i	−0.228943	−	0.171990i
$456$	−5.47960			−0.256606
$457$	11.9041			0.556852			0.278426	−	0.960458i	$-0.410187\pi$
$457$	11.9041			0.556852			0.278426	+	0.960458i	$0.410187\pi$
$458$	−6.71533			−0.313787
$459$	−1.63368	−	1.63368i	−0.0762539	−	0.0762539i
$460$	−1.98044	−	13.9418i	−0.0923385	−	0.650041i
$461$	−21.6193	−	21.6193i	−1.00691	−	1.00691i	−0.999976	−	0.00693591i	$-0.997792\pi$
$461$	−21.6193	−	21.6193i	−1.00691	−	1.00691i	−0.00693591	−	0.999976i	$-0.502208\pi$
$462$		−	0.684892i		−	0.0318641i
$463$			7.74140i			0.359773i	0.983687	+	0.179887i	$0.0575731\pi$
$463$			7.74140i			0.359773i	−0.983687	+	0.179887i	$0.942427\pi$
$464$	−1.15504	−	1.15504i	−0.0536215	−	0.0536215i
$465$	−3.16268	−	22.2645i	−0.146666	−	1.03249i
$466$	−4.61749	−	4.61749i	−0.213901	−	0.213901i
$467$	40.6171			1.87954			0.939768	−	0.341813i	$-0.111041\pi$
$467$	40.6171			1.87954			0.939768	+	0.341813i	$0.111041\pi$
$468$	−5.12767			−0.237027
$469$	−4.00991			−0.185160
$470$	−6.68799	−	5.02426i	−0.308494	−	0.231752i
$471$		−	17.6811i		−	0.814704i
$472$	−1.04438	−	1.04438i	−0.0480714	−	0.0480714i
$473$	−3.29288			−0.151407
$474$	−16.1220			−0.740506
$475$	13.2118	−	24.0020i	0.606200	−	1.10129i
$476$	−0.870290	+	0.870290i	−0.0398897	+	0.0398897i
$477$	0.572887	−	0.572887i	0.0262307	−	0.0262307i
$478$	−13.1078	−	13.1078i	−0.599537	−	0.599537i
$479$	4.76750	−	4.76750i	0.217833	−	0.217833i	−0.589752	−	0.807585i	$-0.700774\pi$
$479$	4.76750	−	4.76750i	0.217833	−	0.217833i	0.807585	+	0.589752i	$0.200774\pi$
$480$	1.78779	+	1.34306i	0.0816012	+	0.0613018i
$481$	−16.4184	+	26.5194i	−0.748613	+	1.20918i
$482$	−12.6538	+	12.6538i	−0.576365	+	0.576365i
$483$	3.35482			0.152649
$484$	−9.34708			−0.424867
$485$	17.8778	−	2.53955i	0.811789	−	0.115315i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−16.5284			−0.748971			−0.374486	−	0.927233i	$-0.622181\pi$
$487$	−16.5284			−0.748971			−0.374486	+	0.927233i	$0.622181\pi$
$488$	3.44882	+	3.44882i	0.156121	+	0.156121i
$489$	6.09026	−	6.09026i	0.275411	−	0.275411i
$490$	14.8686	−	2.11209i	0.671697	−	0.0954147i
$491$	−11.4600			−0.517185			−0.258592	−	0.965987i	$-0.583259\pi$
$491$	−11.4600			−0.517185			−0.258592	+	0.965987i	$0.583259\pi$
$492$	−1.50540	−	1.50540i	−0.0678687	−	0.0678687i
$493$	2.66858	+	2.66858i	0.120187	+	0.120187i
$494$	19.8680	−	19.8680i	0.893902	−	0.893902i
$495$	2.84625	−	0.404311i	0.127929	−	0.0181724i
$496$	−7.11133	+	7.11133i	−0.319308	+	0.319308i
$497$	−1.65203	+	1.65203i	−0.0741036	+	0.0741036i
$498$			16.2920i			0.730062i
$499$	11.0278	+	11.0278i	0.493674	+	0.493674i	0.909462	−	0.415788i	$-0.136494\pi$
$499$	11.0278	+	11.0278i	0.493674	+	0.493674i	−0.415788	+	0.909462i	$0.636494\pi$
$500$	−10.1935	+	4.59275i	−0.455865	+	0.205394i
$501$	15.4431	−	15.4431i	0.689946	−	0.689946i
$502$	0.829972	+	0.829972i	0.0370435	+	0.0370435i
$503$			17.9392i			0.799870i	0.916543	+	0.399935i	$0.130967\pi$
$503$			17.9392i			0.799870i	−0.916543	+	0.399935i	$0.869033\pi$
$504$	−0.376687	+	0.376687i	−0.0167790	+	0.0167790i
$505$	−4.99290	−	35.1488i	−0.222181	−	1.56410i
$506$			8.09653i			0.359935i
$507$	9.39955	−	9.39955i	0.417449	−	0.417449i
$508$	10.6282	−	10.6282i	0.471552	−	0.471552i
$509$	10.1276			0.448897			0.224448	−	0.974486i	$-0.427942\pi$
$509$	10.1276			0.448897			0.224448	+	0.974486i	$0.427942\pi$
$510$	−4.13048	−	3.10297i	−0.182901	−	0.137402i
$511$			7.39097i			0.326957i
$512$		−	1.00000i		−	0.0441942i
$513$	5.47960			0.241930
$514$			9.61238i			0.423984i
$515$	−19.9455	+	2.83327i	−0.878906	+	0.124849i
$516$	1.81107	+	1.81107i	0.0797278	+	0.0797278i
$517$	3.40087	+	3.40087i	0.149570	+	0.149570i
$518$	0.742037	+	3.15428i	0.0326032	+	0.138591i
$519$			1.87211i			0.0821764i
$520$	−11.3519	+	1.61253i	−0.497812	+	0.0707143i
$521$			2.42962i			0.106444i	0.998583	+	0.0532219i	$0.0169491\pi$
$521$			2.42962i			0.106444i	−0.998583	+	0.0532219i	$0.983051\pi$
$522$	1.15504	+	1.15504i	0.0505548	+	0.0505548i
$523$		−	27.3470i		−	1.19580i	−0.801570	−	0.597901i	$-0.796002\pi$
$523$		−	27.3470i		−	1.19580i	0.801570	−	0.597901i	$-0.203998\pi$
$524$	−10.6555	+	10.6555i	−0.465486	+	0.465486i
$525$	−0.741757	−	2.55821i	−0.0323729	−	0.111650i
$526$	−11.2512	−	11.2512i	−0.490576	−	0.490576i
$527$	16.4299	−	16.4299i	0.715696	−	0.715696i
$528$	−0.909099	−	0.909099i	−0.0395635	−	0.0395635i
$529$	−16.6594			−0.724321
$530$	1.08812	−	1.44844i	0.0472650	−	0.0629163i
$531$	1.04438	+	1.04438i	0.0453221	+	0.0453221i
$532$		−	2.91907i		−	0.126558i
$533$	10.9166			0.472850
$534$			11.4460i			0.495317i
$535$	2.68121	−	3.56907i	0.115919	−	0.154304i
$536$	−5.32260	+	5.32260i	−0.229901	+	0.229901i
$537$	25.1735			1.08632
$538$	23.2912			1.00415
$539$	−8.63477			−0.371926
$540$	−1.78779	−	1.34306i	−0.0769344	−	0.0577959i
$541$	24.0214	+	24.0214i	1.03276	+	1.03276i	0.999445	+	0.0333158i	$0.0106067\pi$
$541$	24.0214	+	24.0214i	1.03276	+	1.03276i	0.0333158	+	0.999445i	$0.489393\pi$
$542$		−	13.8775i		−	0.596088i
$543$	1.40516	−	1.40516i	0.0603010	−	0.0603010i
$544$			2.31038i			0.0990567i
$545$	−2.20121	+	2.93012i	−0.0942896	+	0.125513i
$546$		−	2.73159i		−	0.116901i
$547$		−	37.8077i		−	1.61654i	−0.588810	−	0.808271i	$-0.700404\pi$
$547$		−	37.8077i		−	1.61654i	0.588810	−	0.808271i	$-0.299596\pi$
$548$	−8.98795	+	8.98795i	−0.383946	+	0.383946i
$549$	−3.44882	−	3.44882i	−0.147192	−	0.147192i
$550$	6.17401	−	1.79016i	0.263261	−	0.0763327i
$551$	−8.95079			−0.381316
$552$	4.45305	−	4.45305i	0.189535	−	0.189535i
$553$		−	8.58843i		−	0.365217i
$554$	6.57502			0.279346
$555$	−12.6704	+	4.94579i	−0.537829	+	0.209937i
$556$	19.4517			0.824937
$557$			18.1545i			0.769231i	0.923077	+	0.384615i	$0.125666\pi$
$557$			18.1545i			0.769231i	−0.923077	+	0.384615i	$0.874334\pi$
$558$	7.11133	−	7.11133i	0.301047	−	0.301047i
$559$	−13.1332			−0.555474
$560$	−0.715467	+	0.952386i	−0.0302340	+	0.0402457i
$561$	2.10036	+	2.10036i	0.0886774	+	0.0886774i
$562$	−13.5903	+	13.5903i	−0.573272	+	0.573272i
$563$			19.8695i			0.837398i	0.908125	+	0.418699i	$0.137514\pi$
$563$			19.8695i			0.837398i	−0.908125	+	0.418699i	$0.862486\pi$
$564$		−	3.74092i		−	0.157521i
$565$	6.14558	−	0.872982i	0.258547	−	0.0367266i
$566$		−	8.54984i		−	0.359376i
$567$	0.376687	−	0.376687i	0.0158194	−	0.0158194i
$568$			4.38568i			0.184019i
$569$	−6.05236	−	6.05236i	−0.253728	−	0.253728i	0.568769	−	0.822497i	$-0.307420\pi$
$569$	−6.05236	−	6.05236i	−0.253728	−	0.253728i	−0.822497	+	0.568769i	$0.807420\pi$
$570$	12.1310	−	1.72321i	0.508111	−	0.0721772i
$571$	12.1222			0.507297			0.253648	−	0.967296i	$-0.418369\pi$
$571$	12.1222			0.507297			0.253648	+	0.967296i	$0.418369\pi$
$572$	6.59244			0.275644
$573$	6.24313			0.260810
$574$	0.801951	−	0.801951i	0.0334728	−	0.0334728i
$575$	8.76877	+	30.2422i	0.365683	+	1.26119i
$576$			1.00000i			0.0416667i
$577$	36.8080			1.53234			0.766168	−	0.642641i	$-0.222161\pi$
$577$	36.8080			1.53234			0.766168	+	0.642641i	$0.222161\pi$
$578$			11.6621i			0.485081i
$579$	1.48044	+	1.48044i	0.0615249	+	0.0615249i
$580$	2.92032	+	2.19385i	0.121260	+	0.0910946i
$581$	−8.67901			−0.360066
$582$	5.71021	+	5.71021i	0.236696	+	0.236696i
$583$	−0.736538	+	0.736538i	−0.0305043	+	0.0305043i
$584$	9.81049	+	9.81049i	0.405961	+	0.405961i
$585$	11.3519	−	1.61253i	0.469341	−	0.0666701i
$586$	7.61554	−	7.61554i	0.314595	−	0.314595i
$587$			14.5475i			0.600439i	0.953870	+	0.300220i	$0.0970600\pi$
$587$			14.5475i			0.600439i	−0.953870	+	0.300220i	$0.902940\pi$
$588$	4.74908	+	4.74908i	0.195849	+	0.195849i
$589$			55.1080i			2.27068i
$590$	2.64052	+	1.98366i	0.108709	+	0.0816658i
$591$		−	6.71825i		−	0.276352i
$592$	5.17182	+	3.20192i	0.212560	+	0.131598i
$593$	−16.6115	−	16.6115i	−0.682153	−	0.682153i	0.278332	−	0.960485i	$-0.410219\pi$
$593$	−16.6115	−	16.6115i	−0.682153	−	0.682153i	−0.960485	+	0.278332i	$0.910219\pi$
$594$	0.909099	+	0.909099i	0.0373008	+	0.0373008i
$595$	1.65300	−	2.20037i	0.0677664	−	0.0902065i
$596$			15.6534i			0.641190i
$597$	−6.98183			−0.285747
$598$			32.2918i			1.32051i
$599$		−	13.5361i		−	0.553069i	−0.961004	−	0.276535i	$-0.910814\pi$
$599$		−	13.5361i		−	0.553069i	0.961004	−	0.276535i	$-0.0891861\pi$
$600$	−4.38025	−	2.41109i	−0.178823	−	0.0984325i
$601$	8.79388			0.358710			0.179355	−	0.983784i	$-0.442599\pi$
$601$	8.79388			0.358710			0.179355	+	0.983784i	$0.442599\pi$
$602$	−0.964785	+	0.964785i	−0.0393217	+	0.0393217i
$603$	5.32260	−	5.32260i	0.216753	−	0.216753i
$604$			3.10992i			0.126541i
$605$	20.6930	−	2.93944i	0.841289	−	0.119505i
$606$	11.2266	−	11.2266i	0.456050	−	0.456050i
$607$			1.05689i			0.0428979i	0.999770	+	0.0214489i	$0.00682793\pi$
$607$			1.05689i			0.0428979i	−0.999770	+	0.0214489i	$0.993172\pi$
$608$	−3.87466	−	3.87466i	−0.157138	−	0.157138i
$609$	−0.615309	+	0.615309i	−0.0249336	+	0.0249336i
$610$	−8.71973	−	6.55058i	−0.353051	−	0.265225i
$611$	13.5639	+	13.5639i	0.548735	+	0.548735i
$612$		−	2.31038i		−	0.0933915i
$613$	−31.3429	+	31.3429i	−1.26593	+	1.26593i	−0.317753	+	0.948174i	$0.602928\pi$
$613$	−31.3429	+	31.3429i	−1.26593	+	1.26593i	−0.948174	+	0.317753i	$0.897072\pi$
$614$	19.6731	−	19.6731i	0.793940	−	0.793940i
$615$	3.80613	+	2.85931i	0.153478	+	0.115298i
$616$	0.484292	−	0.484292i	0.0195127	−	0.0195127i
$617$	18.9748	+	18.9748i	0.763896	+	0.763896i	0.977024	−	0.213128i	$-0.0683652\pi$
$617$	18.9748	+	18.9748i	0.763896	+	0.763896i	−0.213128	+	0.977024i	$0.568365\pi$
$618$	−6.37065	−	6.37065i	−0.256265	−	0.256265i
$619$	14.1356			0.568157			0.284079	−	0.958801i	$-0.408312\pi$
$619$	14.1356			0.568157			0.284079	+	0.958801i	$0.408312\pi$
$620$	13.5070	−	17.9797i	0.542455	−	0.722083i
$621$	−4.45305	+	4.45305i	−0.178695	+	0.178695i
$622$	3.86047	+	3.86047i	0.154791	+	0.154791i
$623$	−6.09747			−0.244290
$624$	−3.62581	−	3.62581i	−0.145149	−	0.145149i
$625$	21.1224	−	13.3732i	0.844896	−	0.534930i
$626$	18.9968			0.759263
$627$	−7.04490			−0.281346
$628$	12.5025	−	12.5025i	0.498902	−	0.498902i
$629$	−11.9489	−	7.39765i	−0.476432	−	0.294963i
$630$	0.715467	−	0.952386i	0.0285049	−	0.0379440i
$631$	−13.8331	+	13.8331i	−0.550688	+	0.550688i	−0.926639	−	0.375951i	$-0.877316\pi$
$631$	−13.8331	+	13.8331i	−0.550688	+	0.550688i	0.375951	+	0.926639i	$0.377316\pi$
$632$	−11.4000	−	11.4000i	−0.453466	−	0.453466i
$633$	9.30966	−	9.30966i	0.370026	−	0.370026i
$634$	−17.8153	+	17.8153i	−0.707537	+	0.707537i
$635$	−20.1869	+	26.8716i	−0.801094	+	1.06637i
$636$	0.810184			0.0321259
$637$	−34.4385			−1.36450
$638$	−1.48499	−	1.48499i	−0.0587914	−	0.0587914i
$639$		−	4.38568i		−	0.173495i
$640$	0.314477	+	2.21384i	0.0124308	+	0.0875099i
$641$	24.5047			0.967877			0.483938	−	0.875102i	$-0.339206\pi$
$641$	24.5047			0.967877			0.483938	+	0.875102i	$0.339206\pi$
$642$	1.99635			0.0787898
$643$	−1.49125			−0.0588093			−0.0294046	−	0.999568i	$-0.509361\pi$
$643$	−1.49125			−0.0588093			−0.0294046	+	0.999568i	$0.509361\pi$
$644$	2.37221	+	2.37221i	0.0934783	+	0.0934783i
$645$	−4.57896	−	3.43988i	−0.180296	−	0.135445i
$646$	8.95194	+	8.95194i	0.352209	+	0.352209i
$647$		−	32.4023i		−	1.27386i	−0.770920	−	0.636932i	$-0.780203\pi$
$647$		−	32.4023i		−	1.27386i	0.770920	−	0.636932i	$-0.219797\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−1.34271	−	1.34271i	−0.0527062	−	0.0527062i
$650$	24.6241	−	7.13980i	0.965838	−	0.280046i
$651$	3.78832	+	3.78832i	0.148476	+	0.148476i
$652$	8.61293			0.337308
$653$	−49.0619			−1.91994			−0.959971	−	0.280099i	$-0.909633\pi$
$653$	−49.0619			−1.91994			−0.959971	+	0.280099i	$0.909633\pi$
$654$	−1.63896			−0.0640884
$655$	20.2386	−	26.9404i	0.790789	−	1.05265i
$656$		−	2.12896i		−	0.0831218i
$657$	−9.81049	−	9.81049i	−0.382743	−	0.382743i
$658$	1.99285			0.0776894
$659$	11.1464			0.434200			0.217100	−	0.976149i	$-0.430340\pi$
$659$	11.1464			0.434200			0.217100	+	0.976149i	$0.430340\pi$
$660$	2.29849	+	1.72671i	0.0894688	+	0.0672122i
$661$	31.4369	−	31.4369i	1.22275	−	1.22275i	0.256103	−	0.966649i	$-0.417561\pi$
$661$	31.4369	−	31.4369i	1.22275	−	1.22275i	0.966649	−	0.256103i	$-0.0824386\pi$
$662$	−1.11563	+	1.11563i	−0.0433603	+	0.0433603i
$663$	8.37699	+	8.37699i	0.325335	+	0.325335i
$664$	−11.5202	+	11.5202i	−0.447070	+	0.447070i
$665$	0.917981	+	6.46237i	0.0355978	+	0.250600i
$666$	−5.17182	−	3.20192i	−0.200404	−	0.124072i
$667$	7.27396	−	7.27396i	0.281649	−	0.281649i
$668$	21.8398			0.845007
$669$	18.4795			0.714460
$670$	10.1096	−	13.4572i	0.390566	−	0.519898i
$671$	4.43401	+	4.43401i	0.171173	+	0.171173i
$672$	−0.532716			−0.0205500
$673$	−1.81889	−	1.81889i	−0.0701132	−	0.0701132i	0.671181	−	0.741294i	$-0.265787\pi$
$673$	−1.81889	−	1.81889i	−0.0701132	−	0.0701132i	−0.741294	+	0.671181i	$0.765787\pi$
$674$	19.6821	−	19.6821i	0.758126	−	0.758126i
$675$	4.38025	+	2.41109i	0.168596	+	0.0928031i
$676$	13.2930			0.511268
$677$	9.38604	+	9.38604i	0.360735	+	0.360735i	0.864083	−	0.503349i	$-0.167899\pi$
$677$	9.38604	+	9.38604i	0.360735	+	0.360735i	−0.503349	+	0.864083i	$0.667899\pi$
$678$	1.96291	+	1.96291i	0.0753853	+	0.0753853i
$679$	−3.04192	+	3.04192i	−0.116738	+	0.116738i
$680$	−0.726561	−	5.11482i	−0.0278624	−	0.196144i
$681$	−11.3749	+	11.3749i	−0.435885	+	0.435885i
$682$	−9.14275	+	9.14275i	−0.350094	+	0.350094i
$683$		−	0.539905i		−	0.0206589i	−0.999947	−	0.0103295i	$-0.996712\pi$
$683$		−	0.539905i		−	0.0206589i	0.999947	−	0.0103295i	$-0.00328802\pi$
$684$	3.87466	+	3.87466i	0.148151	+	0.148151i
$685$	17.0714	−	22.7244i	0.652265	−	0.868255i
$686$	−5.16672	+	5.16672i	−0.197266	+	0.197266i
$687$	4.74846	+	4.74846i	0.181165	+	0.181165i
$688$			2.56124i			0.0976462i
$689$	−2.93757	+	2.93757i	−0.111913	+	0.111913i
$690$	−8.45798	+	11.2587i	−0.321990	+	0.428613i
$691$			40.4342i			1.53819i	0.639135	+	0.769094i	$0.279292\pi$
$691$			40.4342i			1.53819i	−0.639135	+	0.769094i	$0.720708\pi$
$692$	−1.32378	+	1.32378i	−0.0503226	+	0.0503226i
$693$	−0.484292	+	0.484292i	−0.0183967	+	0.0183967i
$694$	3.98304			0.151194
$695$	−43.0631	+	6.11712i	−1.63348	+	0.232036i
$696$			1.63348i			0.0619167i
$697$			4.91870i			0.186309i
$698$	−7.69090			−0.291105
$699$			6.53012i			0.246992i
$700$	1.28443	−	2.33343i	0.0485469	−	0.0881954i
$701$	23.7123	+	23.7123i	0.895601	+	0.895601i	0.995043	−	0.0994419i	$-0.0317057\pi$
$701$	23.7123	+	23.7123i	0.895601	+	0.895601i	−0.0994419	+	0.995043i	$0.531706\pi$
$702$	3.62581	+	3.62581i	0.136847	+	0.136847i
$703$	32.4454	−	7.63270i	1.22370	−	0.287873i
$704$		−	1.28566i		−	0.0484551i
$705$	1.17643	+	8.28182i	0.0443071	+	0.311911i
$706$			21.0577i			0.792518i
$707$	5.98060	+	5.98060i	0.224924	+	0.224924i
$708$			1.47697i			0.0555080i
$709$	−16.8933	+	16.8933i	−0.634441	+	0.634441i	−0.949179	−	0.314738i	$-0.898083\pi$
$709$	−16.8933	+	16.8933i	−0.634441	+	0.634441i	0.314738	+	0.949179i	$0.398083\pi$
$710$	−1.37919	−	9.70920i	−0.0517602	−	0.364380i
$711$	11.4000	+	11.4000i	0.427532	+	0.427532i
$712$	−8.09354	+	8.09354i	−0.303318	+	0.303318i
$713$	−44.7841	−	44.7841i	−1.67718	−	1.67718i
$714$	1.23078			0.0460607
$715$	−14.5946	+	2.07317i	−0.545808	+	0.0775322i
$716$	17.8003	+	17.8003i	0.665230	+	0.665230i
$717$			18.5372i			0.692285i
$718$	−19.0802			−0.712065
$719$			13.6649i			0.509614i	0.966992	+	0.254807i	$0.0820120\pi$
$719$			13.6649i			0.509614i	−0.966992	+	0.254807i	$0.917988\pi$
$720$	−0.314477	−	2.21384i	−0.0117199	−	0.0825051i
$721$	3.39375	−	3.39375i	0.126390	−	0.126390i
$722$	−11.0260			−0.410345
$723$	17.8952			0.665529
$724$	1.98719			0.0738533
$725$	−7.15504	−	3.93846i	−0.265731	−	0.146271i
$726$	6.60938	+	6.60938i	0.245297	+	0.245297i
$727$			6.24565i			0.231638i	0.993270	+	0.115819i	$0.0369493\pi$
$727$			6.24565i			0.231638i	−0.993270	+	0.115819i	$0.963051\pi$
$728$	1.93153	−	1.93153i	0.0715871	−	0.0715871i
$729$			1.00000i			0.0370370i
$730$	−24.8041	−	18.6337i	−0.918039	−	0.689665i
$731$		−	5.91743i		−	0.218864i
$732$		−	4.87737i		−	0.180273i
$733$	11.6047	−	11.6047i	0.428628	−	0.428628i	−0.459533	−	0.888161i	$-0.651983\pi$
$733$	11.6047	−	11.6047i	0.428628	−	0.428628i	0.888161	+	0.459533i	$0.151983\pi$
$734$	−13.0910	−	13.0910i	−0.483198	−	0.483198i
$735$	−12.0072	−	9.02024i	−0.442892	−	0.332717i
$736$	6.29757			0.232131
$737$	−6.84305	+	6.84305i	−0.252067	+	0.252067i
$738$			2.12896i			0.0783680i
$739$	26.9960			0.993065			0.496533	−	0.868018i	$-0.334606\pi$
$739$	26.9960			0.993065			0.496533	+	0.868018i	$0.334606\pi$
$740$	−12.4565	−	5.46213i	−0.457911	−	0.200792i
$741$	−28.0976			−1.03219
$742$			0.431598i			0.0158445i
$743$	−2.59470	+	2.59470i	−0.0951901	+	0.0951901i	−0.753098	−	0.657908i	$-0.771442\pi$
$743$	−2.59470	+	2.59470i	−0.0951901	+	0.0951901i	0.657908	+	0.753098i	$0.271442\pi$
$744$	10.0569			0.368705
$745$	−4.92265	−	34.6543i	−0.180352	−	1.26963i
$746$	−17.5157	−	17.5157i	−0.641294	−	0.641294i
$747$	11.5202	−	11.5202i	0.421501	−	0.421501i
$748$			2.97036i			0.108607i
$749$			1.06349i			0.0388591i
$750$	10.4554	+	3.96030i	0.381778	+	0.144610i
$751$			37.6977i			1.37561i	0.725897	+	0.687803i	$0.241425\pi$
$751$			37.6977i			1.37561i	−0.725897	+	0.687803i	$0.758575\pi$
$752$	2.64523	−	2.64523i	0.0964617	−	0.0964617i
$753$		−	1.17376i		−	0.0427741i
$754$	−5.92267	−	5.92267i	−0.215691	−	0.215691i
$755$	−0.977999	−	6.88488i	−0.0355930	−	0.250566i
$756$	0.532716			0.0193747
$757$	−27.3872			−0.995406			−0.497703	−	0.867347i	$-0.665823\pi$
$757$	−27.3872			−0.995406			−0.497703	+	0.867347i	$0.665823\pi$
$758$	−21.8739			−0.794494
$759$	5.72511	−	5.72511i	0.207808	−	0.207808i
$760$	9.79638	+	7.35940i	0.355352	+	0.266954i
$761$		−	41.7778i		−	1.51444i	−0.653157	−	0.757222i	$-0.726556\pi$
$761$		−	41.7778i		−	1.51444i	0.653157	−	0.757222i	$-0.273444\pi$
$762$	−15.0306			−0.544502
$763$		−	0.873100i		−	0.0316083i
$764$	4.41456	+	4.41456i	0.159713	+	0.159713i
$765$	0.726561	+	5.11482i	0.0262689	+	0.184927i
$766$	−5.61751			−0.202969
$767$	−5.35522	−	5.35522i	−0.193366	−	0.193366i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	27.6843	+	27.6843i	0.998322	+	0.998322i	0.999999	−	0.00167616i	$-0.000533537\pi$
$769$	27.6843	+	27.6843i	0.998322	+	0.998322i	−0.00167616	+	0.999999i	$0.500534\pi$
$770$	−0.919848	+	1.22444i	−0.0331490	+	0.0441259i
$771$	6.79698	−	6.79698i	0.244787	−	0.244787i
$772$			2.09366i			0.0753524i
$773$	19.1232	+	19.1232i	0.687812	+	0.687812i	0.961748	−	0.273936i	$-0.0883256\pi$
$773$	19.1232	+	19.1232i	0.687812	+	0.687812i	−0.273936	+	0.961748i	$0.588326\pi$
$774$		−	2.56124i		−	0.0920618i
$775$	−24.2482	+	44.0520i	−0.871022	+	1.58239i
$776$			8.07546i			0.289892i
$777$	1.70571	−	2.75511i	0.0611921	−	0.0988391i
$778$	5.37334	+	5.37334i	0.192644	+	0.192644i
$779$	−8.24898	−	8.24898i	−0.295551	−	0.295551i
$780$	9.16721	+	6.88674i	0.328239	+	0.246585i
$781$			5.63849i			0.201761i
$782$	−14.5498			−0.520299
$783$		−	1.63348i		−	0.0583757i
$784$			6.71621i			0.239865i
$785$	−23.7467	+	31.6102i	−0.847558	+	1.12822i
$786$	15.0691			0.537497
$787$	−5.34065	+	5.34065i	−0.190374	+	0.190374i	−0.795858	−	0.605484i	$-0.792980\pi$
$787$	−5.34065	+	5.34065i	−0.190374	+	0.190374i	0.605484	+	0.795858i	$0.292980\pi$
$788$	4.75052	−	4.75052i	0.169230	−	0.169230i
$789$			15.9116i			0.566468i
$790$	28.8227	+	21.6527i	1.02547	+	0.770368i
$791$	−1.04568	+	1.04568i	−0.0371800	+	0.0371800i
$792$			1.28566i			0.0456839i
$793$	17.6844	+	17.6844i	0.627992	+	0.627992i
$794$	−17.9874	+	17.9874i	−0.638349	+	0.638349i
$795$	−1.79362	+	0.254784i	−0.0636132	+	0.00903627i
$796$	−4.93690	−	4.93690i	−0.174984	−	0.174984i
$797$			25.8297i			0.914934i	0.889227	+	0.457467i	$0.151243\pi$
$797$			25.8297i			0.914934i	−0.889227	+	0.457467i	$0.848757\pi$
$798$	−2.06409	+	2.06409i	−0.0730682	+	0.0730682i
$799$	−6.11149	+	6.11149i	−0.216209	+	0.216209i
$800$	−1.39241	−	4.80221i	−0.0492290	−	0.169784i
$801$	8.09354	−	8.09354i	0.285971	−	0.285971i
$802$	−15.1996	−	15.1996i	−0.536718	−	0.536718i
$803$	12.6129	+	12.6129i	0.445101	+	0.445101i
$804$	7.52729			0.265467
$805$	−5.99772	−	4.50570i	−0.211392	−	0.158805i
$806$	−36.4645	+	36.4645i	−1.28441	+	1.28441i
$807$	−16.4693	−	16.4693i	−0.579748	−	0.579748i
$808$	15.8768			0.558545
$809$	−32.2660	−	32.2660i	−1.13441	−	1.13441i	−0.989435	−	0.144976i	$-0.953689\pi$
$809$	−32.2660	−	32.2660i	−1.13441	−	1.13441i	−0.144976	−	0.989435i	$-0.546311\pi$
$810$	0.314477	+	2.21384i	0.0110496	+	0.0777865i
$811$	−16.4212			−0.576628			−0.288314	−	0.957536i	$-0.593095\pi$
$811$	−16.4212			−0.576628			−0.288314	+	0.957536i	$0.593095\pi$
$812$	−0.870179			−0.0305373
$813$	−9.81285	+	9.81285i	−0.344152	+	0.344152i
$814$	6.64920	+	4.11658i	0.233054	+	0.144286i
$815$	−19.0677	+	2.70857i	−0.667912	+	0.0948770i
$816$	1.63368	−	1.63368i	0.0571904	−	0.0571904i
$817$	9.92392	+	9.92392i	0.347194	+	0.347194i
$818$	27.1312	−	27.1312i	0.948620	−	0.948620i
$819$	−1.93153	+	1.93153i	−0.0674930	+	0.0674930i
$820$	0.669508	+	4.71318i	0.0233802	+	0.164591i
$821$	−31.7926			−1.10957			−0.554784	−	0.831994i	$-0.687199\pi$
$821$	−31.7926			−1.10957			−0.554784	+	0.831994i	$0.687199\pi$
$822$	12.7109			0.443343
$823$	−25.1623	−	25.1623i	−0.877102	−	0.877102i	0.116132	−	0.993234i	$-0.462951\pi$
$823$	−25.1623	−	25.1623i	−0.877102	−	0.877102i	−0.993234	+	0.116132i	$0.962951\pi$
$824$		−	9.00947i		−	0.313860i
$825$	−5.63152	−	3.09985i	−0.196064	−	0.107923i
$826$	−0.786807			−0.0273765
$827$	13.8706			0.482329			0.241165	−	0.970484i	$-0.422471\pi$
$827$	13.8706			0.482329			0.241165	+	0.970484i	$0.422471\pi$
$828$	−6.29757			−0.218856
$829$	19.5830	+	19.5830i	0.680147	+	0.680147i	0.960033	−	0.279886i	$-0.0902967\pi$
$829$	19.5830	+	19.5830i	0.680147	+	0.680147i	−0.279886	+	0.960033i	$0.590297\pi$
$830$	21.8810	−	29.1267i	0.759502	−	1.01100i
$831$	−4.64924	−	4.64924i	−0.161280	−	0.161280i
$832$		−	5.12767i		−	0.177770i
$833$		−	15.5170i		−	0.537632i
$834$	−13.7544	−	13.7544i	−0.476277	−	0.476277i
$835$	−48.3499	+	6.86812i	−1.67322	+	0.237681i
$836$	−4.98150	−	4.98150i	−0.172289	−	0.172289i
$837$	−10.0569			−0.347619
$838$	−7.19965			−0.248708
$839$	29.1983			1.00804			0.504019	−	0.863692i	$-0.331854\pi$
$839$	29.1983			1.00804			0.504019	+	0.863692i	$0.331854\pi$
$840$	1.17935	−	0.167527i	0.0406915	−	0.00578023i
$841$		−	26.3318i		−	0.907992i
$842$	−6.17926	−	6.17926i	−0.212951	−	0.212951i
$843$	19.2196			0.661957
$844$	13.1658			0.453187
$845$	−29.4286	+	4.18033i	−1.01237	+	0.143808i
$846$	−2.64523	+	2.64523i	−0.0909449	+	0.0909449i
$847$	−3.52093	+	3.52093i	−0.120980	+	0.120980i
$848$	0.572887	+	0.572887i	0.0196730	+	0.0196730i
$849$	−6.04565	+	6.04565i	−0.207486	+	0.207486i
$850$	3.21699	+	11.0949i	0.110342	+	0.380553i
$851$	−20.1643	+	32.5699i	−0.691223	+	1.11648i
$852$	3.10114	−	3.10114i	0.106243	−	0.106243i
$853$	6.30510			0.215883			0.107941	−	0.994157i	$-0.465574\pi$
$853$	6.30510			0.215883			0.107941	+	0.994157i	$0.465574\pi$
$854$	2.59825			0.0889104
$855$	−9.79638	−	7.35940i	−0.335029	−	0.251686i
$856$	1.41163	+	1.41163i	0.0482487	+	0.0482487i
$857$	−5.70445			−0.194860			−0.0974302	−	0.995242i	$-0.531062\pi$
$857$	−5.70445			−0.194860			−0.0974302	+	0.995242i	$0.531062\pi$
$858$	−4.66156	−	4.66156i	−0.159143	−	0.159143i
$859$	−9.67146	+	9.67146i	−0.329986	+	0.329986i	−0.852581	−	0.522595i	$-0.824964\pi$
$859$	−9.67146	+	9.67146i	−0.329986	+	0.329986i	0.522595	+	0.852581i	$0.324964\pi$
$860$	−0.805450	−	5.67018i	−0.0274656	−	0.193351i
$861$	−1.13413			−0.0386510
$862$	−19.0871	−	19.0871i	−0.650110	−	0.650110i
$863$	−11.4917	−	11.4917i	−0.391181	−	0.391181i	0.483928	−	0.875108i	$-0.339210\pi$
$863$	−11.4917	−	11.4917i	−0.391181	−	0.391181i	−0.875108	+	0.483928i	$0.839210\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	2.51434	−	3.34694i	0.0854903	−	0.113799i
$866$	−27.0193	+	27.0193i	−0.918154	+	0.918154i
$867$	8.24638	−	8.24638i	0.280062	−	0.280062i
$868$			5.35750i			0.181845i
$869$	−14.6565	−	14.6565i	−0.497186	−	0.497186i
$870$	−0.513691	−	3.61626i	−0.0174157	−	0.122603i
$871$	−27.2925	+	27.2925i	−0.924771	+	0.924771i
$872$	−1.15892	−	1.15892i	−0.0392460	−	0.0392460i
$873$		−	8.07546i		−	0.273313i
$874$	24.4009	−	24.4009i	0.825374	−	0.825374i
$875$	−2.10971	+	5.56978i	−0.0713214	+	0.188293i
$876$		−	13.8741i		−	0.468763i
$877$	9.10608	−	9.10608i	0.307490	−	0.307490i	−0.536445	−	0.843935i	$-0.680233\pi$
$877$	9.10608	−	9.10608i	0.307490	−	0.307490i	0.843935	+	0.536445i	$0.180233\pi$
$878$	8.21948	−	8.21948i	0.277394	−	0.277394i
$879$	−10.7700			−0.363263
$880$	0.404311	+	2.84625i	0.0136293	+	0.0959471i
$881$			2.47471i			0.0833752i	0.999131	+	0.0416876i	$0.0132734\pi$
$881$			2.47471i			0.0833752i	−0.999131	+	0.0416876i	$0.986727\pi$
$882$		−	6.71621i		−	0.226147i
$883$	42.6117			1.43400			0.716999	−	0.697075i	$-0.245515\pi$
$883$	42.6117			1.43400			0.716999	+	0.697075i	$0.245515\pi$
$884$			11.8469i			0.398453i
$885$	−0.464474	−	3.26979i	−0.0156131	−	0.109913i
$886$	7.35664	+	7.35664i	0.247151	+	0.247151i
$887$	14.4378	+	14.4378i	0.484774	+	0.484774i	0.906652	−	0.421878i	$-0.138629\pi$
$887$	14.4378	+	14.4378i	0.484774	+	0.484774i	−0.421878	+	0.906652i	$0.638629\pi$
$888$	−1.39293	−	5.92113i	−0.0467437	−	0.198700i
$889$		−	8.00705i		−	0.268548i
$890$	15.3726	−	20.4631i	0.515291	−	0.685924i
$891$		−	1.28566i		−	0.0430712i
$892$	13.0670	+	13.0670i	0.437516	+	0.437516i
$893$		−	20.4987i		−	0.685964i
$894$	11.0687	−	11.0687i	0.370191	−	0.370191i
$895$	−45.0049	−	33.8094i	−1.50435	−	1.13012i
$896$	−0.376687	−	0.376687i	−0.0125842	−	0.0125842i
$897$	22.8338	−	22.8338i	0.762398	−	0.762398i
$898$	−15.3192	−	15.3192i	−0.511207	−	0.511207i
$899$	16.4278			0.547897
$900$	1.39241	+	4.80221i	0.0464135	+	0.160074i
$901$	−1.32359	−	1.32359i	−0.0440950	−	0.0440950i
$902$		−	2.73711i		−	0.0911359i
$903$	1.36441			0.0454048
$904$			2.77598i			0.0923277i
$905$	−4.39933	+	0.624925i	−0.146239	+	0.0207732i
$906$	2.19905	−	2.19905i	0.0730584	−	0.0730584i
$907$	−20.9996			−0.697281			−0.348641	−	0.937256i	$-0.613357\pi$
$907$	−20.9996			−0.697281			−0.348641	+	0.937256i	$0.613357\pi$
$908$	−16.0865			−0.533848
$909$	−15.8768			−0.526601
$910$	−3.66868	+	4.88352i	−0.121615	+	0.161887i
$911$	2.09529	+	2.09529i	0.0694199	+	0.0694199i	0.740964	−	0.671544i	$-0.234369\pi$
$911$	2.09529	+	2.09529i	0.0694199	+	0.0694199i	−0.671544	+	0.740964i	$0.734369\pi$
$912$			5.47960i			0.181448i
$913$	−14.8110	+	14.8110i	−0.490174	+	0.490174i
$914$		−	11.9041i		−	0.393754i
$915$	1.53382	+	10.7977i	0.0507066	+	0.356962i
$916$			6.71533i			0.221881i
$917$			8.02756i			0.265093i
$918$	−1.63368	+	1.63368i	−0.0539196	+	0.0539196i
$919$	−26.2479	−	26.2479i	−0.865840	−	0.865840i	0.126169	−	0.992009i	$-0.459732\pi$
$919$	−26.2479	−	26.2479i	−0.865840	−	0.865840i	−0.992009	+	0.126169i	$0.959732\pi$
$920$	−13.9418	+	1.98044i	−0.459649	+	0.0652932i
$921$	−27.8219			−0.916763
$922$	−21.6193	+	21.6193i	−0.711994	+	0.711994i
$923$			22.4883i			0.740211i
$924$	−0.684892			−0.0225313
$925$	29.2945	+	8.17501i	0.963198	+	0.268793i
$926$	7.74140			0.254398
$927$			9.00947i			0.295910i
$928$	−1.15504	+	1.15504i	−0.0379161	+	0.0379161i
$929$	36.8972			1.21056			0.605279	−	0.796014i	$-0.293062\pi$
$929$	36.8972			1.21056			0.605279	+	0.796014i	$0.293062\pi$
$930$	−22.2645	+	3.16268i	−0.730082	+	0.103708i
$931$	26.0230	+	26.0230i	0.852871	+	0.852871i
$932$	−4.61749	+	4.61749i	−0.151251	+	0.151251i
$933$		−	5.45953i		−	0.178737i
$934$		−	40.6171i		−	1.32903i
$935$	−0.934111	−	6.57592i	−0.0305487	−	0.215056i
$936$			5.12767i			0.167603i
$937$	−6.68552	+	6.68552i	−0.218406	+	0.218406i	−0.807827	−	0.589420i	$-0.799356\pi$
$937$	−6.68552	+	6.68552i	−0.218406	+	0.218406i	0.589420	+	0.807827i	$0.299356\pi$
$938$			4.00991i			0.130928i
$939$	−13.4327	−	13.4327i	−0.438361	−	0.438361i
$940$	−5.02426	+	6.68799i	−0.163873	+	0.218138i
$941$	−5.71005			−0.186142			−0.0930711	−	0.995659i	$-0.529668\pi$
$941$	−5.71005			−0.186142			−0.0930711	+	0.995659i	$0.529668\pi$
$942$	−17.6811			−0.576083
$943$	13.4073			0.436600
$944$	−1.04438	+	1.04438i	−0.0339916	+	0.0339916i
$945$	−1.17935	+	0.167527i	−0.0383643	+	0.00544965i
$946$			3.29288i			0.107061i
$947$	−31.5411			−1.02495			−0.512474	−	0.858703i	$-0.671271\pi$
$947$	−31.5411			−1.02495			−0.512474	+	0.858703i	$0.671271\pi$
$948$			16.1220i			0.523617i
$949$	50.3049	+	50.3049i	1.63297	+	1.63297i
$950$	−24.0020	−	13.2118i	−0.778729	−	0.428648i
$951$	25.1947			0.816993
$952$	0.870290	+	0.870290i	0.0282063	+	0.0282063i
$953$	−41.8752	+	41.8752i	−1.35647	+	1.35647i	−0.478245	+	0.878227i	$0.658727\pi$
$953$	−41.8752	+	41.8752i	−1.35647	+	1.35647i	−0.878227	+	0.478245i	$0.841273\pi$
$954$	−0.572887	−	0.572887i	−0.0185479	−	0.0185479i
$955$	−11.1614	−	8.38487i	−0.361175	−	0.271328i
$956$	−13.1078	+	13.1078i	−0.423936	+	0.423936i
$957$			2.10009i			0.0678864i
$958$	−4.76750	−	4.76750i	−0.154031	−	0.154031i
$959$			6.77129i			0.218656i
$960$	1.34306	−	1.78779i	0.0433469	−	0.0577008i
$961$		−	70.1421i		−	2.26265i
$962$	26.5194	+	16.4184i	0.855019	+	0.529350i
$963$	−1.41163	−	1.41163i	−0.0454893	−	0.0454893i
$964$	12.6538	+	12.6538i	0.407552	+	0.407552i
$965$	−0.658407	−	4.63503i	−0.0211949	−	0.149207i
$966$		−	3.35482i		−	0.107939i
$967$	20.2774			0.652076			0.326038	−	0.945357i	$-0.394286\pi$
$967$	20.2774			0.652076			0.326038	+	0.945357i	$0.394286\pi$
$968$			9.34708i			0.300426i
$969$		−	12.6599i		−	0.406696i
$970$	−2.53955	−	17.8778i	−0.0815399	−	0.574022i
$971$	16.4316			0.527316			0.263658	−	0.964616i	$-0.415071\pi$
$971$	16.4316			0.527316			0.263658	+	0.964616i	$0.415071\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	7.32722	−	7.32722i	0.234900	−	0.234900i
$974$			16.5284i			0.529603i
$975$	−22.4605	−	12.3633i	−0.719311	−	0.395942i
$976$	3.44882	−	3.44882i	0.110394	−	0.110394i
$977$		−	45.6145i		−	1.45934i	−0.683801	−	0.729669i	$-0.739674\pi$
$977$		−	45.6145i		−	1.45934i	0.683801	−	0.729669i	$-0.260326\pi$
$978$	−6.09026	−	6.09026i	−0.194745	−	0.194745i
$979$	−10.4055	+	10.4055i	−0.332563	+	0.332563i
$980$	−2.11209	−	14.8686i	−0.0674684	−	0.474962i
$981$	1.15892	+	1.15892i	0.0370014	+	0.0370014i
$982$			11.4600i			0.365705i
$983$	18.8451	−	18.8451i	0.601066	−	0.601066i	−0.339530	−	0.940595i	$-0.610268\pi$
$983$	18.8451	−	18.8451i	0.601066	−	0.601066i	0.940595	+	0.339530i	$0.110268\pi$
$984$	−1.50540	+	1.50540i	−0.0479904	+	0.0479904i
$985$	−9.02298	+	12.0108i	−0.287496	+	0.382697i
$986$	2.66858	−	2.66858i	0.0849850	−	0.0849850i
$987$	−1.40916	−	1.40916i	−0.0448540	−	0.0448540i
$988$	−19.8680	−	19.8680i	−0.632084	−	0.632084i
$989$	−16.1296			−0.512890
$990$	−0.404311	−	2.84625i	−0.0128498	−	0.0904598i
$991$	28.3442	−	28.3442i	0.900383	−	0.900383i	−0.0950859	−	0.995469i	$-0.530313\pi$
$991$	28.3442	−	28.3442i	0.900383	−	0.900383i	0.995469	+	0.0950859i	$0.0303126\pi$
$992$	7.11133	+	7.11133i	0.225785	+	0.225785i
$993$	1.57774			0.0500682
$994$	1.65203	+	1.65203i	0.0523992	+	0.0523992i
$995$	12.4821	+	9.37699i	0.395708	+	0.297270i
$996$	16.2920			0.516232
$997$	−34.7231			−1.09969			−0.549846	−	0.835266i	$-0.685313\pi$
$997$	−34.7231			−1.09969			−0.549846	+	0.835266i	$0.685313\pi$
$998$	11.0278	−	11.0278i	0.349080	−	0.349080i
$999$	1.39293	+	5.92113i	0.0440704	+	0.187336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.43.6	✓	40
5.2	odd	4		1110.2.o.b.487.15	yes	40
37.31	odd	4		1110.2.o.b.253.15	yes	40
185.142	even	4	inner	1110.2.l.b.697.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.6	✓	40	1.1	even	1	trivial
1110.2.l.b.697.6	yes	40	185.142	even	4	inner
1110.2.o.b.253.15	yes	40	37.31	odd	4
1110.2.o.b.487.15	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.21384 - 0.314477i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.376687 + 0.376687i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.21384 - 0.314477i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.376687 + 0.376687i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-0.314477 - 2.21384i) q^{10} +1.28566i q^{11} +(0.707107 - 0.707107i) q^{12} +5.12767i q^{13} +(0.376687 + 0.376687i) q^{14} +(-1.34306 + 1.78779i) q^{15} +1.00000 q^{16} -2.31038 q^{17} -1.00000 q^{18} +(3.87466 - 3.87466i) q^{19} +(-2.21384 + 0.314477i) q^{20} -0.532716i q^{21} +1.28566 q^{22} +6.29757i q^{23} +(-0.707107 - 0.707107i) q^{24} +(4.80221 - 1.39241i) q^{25} +5.12767 q^{26} +(0.707107 + 0.707107i) q^{27} +(0.376687 - 0.376687i) q^{28} +(-1.15504 - 1.15504i) q^{29} +(1.78779 + 1.34306i) q^{30} +(-7.11133 + 7.11133i) q^{31} -1.00000i q^{32} +(-0.909099 - 0.909099i) q^{33} +2.31038i q^{34} +(-0.715467 + 0.952386i) q^{35} +1.00000i q^{36} +(5.17182 + 3.20192i) q^{37} +(-3.87466 - 3.87466i) q^{38} +(-3.62581 - 3.62581i) q^{39} +(0.314477 + 2.21384i) q^{40} -2.12896i q^{41} -0.532716 q^{42} +2.56124i q^{43} -1.28566i q^{44} +(-0.314477 - 2.21384i) q^{45} +6.29757 q^{46} +(2.64523 - 2.64523i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.71621i q^{49} +(-1.39241 - 4.80221i) q^{50} +(1.63368 - 1.63368i) q^{51} -5.12767i q^{52} +(0.572887 + 0.572887i) q^{53} +(0.707107 - 0.707107i) q^{54} +(0.404311 + 2.84625i) q^{55} +(-0.376687 - 0.376687i) q^{56} +5.47960i q^{57} +(-1.15504 + 1.15504i) q^{58} +(-1.04438 + 1.04438i) q^{59} +(1.34306 - 1.78779i) q^{60} +(3.44882 - 3.44882i) q^{61} +(7.11133 + 7.11133i) q^{62} +(0.376687 + 0.376687i) q^{63} -1.00000 q^{64} +(1.61253 + 11.3519i) q^{65} +(-0.909099 + 0.909099i) q^{66} +(5.32260 + 5.32260i) q^{67} +2.31038 q^{68} +(-4.45305 - 4.45305i) q^{69} +(0.952386 + 0.715467i) q^{70} +4.38568 q^{71} +1.00000 q^{72} +(9.81049 - 9.81049i) q^{73} +(3.20192 - 5.17182i) q^{74} +(-2.41109 + 4.38025i) q^{75} +(-3.87466 + 3.87466i) q^{76} +(-0.484292 - 0.484292i) q^{77} +(-3.62581 + 3.62581i) q^{78} +(-11.4000 + 11.4000i) q^{79} +(2.21384 - 0.314477i) q^{80} -1.00000 q^{81} -2.12896 q^{82} +(11.5202 + 11.5202i) q^{83} +0.532716i q^{84} +(-5.11482 + 0.726561i) q^{85} +2.56124 q^{86} +1.63348 q^{87} -1.28566 q^{88} +(8.09354 + 8.09354i) q^{89} +(-2.21384 + 0.314477i) q^{90} +(-1.93153 - 1.93153i) q^{91} -6.29757i q^{92} -10.0569i q^{93} +(-2.64523 - 2.64523i) q^{94} +(7.35940 - 9.79638i) q^{95} +(0.707107 + 0.707107i) q^{96} +8.07546 q^{97} +6.71621 q^{98} +1.28566 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

Related objects

Downloads

Learn more