LMFDB - Embedded newform 1110.2.l.b.697.10

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			697.10
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.b.43.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07345 - 0.837144i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.93723 - 2.93723i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07345 - 0.837144i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.93723 - 2.93723i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(0.837144 - 2.07345i) q^{10} +1.12978i q^{11} +(0.707107 + 0.707107i) q^{12} +2.10223i q^{13} +(2.93723 - 2.93723i) q^{14} +(0.874200 + 2.05810i) q^{15} +1.00000 q^{16} -3.81919 q^{17} -1.00000 q^{18} +(-0.0424776 - 0.0424776i) q^{19} +(2.07345 + 0.837144i) q^{20} +4.15387i q^{21} -1.12978 q^{22} -7.44945i q^{23} +(-0.707107 + 0.707107i) q^{24} +(3.59838 + 3.47155i) q^{25} -2.10223 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.93723 + 2.93723i) q^{28} +(1.00026 - 1.00026i) q^{29} +(-2.05810 + 0.874200i) q^{30} +(5.55293 + 5.55293i) q^{31} +1.00000i q^{32} +(0.798875 - 0.798875i) q^{33} -3.81919i q^{34} +(3.63131 + 8.54909i) q^{35} -1.00000i q^{36} +(5.91653 + 1.41231i) q^{37} +(0.0424776 - 0.0424776i) q^{38} +(1.48650 - 1.48650i) q^{39} +(-0.837144 + 2.07345i) q^{40} +7.31338i q^{41} -4.15387 q^{42} +6.59679i q^{43} -1.12978i q^{44} +(0.837144 - 2.07345i) q^{45} +7.44945 q^{46} +(3.52289 + 3.52289i) q^{47} +(-0.707107 - 0.707107i) q^{48} +10.2547i q^{49} +(-3.47155 + 3.59838i) q^{50} +(2.70058 + 2.70058i) q^{51} -2.10223i q^{52} +(-6.43055 + 6.43055i) q^{53} +(0.707107 + 0.707107i) q^{54} +(0.945788 - 2.34254i) q^{55} +(-2.93723 + 2.93723i) q^{56} +0.0600724i q^{57} +(1.00026 + 1.00026i) q^{58} +(1.53440 + 1.53440i) q^{59} +(-0.874200 - 2.05810i) q^{60} +(3.13059 + 3.13059i) q^{61} +(-5.55293 + 5.55293i) q^{62} +(2.93723 - 2.93723i) q^{63} -1.00000 q^{64} +(1.75987 - 4.35887i) q^{65} +(0.798875 + 0.798875i) q^{66} +(2.59186 - 2.59186i) q^{67} +3.81919 q^{68} +(-5.26755 + 5.26755i) q^{69} +(-8.54909 + 3.63131i) q^{70} +2.10896 q^{71} +1.00000 q^{72} +(-6.95418 - 6.95418i) q^{73} +(-1.41231 + 5.91653i) q^{74} +(-0.0896820 - 4.99920i) q^{75} +(0.0424776 + 0.0424776i) q^{76} +(3.31842 - 3.31842i) q^{77} +(1.48650 + 1.48650i) q^{78} +(-8.44853 - 8.44853i) q^{79} +(-2.07345 - 0.837144i) q^{80} -1.00000 q^{81} -7.31338 q^{82} +(-2.80605 + 2.80605i) q^{83} -4.15387i q^{84} +(7.91890 + 3.19722i) q^{85} -6.59679 q^{86} -1.41459 q^{87} +1.12978 q^{88} +(-8.09450 + 8.09450i) q^{89} +(2.07345 + 0.837144i) q^{90} +(6.17474 - 6.17474i) q^{91} +7.44945i q^{92} -7.85303i q^{93} +(-3.52289 + 3.52289i) q^{94} +(0.0525152 + 0.123635i) q^{95} +(0.707107 - 0.707107i) q^{96} +10.4722 q^{97} -10.2547 q^{98} -1.12978 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$5$	−2.07345	−	0.837144i	−0.927274	−	0.374382i
$5$	−2.07345	−	0.837144i	−0.927274	−	0.374382i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−2.93723	−	2.93723i	−1.11017	−	1.11017i	−0.993127	−	0.117042i	$-0.962659\pi$
$7$	−2.93723	−	2.93723i	−1.11017	−	1.11017i	−0.117042	−	0.993127i	$-0.537341\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	0.837144	−	2.07345i	0.264728	−	0.655682i
$11$			1.12978i			0.340641i	0.985389	+	0.170321i	$0.0544803\pi$
$11$			1.12978i			0.340641i	−0.985389	+	0.170321i	$0.945520\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$			2.10223i			0.583054i	0.956563	+	0.291527i	$0.0941633\pi$
$13$			2.10223i			0.583054i	−0.956563	+	0.291527i	$0.905837\pi$
$14$	2.93723	−	2.93723i	0.785008	−	0.785008i
$15$	0.874200	+	2.05810i	0.225717	+	0.531399i
$16$	1.00000			0.250000
$17$	−3.81919			−0.926291			−0.463145	−	0.886282i	$-0.653279\pi$
$17$	−3.81919			−0.926291			−0.463145	+	0.886282i	$0.653279\pi$
$18$	−1.00000			−0.235702
$19$	−0.0424776	−	0.0424776i	−0.00974502	−	0.00974502i	0.702217	−	0.711963i	$-0.252193\pi$
$19$	−0.0424776	−	0.0424776i	−0.00974502	−	0.00974502i	−0.711963	+	0.702217i	$0.752193\pi$
$20$	2.07345	+	0.837144i	0.463637	+	0.187191i
$21$			4.15387i			0.906450i
$22$	−1.12978			−0.240870
$23$		−	7.44945i		−	1.55332i	−0.629922	−	0.776659i	$-0.716913\pi$
$23$		−	7.44945i		−	1.55332i	0.629922	−	0.776659i	$-0.283087\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	3.59838	+	3.47155i	0.719676	+	0.694310i
$26$	−2.10223			−0.412281
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.93723	+	2.93723i	0.555085	+	0.555085i
$29$	1.00026	−	1.00026i	0.185744	−	0.185744i	−0.608109	−	0.793854i	$-0.708072\pi$
$29$	1.00026	−	1.00026i	0.185744	−	0.185744i	0.793854	+	0.608109i	$0.208072\pi$
$30$	−2.05810	+	0.874200i	−0.375756	+	0.159606i
$31$	5.55293	+	5.55293i	0.997336	+	0.997336i	0.999996	−	0.00266011i	$-0.000846741\pi$
$31$	5.55293	+	5.55293i	0.997336	+	0.997336i	−0.00266011	+	0.999996i	$0.500847\pi$
$32$			1.00000i			0.176777i
$33$	0.798875	−	0.798875i	0.139066	−	0.139066i
$34$		−	3.81919i		−	0.654986i
$35$	3.63131	+	8.54909i	0.613804	+	1.44506i
$36$		−	1.00000i		−	0.166667i
$37$	5.91653	+	1.41231i	0.972672	+	0.232183i
$37$	5.91653	+	1.41231i	0.972672	+	0.232183i
$38$	0.0424776	−	0.0424776i	0.00689077	−	0.00689077i
$39$	1.48650	−	1.48650i	0.238031	−	0.238031i
$40$	−0.837144	+	2.07345i	−0.132364	+	0.327841i
$41$			7.31338i			1.14216i	0.820895	+	0.571079i	$0.193475\pi$
$41$			7.31338i			1.14216i	−0.820895	+	0.571079i	$0.806525\pi$
$42$	−4.15387			−0.640957
$43$			6.59679i			1.00600i	0.864286	+	0.503001i	$0.167771\pi$
$43$			6.59679i			1.00600i	−0.864286	+	0.503001i	$0.832229\pi$
$44$		−	1.12978i		−	0.170321i
$45$	0.837144	−	2.07345i	0.124794	−	0.309091i
$46$	7.44945			1.09836
$47$	3.52289	+	3.52289i	0.513867	+	0.513867i	0.915709	−	0.401842i	$-0.131630\pi$
$47$	3.52289	+	3.52289i	0.513867	+	0.513867i	−0.401842	+	0.915709i	$0.631630\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			10.2547i			1.46495i
$50$	−3.47155	+	3.59838i	−0.490951	+	0.508888i
$51$	2.70058	+	2.70058i	0.378157	+	0.378157i
$52$		−	2.10223i		−	0.291527i
$53$	−6.43055	+	6.43055i	−0.883304	+	0.883304i	−0.993869	−	0.110565i	$-0.964734\pi$
$53$	−6.43055	+	6.43055i	−0.883304	+	0.883304i	0.110565	+	0.993869i	$0.464734\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	0.945788	−	2.34254i	0.127530	−	0.315868i
$56$	−2.93723	+	2.93723i	−0.392504	+	0.392504i
$57$			0.0600724i			0.00795678i
$58$	1.00026	+	1.00026i	0.131341	+	0.131341i
$59$	1.53440	+	1.53440i	0.199762	+	0.199762i	0.799898	−	0.600136i	$-0.204887\pi$
$59$	1.53440	+	1.53440i	0.199762	+	0.199762i	−0.600136	+	0.799898i	$0.704887\pi$
$60$	−0.874200	−	2.05810i	−0.112859	−	0.265700i
$61$	3.13059	+	3.13059i	0.400830	+	0.400830i	0.878526	−	0.477695i	$-0.158528\pi$
$61$	3.13059	+	3.13059i	0.400830	+	0.400830i	−0.477695	+	0.878526i	$0.658528\pi$
$62$	−5.55293	+	5.55293i	−0.705223	+	0.705223i
$63$	2.93723	−	2.93723i	0.370056	−	0.370056i
$64$	−1.00000			−0.125000
$65$	1.75987	−	4.35887i	0.218285	−	0.540651i
$66$	0.798875	+	0.798875i	0.0983347	+	0.0983347i
$67$	2.59186	−	2.59186i	0.316646	−	0.316646i	−0.530832	−	0.847477i	$-0.678120\pi$
$67$	2.59186	−	2.59186i	0.316646	−	0.316646i	0.847477	+	0.530832i	$0.178120\pi$
$68$	3.81919			0.463145
$69$	−5.26755	+	5.26755i	−0.634139	+	0.634139i
$70$	−8.54909	+	3.63131i	−1.02181	+	0.434025i
$71$	2.10896			0.250287			0.125144	−	0.992139i	$-0.460061\pi$
$71$	2.10896			0.250287			0.125144	+	0.992139i	$0.460061\pi$
$72$	1.00000			0.117851
$73$	−6.95418	−	6.95418i	−0.813925	−	0.813925i	0.171295	−	0.985220i	$-0.445205\pi$
$73$	−6.95418	−	6.95418i	−0.813925	−	0.813925i	−0.985220	+	0.171295i	$0.945205\pi$
$74$	−1.41231	+	5.91653i	−0.164178	+	0.687783i
$75$	−0.0896820	−	4.99920i	−0.0103556	−	0.577257i
$76$	0.0424776	+	0.0424776i	0.00487251	+	0.00487251i
$77$	3.31842	−	3.31842i	0.378170	−	0.378170i
$78$	1.48650	+	1.48650i	0.168313	+	0.168313i
$79$	−8.44853	−	8.44853i	−0.950534	−	0.950534i	0.0482988	−	0.998833i	$-0.484620\pi$
$79$	−8.44853	−	8.44853i	−0.950534	−	0.950534i	−0.998833	+	0.0482988i	$0.984620\pi$
$80$	−2.07345	−	0.837144i	−0.231819	−	0.0935955i
$81$	−1.00000			−0.111111
$82$	−7.31338			−0.807627
$83$	−2.80605	+	2.80605i	−0.308003	+	0.308003i	−0.844135	−	0.536131i	$-0.819885\pi$
$83$	−2.80605	+	2.80605i	−0.308003	+	0.308003i	0.536131	+	0.844135i	$0.319885\pi$
$84$		−	4.15387i		−	0.453225i
$85$	7.91890	+	3.19722i	0.858926	+	0.346787i
$86$	−6.59679			−0.711350
$87$	−1.41459			−0.151660
$88$	1.12978			0.120435
$89$	−8.09450	+	8.09450i	−0.858015	+	0.858015i	−0.991104	−	0.133089i	$-0.957511\pi$
$89$	−8.09450	+	8.09450i	−0.858015	+	0.858015i	0.133089	+	0.991104i	$0.457511\pi$
$90$	2.07345	+	0.837144i	0.218561	+	0.0882427i
$91$	6.17474	−	6.17474i	0.647289	−	0.647289i
$92$			7.44945i			0.776659i
$93$		−	7.85303i		−	0.814322i
$94$	−3.52289	+	3.52289i	−0.363359	+	0.363359i
$95$	0.0525152	+	0.123635i	0.00538795	+	0.0126847i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	10.4722			1.06329			0.531646	−	0.846966i	$-0.321574\pi$
$97$	10.4722			1.06329			0.531646	+	0.846966i	$0.321574\pi$
$98$	−10.2547			−1.03588
$99$	−1.12978			−0.113547
$100$	−3.59838	−	3.47155i	−0.359838	−	0.347155i
$101$		−	6.85371i		−	0.681970i	−0.940069	−	0.340985i	$-0.889240\pi$
$101$		−	6.85371i		−	0.681970i	0.940069	−	0.340985i	$-0.110760\pi$
$102$	−2.70058	+	2.70058i	−0.267397	+	0.267397i
$103$	11.0473			1.08852			0.544262	−	0.838915i	$-0.316810\pi$
$103$	11.0473			1.08852			0.544262	+	0.838915i	$0.316810\pi$
$104$	2.10223			0.206141
$105$	3.47739	−	8.61284i	0.339359	−	0.840528i
$106$	−6.43055	−	6.43055i	−0.624591	−	0.624591i
$107$	2.67190	+	2.67190i	0.258303	+	0.258303i	0.824363	−	0.566061i	$-0.191533\pi$
$107$	2.67190	+	2.67190i	0.258303	+	0.258303i	−0.566061	+	0.824363i	$0.691533\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−1.57675	−	1.57675i	−0.151025	−	0.151025i	0.627551	−	0.778576i	$-0.284057\pi$
$109$	−1.57675	−	1.57675i	−0.151025	−	0.151025i	−0.778576	+	0.627551i	$0.784057\pi$
$110$	2.34254	+	0.945788i	0.223352	+	0.0901773i
$111$	−3.18497	−	5.18228i	−0.302304	−	0.491880i
$112$	−2.93723	−	2.93723i	−0.277542	−	0.277542i
$113$	−13.9588			−1.31314			−0.656568	−	0.754267i	$-0.727992\pi$
$113$	−13.9588			−1.31314			−0.656568	+	0.754267i	$0.727992\pi$
$114$	−0.0600724			−0.00562629
$115$	−6.23626	+	15.4460i	−0.581534	+	1.44035i
$116$	−1.00026	+	1.00026i	−0.0928722	+	0.0928722i
$117$	−2.10223			−0.194351
$118$	−1.53440	+	1.53440i	−0.141253	+	0.141253i
$119$	11.2179	+	11.2179i	1.02834	+	1.02834i
$120$	2.05810	−	0.874200i	0.187878	−	0.0798031i
$121$	9.72360			0.883964
$122$	−3.13059	+	3.13059i	−0.283430	+	0.283430i
$123$	5.17134	−	5.17134i	0.466284	−	0.466284i
$124$	−5.55293	−	5.55293i	−0.498668	−	0.498668i
$125$	−4.55487	−	10.2104i	−0.407400	−	0.913250i
$126$	2.93723	+	2.93723i	0.261669	+	0.261669i
$127$	8.02624	+	8.02624i	0.712214	+	0.712214i	0.966998	−	0.254784i	$-0.0820044\pi$
$127$	8.02624	+	8.02624i	0.712214	+	0.712214i	−0.254784	+	0.966998i	$0.582004\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.66464	−	4.66464i	0.410698	−	0.410698i
$130$	4.35887	+	1.75987i	0.382298	+	0.154351i
$131$	4.61659	+	4.61659i	0.403353	+	0.403353i	0.879413	−	0.476060i	$-0.157935\pi$
$131$	4.61659	+	4.61659i	0.403353	+	0.403353i	−0.476060	+	0.879413i	$0.657935\pi$
$132$	−0.798875	+	0.798875i	−0.0695331	+	0.0695331i
$133$			0.249533i			0.0216373i
$134$	2.59186	+	2.59186i	0.223902	+	0.223902i
$135$	−2.05810	+	0.874200i	−0.177133	+	0.0752391i
$136$			3.81919i			0.327493i
$137$	−12.7568	−	12.7568i	−1.08989	−	1.08989i	−0.995539	−	0.0943459i	$-0.969924\pi$
$137$	−12.7568	−	12.7568i	−1.08989	−	1.08989i	−0.0943459	−	0.995539i	$-0.530076\pi$
$138$	−5.26755	−	5.26755i	−0.448404	−	0.448404i
$139$	−10.7050			−0.907987			−0.453993	−	0.891005i	$-0.650001\pi$
$139$	−10.7050			−0.907987			−0.453993	+	0.891005i	$0.650001\pi$
$140$	−3.63131	−	8.54909i	−0.306902	−	0.722530i
$141$		−	4.98212i		−	0.419570i
$142$			2.10896i			0.176980i
$143$	−2.37506			−0.198612
$144$			1.00000i			0.0833333i
$145$	−2.91136	+	1.23663i	−0.241776	+	0.102697i
$146$	6.95418	−	6.95418i	0.575532	−	0.575532i
$147$	7.25114	−	7.25114i	0.598064	−	0.598064i
$148$	−5.91653	−	1.41231i	−0.486336	−	0.116091i
$149$			21.7914i			1.78522i	0.450832	+	0.892609i	$0.351127\pi$
$149$			21.7914i			1.78522i	−0.450832	+	0.892609i	$0.648873\pi$
$150$	4.99920	−	0.0896820i	0.408183	−	0.00732250i
$151$		−	1.57215i		−	0.127940i	−0.997952	−	0.0639698i	$-0.979624\pi$
$151$		−	1.57215i		−	0.127940i	0.997952	−	0.0639698i	$-0.0203761\pi$
$152$	−0.0424776	+	0.0424776i	−0.00344539	+	0.00344539i
$153$		−	3.81919i		−	0.308764i
$154$	3.31842	+	3.31842i	0.267406	+	0.267406i
$155$	−6.86512	−	16.1623i	−0.551420	−	1.29819i
$156$	−1.48650	+	1.48650i	−0.119015	+	0.119015i
$157$	0.999991	+	0.999991i	0.0798079	+	0.0798079i	0.745884	−	0.666076i	$-0.232027\pi$
$157$	0.999991	+	0.999991i	0.0798079	+	0.0798079i	−0.666076	+	0.745884i	$0.732027\pi$
$158$	8.44853	−	8.44853i	0.672129	−	0.672129i
$159$	9.09418			0.721215
$160$	0.837144	−	2.07345i	0.0661820	−	0.163921i
$161$	−21.8808	+	21.8808i	−1.72445	+	1.72445i
$162$		−	1.00000i		−	0.0785674i
$163$	19.9337			1.56133			0.780664	−	0.624952i	$-0.214881\pi$
$163$	19.9337			1.56133			0.780664	+	0.624952i	$0.214881\pi$
$164$		−	7.31338i		−	0.571079i
$165$	−2.32520	+	0.987653i	−0.181016	+	0.0768887i
$166$	−2.80605	−	2.80605i	−0.217791	−	0.217791i
$167$	−2.23975			−0.173317			−0.0866586	−	0.996238i	$-0.527619\pi$
$167$	−2.23975			−0.173317			−0.0866586	+	0.996238i	$0.527619\pi$
$168$	4.15387			0.320478
$169$	8.58063			0.660048
$170$	−3.19722	+	7.91890i	−0.245215	+	0.607352i
$171$	0.0424776	−	0.0424776i	0.00324834	−	0.00324834i
$172$		−	6.59679i		−	0.503001i
$173$	6.82631	+	6.82631i	0.518995	+	0.518995i	0.917267	−	0.398272i	$-0.130390\pi$
$173$	6.82631	+	6.82631i	0.518995	+	0.518995i	−0.398272	+	0.917267i	$0.630390\pi$
$174$		−	1.41459i		−	0.107240i
$175$	−0.372528	−	20.7660i	−0.0281604	−	1.56976i
$176$			1.12978i			0.0851603i
$177$		−	2.16997i		−	0.163105i
$178$	−8.09450	−	8.09450i	−0.606709	−	0.606709i
$179$	1.80725	−	1.80725i	0.135080	−	0.135080i	−0.636334	−	0.771414i	$-0.719550\pi$
$179$	1.80725	−	1.80725i	0.135080	−	0.135080i	0.771414	+	0.636334i	$0.219550\pi$
$180$	−0.837144	+	2.07345i	−0.0623970	+	0.154546i
$181$	16.0321			1.19166			0.595828	−	0.803112i	$-0.296824\pi$
$181$	16.0321			1.19166			0.595828	+	0.803112i	$0.296824\pi$
$182$	6.17474	+	6.17474i	0.457702	+	0.457702i
$183$		−	4.42732i		−	0.327277i
$184$	−7.44945			−0.549181
$185$	−11.0853	−	7.88135i	−0.815009	−	0.579448i
$186$	7.85303			0.575812
$187$		−	4.31485i		−	0.315533i
$188$	−3.52289	−	3.52289i	−0.256933	−	0.256933i
$189$	−4.15387			−0.302150
$190$	−0.123635	+	0.0525152i	−0.00896942	+	0.00380985i
$191$	3.79156	−	3.79156i	0.274348	−	0.274348i	−0.556500	−	0.830848i	$-0.687856\pi$
$191$	3.79156	−	3.79156i	0.274348	−	0.274348i	0.830848	+	0.556500i	$0.187856\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$			6.10797i			0.439661i	0.975538	+	0.219831i	$0.0705504\pi$
$193$			6.10797i			0.439661i	−0.975538	+	0.219831i	$0.929450\pi$
$194$			10.4722i			0.751861i
$195$	−4.32660	+	1.83777i	−0.309834	+	0.131605i
$196$		−	10.2547i		−	0.732476i
$197$	−16.3684	−	16.3684i	−1.16620	−	1.16620i	−0.983094	−	0.183104i	$-0.941385\pi$
$197$	−16.3684	−	16.3684i	−1.16620	−	1.16620i	−0.183104	−	0.983094i	$-0.558615\pi$
$198$		−	1.12978i		−	0.0802899i
$199$	−14.9530	+	14.9530i	−1.05999	+	1.05999i	−0.0619052	+	0.998082i	$0.519718\pi$
$199$	−14.9530	+	14.9530i	−1.05999	+	1.05999i	−0.998082	+	0.0619052i	$0.980282\pi$
$200$	3.47155	−	3.59838i	0.245476	−	0.254444i
$201$	−3.66544			−0.258540
$202$	6.85371			0.482225
$203$	−5.87602			−0.412416
$204$	−2.70058	−	2.70058i	−0.189078	−	0.189078i
$205$	6.12235	−	15.1639i	0.427603	−	1.05909i
$206$			11.0473i			0.769702i
$207$	7.44945			0.517772
$208$			2.10223i			0.145763i
$209$	0.0479903	−	0.0479903i	0.00331956	−	0.00331956i
$210$	8.61284	+	3.47739i	0.594343	+	0.239963i
$211$	−6.95993			−0.479142			−0.239571	−	0.970879i	$-0.577007\pi$
$211$	−6.95993			−0.479142			−0.239571	+	0.970879i	$0.577007\pi$
$212$	6.43055	−	6.43055i	0.441652	−	0.441652i
$213$	−1.49126	−	1.49126i	−0.102179	−	0.102179i
$214$	−2.67190	+	2.67190i	−0.182647	+	0.182647i
$215$	5.52247	−	13.6781i	0.376629	−	0.932839i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$		−	32.6205i		−	2.21442i
$218$	1.57675	−	1.57675i	0.106791	−	0.106791i
$219$			9.83469i			0.664567i
$220$	−0.945788	+	2.34254i	−0.0637650	+	0.157934i
$221$		−	8.02883i		−	0.540077i
$222$	5.18228	−	3.18497i	0.347812	−	0.213761i
$223$	−1.57965	+	1.57965i	−0.105781	+	0.105781i	−0.758017	−	0.652235i	$-0.773831\pi$
$223$	−1.57965	+	1.57965i	−0.105781	+	0.105781i	0.652235	+	0.758017i	$0.273831\pi$
$224$	2.93723	−	2.93723i	0.196252	−	0.196252i
$225$	−3.47155	+	3.59838i	−0.231437	+	0.239892i
$226$		−	13.9588i		−	0.928527i
$227$	−0.343113			−0.0227732			−0.0113866	−	0.999935i	$-0.503625\pi$
$227$	−0.343113			−0.0227732			−0.0113866	+	0.999935i	$0.503625\pi$
$228$		−	0.0600724i		−	0.00397839i
$229$			29.6963i			1.96239i	0.193028	+	0.981193i	$0.438169\pi$
$229$			29.6963i			1.96239i	−0.193028	+	0.981193i	$0.561831\pi$
$230$	−15.4460	−	6.23626i	−1.01848	−	0.411207i
$231$	−4.69296			−0.308774
$232$	−1.00026	−	1.00026i	−0.0656706	−	0.0656706i
$233$	4.57105	+	4.57105i	0.299459	+	0.299459i	0.840802	−	0.541343i	$-0.182084\pi$
$233$	4.57105	+	4.57105i	0.299459	+	0.299459i	−0.541343	+	0.840802i	$0.682084\pi$
$234$		−	2.10223i		−	0.137427i
$235$	−4.35537	−	10.2537i	−0.284113	−	0.668878i
$236$	−1.53440	−	1.53440i	−0.0998809	−	0.0998809i
$237$			11.9480i			0.776108i
$238$	−11.2179	+	11.2179i	−0.727146	+	0.727146i
$239$	12.3303	+	12.3303i	0.797581	+	0.797581i	0.982714	−	0.185133i	$-0.0592715\pi$
$239$	12.3303	+	12.3303i	0.797581	+	0.797581i	−0.185133	+	0.982714i	$0.559272\pi$
$240$	0.874200	+	2.05810i	0.0564293	+	0.132850i
$241$	−19.4485	+	19.4485i	−1.25279	+	1.25279i	−0.298326	+	0.954464i	$0.596428\pi$
$241$	−19.4485	+	19.4485i	−1.25279	+	1.25279i	−0.954464	+	0.298326i	$0.903572\pi$
$242$			9.72360i			0.625057i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−3.13059	−	3.13059i	−0.200415	−	0.200415i
$245$	8.58463	−	21.2625i	0.548452	−	1.35841i
$246$	5.17134	+	5.17134i	0.329712	+	0.329712i
$247$	0.0892976	−	0.0892976i	0.00568187	−	0.00568187i
$248$	5.55293	−	5.55293i	0.352612	−	0.352612i
$249$	3.96835			0.251484
$250$	10.2104	−	4.55487i	0.645765	−	0.288075i
$251$	−5.33183	−	5.33183i	−0.336542	−	0.336542i	0.518522	−	0.855064i	$-0.326482\pi$
$251$	−5.33183	−	5.33183i	−0.336542	−	0.336542i	−0.855064	+	0.518522i	$0.826482\pi$
$252$	−2.93723	+	2.93723i	−0.185028	+	0.185028i
$253$	8.41623			0.529124
$254$	−8.02624	+	8.02624i	−0.503611	+	0.503611i
$255$	−3.33874	−	7.86028i	−0.209080	−	0.492230i
$256$	1.00000			0.0625000
$257$	−0.0742306			−0.00463038			−0.00231519	−	0.999997i	$-0.500737\pi$
$257$	−0.0742306			−0.00463038			−0.00231519	+	0.999997i	$0.500737\pi$
$258$	4.66464	+	4.66464i	0.290408	+	0.290408i
$259$	−13.2299	−	21.5265i	−0.822069	−	1.33759i
$260$	−1.75987	+	4.35887i	−0.109142	+	0.270325i
$261$	1.00026	+	1.00026i	0.0619148	+	0.0619148i
$262$	−4.61659	+	4.61659i	−0.285214	+	0.285214i
$263$	−10.0575	−	10.0575i	−0.620173	−	0.620173i	0.325402	−	0.945576i	$-0.394500\pi$
$263$	−10.0575	−	10.0575i	−0.620173	−	0.620173i	−0.945576	+	0.325402i	$0.894500\pi$
$264$	−0.798875	−	0.798875i	−0.0491673	−	0.0491673i
$265$	18.7167	−	7.95012i	1.14976	−	0.488372i
$266$	−0.249533			−0.0152998
$267$	11.4474			0.700567
$268$	−2.59186	+	2.59186i	−0.158323	+	0.158323i
$269$			0.705488i			0.0430144i	0.999769	+	0.0215072i	$0.00684648\pi$
$269$			0.705488i			0.0430144i	−0.999769	+	0.0215072i	$0.993154\pi$
$270$	−0.874200	−	2.05810i	−0.0532021	−	0.125252i
$271$	26.3349			1.59973			0.799865	−	0.600180i	$-0.204904\pi$
$271$	26.3349			1.59973			0.799865	+	0.600180i	$0.204904\pi$
$272$	−3.81919			−0.231573
$273$	−8.73240			−0.528509
$274$	12.7568	−	12.7568i	0.770665	−	0.770665i
$275$	−3.92209	+	4.06538i	−0.236511	+	0.245151i
$276$	5.26755	−	5.26755i	0.317070	−	0.317070i
$277$			8.82636i			0.530325i	0.964204	+	0.265162i	$0.0854256\pi$
$277$			8.82636i			0.530325i	−0.964204	+	0.265162i	$0.914574\pi$
$278$		−	10.7050i		−	0.642044i
$279$	−5.55293	+	5.55293i	−0.332445	+	0.332445i
$280$	8.54909	−	3.63131i	0.510906	−	0.217013i
$281$	−11.2760	+	11.2760i	−0.672668	+	0.672668i	−0.958330	−	0.285662i	$-0.907787\pi$
$281$	−11.2760	+	11.2760i	−0.672668	+	0.672668i	0.285662	+	0.958330i	$0.407787\pi$
$282$	4.98212			0.296681
$283$	21.3959			1.27185			0.635927	−	0.771749i	$-0.280618\pi$
$283$	21.3959			1.27185			0.635927	+	0.771749i	$0.280618\pi$
$284$	−2.10896			−0.125144
$285$	0.0502892	−	0.124557i	0.00297888	−	0.00737812i
$286$		−	2.37506i		−	0.140440i
$287$	21.4811	−	21.4811i	1.26799	−	1.26799i
$288$	−1.00000			−0.0589256
$289$	−2.41375			−0.141986
$290$	−1.23663	−	2.91136i	−0.0726175	−	0.170961i
$291$	−7.40498	−	7.40498i	−0.434087	−	0.434087i
$292$	6.95418	+	6.95418i	0.406962	+	0.406962i
$293$	−10.0273	+	10.0273i	−0.585801	+	0.585801i	−0.936491	−	0.350690i	$-0.885947\pi$
$293$	−10.0273	+	10.0273i	−0.585801	+	0.585801i	0.350690	+	0.936491i	$0.385947\pi$
$294$	7.25114	+	7.25114i	0.422895	+	0.422895i
$295$	−1.89699	−	4.46601i	−0.110447	−	0.260021i
$296$	1.41231	−	5.91653i	0.0820890	−	0.343892i
$297$	0.798875	+	0.798875i	0.0463554	+	0.0463554i
$298$	−21.7914			−1.26234
$299$	15.6605			0.905668
$300$	0.0896820	+	4.99920i	0.00517779	+	0.288629i
$301$	19.3763	−	19.3763i	1.11683	−	1.11683i
$302$	1.57215			0.0904669
$303$	−4.84630	+	4.84630i	−0.278413	+	0.278413i
$304$	−0.0424776	−	0.0424776i	−0.00243626	−	0.00243626i
$305$	−3.87036	−	9.11186i	−0.221616	−	0.521744i
$306$	3.81919			0.218329
$307$	−15.3558	+	15.3558i	−0.876403	+	0.876403i	−0.993160	−	0.116758i	$-0.962750\pi$
$307$	−15.3558	+	15.3558i	−0.876403	+	0.876403i	0.116758	+	0.993160i	$0.462750\pi$
$308$	−3.31842	+	3.31842i	−0.189085	+	0.189085i
$309$	−7.81163	−	7.81163i	−0.444388	−	0.444388i
$310$	16.1623	−	6.86512i	0.917959	−	0.389913i
$311$	21.4671	+	21.4671i	1.21729	+	1.21729i	0.968578	+	0.248710i	$0.0800065\pi$
$311$	21.4671	+	21.4671i	1.21729	+	1.21729i	0.248710	+	0.968578i	$0.419994\pi$
$312$	−1.48650	−	1.48650i	−0.0841566	−	0.0841566i
$313$		−	11.8966i		−	0.672435i	−0.941784	−	0.336217i	$-0.890852\pi$
$313$		−	11.8966i		−	0.672435i	0.941784	−	0.336217i	$-0.109148\pi$
$314$	−0.999991	+	0.999991i	−0.0564327	+	0.0564327i
$315$	−8.54909	+	3.63131i	−0.481686	+	0.204601i
$316$	8.44853	+	8.44853i	0.475267	+	0.475267i
$317$	21.4453	−	21.4453i	1.20449	−	1.20449i	0.231701	−	0.972787i	$-0.425571\pi$
$317$	21.4453	−	21.4453i	1.20449	−	1.20449i	0.972787	−	0.231701i	$-0.0744292\pi$
$318$			9.09418i			0.509976i
$319$	1.13008	+	1.13008i	0.0632722	+	0.0632722i
$320$	2.07345	+	0.837144i	0.115909	+	0.0467978i
$321$		−	3.77864i		−	0.210903i
$322$	−21.8808	−	21.8808i	−1.21937	−	1.21937i
$323$	0.162230	+	0.162230i	0.00902672	+	0.00902672i
$324$	1.00000			0.0555556
$325$	−7.29800	+	7.56462i	−0.404820	+	0.419610i
$326$			19.9337i			1.10402i
$327$			2.22985i			0.123311i
$328$	7.31338			0.403814
$329$		−	20.6951i		−	1.14096i
$330$	−0.987653	−	2.32520i	−0.0543685	−	0.127998i
$331$	−1.31507	+	1.31507i	−0.0722829	+	0.0722829i	−0.742324	−	0.670041i	$-0.766276\pi$
$331$	−1.31507	+	1.31507i	−0.0722829	+	0.0722829i	0.670041	+	0.742324i	$0.266276\pi$
$332$	2.80605	−	2.80605i	0.154002	−	0.154002i
$333$	−1.41231	+	5.91653i	−0.0773942	+	0.324224i
$334$		−	2.23975i		−	0.122554i
$335$	−7.54384	+	3.20433i	−0.412164	+	0.175071i
$336$			4.15387i			0.226612i
$337$	−14.7026	+	14.7026i	−0.800900	+	0.800900i	−0.983236	−	0.182336i	$-0.941634\pi$
$337$	−14.7026	+	14.7026i	−0.800900	+	0.800900i	0.182336	+	0.983236i	$0.441634\pi$
$338$			8.58063i			0.466725i
$339$	9.87038	+	9.87038i	0.536085	+	0.536085i
$340$	−7.91890	−	3.19722i	−0.429463	−	0.173393i
$341$	−6.27359	+	6.27359i	−0.339734	+	0.339734i
$342$	0.0424776	+	0.0424776i	0.00229692	+	0.00229692i
$343$	9.55971	−	9.55971i	0.516176	−	0.516176i
$344$	6.59679			0.355675
$345$	15.3317	−	6.51230i	0.825431	−	0.350611i
$346$	−6.82631	+	6.82631i	−0.366985	+	0.366985i
$347$			31.6430i			1.69868i	0.527843	+	0.849342i	$0.323001\pi$
$347$			31.6430i			1.69868i	−0.527843	+	0.849342i	$0.676999\pi$
$348$	1.41459			0.0758299
$349$		−	21.1235i		−	1.13072i	−0.824846	−	0.565358i	$-0.808738\pi$
$349$		−	21.1235i		−	1.13072i	0.824846	−	0.565358i	$-0.191262\pi$
$350$	20.7660	−	0.372528i	1.10999	−	0.0199124i
$351$	1.48650	+	1.48650i	0.0793436	+	0.0793436i
$352$	−1.12978			−0.0602174
$353$	−34.4460			−1.83338			−0.916689	−	0.399602i	$-0.869148\pi$
$353$	−34.4460			−1.83338			−0.916689	+	0.399602i	$0.869148\pi$
$354$	2.16997			0.115333
$355$	−4.37282	−	1.76550i	−0.232085	−	0.0937032i
$356$	8.09450	−	8.09450i	0.429008	−	0.429008i
$357$		−	15.8645i		−	0.839636i
$358$	1.80725	+	1.80725i	0.0955161	+	0.0955161i
$359$		−	12.0502i		−	0.635987i	−0.948093	−	0.317994i	$-0.896991\pi$
$359$		−	12.0502i		−	0.635987i	0.948093	−	0.317994i	$-0.103009\pi$
$360$	−2.07345	−	0.837144i	−0.109280	−	0.0441214i
$361$		−	18.9964i		−	0.999810i
$362$			16.0321i			0.842628i
$363$	−6.87562	−	6.87562i	−0.360877	−	0.360877i
$364$	−6.17474	+	6.17474i	−0.323644	+	0.323644i
$365$	8.59748	+	20.2408i	0.450013	+	1.05945i
$366$	4.42732			0.231420
$367$	−10.7675	−	10.7675i	−0.562060	−	0.562060i	0.367832	−	0.929892i	$-0.380100\pi$
$367$	−10.7675	−	10.7675i	−0.562060	−	0.562060i	−0.929892	+	0.367832i	$0.880100\pi$
$368$		−	7.44945i		−	0.388329i
$369$	−7.31338			−0.380719
$370$	7.88135	−	11.0853i	0.409732	−	0.576298i
$371$	37.7761			1.96124
$372$			7.85303i			0.407161i
$373$	−0.907328	−	0.907328i	−0.0469797	−	0.0469797i	0.683227	−	0.730206i	$-0.260576\pi$
$373$	−0.907328	−	0.907328i	−0.0469797	−	0.0469797i	−0.730206	+	0.683227i	$0.760576\pi$
$374$	4.31485			0.223115
$375$	−3.99910	+	10.4407i	−0.206512	+	0.539153i
$376$	3.52289	−	3.52289i	0.181679	−	0.181679i
$377$	2.10279	+	2.10279i	0.108299	+	0.108299i
$378$		−	4.15387i		−	0.213652i
$379$		−	30.6276i		−	1.57323i	−0.617442	−	0.786617i	$-0.711831\pi$
$379$		−	30.6276i		−	1.57323i	0.617442	−	0.786617i	$-0.288169\pi$
$380$	−0.0525152	−	0.123635i	−0.00269397	−	0.00634234i
$381$		−	11.3508i		−	0.581520i
$382$	3.79156	+	3.79156i	0.193993	+	0.193993i
$383$			36.9850i			1.88985i	0.327293	+	0.944923i	$0.393864\pi$
$383$			36.9850i			1.88985i	−0.327293	+	0.944923i	$0.606136\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−9.65858	+	4.10258i	−0.492247	+	0.209087i
$386$	−6.10797			−0.310887
$387$	−6.59679			−0.335334
$388$	−10.4722			−0.531646
$389$	−2.10277	−	2.10277i	−0.106615	−	0.106615i	0.651787	−	0.758402i	$-0.274020\pi$
$389$	−2.10277	−	2.10277i	−0.106615	−	0.106615i	−0.758402	+	0.651787i	$0.774020\pi$
$390$	−1.83777	−	4.32660i	−0.0930591	−	0.219086i
$391$			28.4509i			1.43882i
$392$	10.2547			0.517939
$393$		−	6.52884i		−	0.329336i
$394$	16.3684	−	16.3684i	0.824626	−	0.824626i
$395$	10.4450	+	24.5902i	0.525543	+	1.23727i
$396$	1.12978			0.0567736
$397$	5.65369	−	5.65369i	0.283750	−	0.283750i	−0.550852	−	0.834603i	$-0.685697\pi$
$397$	5.65369	−	5.65369i	0.283750	−	0.283750i	0.834603	+	0.550852i	$0.185697\pi$
$398$	−14.9530	−	14.9530i	−0.749524	−	0.749524i
$399$	0.176446	−	0.176446i	0.00883337	−	0.00883337i
$400$	3.59838	+	3.47155i	0.179919	+	0.173578i
$401$	17.2850	+	17.2850i	0.863170	+	0.863170i	0.991705	−	0.128535i	$-0.0410274\pi$
$401$	17.2850	+	17.2850i	0.863170	+	0.863170i	−0.128535	+	0.991705i	$0.541027\pi$
$402$		−	3.66544i		−	0.182815i
$403$	−11.6735	+	11.6735i	−0.581501	+	0.581501i
$404$			6.85371i			0.340985i
$405$	2.07345	+	0.837144i	0.103030	+	0.0415980i
$406$		−	5.87602i		−	0.291622i
$407$	−1.59560	+	6.68438i	−0.0790910	+	0.331332i
$408$	2.70058	−	2.70058i	0.133699	−	0.133699i
$409$	−17.8635	+	17.8635i	−0.883295	+	0.883295i	−0.993868	−	0.110573i	$-0.964731\pi$
$409$	−17.8635	+	17.8635i	−0.883295	+	0.883295i	0.110573	+	0.993868i	$0.464731\pi$
$410$	15.1639	+	6.12235i	0.748892	+	0.302361i
$411$			18.0408i			0.889888i
$412$	−11.0473			−0.544262
$413$		−	9.01377i		−	0.443539i
$414$			7.44945i			0.366120i
$415$	8.16726	−	3.46913i	0.400915	−	0.170293i
$416$	−2.10223			−0.103070
$417$	7.56958	+	7.56958i	0.370684	+	0.370684i
$418$	0.0479903	+	0.0479903i	0.00234728	+	0.00234728i
$419$		−	13.1163i		−	0.640772i	−0.947287	−	0.320386i	$-0.896187\pi$
$419$		−	13.1163i		−	0.640772i	0.947287	−	0.320386i	$-0.103813\pi$
$420$	−3.47739	+	8.61284i	−0.169679	+	0.420264i
$421$	1.41752	+	1.41752i	0.0690858	+	0.0690858i	0.740805	−	0.671720i	$-0.234444\pi$
$421$	1.41752	+	1.41752i	0.0690858	+	0.0690858i	−0.671720	+	0.740805i	$0.734444\pi$
$422$		−	6.95993i		−	0.338804i
$423$	−3.52289	+	3.52289i	−0.171289	+	0.171289i
$424$	6.43055	+	6.43055i	0.312295	+	0.312295i
$425$	−13.7429	−	13.2585i	−0.666629	−	0.643133i
$426$	1.49126	−	1.49126i	0.0722518	−	0.0722518i
$427$		−	18.3905i		−	0.889979i
$428$	−2.67190	−	2.67190i	−0.129151	−	0.129151i
$429$	1.67942	+	1.67942i	0.0810831	+	0.0810831i
$430$	13.6781	+	5.52247i	0.659617	+	0.266317i
$431$	−21.4522	−	21.4522i	−1.03331	−	1.03331i	−0.999426	−	0.0338889i	$-0.989211\pi$
$431$	−21.4522	−	21.4522i	−1.03331	−	1.03331i	−0.0338889	−	0.999426i	$-0.510789\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−26.2287	+	26.2287i	−1.26047	+	1.26047i	−0.309607	+	0.950865i	$0.600197\pi$
$433$	−26.2287	+	26.2287i	−1.26047	+	1.26047i	−0.950865	+	0.309607i	$0.899803\pi$
$434$	32.6205			1.56583
$435$	2.93308	+	1.18421i	0.140630	+	0.0567787i
$436$	1.57675	+	1.57675i	0.0755124	+	0.0755124i
$437$	−0.316434	+	0.316434i	−0.0151371	+	0.0151371i
$438$	−9.83469			−0.469920
$439$	−10.4737	+	10.4737i	−0.499884	+	0.499884i	−0.911402	−	0.411518i	$-0.864999\pi$
$439$	−10.4737	+	10.4737i	−0.499884	+	0.499884i	0.411518	+	0.911402i	$0.364999\pi$
$440$	−2.34254	−	0.945788i	−0.111676	−	0.0450887i
$441$	−10.2547			−0.488317
$442$	8.02883			0.381892
$443$	5.10023	+	5.10023i	0.242319	+	0.242319i	0.817809	−	0.575490i	$-0.195189\pi$
$443$	5.10023	+	5.10023i	0.242319	+	0.242319i	−0.575490	+	0.817809i	$0.695189\pi$
$444$	3.18497	+	5.18228i	0.151152	+	0.245940i
$445$	23.5598	−	10.0073i	1.11684	−	0.474390i
$446$	−1.57965	−	1.57965i	−0.0747987	−	0.0747987i
$447$	15.4088	−	15.4088i	0.728812	−	0.728812i
$448$	2.93723	+	2.93723i	0.138771	+	0.138771i
$449$	−1.76700	−	1.76700i	−0.0833897	−	0.0833897i	0.664182	−	0.747571i	$-0.268780\pi$
$449$	−1.76700	−	1.76700i	−0.0833897	−	0.0833897i	−0.747571	+	0.664182i	$0.768780\pi$
$450$	−3.59838	−	3.47155i	−0.169629	−	0.163650i
$451$	−8.26250			−0.389066
$452$	13.9588			0.656568
$453$	−1.11168	+	1.11168i	−0.0522311	+	0.0522311i
$454$		−	0.343113i		−	0.0161031i
$455$	−17.9722	+	7.63386i	−0.842547	+	0.357881i
$456$	0.0600724			0.00281315
$457$	−31.6204			−1.47914			−0.739570	−	0.673080i	$-0.764971\pi$
$457$	−31.6204			−1.47914			−0.739570	+	0.673080i	$0.764971\pi$
$458$	−29.6963			−1.38762
$459$	−2.70058	+	2.70058i	−0.126052	+	0.126052i
$460$	6.23626	−	15.4460i	0.290767	−	0.720176i
$461$	8.01857	−	8.01857i	0.373462	−	0.373462i	−0.495274	−	0.868737i	$-0.664932\pi$
$461$	8.01857	−	8.01857i	0.373462	−	0.373462i	0.868737	+	0.495274i	$0.164932\pi$
$462$		−	4.69296i		−	0.218336i
$463$		−	13.1675i		−	0.611945i	−0.952040	−	0.305973i	$-0.901018\pi$
$463$		−	13.1675i		−	0.611945i	0.952040	−	0.305973i	$-0.0989816\pi$
$464$	1.00026	−	1.00026i	0.0464361	−	0.0464361i
$465$	−6.57412	+	16.2829i	−0.304868	+	0.755100i
$466$	−4.57105	+	4.57105i	−0.211750	+	0.211750i
$467$	−2.65254			−0.122745			−0.0613725	−	0.998115i	$-0.519548\pi$
$467$	−2.65254			−0.122745			−0.0613725	+	0.998115i	$0.519548\pi$
$468$	2.10223			0.0971756
$469$	−15.2258			−0.703061
$470$	10.2537	−	4.35537i	0.472968	−	0.200898i
$471$		−	1.41420i		−	0.0651629i
$472$	1.53440	−	1.53440i	0.0706264	−	0.0706264i
$473$	−7.45292			−0.342686
$474$	−11.9480			−0.548791
$475$	−0.00538741	−	0.300313i	−0.000247191	−	0.0137793i
$476$	−11.2179	−	11.2179i	−0.514170	−	0.514170i
$477$	−6.43055	−	6.43055i	−0.294435	−	0.294435i
$478$	−12.3303	+	12.3303i	−0.563975	+	0.563975i
$479$	5.91428	+	5.91428i	0.270230	+	0.270230i	0.829193	−	0.558963i	$-0.188800\pi$
$479$	5.91428	+	5.91428i	0.270230	+	0.270230i	−0.558963	+	0.829193i	$0.688800\pi$
$480$	−2.05810	+	0.874200i	−0.0939390	+	0.0399016i
$481$	−2.96901	+	12.4379i	−0.135375	+	0.567120i
$482$	−19.4485	−	19.4485i	−0.885856	−	0.885856i
$483$	30.9441			1.40800
$484$	−9.72360			−0.441982
$485$	−21.7136	−	8.76675i	−0.985964	−	0.398078i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	15.5782			0.705915			0.352957	−	0.935639i	$-0.385176\pi$
$487$	15.5782			0.705915			0.352957	+	0.935639i	$0.385176\pi$
$488$	3.13059	−	3.13059i	0.141715	−	0.141715i
$489$	−14.0952	−	14.0952i	−0.637409	−	0.637409i
$490$	21.2625	+	8.58463i	0.960543	+	0.387814i
$491$	19.8002			0.893571			0.446785	−	0.894641i	$-0.352569\pi$
$491$	19.8002			0.893571			0.446785	+	0.894641i	$0.352569\pi$
$492$	−5.17134	+	5.17134i	−0.233142	+	0.233142i
$493$	−3.82020	+	3.82020i	−0.172053	+	0.172053i
$494$	0.0892976	+	0.0892976i	0.00401769	+	0.00401769i
$495$	2.34254	+	0.945788i	0.105289	+	0.0425100i
$496$	5.55293	+	5.55293i	0.249334	+	0.249334i
$497$	−6.19450	−	6.19450i	−0.277861	−	0.277861i
$498$			3.96835i			0.177826i
$499$	6.66081	−	6.66081i	0.298179	−	0.298179i	−0.542122	−	0.840300i	$-0.682379\pi$
$499$	6.66081	−	6.66081i	0.298179	−	0.298179i	0.840300	+	0.542122i	$0.182379\pi$
$500$	4.55487	+	10.2104i	0.203700	+	0.456625i
$501$	1.58374	+	1.58374i	0.0707564	+	0.0707564i
$502$	5.33183	−	5.33183i	0.237971	−	0.237971i
$503$		−	20.9403i		−	0.933681i	−0.884341	−	0.466841i	$-0.845392\pi$
$503$		−	20.9403i		−	0.933681i	0.884341	−	0.466841i	$-0.154608\pi$
$504$	−2.93723	−	2.93723i	−0.130835	−	0.130835i
$505$	−5.73754	+	14.2108i	−0.255317	+	0.632373i
$506$			8.41623i			0.374147i
$507$	−6.06742	−	6.06742i	−0.269464	−	0.269464i
$508$	−8.02624	−	8.02624i	−0.356107	−	0.356107i
$509$	18.1652			0.805159			0.402580	−	0.915385i	$-0.368114\pi$
$509$	18.1652			0.805159			0.402580	+	0.915385i	$0.368114\pi$
$510$	7.86028	−	3.33874i	0.348059	−	0.147842i
$511$			40.8521i			1.80719i
$512$			1.00000i			0.0441942i
$513$	−0.0600724			−0.00265226
$514$		−	0.0742306i		−	0.00327417i
$515$	−22.9060	−	9.24819i	−1.00936	−	0.407524i
$516$	−4.66464	+	4.66464i	−0.205349	+	0.205349i
$517$	−3.98009	+	3.98009i	−0.175044	+	0.175044i
$518$	21.5265	−	13.2299i	0.945821	−	0.581290i
$519$		−	9.65387i		−	0.423758i
$520$	−4.35887	−	1.75987i	−0.191149	−	0.0771754i
$521$			44.3755i			1.94413i	0.234718	+	0.972063i	$0.424583\pi$
$521$			44.3755i			1.94413i	−0.234718	+	0.972063i	$0.575417\pi$
$522$	−1.00026	+	1.00026i	−0.0437804	+	0.0437804i
$523$			32.3600i			1.41500i	0.706712	+	0.707502i	$0.250178\pi$
$523$			32.3600i			1.41500i	−0.706712	+	0.707502i	$0.749822\pi$
$524$	−4.61659	−	4.61659i	−0.201676	−	0.201676i
$525$	−14.4204	+	14.9472i	−0.629357	+	0.652350i
$526$	10.0575	−	10.0575i	0.438529	−	0.438529i
$527$	−21.2077	−	21.2077i	−0.923823	−	0.923823i
$528$	0.798875	−	0.798875i	0.0347666	−	0.0347666i
$529$	−32.4943			−1.41279
$530$	7.95012	+	18.7167i	0.345331	+	0.813002i
$531$	−1.53440	+	1.53440i	−0.0665873	+	0.0665873i
$532$		−	0.249533i		−	0.0108186i
$533$	−15.3744			−0.665939
$534$			11.4474i			0.495375i
$535$	−3.30329	−	7.77682i	−0.142813	−	0.336221i
$536$	−2.59186	−	2.59186i	−0.111951	−	0.111951i
$537$	−2.55584			−0.110293
$538$	−0.705488			−0.0304158
$539$	−11.5855			−0.499023
$540$	2.05810	−	0.874200i	0.0885665	−	0.0376196i
$541$	−26.5457	+	26.5457i	−1.14129	+	1.14129i	−0.153072	+	0.988215i	$0.548917\pi$
$541$	−26.5457	+	26.5457i	−1.14129	+	1.14129i	−0.988215	+	0.153072i	$0.951083\pi$
$542$			26.3349i			1.13118i
$543$	−11.3364	−	11.3364i	−0.486491	−	0.486491i
$544$		−	3.81919i		−	0.163747i
$545$	1.94934	+	4.58926i	0.0835004	+	0.196582i
$546$		−	8.73240i		−	0.373712i
$547$		−	15.8829i		−	0.679106i	−0.940587	−	0.339553i	$-0.889724\pi$
$547$		−	15.8829i		−	0.679106i	0.940587	−	0.339553i	$-0.110276\pi$
$548$	12.7568	+	12.7568i	0.544943	+	0.544943i
$549$	−3.13059	+	3.13059i	−0.133610	+	0.133610i
$550$	−4.06538	−	3.92209i	−0.173348	−	0.167238i
$551$	−0.0849776			−0.00362017
$552$	5.26755	+	5.26755i	0.224202	+	0.224202i
$553$			49.6306i			2.11051i
$554$	−8.82636			−0.374996
$555$	2.26555	+	13.4115i	0.0961673	+	0.569285i
$556$	10.7050			0.453993
$557$		−	2.64519i		−	0.112080i	−0.998429	−	0.0560402i	$-0.982152\pi$
$557$		−	2.64519i		−	0.112080i	0.998429	−	0.0560402i	$-0.0178475\pi$
$558$	−5.55293	−	5.55293i	−0.235074	−	0.235074i
$559$	−13.8680			−0.586553
$560$	3.63131	+	8.54909i	0.153451	+	0.361265i
$561$	−3.05106	+	3.05106i	−0.128816	+	0.128816i
$562$	−11.2760	−	11.2760i	−0.475648	−	0.475648i
$563$			34.7341i			1.46387i	0.681377	+	0.731933i	$0.261382\pi$
$563$			34.7341i			1.46387i	−0.681377	+	0.731933i	$0.738618\pi$
$564$			4.98212i			0.209785i
$565$	28.9429	+	11.6855i	1.21764	+	0.491614i
$566$			21.3959i			0.899337i
$567$	2.93723	+	2.93723i	0.123352	+	0.123352i
$568$		−	2.10896i		−	0.0884900i
$569$	−26.8268	+	26.8268i	−1.12464	+	1.12464i	−0.133603	+	0.991035i	$0.542655\pi$
$569$	−26.8268	+	26.8268i	−1.12464	+	1.12464i	−0.991035	+	0.133603i	$0.957345\pi$
$570$	0.124557	+	0.0502892i	0.00521712	+	0.00210638i
$571$	17.9771			0.752318			0.376159	−	0.926555i	$-0.377245\pi$
$571$	17.9771			0.752318			0.376159	+	0.926555i	$0.377245\pi$
$572$	2.37506			0.0993061
$573$	−5.36208			−0.224004
$574$	21.4811	+	21.4811i	0.896603	+	0.896603i
$575$	25.8611	−	26.8059i	1.07848	−	1.11789i
$576$		−	1.00000i		−	0.0416667i
$577$	−6.76864			−0.281782			−0.140891	−	0.990025i	$-0.544997\pi$
$577$	−6.76864			−0.281782			−0.140891	+	0.990025i	$0.544997\pi$
$578$		−	2.41375i		−	0.100399i
$579$	4.31898	−	4.31898i	0.179491	−	0.179491i
$580$	2.91136	−	1.23663i	0.120888	−	0.0513483i
$581$	16.4840			0.683872
$582$	7.40498	−	7.40498i	0.306946	−	0.306946i
$583$	−7.26511	−	7.26511i	−0.300890	−	0.300890i
$584$	−6.95418	+	6.95418i	−0.287766	+	0.287766i
$585$	4.35887	+	1.75987i	0.180217	+	0.0727617i
$586$	−10.0273	−	10.0273i	−0.414224	−	0.414224i
$587$		−	13.0624i		−	0.539143i	−0.962980	−	0.269571i	$-0.913118\pi$
$587$		−	13.0624i		−	0.539143i	0.962980	−	0.269571i	$-0.0868820\pi$
$588$	−7.25114	+	7.25114i	−0.299032	+	0.299032i
$589$		−	0.471750i		−	0.0194381i
$590$	4.46601	−	1.89699i	0.183863	−	0.0780976i
$591$			23.1484i			0.952196i
$592$	5.91653	+	1.41231i	0.243168	+	0.0580457i
$593$	10.6406	−	10.6406i	0.436957	−	0.436957i	−0.454030	−	0.890986i	$-0.650014\pi$
$593$	10.6406	−	10.6406i	0.436957	−	0.436957i	0.890986	+	0.454030i	$0.150014\pi$
$594$	−0.798875	+	0.798875i	−0.0327782	+	0.0327782i
$595$	−13.8687	−	32.6506i	−0.568561	−	1.33855i
$596$		−	21.7914i		−	0.892609i
$597$	21.1467			0.865476
$598$			15.6605i			0.640404i
$599$		−	23.4022i		−	0.956189i	−0.878309	−	0.478094i	$-0.841328\pi$
$599$		−	23.4022i		−	0.956189i	0.878309	−	0.478094i	$-0.158672\pi$
$600$	−4.99920	+	0.0896820i	−0.204091	+	0.00366125i
$601$	−22.5030			−0.917918			−0.458959	−	0.888457i	$-0.651778\pi$
$601$	−22.5030			−0.917918			−0.458959	+	0.888457i	$0.651778\pi$
$602$	19.3763	+	19.3763i	0.789719	+	0.789719i
$603$	2.59186	+	2.59186i	0.105549	+	0.105549i
$604$			1.57215i			0.0639698i
$605$	−20.1614	−	8.14005i	−0.819677	−	0.330940i
$606$	−4.84630	−	4.84630i	−0.196868	−	0.196868i
$607$			35.7595i			1.45143i	0.687993	+	0.725717i	$0.258492\pi$
$607$			35.7595i			1.45143i	−0.687993	+	0.725717i	$0.741508\pi$
$608$	0.0424776	−	0.0424776i	0.00172269	−	0.00172269i
$609$	4.15497	+	4.15497i	0.168368	+	0.168368i
$610$	9.11186	−	3.87036i	0.368928	−	0.156706i
$611$	−7.40593	+	7.40593i	−0.299612	+	0.299612i
$612$			3.81919i			0.154382i
$613$	7.70270	+	7.70270i	0.311109	+	0.311109i	0.845339	−	0.534230i	$-0.179398\pi$
$613$	7.70270	+	7.70270i	0.311109	+	0.311109i	−0.534230	+	0.845339i	$0.679398\pi$
$614$	−15.3558	−	15.3558i	−0.619710	−	0.619710i
$615$	−15.0517	+	6.39335i	−0.606941	+	0.257805i
$616$	−3.31842	−	3.31842i	−0.133703	−	0.133703i
$617$	14.9706	−	14.9706i	0.602695	−	0.602695i	−0.338332	−	0.941027i	$-0.609863\pi$
$617$	14.9706	−	14.9706i	0.602695	−	0.602695i	0.941027	+	0.338332i	$0.109863\pi$
$618$	7.81163	−	7.81163i	0.314230	−	0.314230i
$619$	18.5620			0.746068			0.373034	−	0.927818i	$-0.378317\pi$
$619$	18.5620			0.746068			0.373034	+	0.927818i	$0.378317\pi$
$620$	6.86512	+	16.1623i	0.275710	+	0.649095i
$621$	−5.26755	−	5.26755i	−0.211380	−	0.211380i
$622$	−21.4671	+	21.4671i	−0.860752	+	0.860752i
$623$	47.5509			1.90509
$624$	1.48650	−	1.48650i	0.0595077	−	0.0595077i
$625$	0.896676	+	24.9839i	0.0358670	+	0.999357i
$626$	11.8966			0.475483
$627$	−0.0678685			−0.00271041
$628$	−0.999991	−	0.999991i	−0.0399040	−	0.0399040i
$629$	−22.5964	−	5.39390i	−0.900977	−	0.215069i
$630$	−3.63131	−	8.54909i	−0.144675	−	0.340604i
$631$	10.3185	+	10.3185i	0.410774	+	0.410774i	0.882008	−	0.471234i	$-0.156191\pi$
$631$	10.3185	+	10.3185i	0.410774	+	0.410774i	−0.471234	+	0.882008i	$0.656191\pi$
$632$	−8.44853	+	8.44853i	−0.336065	+	0.336065i
$633$	4.92142	+	4.92142i	0.195609	+	0.195609i
$634$	21.4453	+	21.4453i	0.851702	+	0.851702i
$635$	−9.92288	−	23.3611i	−0.393778	−	0.927058i
$636$	−9.09418			−0.360608
$637$	−21.5577			−0.854146
$638$	−1.13008	+	1.13008i	−0.0447402	+	0.0447402i
$639$			2.10896i			0.0834291i
$640$	−0.837144	+	2.07345i	−0.0330910	+	0.0819603i
$641$	5.52209			0.218109			0.109055	−	0.994036i	$-0.465218\pi$
$641$	5.52209			0.218109			0.109055	+	0.994036i	$0.465218\pi$
$642$	3.77864			0.149131
$643$	23.5970			0.930576			0.465288	−	0.885159i	$-0.345951\pi$
$643$	23.5970			0.930576			0.465288	+	0.885159i	$0.345951\pi$
$644$	21.8808	−	21.8808i	0.862223	−	0.862223i
$645$	−13.5769	+	5.76691i	−0.534588	+	0.227072i
$646$	−0.162230	+	0.162230i	−0.00638286	+	0.00638286i
$647$			32.6973i			1.28547i	0.766090	+	0.642733i	$0.222199\pi$
$647$			32.6973i			1.28547i	−0.766090	+	0.642733i	$0.777801\pi$
$648$			1.00000i			0.0392837i
$649$	−1.73353	+	1.73353i	−0.0680471	+	0.0680471i
$650$	−7.56462	−	7.29800i	−0.296709	−	0.286251i
$651$	−23.0662	+	23.0662i	−0.904035	+	0.904035i
$652$	−19.9337			−0.780664
$653$	−16.1246			−0.631003			−0.315501	−	0.948925i	$-0.602173\pi$
$653$	−16.1246			−0.631003			−0.315501	+	0.948925i	$0.602173\pi$
$654$	−2.22985			−0.0871942
$655$	−5.70751	−	13.4370i	−0.223011	−	0.525027i
$656$			7.31338i			0.285539i
$657$	6.95418	−	6.95418i	0.271308	−	0.271308i
$658$	20.6951			0.806779
$659$	13.1116			0.510755			0.255377	−	0.966841i	$-0.417800\pi$
$659$	13.1116			0.510755			0.255377	+	0.966841i	$0.417800\pi$
$660$	2.32520	−	0.987653i	0.0905082	−	0.0384443i
$661$	−5.13385	−	5.13385i	−0.199684	−	0.199684i	0.600181	−	0.799864i	$-0.295095\pi$
$661$	−5.13385	−	5.13385i	−0.199684	−	0.199684i	−0.799864	+	0.600181i	$0.795095\pi$
$662$	−1.31507	−	1.31507i	−0.0511117	−	0.0511117i
$663$	−5.67724	+	5.67724i	−0.220486	+	0.220486i
$664$	2.80605	+	2.80605i	0.108896	+	0.108896i
$665$	0.208895	−	0.517394i	0.00810060	−	0.0200637i
$666$	−5.91653	−	1.41231i	−0.229261	−	0.0547260i
$667$	−7.45142	−	7.45142i	−0.288520	−	0.288520i
$668$	2.23975			0.0866586
$669$	2.23397			0.0863701
$670$	−3.20433	−	7.54384i	−0.123794	−	0.291444i
$671$	−3.53687	+	3.53687i	−0.136539	+	0.136539i
$672$	−4.15387			−0.160239
$673$	−8.33275	+	8.33275i	−0.321204	+	0.321204i	−0.849229	−	0.528025i	$-0.822933\pi$
$673$	−8.33275	+	8.33275i	−0.321204	+	0.321204i	0.528025	+	0.849229i	$0.322933\pi$
$674$	−14.7026	−	14.7026i	−0.566322	−	0.566322i
$675$	4.99920	−	0.0896820i	0.192419	−	0.00345186i
$676$	−8.58063			−0.330024
$677$	3.81491	−	3.81491i	0.146619	−	0.146619i	−0.629987	−	0.776606i	$-0.716940\pi$
$677$	3.81491	−	3.81491i	0.146619	−	0.146619i	0.776606	+	0.629987i	$0.216940\pi$
$678$	−9.87038	+	9.87038i	−0.379069	+	0.379069i
$679$	−30.7593	−	30.7593i	−1.18043	−	1.18043i
$680$	3.19722	−	7.91890i	0.122608	−	0.303676i
$681$	0.242618	+	0.242618i	0.00929714	+	0.00929714i
$682$	−6.27359	−	6.27359i	−0.240228	−	0.240228i
$683$		−	40.4422i		−	1.54748i	−0.633505	−	0.773739i	$-0.718384\pi$
$683$		−	40.4422i		−	1.54748i	0.633505	−	0.773739i	$-0.281616\pi$
$684$	−0.0424776	+	0.0424776i	−0.00162417	+	0.00162417i
$685$	15.7713	+	37.1298i	0.602589	+	1.41866i
$686$	9.55971	+	9.55971i	0.364991	+	0.364991i
$687$	20.9985	−	20.9985i	0.801141	−	0.801141i
$688$			6.59679i			0.251500i
$689$	−13.5185	−	13.5185i	−0.515014	−	0.515014i
$690$	6.51230	+	15.3317i	0.247919	+	0.583668i
$691$		−	18.2232i		−	0.693245i	−0.938005	−	0.346622i	$-0.887329\pi$
$691$		−	18.2232i		−	0.693245i	0.938005	−	0.346622i	$-0.112671\pi$
$692$	−6.82631	−	6.82631i	−0.259498	−	0.259498i
$693$	3.31842	+	3.31842i	0.126057	+	0.126057i
$694$	−31.6430			−1.20115
$695$	22.1963	+	8.96163i	0.841953	+	0.339934i
$696$			1.41459i			0.0536198i
$697$		−	27.9312i		−	1.05797i
$698$	21.1235			0.799537
$699$		−	6.46444i		−	0.244508i
$700$	0.372528	+	20.7660i	0.0140802	+	0.784882i
$701$	22.7697	−	22.7697i	0.859999	−	0.859999i	−0.131339	−	0.991338i	$-0.541928\pi$
$701$	22.7697	−	22.7697i	0.859999	−	0.859999i	0.991338	+	0.131339i	$0.0419276\pi$
$702$	−1.48650	+	1.48650i	−0.0561044	+	0.0561044i
$703$	−0.191328	−	0.311312i	−0.00721609	−	0.0117413i
$704$		−	1.12978i		−	0.0425802i
$705$	−4.17075	+	10.3302i	−0.157080	+	0.389057i
$706$		−	34.4460i		−	1.29639i
$707$	−20.1309	+	20.1309i	−0.757102	+	0.757102i
$708$			2.16997i			0.0815524i
$709$	36.5765	+	36.5765i	1.37366	+	1.37366i	0.854953	+	0.518706i	$0.173586\pi$
$709$	36.5765	+	36.5765i	1.37366	+	1.37366i	0.518706	+	0.854953i	$0.326414\pi$
$710$	1.76550	−	4.37282i	0.0662581	−	0.164109i
$711$	8.44853	−	8.44853i	0.316845	−	0.316845i
$712$	8.09450	+	8.09450i	0.303354	+	0.303354i
$713$	41.3663	−	41.3663i	1.54918	−	1.54918i
$714$	15.8645			0.593712
$715$	4.92456	+	1.98826i	0.184168	+	0.0743569i
$716$	−1.80725	+	1.80725i	−0.0675401	+	0.0675401i
$717$		−	17.4377i		−	0.651222i
$718$	12.0502			0.449711
$719$			17.7477i			0.661876i	0.943652	+	0.330938i	$0.107365\pi$
$719$			17.7477i			0.661876i	−0.943652	+	0.330938i	$0.892635\pi$
$720$	0.837144	−	2.07345i	0.0311985	−	0.0772729i
$721$	−32.4485	−	32.4485i	−1.20845	−	1.20845i
$722$	18.9964			0.706972
$723$	27.5044			1.02290
$724$	−16.0321			−0.595828
$725$	7.07180	−	0.126863i	0.262640	−	0.00471157i
$726$	6.87562	−	6.87562i	0.255178	−	0.255178i
$727$			42.7261i			1.58462i	0.610117	+	0.792311i	$0.291122\pi$
$727$			42.7261i			1.58462i	−0.610117	+	0.792311i	$0.708878\pi$
$728$	−6.17474	−	6.17474i	−0.228851	−	0.228851i
$729$		−	1.00000i		−	0.0370370i
$730$	−20.2408	+	8.59748i	−0.749145	+	0.318207i
$731$		−	25.1944i		−	0.931850i
$732$			4.42732i			0.163638i
$733$	14.8671	+	14.8671i	0.549131	+	0.549131i	0.926189	−	0.377059i	$-0.123065\pi$
$733$	14.8671	+	14.8671i	0.549131	+	0.549131i	−0.377059	+	0.926189i	$0.623065\pi$
$734$	10.7675	−	10.7675i	0.397437	−	0.397437i
$735$	−21.1051	+	8.96462i	−0.778474	+	0.330665i
$736$	7.44945			0.274590
$737$	2.92823	+	2.92823i	0.107863	+	0.107863i
$738$		−	7.31338i		−	0.269209i
$739$	9.68871			0.356405			0.178202	−	0.983994i	$-0.442972\pi$
$739$	9.68871			0.356405			0.178202	+	0.983994i	$0.442972\pi$
$740$	11.0853	+	7.88135i	0.407505	+	0.289724i
$741$	−0.126286			−0.00463923
$742$			37.7761i			1.38680i
$743$	2.02271	+	2.02271i	0.0742059	+	0.0742059i	0.743236	−	0.669030i	$-0.233290\pi$
$743$	2.02271	+	2.02271i	0.0742059	+	0.0742059i	−0.669030	+	0.743236i	$0.733290\pi$
$744$	−7.85303			−0.287906
$745$	18.2425	−	45.1833i	0.668354	−	1.65539i
$746$	0.907328	−	0.907328i	0.0332196	−	0.0332196i
$747$	−2.80605	−	2.80605i	−0.102668	−	0.102668i
$748$			4.31485i			0.157766i
$749$		−	15.6960i		−	0.573519i
$750$	−10.4407	−	3.99910i	−0.381239	−	0.146026i
$751$		−	22.8435i		−	0.833572i	−0.909005	−	0.416786i	$-0.863156\pi$
$751$		−	22.8435i		−	0.833572i	0.909005	−	0.416786i	$-0.136844\pi$
$752$	3.52289	+	3.52289i	0.128467	+	0.128467i
$753$			7.54034i			0.274785i
$754$	−2.10279	+	2.10279i	−0.0765790	+	0.0765790i
$755$	−1.31611	+	3.25977i	−0.0478983	+	0.118635i
$756$	4.15387			0.151075
$757$	−6.59491			−0.239696			−0.119848	−	0.992792i	$-0.538241\pi$
$757$	−6.59491			−0.239696			−0.119848	+	0.992792i	$0.538241\pi$
$758$	30.6276			1.11244
$759$	−5.95118	−	5.95118i	−0.216014	−	0.216014i
$760$	0.123635	−	0.0525152i	0.00448471	−	0.00190493i
$761$		−	38.8564i		−	1.40855i	−0.709930	−	0.704273i	$-0.751273\pi$
$761$		−	38.8564i		−	1.40855i	0.709930	−	0.704273i	$-0.248727\pi$
$762$	11.3508			0.411197
$763$			9.26253i			0.335326i
$764$	−3.79156	+	3.79156i	−0.137174	+	0.137174i
$765$	−3.19722	+	7.91890i	−0.115596	+	0.286309i
$766$	−36.9850			−1.33632
$767$	−3.22566	+	3.22566i	−0.116472	+	0.116472i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−11.6459	+	11.6459i	−0.419962	+	0.419962i	−0.885191	−	0.465228i	$-0.845972\pi$
$769$	−11.6459	+	11.6459i	−0.419962	+	0.419962i	0.465228	+	0.885191i	$0.345972\pi$
$770$	−4.10258	−	9.65858i	−0.147847	−	0.348071i
$771$	0.0524889	+	0.0524889i	0.00189034	+	0.00189034i
$772$		−	6.10797i		−	0.219831i
$773$	−2.91229	+	2.91229i	−0.104748	+	0.104748i	−0.757538	−	0.652791i	$-0.773598\pi$
$773$	−2.91229	+	2.91229i	−0.104748	+	0.104748i	0.652791	+	0.757538i	$0.273598\pi$
$774$		−	6.59679i		−	0.237117i
$775$	0.704276	+	39.2589i	0.0252983	+	1.41022i
$776$		−	10.4722i		−	0.375931i
$777$	−5.86657	+	24.5765i	−0.210462	+	0.881678i
$778$	2.10277	−	2.10277i	0.0753880	−	0.0753880i
$779$	0.310654	−	0.310654i	0.0111303	−	0.0111303i
$780$	4.32660	−	1.83777i	0.154917	−	0.0658027i
$781$			2.38266i			0.0852582i
$782$	−28.4509			−1.01740
$783$		−	1.41459i		−	0.0505532i
$784$			10.2547i			0.366238i
$785$	−1.23629	−	2.91057i	−0.0441252	−	0.103883i
$786$	6.52884			0.232876
$787$	16.8342	+	16.8342i	0.600076	+	0.600076i	0.940332	−	0.340257i	$-0.110514\pi$
$787$	16.8342	+	16.8342i	0.600076	+	0.600076i	−0.340257	+	0.940332i	$0.610514\pi$
$788$	16.3684	+	16.3684i	0.583099	+	0.583099i
$789$			14.2235i			0.506369i
$790$	−24.5902	+	10.4450i	−0.874881	+	0.371615i
$791$	41.0003	+	41.0003i	1.45780	+	1.45780i
$792$			1.12978i			0.0401450i
$793$	−6.58121	+	6.58121i	−0.233706	+	0.233706i
$794$	5.65369	+	5.65369i	0.200642	+	0.200642i
$795$	−18.8563	−	7.61313i	−0.668764	−	0.270010i
$796$	14.9530	−	14.9530i	0.529994	−	0.529994i
$797$			51.3349i			1.81837i	0.416388	+	0.909187i	$0.363296\pi$
$797$			51.3349i			1.81837i	−0.416388	+	0.909187i	$0.636704\pi$
$798$	0.176446	+	0.176446i	0.00624614	+	0.00624614i
$799$	−13.4546	−	13.4546i	−0.475990	−	0.475990i
$800$	−3.47155	+	3.59838i	−0.122738	+	0.127222i
$801$	−8.09450	−	8.09450i	−0.286005	−	0.286005i
$802$	−17.2850	+	17.2850i	−0.610354	+	0.610354i
$803$	7.85669	−	7.85669i	0.277256	−	0.277256i
$804$	3.66544			0.129270
$805$	63.6860	−	27.0513i	2.24464	−	0.953433i
$806$	−11.6735	−	11.6735i	−0.411183	−	0.411183i
$807$	0.498856	−	0.498856i	0.0175606	−	0.0175606i
$808$	−6.85371			−0.241113
$809$	20.1713	−	20.1713i	0.709186	−	0.709186i	−0.257178	−	0.966364i	$-0.582793\pi$
$809$	20.1713	−	20.1713i	0.709186	−	0.709186i	0.966364	+	0.257178i	$0.0827927\pi$
$810$	−0.837144	+	2.07345i	−0.0294142	+	0.0728536i
$811$	18.3009			0.642630			0.321315	−	0.946972i	$-0.395875\pi$
$811$	18.3009			0.642630			0.321315	+	0.946972i	$0.395875\pi$
$812$	5.87602			0.206208
$813$	−18.6216	−	18.6216i	−0.653087	−	0.653087i
$814$	−6.68438	−	1.59560i	−0.234287	−	0.0559258i
$815$	−41.3315	−	16.6874i	−1.44778	−	0.584533i
$816$	2.70058	+	2.70058i	0.0945392	+	0.0945392i
$817$	0.280216	−	0.280216i	0.00980351	−	0.00980351i
$818$	−17.8635	−	17.8635i	−0.624584	−	0.624584i
$819$	6.17474	+	6.17474i	0.215763	+	0.215763i
$820$	−6.12235	+	15.1639i	−0.213802	+	0.529547i
$821$	44.4703			1.55202			0.776012	−	0.630718i	$-0.217240\pi$
$821$	44.4703			1.55202			0.776012	+	0.630718i	$0.217240\pi$
$822$	−18.0408			−0.629246
$823$	−32.3201	+	32.3201i	−1.12661	+	1.12661i	−0.135883	+	0.990725i	$0.543387\pi$
$823$	−32.3201	+	32.3201i	−1.12661	+	1.12661i	−0.990725	+	0.135883i	$0.956613\pi$
$824$		−	11.0473i		−	0.384851i
$825$	5.64799	−	0.101321i	0.196638	−	0.00352754i
$826$	9.01377			0.313629
$827$	−31.5214			−1.09611			−0.548054	−	0.836443i	$-0.684631\pi$
$827$	−31.5214			−1.09611			−0.548054	+	0.836443i	$0.684631\pi$
$828$	−7.44945			−0.258886
$829$	5.62251	−	5.62251i	0.195278	−	0.195278i	−0.602694	−	0.797972i	$-0.705906\pi$
$829$	5.62251	−	5.62251i	0.195278	−	0.195278i	0.797972	+	0.602694i	$0.205906\pi$
$830$	3.46913	+	8.16726i	0.120415	+	0.283490i
$831$	6.24118	−	6.24118i	0.216504	−	0.216504i
$832$		−	2.10223i		−	0.0728817i
$833$		−	39.1646i		−	1.35697i
$834$	−7.56958	+	7.56958i	−0.262113	+	0.262113i
$835$	4.64401	+	1.87499i	0.160713	+	0.0648868i
$836$	−0.0479903	+	0.0479903i	−0.00165978	+	0.00165978i
$837$	7.85303			0.271441
$838$	13.1163			0.453094
$839$	−21.8089			−0.752926			−0.376463	−	0.926432i	$-0.622860\pi$
$839$	−21.8089			−0.752926			−0.376463	+	0.926432i	$0.622860\pi$
$840$	−8.61284	−	3.47739i	−0.297171	−	0.119981i
$841$			26.9989i			0.930998i
$842$	−1.41752	+	1.41752i	−0.0488510	+	0.0488510i
$843$	15.9466			0.549231
$844$	6.95993			0.239571
$845$	−17.7915	−	7.18322i	−0.612046	−	0.247110i
$846$	−3.52289	−	3.52289i	−0.121120	−	0.121120i
$847$	−28.5605	−	28.5605i	−0.981349	−	0.981349i
$848$	−6.43055	+	6.43055i	−0.220826	+	0.220826i
$849$	−15.1292	−	15.1292i	−0.519232	−	0.519232i
$850$	13.2585	−	13.7429i	0.454764	−	0.471378i
$851$	10.5209	−	44.0749i	0.360653	−	1.51087i
$852$	1.49126	+	1.49126i	0.0510897	+	0.0510897i
$853$	25.7642			0.882150			0.441075	−	0.897470i	$-0.354597\pi$
$853$	25.7642			0.882150			0.441075	+	0.897470i	$0.354597\pi$
$854$	18.3905			0.629310
$855$	−0.123635	+	0.0525152i	−0.00422822	+	0.00179598i
$856$	2.67190	−	2.67190i	0.0913237	−	0.0913237i
$857$	42.1740			1.44064			0.720319	−	0.693643i	$-0.243996\pi$
$857$	42.1740			1.44064			0.720319	+	0.693643i	$0.243996\pi$
$858$	−1.67942	+	1.67942i	−0.0573344	+	0.0573344i
$859$	21.7251	+	21.7251i	0.741250	+	0.741250i	0.972819	−	0.231568i	$-0.0743857\pi$
$859$	21.7251	+	21.7251i	0.741250	+	0.741250i	−0.231568	+	0.972819i	$0.574386\pi$
$860$	−5.52247	+	13.6781i	−0.188314	+	0.466420i
$861$	−30.3788			−1.03531
$862$	21.4522	−	21.4522i	0.730664	−	0.730664i
$863$	−1.51284	+	1.51284i	−0.0514976	+	0.0514976i	−0.732387	−	0.680889i	$-0.761594\pi$
$863$	−1.51284	+	1.51284i	−0.0514976	+	0.0514976i	0.680889	+	0.732387i	$0.261594\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−8.43941	−	19.8686i	−0.286948	−	0.675553i
$866$	−26.2287	−	26.2287i	−0.891288	−	0.891288i
$867$	1.70678	+	1.70678i	0.0579653	+	0.0579653i
$868$			32.6205i			1.10721i
$869$	9.54498	−	9.54498i	0.323791	−	0.323791i
$870$	−1.18421	+	2.93308i	−0.0401486	+	0.0994406i
$871$	5.44868	+	5.44868i	0.184622	+	0.184622i
$872$	−1.57675	+	1.57675i	−0.0533953	+	0.0533953i
$873$			10.4722i			0.354431i
$874$	−0.316434	−	0.316434i	−0.0107036	−	0.0107036i
$875$	−16.6117	+	43.3692i	−0.561579	+	1.46614i
$876$		−	9.83469i		−	0.332283i
$877$	33.4428	+	33.4428i	1.12928	+	1.12928i	0.990294	+	0.138990i	$0.0443855\pi$
$877$	33.4428	+	33.4428i	1.12928	+	1.12928i	0.138990	+	0.990294i	$0.455615\pi$
$878$	−10.4737	−	10.4737i	−0.353472	−	0.353472i
$879$	14.1807			0.478305
$880$	0.945788	−	2.34254i	0.0318825	−	0.0789670i
$881$			15.3576i			0.517411i	0.965956	+	0.258706i	$0.0832959\pi$
$881$			15.3576i			0.517411i	−0.965956	+	0.258706i	$0.916704\pi$
$882$		−	10.2547i		−	0.345293i
$883$	2.26602			0.0762575			0.0381287	−	0.999273i	$-0.487860\pi$
$883$	2.26602			0.0762575			0.0381287	+	0.999273i	$0.487860\pi$
$884$			8.02883i			0.270039i
$885$	−1.81658	+	4.49932i	−0.0610635	+	0.151243i
$886$	−5.10023	+	5.10023i	−0.171346	+	0.171346i
$887$	10.1536	−	10.1536i	0.340926	−	0.340926i	−0.515789	−	0.856715i	$-0.672501\pi$
$887$	10.1536	−	10.1536i	0.340926	−	0.340926i	0.856715	+	0.515789i	$0.172501\pi$
$888$	−5.18228	+	3.18497i	−0.173906	+	0.106880i
$889$		−	47.1499i		−	1.58136i
$890$	10.0073	+	23.5598i	0.335445	+	0.789726i
$891$		−	1.12978i		−	0.0378490i
$892$	1.57965	−	1.57965i	0.0528907	−	0.0528907i
$893$		−	0.299288i		−	0.0100153i
$894$	15.4088	+	15.4088i	0.515348	+	0.515348i
$895$	−5.26017	+	2.23431i	−0.175828	+	0.0746848i
$896$	−2.93723	+	2.93723i	−0.0981260	+	0.0981260i
$897$	−11.0736	−	11.0736i	−0.369737	−	0.369737i
$898$	1.76700	−	1.76700i	0.0589654	−	0.0589654i
$899$	11.1088			0.370499
$900$	3.47155	−	3.59838i	0.115718	−	0.119946i
$901$	24.5595	−	24.5595i	0.818197	−	0.818197i
$902$		−	8.26250i		−	0.275111i
$903$	−27.4022			−0.911889
$904$			13.9588i			0.464263i
$905$	−33.2417	−	13.4212i	−1.10499	−	0.446135i
$906$	−1.11168	−	1.11168i	−0.0369330	−	0.0369330i
$907$	17.3963			0.577634			0.288817	−	0.957384i	$-0.406738\pi$
$907$	17.3963			0.577634			0.288817	+	0.957384i	$0.406738\pi$
$908$	0.343113			0.0113866
$909$	6.85371			0.227323
$910$	−7.63386	−	17.9722i	−0.253060	−	0.595771i
$911$	−42.0562	+	42.0562i	−1.39338	+	1.39338i	−0.575776	+	0.817607i	$0.695300\pi$
$911$	−42.0562	+	42.0562i	−1.39338	+	1.39338i	−0.817607	+	0.575776i	$0.804700\pi$
$912$			0.0600724i			0.00198919i
$913$	−3.17021	−	3.17021i	−0.104919	−	0.104919i
$914$		−	31.6204i		−	1.04591i
$915$	−3.70630	+	9.17981i	−0.122527	+	0.303475i
$916$		−	29.6963i		−	0.981193i
$917$		−	27.1200i		−	0.895580i
$918$	−2.70058	−	2.70058i	−0.0891324	−	0.0891324i
$919$	29.6536	−	29.6536i	0.978181	−	0.978181i	−0.0215857	−	0.999767i	$-0.506871\pi$
$919$	29.6536	−	29.6536i	0.978181	−	0.978181i	0.999767	+	0.0215857i	$0.00687148\pi$
$920$	15.4460	+	6.23626i	0.509241	+	0.205603i
$921$	21.7164			0.715580
$922$	8.01857	+	8.01857i	0.264078	+	0.264078i
$923$			4.43352i			0.145931i
$924$	4.69296			0.154387
$925$	16.3870	+	25.6216i	0.538802	+	0.842432i
$926$	13.1675			0.432711
$927$			11.0473i			0.362841i
$928$	1.00026	+	1.00026i	0.0328353	+	0.0328353i
$929$	6.81010			0.223432			0.111716	−	0.993740i	$-0.464365\pi$
$929$	6.81010			0.223432			0.111716	+	0.993740i	$0.464365\pi$
$930$	−16.2829	−	6.57412i	−0.533936	−	0.215574i
$931$	0.435593	−	0.435593i	0.0142760	−	0.0142760i
$932$	−4.57105	−	4.57105i	−0.149730	−	0.149730i
$933$		−	30.3591i		−	0.993911i
$934$		−	2.65254i		−	0.0867938i
$935$	−3.61215	+	8.94661i	−0.118130	+	0.292586i
$936$			2.10223i			0.0687136i
$937$	−29.9829	−	29.9829i	−0.979500	−	0.979500i	0.0202941	−	0.999794i	$-0.493540\pi$
$937$	−29.9829	−	29.9829i	−0.979500	−	0.979500i	−0.999794	+	0.0202941i	$0.993540\pi$
$938$		−	15.2258i		−	0.497139i
$939$	−8.41215	+	8.41215i	−0.274520	+	0.274520i
$940$	4.35537	+	10.2537i	0.142056	+	0.334439i
$941$	4.40416			0.143571			0.0717857	−	0.997420i	$-0.477130\pi$
$941$	4.40416			0.143571			0.0717857	+	0.997420i	$0.477130\pi$
$942$	1.41420			0.0460771
$943$	54.4806			1.77413
$944$	1.53440	+	1.53440i	0.0499404	+	0.0499404i
$945$	8.61284	+	3.47739i	0.280176	+	0.113120i
$946$		−	7.45292i		−	0.242315i
$947$	42.5294			1.38202			0.691011	−	0.722845i	$-0.257166\pi$
$947$	42.5294			1.38202			0.691011	+	0.722845i	$0.257166\pi$
$948$		−	11.9480i		−	0.388054i
$949$	14.6193	−	14.6193i	0.474562	−	0.474562i
$950$	0.300313	−	0.00538741i	0.00974345	−	0.000174791i
$951$	−30.3282			−0.983461
$952$	11.2179	−	11.2179i	0.363573	−	0.363573i
$953$	25.4342	+	25.4342i	0.823894	+	0.823894i	0.986664	−	0.162770i	$-0.0520429\pi$
$953$	25.4342	+	25.4342i	0.823894	+	0.823894i	−0.162770	+	0.986664i	$0.552043\pi$
$954$	6.43055	−	6.43055i	0.208197	−	0.208197i
$955$	−11.0357	+	4.68753i	−0.357107	+	0.151685i
$956$	−12.3303	−	12.3303i	−0.398790	−	0.398790i
$957$		−	1.59817i		−	0.0516616i
$958$	−5.91428	+	5.91428i	−0.191082	+	0.191082i
$959$			74.9393i			2.41991i
$960$	−0.874200	−	2.05810i	−0.0282147	−	0.0664249i
$961$			30.6701i			0.989360i
$962$	−12.4379	−	2.96901i	−0.401015	−	0.0957246i
$963$	−2.67190	+	2.67190i	−0.0861008	+	0.0861008i
$964$	19.4485	−	19.4485i	0.626395	−	0.626395i
$965$	5.11325	−	12.6646i	0.164601	−	0.407687i
$966$			30.9441i			0.995609i
$967$	25.3173			0.814150			0.407075	−	0.913395i	$-0.366549\pi$
$967$	25.3173			0.814150			0.407075	+	0.913395i	$0.366549\pi$
$968$		−	9.72360i		−	0.312528i
$969$		−	0.229428i		−	0.00737029i
$970$	8.76675	−	21.7136i	0.281483	−	0.697182i
$971$	−50.4955			−1.62048			−0.810239	−	0.586100i	$-0.800663\pi$
$971$	−50.4955			−1.62048			−0.810239	+	0.586100i	$0.800663\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	31.4431	+	31.4431i	1.00802	+	1.00802i
$974$			15.5782i			0.499157i
$975$	10.5095	−	0.188532i	0.336572	−	0.00603786i
$976$	3.13059	+	3.13059i	0.100208	+	0.100208i
$977$		−	24.4091i		−	0.780917i	−0.920621	−	0.390459i	$-0.872316\pi$
$977$		−	24.4091i		−	0.780917i	0.920621	−	0.390459i	$-0.127684\pi$
$978$	14.0952	−	14.0952i	0.450716	−	0.450716i
$979$	−9.14500	−	9.14500i	−0.292276	−	0.292276i
$980$	−8.58463	+	21.2625i	−0.274226	+	0.679206i
$981$	1.57675	−	1.57675i	0.0503416	−	0.0503416i
$982$			19.8002i			0.631850i
$983$	−10.2716	−	10.2716i	−0.327613	−	0.327613i	0.524065	−	0.851678i	$-0.324415\pi$
$983$	−10.2716	−	10.2716i	−0.327613	−	0.327613i	−0.851678	+	0.524065i	$0.824415\pi$
$984$	−5.17134	−	5.17134i	−0.164856	−	0.164856i
$985$	20.2363	+	47.6416i	0.644782	+	1.51799i
$986$	−3.82020	−	3.82020i	−0.121660	−	0.121660i
$987$	−14.6336	+	14.6336i	−0.465794	+	0.465794i
$988$	−0.0892976	+	0.0892976i	−0.00284094	+	0.00284094i
$989$	49.1425			1.56264
$990$	−0.945788	+	2.34254i	−0.0300591	+	0.0744508i
$991$	−27.4329	−	27.4329i	−0.871435	−	0.871435i	0.121194	−	0.992629i	$-0.461328\pi$
$991$	−27.4329	−	27.4329i	−0.871435	−	0.871435i	−0.992629	+	0.121194i	$0.961328\pi$
$992$	−5.55293	+	5.55293i	−0.176306	+	0.176306i
$993$	1.85979			0.0590188
$994$	6.19450	−	6.19450i	0.196478	−	0.196478i
$995$	43.5220	−	18.4864i	1.37974	−	0.586059i
$996$	−3.96835			−0.125742
$997$	47.3611			1.49994			0.749971	−	0.661471i	$-0.230067\pi$
$997$	47.3611			1.49994			0.749971	+	0.661471i	$0.230067\pi$
$998$	6.66081	+	6.66081i	0.210844	+	0.210844i
$999$	5.18228	−	3.18497i	0.163960	−	0.100768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.697.10	yes	40
5.3	odd	4		1110.2.o.b.253.11	yes	40
37.6	odd	4		1110.2.o.b.487.11	yes	40
185.43	even	4	inner	1110.2.l.b.43.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.10	✓	40	185.43	even	4	inner
1110.2.l.b.697.10	yes	40	1.1	even	1	trivial
1110.2.o.b.253.11	yes	40	5.3	odd	4
1110.2.o.b.487.11	yes	40	37.6	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07345 - 0.837144i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.93723 - 2.93723i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07345 - 0.837144i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.93723 - 2.93723i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(0.837144 - 2.07345i) q^{10} +1.12978i q^{11} +(0.707107 + 0.707107i) q^{12} +2.10223i q^{13} +(2.93723 - 2.93723i) q^{14} +(0.874200 + 2.05810i) q^{15} +1.00000 q^{16} -3.81919 q^{17} -1.00000 q^{18} +(-0.0424776 - 0.0424776i) q^{19} +(2.07345 + 0.837144i) q^{20} +4.15387i q^{21} -1.12978 q^{22} -7.44945i q^{23} +(-0.707107 + 0.707107i) q^{24} +(3.59838 + 3.47155i) q^{25} -2.10223 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.93723 + 2.93723i) q^{28} +(1.00026 - 1.00026i) q^{29} +(-2.05810 + 0.874200i) q^{30} +(5.55293 + 5.55293i) q^{31} +1.00000i q^{32} +(0.798875 - 0.798875i) q^{33} -3.81919i q^{34} +(3.63131 + 8.54909i) q^{35} -1.00000i q^{36} +(5.91653 + 1.41231i) q^{37} +(0.0424776 - 0.0424776i) q^{38} +(1.48650 - 1.48650i) q^{39} +(-0.837144 + 2.07345i) q^{40} +7.31338i q^{41} -4.15387 q^{42} +6.59679i q^{43} -1.12978i q^{44} +(0.837144 - 2.07345i) q^{45} +7.44945 q^{46} +(3.52289 + 3.52289i) q^{47} +(-0.707107 - 0.707107i) q^{48} +10.2547i q^{49} +(-3.47155 + 3.59838i) q^{50} +(2.70058 + 2.70058i) q^{51} -2.10223i q^{52} +(-6.43055 + 6.43055i) q^{53} +(0.707107 + 0.707107i) q^{54} +(0.945788 - 2.34254i) q^{55} +(-2.93723 + 2.93723i) q^{56} +0.0600724i q^{57} +(1.00026 + 1.00026i) q^{58} +(1.53440 + 1.53440i) q^{59} +(-0.874200 - 2.05810i) q^{60} +(3.13059 + 3.13059i) q^{61} +(-5.55293 + 5.55293i) q^{62} +(2.93723 - 2.93723i) q^{63} -1.00000 q^{64} +(1.75987 - 4.35887i) q^{65} +(0.798875 + 0.798875i) q^{66} +(2.59186 - 2.59186i) q^{67} +3.81919 q^{68} +(-5.26755 + 5.26755i) q^{69} +(-8.54909 + 3.63131i) q^{70} +2.10896 q^{71} +1.00000 q^{72} +(-6.95418 - 6.95418i) q^{73} +(-1.41231 + 5.91653i) q^{74} +(-0.0896820 - 4.99920i) q^{75} +(0.0424776 + 0.0424776i) q^{76} +(3.31842 - 3.31842i) q^{77} +(1.48650 + 1.48650i) q^{78} +(-8.44853 - 8.44853i) q^{79} +(-2.07345 - 0.837144i) q^{80} -1.00000 q^{81} -7.31338 q^{82} +(-2.80605 + 2.80605i) q^{83} -4.15387i q^{84} +(7.91890 + 3.19722i) q^{85} -6.59679 q^{86} -1.41459 q^{87} +1.12978 q^{88} +(-8.09450 + 8.09450i) q^{89} +(2.07345 + 0.837144i) q^{90} +(6.17474 - 6.17474i) q^{91} +7.44945i q^{92} -7.85303i q^{93} +(-3.52289 + 3.52289i) q^{94} +(0.0525152 + 0.123635i) q^{95} +(0.707107 - 0.707107i) q^{96} +10.4722 q^{97} -10.2547 q^{98} -1.12978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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