LMFDB - Embedded newform 429.2.s.a.166.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.s (of order $6$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.5
Character	$\chi$	$=$	429.166
Dual form			429.2.s.a.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.761768 + 0.439807i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.613140 + 1.06199i) q^{4} +3.40975i q^{5} +(-0.761768 - 0.439807i) q^{6} +(4.33112 + 2.50057i) q^{7} -2.83788i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.761768 + 0.439807i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.613140 + 1.06199i) q^{4} +3.40975i q^{5} +(-0.761768 - 0.439807i) q^{6} +(4.33112 + 2.50057i) q^{7} -2.83788i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.49963 - 2.59744i) q^{10} +(0.866025 - 0.500000i) q^{11} -1.22628 q^{12} +(2.75617 + 2.32455i) q^{13} -4.39907 q^{14} +(-2.95293 + 1.70487i) q^{15} +(0.0218405 + 0.0378288i) q^{16} +(2.58602 - 4.47912i) q^{17} -0.879614i q^{18} +(-0.950353 - 0.548686i) q^{19} +(-3.62111 - 2.09065i) q^{20} +5.00114i q^{21} +(-0.439807 + 0.761768i) q^{22} +(-1.23550 - 2.13996i) q^{23} +(2.45768 - 1.41894i) q^{24} -6.62638 q^{25} +(-3.12191 - 0.558588i) q^{26} -1.00000 q^{27} +(-5.31116 + 3.06640i) q^{28} +(-2.18481 - 3.78420i) q^{29} +(1.49963 - 2.59744i) q^{30} -3.68100i q^{31} +(4.88208 + 2.81867i) q^{32} +(0.866025 + 0.500000i) q^{33} +4.54940i q^{34} +(-8.52631 + 14.7680i) q^{35} +(-0.613140 - 1.06199i) q^{36} +(1.62178 - 0.936337i) q^{37} +0.965265 q^{38} +(-0.635038 + 3.54919i) q^{39} +9.67646 q^{40} +(-4.64689 + 2.68288i) q^{41} +(-2.19954 - 3.80971i) q^{42} +(2.82091 - 4.88596i) q^{43} +1.22628i q^{44} +(-2.95293 - 1.70487i) q^{45} +(1.88234 + 1.08677i) q^{46} -8.84511i q^{47} +(-0.0218405 + 0.0378288i) q^{48} +(9.00571 + 15.5983i) q^{49} +(5.04776 - 2.91433i) q^{50} +5.17204 q^{51} +(-4.15856 + 1.50174i) q^{52} -2.84315 q^{53} +(0.761768 - 0.439807i) q^{54} +(1.70487 + 2.95293i) q^{55} +(7.09632 - 12.2912i) q^{56} -1.09737i q^{57} +(3.32863 + 1.92179i) q^{58} +(1.23833 + 0.714950i) q^{59} -4.18130i q^{60} +(-0.730589 + 1.26542i) q^{61} +(1.61893 + 2.80407i) q^{62} +(-4.33112 + 2.50057i) q^{63} -5.04604 q^{64} +(-7.92614 + 9.39783i) q^{65} -0.879614 q^{66} +(8.61171 - 4.97197i) q^{67} +(3.17118 + 5.49265i) q^{68} +(1.23550 - 2.13996i) q^{69} -14.9997i q^{70} +(-10.7542 - 6.20896i) q^{71} +(2.45768 + 1.41894i) q^{72} -12.1774i q^{73} +(-0.823616 + 1.42654i) q^{74} +(-3.31319 - 5.73861i) q^{75} +(1.16540 - 0.672843i) q^{76} +5.00114 q^{77} +(-1.07721 - 2.98295i) q^{78} -12.9175 q^{79} +(-0.128987 + 0.0744706i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.35990 - 4.08747i) q^{82} +3.29589i q^{83} +(-5.31116 - 3.06640i) q^{84} +(15.2727 + 8.81768i) q^{85} +4.96262i q^{86} +(2.18481 - 3.78420i) q^{87} +(-1.41894 - 2.45768i) q^{88} +(2.75762 - 1.59211i) q^{89} +2.99926 q^{90} +(6.12457 + 16.9599i) q^{91} +3.03015 q^{92} +(3.18784 - 1.84050i) q^{93} +(3.89014 + 6.73792i) q^{94} +(1.87088 - 3.24046i) q^{95} +5.63734i q^{96} +(15.5099 + 8.95467i) q^{97} +(-13.7205 - 7.92155i) q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.761768	+	0.439807i	−0.538651	+	0.310991i	−0.744532	−	0.667587i	$-0.767327\pi$
$2$	−0.761768	+	0.439807i	−0.538651	+	0.310991i	0.205881	+	0.978577i	$0.433994\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.613140	+	1.06199i	−0.306570	+	0.530994i
$5$			3.40975i			1.52489i	0.647056	+	0.762443i	$0.276000\pi$
$5$			3.40975i			1.52489i	−0.647056	+	0.762443i	$0.724000\pi$
$6$	−0.761768	−	0.439807i	−0.310991	−	0.179550i
$7$	4.33112	+	2.50057i	1.63701	+	0.945127i	0.981856	+	0.189630i	$0.0607289\pi$
$7$	4.33112	+	2.50057i	1.63701	+	0.945127i	0.655152	+	0.755497i	$0.272604\pi$
$8$		−	2.83788i		−	1.00334i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.49963	−	2.59744i	−0.474225	−	0.821382i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	−1.22628			−0.353996
$13$	2.75617	+	2.32455i	0.764423	+	0.644715i
$13$	2.75617	+	2.32455i	0.764423	+	0.644715i
$14$	−4.39907			−1.17570
$15$	−2.95293	+	1.70487i	−0.762443	+	0.440197i
$16$	0.0218405	+	0.0378288i	0.00546012	+	0.00945721i
$17$	2.58602	−	4.47912i	0.627202	−	1.08635i	−0.360908	−	0.932601i	$-0.617533\pi$
$17$	2.58602	−	4.47912i	0.627202	−	1.08635i	0.988111	−	0.153745i	$-0.0491335\pi$
$18$		−	0.879614i		−	0.207327i
$19$	−0.950353	−	0.548686i	−0.218026	−	0.125877i	0.387010	−	0.922076i	$-0.373508\pi$
$19$	−0.950353	−	0.548686i	−0.218026	−	0.125877i	−0.605036	+	0.796198i	$0.706841\pi$
$20$	−3.62111	−	2.09065i	−0.809706	−	0.467484i
$21$			5.00114i			1.09134i
$22$	−0.439807	+	0.761768i	−0.0937672	+	0.162410i
$23$	−1.23550	−	2.13996i	−0.257620	−	0.446212i	0.707984	−	0.706229i	$-0.249605\pi$
$23$	−1.23550	−	2.13996i	−0.257620	−	0.446212i	−0.965604	+	0.260017i	$0.916272\pi$
$24$	2.45768	−	1.41894i	0.501671	−	0.289640i
$25$	−6.62638			−1.32528
$26$	−3.12191	−	0.558588i	−0.612258	−	0.109548i
$27$	−1.00000			−0.192450
$28$	−5.31116	+	3.06640i	−1.00371	+	0.579495i
$29$	−2.18481	−	3.78420i	−0.405709	−	0.702708i	0.588695	−	0.808355i	$-0.299642\pi$
$29$	−2.18481	−	3.78420i	−0.405709	−	0.702708i	−0.994404	+	0.105647i	$0.966309\pi$
$30$	1.49963	−	2.59744i	0.273794	−	0.474225i
$31$		−	3.68100i		−	0.661128i	−0.943784	−	0.330564i	$-0.892761\pi$
$31$		−	3.68100i		−	0.661128i	0.943784	−	0.330564i	$-0.107239\pi$
$32$	4.88208	+	2.81867i	0.863038	+	0.498275i
$33$	0.866025	+	0.500000i	0.150756	+	0.0870388i
$34$			4.54940i			0.780216i
$35$	−8.52631	+	14.7680i	−1.44121	+	2.49625i
$36$	−0.613140	−	1.06199i	−0.102190	−	0.176998i
$37$	1.62178	−	0.936337i	0.266620	−	0.153933i	−0.360731	−	0.932670i	$-0.617473\pi$
$37$	1.62178	−	0.936337i	0.266620	−	0.153933i	0.627350	+	0.778737i	$0.284139\pi$
$38$	0.965265			0.156587
$39$	−0.635038	+	3.54919i	−0.101687	+	0.568325i
$40$	9.67646			1.52998
$41$	−4.64689	+	2.68288i	−0.725722	+	0.418996i	−0.816855	−	0.576843i	$-0.804284\pi$
$41$	−4.64689	+	2.68288i	−0.725722	+	0.418996i	0.0911334	+	0.995839i	$0.470951\pi$
$42$	−2.19954	−	3.80971i	−0.339396	−	0.587851i
$43$	2.82091	−	4.88596i	0.430185	−	0.745102i	−0.566704	−	0.823921i	$-0.691782\pi$
$43$	2.82091	−	4.88596i	0.430185	−	0.745102i	0.996889	+	0.0788197i	$0.0251151\pi$
$44$			1.22628i			0.184869i
$45$	−2.95293	−	1.70487i	−0.440197	−	0.254148i
$46$	1.88234	+	1.08677i	0.277535	+	0.160235i
$47$		−	8.84511i		−	1.29019i	−0.764102	−	0.645096i	$-0.776817\pi$
$47$		−	8.84511i		−	1.29019i	0.764102	−	0.645096i	$-0.223183\pi$
$48$	−0.0218405	+	0.0378288i	−0.00315240	+	0.00546012i
$49$	9.00571	+	15.5983i	1.28653	+	2.22834i
$50$	5.04776	−	2.91433i	0.713861	−	0.412148i
$51$	5.17204			0.724231
$52$	−4.15856	+	1.50174i	−0.576689	+	0.208254i
$53$	−2.84315			−0.390537			−0.195269	−	0.980750i	$-0.562558\pi$
$53$	−2.84315			−0.390537			−0.195269	+	0.980750i	$0.562558\pi$
$54$	0.761768	−	0.439807i	0.103664	−	0.0598502i
$55$	1.70487	+	2.95293i	0.229885	+	0.398173i
$56$	7.09632	−	12.2912i	0.948286	−	1.64248i
$57$		−	1.09737i		−	0.145351i
$58$	3.32863	+	1.92179i	0.437071	+	0.252343i
$59$	1.23833	+	0.714950i	0.161217	+	0.0930786i	0.578438	−	0.815726i	$-0.303663\pi$
$59$	1.23833	+	0.714950i	0.161217	+	0.0930786i	−0.417221	+	0.908805i	$0.636996\pi$
$60$		−	4.18130i		−	0.539804i
$61$	−0.730589	+	1.26542i	−0.0935423	+	0.162020i	−0.908999	−	0.416798i	$-0.863152\pi$
$61$	−0.730589	+	1.26542i	−0.0935423	+	0.162020i	0.815457	+	0.578818i	$0.196486\pi$
$62$	1.61893	+	2.80407i	0.205604	+	0.356117i
$63$	−4.33112	+	2.50057i	−0.545669	+	0.315042i
$64$	−5.04604			−0.630755
$65$	−7.92614	+	9.39783i	−0.983116	+	1.16566i
$66$	−0.879614			−0.108273
$67$	8.61171	−	4.97197i	1.05209	−	0.607423i	0.128854	−	0.991664i	$-0.458870\pi$
$67$	8.61171	−	4.97197i	1.05209	−	0.607423i	0.923233	+	0.384241i	$0.125537\pi$
$68$	3.17118	+	5.49265i	0.384563	+	0.666082i
$69$	1.23550	−	2.13996i	0.148737	−	0.257620i
$70$		−	14.9997i		−	1.79281i
$71$	−10.7542	−	6.20896i	−1.27629	−	0.736867i	−0.300127	−	0.953899i	$-0.597029\pi$
$71$	−10.7542	−	6.20896i	−1.27629	−	0.736867i	−0.976165	+	0.217032i	$0.930362\pi$
$72$	2.45768	+	1.41894i	0.289640	+	0.167224i
$73$		−	12.1774i		−	1.42525i	−0.701544	−	0.712626i	$-0.747506\pi$
$73$		−	12.1774i		−	1.42525i	0.701544	−	0.712626i	$-0.252494\pi$
$74$	−0.823616	+	1.42654i	−0.0957434	+	0.165832i
$75$	−3.31319	−	5.73861i	−0.382574	−	0.662638i
$76$	1.16540	−	0.672843i	0.133680	−	0.0771804i
$77$	5.00114			0.569933
$78$	−1.07721	−	2.98295i	−0.121970	−	0.337753i
$79$	−12.9175			−1.45333			−0.726666	−	0.686991i	$-0.758931\pi$
$79$	−12.9175			−1.45333			−0.726666	+	0.686991i	$0.758931\pi$
$80$	−0.128987	+	0.0744706i	−0.0144212	+	0.00832606i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.35990	−	4.08747i	0.260607	−	0.451385i
$83$			3.29589i			0.361771i	0.983504	+	0.180885i	$0.0578963\pi$
$83$			3.29589i			0.361771i	−0.983504	+	0.180885i	$0.942104\pi$
$84$	−5.31116	−	3.06640i	−0.579495	−	0.334571i
$85$	15.2727	+	8.81768i	1.65655	+	0.956412i
$86$			4.96262i			0.535133i
$87$	2.18481	−	3.78420i	0.234236	−	0.405709i
$88$	−1.41894	−	2.45768i	−0.151260	−	0.261989i
$89$	2.75762	−	1.59211i	0.292307	−	0.168764i	−0.346675	−	0.937985i	$-0.612689\pi$
$89$	2.75762	−	1.59211i	0.292307	−	0.168764i	0.638982	+	0.769222i	$0.279356\pi$
$90$	2.99926			0.316150
$91$	6.12457	+	16.9599i	0.642029	+	1.77788i
$92$	3.03015			0.315915
$93$	3.18784	−	1.84050i	0.330564	−	0.190851i
$94$	3.89014	+	6.73792i	0.401237	+	0.694963i
$95$	1.87088	−	3.24046i	0.191948	−	0.332465i
$96$			5.63734i			0.575358i
$97$	15.5099	+	8.95467i	1.57480	+	0.909209i	0.995568	+	0.0940424i	$0.0299789\pi$
$97$	15.5099	+	8.95467i	1.57480	+	0.909209i	0.579227	+	0.815166i	$0.303354\pi$
$98$	−13.7205	−	7.92155i	−1.38598	−	0.800197i
$99$			1.00000i			0.100504i
$100$	4.06289	−	7.03714i	0.406289	−	0.703714i
$101$	−2.84316	−	4.92449i	−0.282905	−	0.490005i	0.689194	−	0.724577i	$-0.257965\pi$
$101$	−2.84316	−	4.92449i	−0.282905	−	0.490005i	−0.972099	+	0.234572i	$0.924631\pi$
$102$	−3.93990	+	2.27470i	−0.390108	+	0.225229i
$103$	−7.59244			−0.748106			−0.374053	−	0.927407i	$-0.622032\pi$
$103$	−7.59244			−0.748106			−0.374053	+	0.927407i	$0.622032\pi$
$104$	6.59680	−	7.82167i	0.646870	−	0.766978i
$105$	−17.0526			−1.66417
$106$	2.16582	−	1.25044i	0.210363	−	0.121453i
$107$	7.24562	+	12.5498i	0.700461	+	1.21323i	0.968305	+	0.249771i	$0.0803555\pi$
$107$	7.24562	+	12.5498i	0.700461	+	1.21323i	−0.267844	+	0.963462i	$0.586311\pi$
$108$	0.613140	−	1.06199i	0.0589994	−	0.102190i
$109$		−	19.2493i		−	1.84375i	−0.387493	−	0.921873i	$-0.626659\pi$
$109$		−	19.2493i		−	1.84375i	0.387493	−	0.921873i	$-0.373341\pi$
$110$	−2.59744	−	1.49963i	−0.247656	−	0.142984i
$111$	1.62178	+	0.936337i	0.153933	+	0.0888732i
$112$			0.218455i			0.0206420i
$113$	−3.56685	+	6.17797i	−0.335541	+	0.581175i	−0.983589	−	0.180425i	$-0.942253\pi$
$113$	−3.56685	+	6.17797i	−0.335541	+	0.581175i	0.648047	+	0.761600i	$0.275586\pi$
$114$	0.482632	+	0.835944i	0.0452027	+	0.0782933i
$115$	7.29671	−	4.21276i	0.680422	−	0.392842i
$116$	5.35837			0.497512
$117$	−3.39120	+	1.22463i	−0.313517	+	0.113217i
$118$	−1.25776			−0.115786
$119$	22.4007	−	12.9331i	2.05347	−	1.18557i
$120$	4.83823	+	8.38006i	0.441668	+	0.764991i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	1.28527i		−	0.116363i
$123$	−4.64689	−	2.68288i	−0.418996	−	0.241907i
$124$	3.90918	+	2.25697i	0.351055	+	0.202682i
$125$		−	5.54554i		−	0.496008i
$126$	2.19954	−	3.80971i	0.195950	−	0.339396i
$127$	2.40326	+	4.16258i	0.213255	+	0.369369i	0.952731	−	0.303814i	$-0.0982601\pi$
$127$	2.40326	+	4.16258i	0.213255	+	0.369369i	−0.739476	+	0.673183i	$0.764927\pi$
$128$	−5.92024	+	3.41805i	−0.523280	+	0.302116i
$129$	5.64182			0.496734
$130$	1.90465	−	10.6449i	0.167048	−	0.933623i
$131$	20.0968			1.75587			0.877934	−	0.478782i	$-0.158922\pi$
$131$	20.0968			1.75587			0.877934	+	0.478782i	$0.158922\pi$
$132$	−1.06199	+	0.613140i	−0.0924343	+	0.0533670i
$133$	−2.74406	−	4.75285i	−0.237940	−	0.412124i
$134$	−4.37341	+	7.57498i	−0.377805	+	0.654378i
$135$		−	3.40975i		−	0.293464i
$136$	−12.7112	−	7.33882i	−1.08998	−	0.629299i
$137$	−9.80999	−	5.66380i	−0.838124	−	0.483891i	0.0185021	−	0.999829i	$-0.494110\pi$
$137$	−9.80999	−	5.66380i	−0.838124	−	0.483891i	−0.856626	+	0.515938i	$0.827444\pi$
$138$			2.17353i			0.185023i
$139$	−3.36002	+	5.81973i	−0.284993	+	0.493623i	−0.972608	−	0.232453i	$-0.925325\pi$
$139$	−3.36002	+	5.81973i	−0.284993	+	0.493623i	0.687614	+	0.726076i	$0.258658\pi$
$140$	−10.4556	−	18.1097i	−0.883663	−	1.53055i
$141$	7.66009	−	4.42255i	0.645096	−	0.372446i
$142$	10.9230			0.916635
$143$	3.54919	+	0.635038i	0.296798	+	0.0531045i
$144$	−0.0436810			−0.00364008
$145$	12.9032	−	7.44965i	1.07155	−	0.618659i
$146$	5.35569	+	9.27632i	0.443240	+	0.767714i
$147$	−9.00571	+	15.5983i	−0.742778	+	1.28653i
$148$			2.29642i			0.188765i
$149$	6.45367	+	3.72603i	0.528706	+	0.305248i	0.740489	−	0.672068i	$-0.234594\pi$
$149$	6.45367	+	3.72603i	0.528706	+	0.305248i	−0.211784	+	0.977317i	$0.567927\pi$
$150$	5.04776	+	2.91433i	0.412148	+	0.237954i
$151$			5.94468i			0.483771i	0.970305	+	0.241886i	$0.0777658\pi$
$151$			5.94468i			0.483771i	−0.970305	+	0.241886i	$0.922234\pi$
$152$	−1.55711	+	2.69699i	−0.126298	+	0.218755i
$153$	2.58602	+	4.47912i	0.209067	+	0.362115i
$154$	−3.80971	+	2.19954i	−0.306995	+	0.177244i
$155$	12.5513			1.00814
$156$	−3.37983	−	2.85055i	−0.270603	−	0.228227i
$157$	−15.4935			−1.23651			−0.618256	−	0.785977i	$-0.712160\pi$
$157$	−15.4935			−1.23651			−0.618256	+	0.785977i	$0.712160\pi$
$158$	9.84014	−	5.68121i	0.782839	−	0.451972i
$159$	−1.42158	−	2.46224i	−0.112738	−	0.195269i
$160$	−9.61095	+	16.6467i	−0.759812	+	1.31603i
$161$		−	12.3579i		−	0.973936i
$162$	0.761768	+	0.439807i	0.0598502	+	0.0345545i
$163$	−6.81948	−	3.93723i	−0.534143	−	0.308387i	0.208559	−	0.978010i	$-0.433123\pi$
$163$	−6.81948	−	3.93723i	−0.534143	−	0.308387i	−0.742702	+	0.669622i	$0.766456\pi$
$164$		−	6.57992i		−	0.513805i
$165$	−1.70487	+	2.95293i	−0.132724	+	0.229885i
$166$	−1.44956	−	2.51070i	−0.112507	−	0.194868i
$167$	6.73045	−	3.88583i	0.520818	−	0.300694i	−0.216451	−	0.976293i	$-0.569448\pi$
$167$	6.73045	−	3.88583i	0.520818	−	0.300694i	0.737269	+	0.675599i	$0.236115\pi$
$168$	14.1926			1.09499
$169$	2.19291	+	12.8137i	0.168686	+	0.985670i
$170$	−15.5123			−1.18974
$171$	0.950353	−	0.548686i	0.0726753	−	0.0419591i
$172$	3.45922	+	5.99155i	0.263763	+	0.456851i
$173$	−11.4071	+	19.7577i	−0.867267	+	1.50215i	−0.00248858	+	0.999997i	$0.500792\pi$
$173$	−11.4071	+	19.7577i	−0.867267	+	1.50215i	−0.864778	+	0.502154i	$0.832541\pi$
$174$			3.84358i			0.291381i
$175$	−28.6996	−	16.5697i	−2.16949	−	1.25255i
$176$	0.0378288	+	0.0218405i	0.00285146	+	0.00164629i
$177$			1.42990i			0.107478i
$178$	−1.40044	+	2.42564i	−0.104968	+	0.181810i
$179$	9.40751	+	16.2943i	0.703150	+	1.21789i	0.967355	+	0.253425i	$0.0815572\pi$
$179$	9.40751	+	16.2943i	0.703150	+	1.21789i	−0.264205	+	0.964467i	$0.585109\pi$
$180$	3.62111	−	2.09065i	0.269902	−	0.155828i
$181$	−19.8421			−1.47485			−0.737427	−	0.675427i	$-0.763959\pi$
$181$	−19.8421			−1.47485			−0.737427	+	0.675427i	$0.763959\pi$
$182$	−12.1246	−	10.2259i	−0.898734	−	0.757993i
$183$	−1.46118			−0.108013
$184$	−6.07294	+	3.50621i	−0.447703	+	0.258481i
$185$	3.19267	+	5.52987i	0.234730	+	0.406564i
$186$	−1.61893	+	2.80407i	−0.118706	+	0.205604i
$187$		−	5.17204i		−	0.378217i
$188$	9.39341	+	5.42329i	0.685085	+	0.395534i
$189$	−4.33112	−	2.50057i	−0.315042	−	0.181890i
$190$			3.29131i			0.238777i
$191$	−4.34762	+	7.53029i	−0.314583	+	0.544873i	−0.979349	−	0.202179i	$-0.935198\pi$
$191$	−4.34762	+	7.53029i	−0.314583	+	0.544873i	0.664766	+	0.747052i	$0.268531\pi$
$192$	−2.52302	−	4.37000i	−0.182083	−	0.315378i
$193$	−23.9466	+	13.8256i	−1.72371	+	0.995187i	−0.812860	+	0.582459i	$0.802091\pi$
$193$	−23.9466	+	13.8256i	−1.72371	+	0.995187i	−0.910854	+	0.412728i	$0.864576\pi$
$194$	−15.7533			−1.13102
$195$	−12.1018	−	2.16532i	−0.866630	−	0.155062i
$196$	−22.0870			−1.57764
$197$	−16.6423	+	9.60845i	−1.18572	+	0.684574i	−0.957330	−	0.288997i	$-0.906678\pi$
$197$	−16.6423	+	9.60845i	−1.18572	+	0.684574i	−0.228386	+	0.973571i	$0.573345\pi$
$198$	−0.439807	−	0.761768i	−0.0312557	−	0.0541365i
$199$	3.11410	−	5.39379i	0.220753	−	0.382355i	−0.734284	−	0.678843i	$-0.762482\pi$
$199$	3.11410	−	5.39379i	0.220753	−	0.382355i	0.955037	+	0.296487i	$0.0958152\pi$
$200$			18.8049i			1.32970i
$201$	8.61171	+	4.97197i	0.607423	+	0.350696i
$202$	4.33165	+	2.50088i	0.304774	+	0.175961i
$203$		−	21.8531i		−	1.53379i
$204$	−3.17118	+	5.49265i	−0.222027	+	0.384563i
$205$	−9.14794	−	15.8447i	−0.638920	−	1.10664i
$206$	5.78368	−	3.33921i	0.402968	−	0.232654i
$207$	2.47101			0.171747
$208$	−0.0277391	+	0.155032i	−0.00192336	+	0.0107495i
$209$	−1.09737			−0.0759069
$210$	12.9901	−	7.49987i	0.896405	−	0.517540i
$211$	13.8203	+	23.9375i	0.951429	+	1.64792i	0.742335	+	0.670028i	$0.233718\pi$
$211$	13.8203	+	23.9375i	0.951429	+	1.64792i	0.209094	+	0.977896i	$0.432949\pi$
$212$	1.74325	−	3.01940i	0.119727	−	0.207373i
$213$		−	12.4179i		−	0.850861i
$214$	−11.0390	−	6.37335i	−0.754608	−	0.435673i
$215$	16.6599	+	9.61859i	1.13619	+	0.655982i
$216$			2.83788i			0.193093i
$217$	9.20461	−	15.9429i	0.624850	−	1.08227i
$218$	8.46596	+	14.6635i	0.573387	+	0.993136i
$219$	10.5459	−	6.08868i	0.712626	−	0.411435i
$220$	−4.18130			−0.281903
$221$	17.5395	−	6.33386i	1.17983	−	0.426062i
$222$	−1.64723			−0.110555
$223$	−5.58549	+	3.22478i	−0.374032	+	0.215947i	−0.675218	−	0.737618i	$-0.735951\pi$
$223$	−5.58549	+	3.22478i	−0.374032	+	0.215947i	0.301187	+	0.953565i	$0.402617\pi$
$224$	14.0966	+	24.4160i	0.941866	+	1.63136i
$225$	3.31319	−	5.73861i	0.220879	−	0.382574i
$226$		−	6.27491i		−	0.417401i
$227$	4.64378	+	2.68109i	0.308218	+	0.177950i	0.646129	−	0.763228i	$-0.276387\pi$
$227$	4.64378	+	2.68109i	0.308218	+	0.177950i	−0.337911	+	0.941178i	$0.609720\pi$
$228$	1.16540	+	0.672843i	0.0771804	+	0.0445601i
$229$		−	24.4129i		−	1.61325i	−0.591063	−	0.806625i	$-0.701292\pi$
$229$		−	24.4129i		−	1.61325i	0.591063	−	0.806625i	$-0.298708\pi$
$230$	−3.70560	+	6.41829i	−0.244340	+	0.423209i
$231$	2.50057	+	4.33112i	0.164525	+	0.284966i
$232$	−10.7391	+	6.20023i	−0.705057	+	0.407065i
$233$	−18.1952			−1.19201			−0.596003	−	0.802982i	$-0.703246\pi$
$233$	−18.1952			−1.19201			−0.596003	+	0.802982i	$0.703246\pi$
$234$	2.04471	−	2.42436i	0.133667	−	0.158486i
$235$	30.1596			1.96739
$236$	−1.51854	+	0.876729i	−0.0988484	+	0.0570702i
$237$	−6.45875	−	11.1869i	−0.419541	−	0.726666i
$238$	−11.3761	+	19.7040i	−0.737403	+	1.27722i
$239$			8.40576i			0.543724i	0.962336	+	0.271862i	$0.0876393\pi$
$239$			8.40576i			0.543724i	−0.962336	+	0.271862i	$0.912361\pi$
$240$	−0.128987	−	0.0744706i	−0.00832606	−	0.00480705i
$241$	−9.20921	−	5.31694i	−0.593217	−	0.342494i	0.173151	−	0.984895i	$-0.444605\pi$
$241$	−9.20921	−	5.31694i	−0.593217	−	0.342494i	−0.766369	+	0.642401i	$0.777938\pi$
$242$			0.879614i			0.0565437i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.895906	−	1.55175i	−0.0573545	−	0.0993409i
$245$	−53.1864	+	30.7072i	−3.39796	+	1.96181i
$246$	4.71980			0.300923
$247$	−1.34388	−	3.72142i	−0.0855091	−	0.236788i
$248$	−10.4462			−0.663337
$249$	−2.85432	+	1.64794i	−0.180885	+	0.104434i
$250$	2.43897	+	4.22441i	0.154254	+	0.267175i
$251$	3.55436	−	6.15633i	0.224349	−	0.388584i	−0.731775	−	0.681547i	$-0.761308\pi$
$251$	3.55436	−	6.15633i	0.224349	−	0.388584i	0.956124	+	0.292962i	$0.0946410\pi$
$252$		−	6.13280i		−	0.386330i
$253$	−2.13996	−	1.23550i	−0.134538	−	0.0776755i
$254$	−3.66146	−	2.11394i	−0.229740	−	0.132641i
$255$			17.6354i			1.10437i
$256$	8.05261	−	13.9475i	0.503288	−	0.871721i
$257$	−10.3643	−	17.9515i	−0.646507	−	1.11978i	−0.983951	−	0.178437i	$-0.942896\pi$
$257$	−10.3643	−	17.9515i	−0.646507	−	1.11978i	0.337444	−	0.941345i	$-0.390438\pi$
$258$	−4.29776	+	2.48131i	−0.267567	+	0.154480i
$259$	9.36551			0.581945
$260$	−5.12057	−	14.1797i	−0.317564	−	0.879385i
$261$	4.36962			0.270473
$262$	−15.3091	+	8.83872i	−0.945801	+	0.546058i
$263$	11.5968	+	20.0863i	0.715091	+	1.23857i	0.962924	+	0.269771i	$0.0869481\pi$
$263$	11.5968	+	20.0863i	0.715091	+	1.23857i	−0.247834	+	0.968803i	$0.579719\pi$
$264$	1.41894	−	2.45768i	0.0873297	−	0.151260i
$265$		−	9.69444i		−	0.595524i
$266$	4.18067	+	2.41371i	0.256333	+	0.147994i
$267$	2.75762	+	1.59211i	0.168764	+	0.0974357i
$268$			12.1940i			0.744870i
$269$	7.79655	−	13.5040i	0.475364	−	0.823355i	−0.524238	−	0.851572i	$-0.675650\pi$
$269$	7.79655	−	13.5040i	0.475364	−	0.823355i	0.999602	+	0.0282170i	$0.00898295\pi$
$270$	1.49963	+	2.59744i	0.0912646	+	0.158075i
$271$	−0.267146	+	0.154237i	−0.0162280	+	0.00936923i	−0.508092	−	0.861303i	$-0.669649\pi$
$271$	−0.267146	+	0.154237i	−0.0162280	+	0.00936923i	0.491864	+	0.870672i	$0.336316\pi$
$272$	0.225920			0.0136984
$273$	−11.6254	+	13.7840i	−0.703602	+	0.834244i
$274$	9.96392			0.601942
$275$	−5.73861	+	3.31319i	−0.346051	+	0.199793i
$276$	1.51507	+	2.62418i	0.0911967	+	0.157957i
$277$	2.48028	−	4.29597i	0.149026	−	0.258120i	−0.781842	−	0.623477i	$-0.785720\pi$
$277$	2.48028	−	4.29597i	0.149026	−	0.258120i	0.930868	+	0.365357i	$0.119053\pi$
$278$		−	5.91105i		−	0.354521i
$279$	3.18784	+	1.84050i	0.190851	+	0.110188i
$280$	41.9098	+	24.1967i	2.50459	+	1.44603i
$281$			11.3485i			0.676995i	0.940967	+	0.338498i	$0.109919\pi$
$281$			11.3485i			0.676995i	−0.940967	+	0.338498i	$0.890081\pi$
$282$	−3.89014	+	6.73792i	−0.231654	+	0.401237i
$283$	−5.54097	−	9.59724i	−0.329376	−	0.570497i	0.653012	−	0.757348i	$-0.273505\pi$
$283$	−5.54097	−	9.59724i	−0.329376	−	0.570497i	−0.982388	+	0.186851i	$0.940172\pi$
$284$	13.1877	−	7.61391i	0.782545	−	0.451803i
$285$	3.74176			0.221643
$286$	−2.98295	+	1.07721i	−0.176386	+	0.0636965i
$287$	−26.8349			−1.58402
$288$	−4.88208	+	2.81867i	−0.287679	+	0.166092i
$289$	−4.87502	−	8.44378i	−0.286766	−	0.496693i
$290$	−6.55281	+	11.3498i	−0.384794	+	0.666483i
$291$			17.9093i			1.04986i
$292$	12.9322	+	7.46642i	0.756801	+	0.436939i
$293$	13.8651	+	8.00504i	0.810010	+	0.467660i	0.846959	−	0.531657i	$-0.178431\pi$
$293$	13.8651	+	8.00504i	0.810010	+	0.467660i	−0.0369492	+	0.999317i	$0.511764\pi$
$294$		−	15.8431i		−	0.923988i
$295$	−2.43780	+	4.22239i	−0.141934	+	0.245837i
$296$	−2.65721	−	4.60243i	−0.154447	−	0.267511i
$297$	−0.866025	+	0.500000i	−0.0502519	+	0.0290129i
$298$	−6.55494			−0.379717
$299$	1.56918	−	8.77007i	0.0907483	−	0.507186i
$300$	8.12579			0.469143
$301$	24.4354	−	14.1078i	1.40843	−	0.813158i
$302$	−2.61451	−	4.52847i	−0.150448	−	0.260584i
$303$	2.84316	−	4.92449i	0.163335	−	0.282905i
$304$		−	0.0479343i		−	0.00274922i
$305$	−4.31475	−	2.49112i	−0.247062	−	0.142641i
$306$	−3.93990	−	2.27470i	−0.225229	−	0.130036i
$307$		−	5.32938i		−	0.304164i	−0.988368	−	0.152082i	$-0.951402\pi$
$307$		−	5.32938i		−	0.304164i	0.988368	−	0.152082i	$-0.0485978\pi$
$308$	−3.06640	+	5.31116i	−0.174724	+	0.302631i
$309$	−3.79622	−	6.57525i	−0.215959	−	0.374053i
$310$	−9.56117	+	5.52015i	−0.543038	+	0.313523i
$311$	4.48211			0.254157			0.127079	−	0.991893i	$-0.459440\pi$
$311$	4.48211			0.254157			0.127079	+	0.991893i	$0.459440\pi$
$312$	10.0722	+	1.80216i	0.570224	+	0.102027i
$313$	−11.7899			−0.666406			−0.333203	−	0.942855i	$-0.608129\pi$
$313$	−11.7899			−0.666406			−0.333203	+	0.942855i	$0.608129\pi$
$314$	11.8024	−	6.81413i	0.666049	−	0.384544i
$315$	−8.52631	−	14.7680i	−0.480403	−	0.832083i
$316$	7.92023	−	13.7182i	0.445548	−	0.771711i
$317$		−	24.2780i		−	1.36359i	−0.731545	−	0.681793i	$-0.761201\pi$
$317$		−	24.2780i		−	1.36359i	0.731545	−	0.681793i	$-0.238799\pi$
$318$	2.16582	+	1.25044i	0.121453	+	0.0701211i
$319$	−3.78420	−	2.18481i	−0.211875	−	0.122326i
$320$		−	17.2057i		−	0.961830i
$321$	−7.24562	+	12.5498i	−0.404411	+	0.700461i
$322$	5.43507	+	9.41382i	0.302885	+	0.524612i
$323$	−4.91527	+	2.83783i	−0.273493	+	0.157901i
$324$	1.22628			0.0681266
$325$	−18.2634	−	15.4034i	−1.01307	−	0.854425i
$326$	6.92648			0.383622
$327$	16.6704	−	9.62463i	0.921873	−	0.532243i
$328$	7.61369	+	13.1873i	0.420396	+	0.728147i
$329$	22.1178	−	38.3092i	1.21939	−	2.11205i
$330$		−	2.99926i		−	0.165104i
$331$	6.68289	+	3.85837i	0.367325	+	0.212075i	0.672289	−	0.740289i	$-0.265311\pi$
$331$	6.68289	+	3.85837i	0.367325	+	0.212075i	−0.304964	+	0.952364i	$0.598645\pi$
$332$	−3.50020	−	2.02084i	−0.192098	−	0.110908i
$333$			1.87267i			0.102622i
$334$	−3.41803	+	5.92020i	−0.187026	+	0.323939i
$335$	16.9532	+	29.3637i	0.926250	+	1.60431i
$336$	−0.189187	+	0.109227i	−0.0103210	+	0.00595884i
$337$	−1.22268			−0.0666034			−0.0333017	−	0.999445i	$-0.510602\pi$
$337$	−1.22268			−0.0666034			−0.0333017	+	0.999445i	$0.510602\pi$
$338$	−7.30605	−	8.79662i	−0.397397	−	0.478473i
$339$	−7.13371			−0.387450
$340$	−18.7286	+	10.8129i	−1.01570	+	0.586414i
$341$	−1.84050	−	3.18784i	−0.0996688	−	0.172631i
$342$	−0.482632	+	0.835944i	−0.0260978	+	0.0452027i
$343$			55.0697i			2.97348i
$344$	−13.8658	−	8.00540i	−0.747592	−	0.431622i
$345$	7.29671	+	4.21276i	0.392842	+	0.226807i
$346$		−	20.0677i		−	1.07885i
$347$	−1.05662	+	1.83012i	−0.0567225	+	0.0982462i	−0.892992	−	0.450072i	$-0.851398\pi$
$347$	−1.05662	+	1.83012i	−0.0567225	+	0.0982462i	0.836270	+	0.548318i	$0.184732\pi$
$348$	2.67919	+	4.64049i	0.143619	+	0.248756i
$349$	11.3688	−	6.56378i	0.608558	−	0.351351i	−0.163843	−	0.986486i	$-0.552389\pi$
$349$	11.3688	−	6.56378i	0.608558	−	0.351351i	0.772401	+	0.635135i	$0.219056\pi$
$350$	29.1499			1.55813
$351$	−2.75617	−	2.32455i	−0.147113	−	0.124075i
$352$	5.63734			0.300471
$353$	−9.94652	+	5.74263i	−0.529400	+	0.305649i	−0.740772	−	0.671756i	$-0.765540\pi$
$353$	−9.94652	+	5.74263i	−0.529400	+	0.305649i	0.211372	+	0.977406i	$0.432207\pi$
$354$	−0.628880	−	1.08925i	−0.0334246	−	0.0578931i
$355$	21.1710	−	36.6692i	1.12364	−	1.94620i
$356$			3.90475i			0.206951i
$357$	22.4007	+	12.9331i	1.18557	+	0.684490i
$358$	−14.3327	−	8.27498i	−0.757506	−	0.437346i
$359$		−	22.2266i		−	1.17307i	−0.809922	−	0.586537i	$-0.800491\pi$
$359$		−	22.2266i		−	1.17307i	0.809922	−	0.586537i	$-0.199509\pi$
$360$	−4.83823	+	8.38006i	−0.254997	+	0.441668i
$361$	−8.89789	−	15.4116i	−0.468310	−	0.811136i
$362$	15.1151	−	8.72671i	0.794432	−	0.458666i
$363$	1.00000			0.0524864
$364$	−21.7664	−	3.89456i	−1.14087	−	0.204130i
$365$	41.5217			2.17335
$366$	1.11308	−	0.642636i	0.0581815	−	0.0335911i
$367$	−6.74713	−	11.6864i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$367$	−6.74713	−	11.6864i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$368$	0.0539680	−	0.0934754i	0.00281328	−	0.00487274i
$369$		−	5.36576i		−	0.279330i
$370$	−4.86415	−	2.80832i	−0.252875	−	0.145998i
$371$	−12.3140	−	7.10951i	−0.639312	−	0.369107i
$372$			4.51394i			0.234037i
$373$	−7.58949	+	13.1454i	−0.392969	+	0.680642i	−0.992840	−	0.119455i	$-0.961885\pi$
$373$	−7.58949	+	13.1454i	−0.392969	+	0.680642i	0.599871	+	0.800097i	$0.295219\pi$
$374$	2.27470	+	3.93990i	0.117622	+	0.203727i
$375$	4.80258	−	2.77277i	0.248004	−	0.143185i
$376$	−25.1014			−1.29450
$377$	2.77487	−	15.5086i	0.142913	−	0.798733i
$378$	4.39907			0.226264
$379$	−4.05968	+	2.34386i	−0.208532	+	0.120396i	−0.600629	−	0.799528i	$-0.705083\pi$
$379$	−4.05968	+	2.34386i	−0.208532	+	0.120396i	0.392097	+	0.919924i	$0.371750\pi$
$380$	2.29422	+	3.97371i	0.117691	+	0.203847i
$381$	−2.40326	+	4.16258i	−0.123123	+	0.213255i
$382$		−	7.64845i		−	0.391329i
$383$	11.5588	+	6.67346i	0.590625	+	0.340998i	0.765345	−	0.643621i	$-0.222569\pi$
$383$	11.5588	+	6.67346i	0.590625	+	0.340998i	−0.174719	+	0.984618i	$0.555902\pi$
$384$	−5.92024	−	3.41805i	−0.302116	−	0.174427i
$385$			17.0526i			0.869082i
$386$	12.1612	−	21.0638i	0.618987	−	1.07212i
$387$	2.82091	+	4.88596i	0.143395	+	0.248367i
$388$	−19.0195	+	10.9809i	−0.965569	+	0.557472i
$389$	−4.48568			−0.227433			−0.113717	−	0.993513i	$-0.536276\pi$
$389$	−4.48568			−0.227433			−0.113717	+	0.993513i	$0.536276\pi$
$390$	10.1711	−	3.67300i	0.515034	−	0.185990i
$391$	−12.7802			−0.646321
$392$	44.2662	−	25.5571i	2.23578	−	1.29083i
$393$	10.0484	+	17.4044i	0.506875	+	0.877934i
$394$	8.45173	−	14.6388i	0.425792	−	0.737493i
$395$		−	44.0454i		−	2.21616i
$396$	−1.06199	−	0.613140i	−0.0533670	−	0.0308114i
$397$	23.0445	+	13.3048i	1.15657	+	0.667747i	0.950480	−	0.310786i	$-0.100592\pi$
$397$	23.0445	+	13.3048i	1.15657	+	0.667747i	0.206091	+	0.978533i	$0.433926\pi$
$398$			5.47842i			0.274608i
$399$	2.74406	−	4.75285i	0.137375	−	0.237940i
$400$	−0.144723	−	0.250668i	−0.00723617	−	0.0125334i
$401$	−12.8424	+	7.41458i	−0.641320	+	0.370266i	−0.785123	−	0.619340i	$-0.787400\pi$
$401$	−12.8424	+	7.41458i	−0.641320	+	0.370266i	0.143803	+	0.989606i	$0.454067\pi$
$402$	−8.74683			−0.436252
$403$	8.55669	−	10.1455i	0.426239	−	0.505381i
$404$	6.97300			0.346920
$405$	2.95293	−	1.70487i	0.146732	−	0.0847159i
$406$	9.61114	+	16.6470i	0.476993	+	0.826175i
$407$	0.936337	−	1.62178i	0.0464125	−	0.0803888i
$408$		−	14.6776i		−	0.726652i
$409$	−14.6134	−	8.43707i	−0.722588	−	0.417186i	0.0931164	−	0.995655i	$-0.470317\pi$
$409$	−14.6134	−	8.43707i	−0.722588	−	0.417186i	−0.815705	+	0.578469i	$0.803650\pi$
$410$	13.9372	+	8.04666i	0.688310	+	0.397396i
$411$		−	11.3276i		−	0.558749i
$412$	4.65523	−	8.06309i	0.229347	−	0.397240i
$413$	3.57557	+	6.19307i	0.175942	+	0.304741i
$414$	−1.88234	+	1.08677i	−0.0925117	+	0.0534117i
$415$	−11.2381			−0.551659
$416$	6.90368	+	19.1174i	0.338481	+	0.937306i
$417$	−6.72004			−0.329082
$418$	0.835944	−	0.482632i	0.0408873	−	0.0236063i
$419$	−4.78424	−	8.28655i	−0.233725	−	0.404824i	0.725176	−	0.688563i	$-0.241758\pi$
$419$	−4.78424	−	8.28655i	−0.233725	−	0.404824i	−0.958901	+	0.283739i	$0.908425\pi$
$420$	10.4556	−	18.1097i	0.510183	−	0.883663i
$421$			28.3549i			1.38193i	0.722886	+	0.690967i	$0.242815\pi$
$421$			28.3549i			1.38193i	−0.722886	+	0.690967i	$0.757185\pi$
$422$	−21.0557	−	12.1565i	−1.02498	−	0.591771i
$423$	7.66009	+	4.42255i	0.372446	+	0.215032i
$424$			8.06853i			0.391842i
$425$	−17.1360	+	29.6803i	−0.831216	+	1.43971i
$426$	5.46148	+	9.45957i	0.264610	+	0.458318i
$427$	−6.32853	+	3.65378i	−0.306259	+	0.176819i
$428$	−17.7703			−0.858961
$429$	1.22463	+	3.39120i	0.0591259	+	0.163729i
$430$	−16.9213			−0.816017
$431$	21.7411	−	12.5522i	1.04723	−	0.604620i	0.125360	−	0.992111i	$-0.459992\pi$
$431$	21.7411	−	12.5522i	1.04723	−	0.604620i	0.921873	+	0.387491i	$0.126658\pi$
$432$	−0.0218405	−	0.0378288i	−0.00105080	−	0.00182004i
$433$	0.892413	−	1.54570i	0.0428866	−	0.0742818i	−0.843785	−	0.536681i	$-0.819678\pi$
$433$	0.892413	−	1.54570i	0.0428866	−	0.0742818i	0.886672	+	0.462399i	$0.153011\pi$
$434$			16.1930i			0.777289i
$435$	12.9032	+	7.44965i	0.618659	+	0.357183i
$436$	20.4425	+	11.8025i	0.979019	+	0.565237i
$437$			2.71162i			0.129714i
$438$	−5.35569	+	9.27632i	−0.255905	+	0.443240i
$439$	7.48846	+	12.9704i	0.357405	+	0.619043i	0.987526	−	0.157453i	$-0.0503284\pi$
$439$	7.48846	+	12.9704i	0.357405	+	0.619043i	−0.630122	+	0.776496i	$0.716995\pi$
$440$	8.38006	−	4.83823i	0.399504	−	0.230653i
$441$	−18.0114			−0.857687
$442$	−10.5753	+	12.5389i	−0.503017	+	0.596415i
$443$	−13.7138			−0.651564			−0.325782	−	0.945445i	$-0.605628\pi$
$443$	−13.7138			−0.651564			−0.325782	+	0.945445i	$0.605628\pi$
$444$	−1.98876	+	1.14821i	−0.0943824	+	0.0544917i
$445$	5.42870	+	9.40279i	0.257345	+	0.445735i
$446$	2.83656	−	4.91307i	0.134315	−	0.232641i
$447$			7.45206i			0.352470i
$448$	−21.8550	−	12.6180i	−1.03255	−	0.596144i
$449$	−15.0297	−	8.67743i	−0.709298	−	0.409513i	0.101503	−	0.994835i	$-0.467635\pi$
$449$	−15.0297	−	8.67743i	−0.709298	−	0.409513i	−0.810801	+	0.585322i	$0.800968\pi$
$450$			5.82865i			0.274765i
$451$	−2.68288	+	4.64689i	−0.126332	+	0.218813i
$452$	−4.37396	−	7.57592i	−0.205734	−	0.356341i
$453$	−5.14824	+	2.97234i	−0.241886	+	0.139653i
$454$	−4.71664			−0.221363
$455$	−57.8290	+	20.8832i	−2.71106	+	0.979021i
$456$	−3.11421			−0.145836
$457$	22.0856	−	12.7511i	1.03312	−	0.596472i	0.115243	−	0.993337i	$-0.463235\pi$
$457$	22.0856	−	12.7511i	1.03312	−	0.596472i	0.917877	+	0.396866i	$0.129902\pi$
$458$	10.7370	+	18.5970i	0.501706	+	0.868980i
$459$	−2.58602	+	4.47912i	−0.120705	+	0.209067i
$460$			10.3320i			0.481733i
$461$	23.1743	+	13.3797i	1.07933	+	0.623153i	0.930716	−	0.365742i	$-0.119185\pi$
$461$	23.1743	+	13.3797i	1.07933	+	0.623153i	0.148616	+	0.988895i	$0.452518\pi$
$462$	−3.80971	−	2.19954i	−0.177244	−	0.102332i
$463$		−	40.3958i		−	1.87735i	−0.344797	−	0.938677i	$-0.612052\pi$
$463$		−	40.3958i		−	1.87735i	0.344797	−	0.938677i	$-0.387948\pi$
$464$	0.0954346	−	0.165298i	0.00443044	−	0.00767375i
$465$	6.27565	+	10.8697i	0.291026	+	0.504072i
$466$	13.8605	−	8.00237i	0.642076	−	0.370703i
$467$	5.47728			0.253458			0.126729	−	0.991937i	$-0.459552\pi$
$467$	5.47728			0.253458			0.126729	+	0.991937i	$0.459552\pi$
$468$	0.778734	−	4.35229i	0.0359970	−	0.201185i
$469$	49.7311			2.29637
$470$	−22.9746	+	13.2644i	−1.05974	+	0.611841i
$471$	−7.74673	−	13.4177i	−0.356950	−	0.618256i
$472$	2.02894	−	3.51423i	0.0933897	−	0.161756i
$473$		−	5.64182i		−	0.259411i
$474$	9.84014	+	5.68121i	0.451972	+	0.260946i
$475$	6.29740	+	3.63580i	0.288944	+	0.166822i
$476$			31.7191i			1.45384i
$477$	1.42158	−	2.46224i	0.0650895	−	0.112738i
$478$	−3.69691	−	6.40324i	−0.169093	−	0.292877i
$479$	−0.930887	+	0.537448i	−0.0425333	+	0.0245566i	−0.521116	−	0.853486i	$-0.674484\pi$
$479$	−0.930887	+	0.537448i	−0.0425333	+	0.0245566i	0.478583	+	0.878043i	$0.341151\pi$
$480$	−19.2219			−0.877356
$481$	6.64647	+	1.18922i	0.303053	+	0.0542238i
$482$	9.35371			0.426050
$483$	10.7022	−	6.17893i	0.486968	−	0.281151i
$484$	0.613140	+	1.06199i	0.0278700	+	0.0482722i
$485$	−30.5331	+	52.8850i	−1.38644	+	2.40138i
$486$			0.879614i			0.0399001i
$487$	1.23860	+	0.715107i	0.0561264	+	0.0324046i	0.527801	−	0.849368i	$-0.323017\pi$
$487$	1.23860	+	0.715107i	0.0561264	+	0.0324046i	−0.471674	+	0.881773i	$0.656350\pi$
$488$	3.59110	+	2.07332i	0.162561	+	0.0938549i
$489$		−	7.87446i		−	0.356095i
$490$	27.0105	−	46.7835i	1.22021	−	2.11346i
$491$	3.50398	+	6.06907i	0.158132	+	0.273893i	0.934195	−	0.356762i	$-0.116119\pi$
$491$	3.50398	+	6.06907i	0.158132	+	0.273893i	−0.776063	+	0.630656i	$0.782786\pi$
$492$	5.69838	−	3.28996i	0.256903	−	0.148323i
$493$	−22.5999			−1.01785
$494$	2.66043	+	2.24381i	0.119698	+	0.100954i
$495$	−3.40975			−0.153257
$496$	0.139248	−	0.0803949i	0.00625242	−	0.00360984i
$497$	−31.0519	−	53.7834i	−1.39287	−	2.41252i
$498$	1.44956	−	2.51070i	0.0649561	−	0.112507i
$499$			42.6766i			1.91047i	0.295853	+	0.955233i	$0.404396\pi$
$499$			42.6766i			1.91047i	−0.295853	+	0.955233i	$0.595604\pi$
$500$	5.88930	+	3.40019i	0.263377	+	0.152061i
$501$	6.73045	+	3.88583i	0.300694	+	0.173606i
$502$			6.25293i			0.279082i
$503$	3.61113	−	6.25466i	0.161012	−	0.278882i	−0.774220	−	0.632917i	$-0.781857\pi$
$503$	3.61113	−	6.25466i	0.161012	−	0.278882i	0.935232	+	0.354035i	$0.115191\pi$
$504$	7.09632	+	12.2912i	0.316095	+	0.547493i
$505$	16.7913	−	9.69444i	0.747202	−	0.431397i
$506$	2.17353			0.0966253
$507$	−10.0005	+	8.30597i	−0.444140	+	0.368881i
$508$	−5.89415			−0.261510
$509$	0.123541	−	0.0713264i	0.00547586	−	0.00316149i	−0.497260	−	0.867602i	$-0.665660\pi$
$509$	0.123541	−	0.0713264i	0.00547586	−	0.00316149i	0.502735	+	0.864440i	$0.332327\pi$
$510$	−7.75616	−	13.4341i	−0.343448	−	0.594870i
$511$	30.4503	−	52.7415i	1.34704	−	2.33315i
$512$			0.494167i			0.0218393i
$513$	0.950353	+	0.548686i	0.0419591	+	0.0242251i
$514$	15.7904	+	9.11658i	0.696484	+	0.402115i
$515$		−	25.8883i		−	1.14078i
$516$	−3.45922	+	5.99155i	−0.152284	+	0.263763i
$517$	−4.42255	−	7.66009i	−0.194504	−	0.336890i
$518$	−7.13435	+	4.11902i	−0.313465	+	0.180979i
$519$	−22.8142			−1.00143
$520$	26.6699	+	22.4934i	1.16955	+	0.986402i
$521$	−6.09268			−0.266925			−0.133463	−	0.991054i	$-0.542610\pi$
$521$	−6.09268			−0.266925			−0.133463	+	0.991054i	$0.542610\pi$
$522$	−3.32863	+	1.92179i	−0.145690	+	0.0841144i
$523$	−10.8072	−	18.7186i	−0.472566	−	0.818508i	0.526942	−	0.849902i	$-0.323339\pi$
$523$	−10.8072	−	18.7186i	−0.472566	−	0.818508i	−0.999507	+	0.0313940i	$0.990005\pi$
$524$	−12.3222	+	21.3426i	−0.538296	+	0.932356i
$525$		−	33.1395i		−	1.44632i
$526$	−17.6682	−	10.2007i	−0.770369	−	0.444773i
$527$	−16.4877	−	9.51916i	−0.718214	−	0.414661i
$528$			0.0436810i			0.00190097i
$529$	8.44706	−	14.6307i	0.367263	−	0.636119i
$530$	4.26368	+	7.38491i	0.185202	+	0.320780i
$531$	−1.23833	+	0.714950i	−0.0537390	+	0.0310262i
$532$	6.72996			0.291781
$533$	−19.0441	−	3.40746i	−0.824891	−	0.147594i
$534$	−2.80089			−0.121206
$535$	−42.7916	+	24.7057i	−1.85004	+	1.06812i
$536$	−14.1099	−	24.4390i	−0.609453	−	1.05560i
$537$	−9.40751	+	16.2943i	−0.405964	+	0.703150i
$538$			13.7159i			0.591335i
$539$	15.5983	+	9.00571i	0.671868	+	0.387903i
$540$	3.62111	+	2.09065i	0.155828	+	0.0899673i
$541$		−	38.6879i		−	1.66332i	−0.555284	−	0.831661i	$-0.687390\pi$
$541$		−	38.6879i		−	1.66332i	0.555284	−	0.831661i	$-0.312610\pi$
$542$	0.135669	−	0.234986i	0.00582749	−	0.0100935i
$543$	−9.92106	−	17.1838i	−0.425754	−	0.737427i
$544$	25.2503	−	14.5783i	1.08260	−	0.625039i
$545$	65.6351			2.81150
$546$	2.79358	−	15.6131i	0.119554	−	0.668181i
$547$	20.8960			0.893447			0.446724	−	0.894672i	$-0.352591\pi$
$547$	20.8960			0.893447			0.446724	+	0.894672i	$0.352591\pi$
$548$	12.0298	−	6.94540i	0.513887	−	0.296693i
$549$	−0.730589	−	1.26542i	−0.0311808	−	0.0540067i
$550$	2.91433	−	5.04776i	0.124267	−	0.215237i
$551$			4.79510i			0.204278i
$552$	−6.07294	−	3.50621i	−0.258481	−	0.149234i
$553$	−55.9472	−	32.3011i	−2.37912	−	1.37358i
$554$			4.36338i			0.185382i
$555$	−3.19267	+	5.52987i	−0.135521	+	0.234730i
$556$	−4.12033	−	7.13661i	−0.174741	−	0.302660i
$557$	1.87435	−	1.08216i	0.0794188	−	0.0458524i	−0.459765	−	0.888041i	$-0.652066\pi$
$557$	1.87435	−	1.08216i	0.0794188	−	0.0458524i	0.539183	+	0.842188i	$0.318733\pi$
$558$	−3.23786			−0.137070
$559$	19.1326	−	6.90916i	0.809221	−	0.292226i
$560$	−0.744876			−0.0314767
$561$	4.47912	−	2.58602i	0.189109	−	0.109182i
$562$	−4.99115	−	8.64493i	−0.210539	−	0.364664i
$563$	−5.80824	+	10.0602i	−0.244788	+	0.423985i	−0.962072	−	0.272796i	$-0.912052\pi$
$563$	−5.80824	+	10.0602i	−0.244788	+	0.423985i	0.717284	+	0.696781i	$0.245385\pi$
$564$			10.8466i			0.456723i
$565$	−21.0653	−	12.1621i	−0.886225	−	0.511662i
$566$	8.44187	+	4.87391i	0.354838	+	0.204866i
$567$		−	5.00114i		−	0.210028i
$568$	−17.6203	+	30.5192i	−0.739330	+	1.28056i
$569$	−2.71031	−	4.69440i	−0.113622	−	0.196800i	0.803606	−	0.595162i	$-0.202912\pi$
$569$	−2.71031	−	4.69440i	−0.113622	−	0.196800i	−0.917228	+	0.398362i	$0.869579\pi$
$570$	−2.85036	+	1.64565i	−0.119388	+	0.0689289i
$571$	42.7522			1.78912			0.894562	−	0.446944i	$-0.147488\pi$
$571$	42.7522			1.78912			0.894562	+	0.446944i	$0.147488\pi$
$572$	−2.85055	+	3.37983i	−0.119187	+	0.141318i
$573$	−8.69523			−0.363249
$574$	20.4420	−	11.8022i	0.853232	−	0.492614i
$575$	8.18692	+	14.1802i	0.341418	+	0.591353i
$576$	2.52302	−	4.37000i	0.105126	−	0.182083i
$577$		−	5.28596i		−	0.220058i	−0.993928	−	0.110029i	$-0.964906\pi$
$577$		−	5.28596i		−	0.220058i	0.993928	−	0.110029i	$-0.0350943\pi$
$578$	7.42727	+	4.28813i	0.308934	+	0.178363i
$579$	−23.9466	−	13.8256i	−0.995187	−	0.574571i
$580$			18.2707i			0.758649i
$581$	−8.24160	+	14.2749i	−0.341919	+	0.592222i
$582$	−7.87665	−	13.6428i	−0.326498	−	0.565510i
$583$	−2.46224	+	1.42158i	−0.101976	+	0.0588757i
$584$	−34.5579			−1.43002
$585$	−4.17569	−	11.5632i	−0.172644	−	0.478078i
$586$	−14.0827			−0.581751
$587$	−14.8476	+	8.57227i	−0.612826	+	0.353815i	−0.774071	−	0.633099i	$-0.781783\pi$
$587$	−14.8476	+	8.57227i	−0.612826	+	0.353815i	0.161244	+	0.986914i	$0.448449\pi$
$588$	−11.0435	−	19.1279i	−0.455427	−	0.788822i
$589$	−2.01972	+	3.49825i	−0.0832210	+	0.144143i
$590$		−	4.28865i		−	0.176561i
$591$	−16.6423	−	9.60845i	−0.684574	−	0.395239i
$592$	0.0708411	+	0.0409001i	0.00291155	+	0.00168099i
$593$			36.7188i			1.50786i	0.656955	+	0.753930i	$0.271844\pi$
$593$			36.7188i			1.50786i	−0.656955	+	0.753930i	$0.728156\pi$
$594$	0.439807	−	0.761768i	0.0180455	−	0.0312557i
$595$	44.0985	+	76.3808i	1.80786	+	3.13131i
$596$	−7.91401	+	4.56915i	−0.324170	+	0.187160i
$597$	6.22821			0.254904
$598$	2.66178	+	7.37090i	0.108848	+	0.301418i
$599$	−41.2327			−1.68472			−0.842361	−	0.538913i	$-0.818835\pi$
$599$	−41.2327			−1.68472			−0.842361	+	0.538913i	$0.818835\pi$
$600$	−16.2855	+	9.40243i	−0.664852	+	0.383853i
$601$	−9.00370	−	15.5949i	−0.367269	−	0.636128i	0.621869	−	0.783122i	$-0.286374\pi$
$601$	−9.00370	−	15.5949i	−0.367269	−	0.636128i	−0.989137	+	0.146993i	$0.953040\pi$
$602$	−12.4094	+	21.4937i	−0.505769	+	0.876017i
$603$			9.94394i			0.404949i
$604$	−6.31318	−	3.64492i	−0.256880	−	0.148310i
$605$	2.95293	+	1.70487i	0.120054	+	0.0693130i
$606$			5.00176i			0.203183i
$607$	−10.3301	+	17.8923i	−0.419286	+	0.726225i	−0.995868	−	0.0908145i	$-0.971053\pi$
$607$	−10.3301	+	17.8923i	−0.419286	+	0.726225i	0.576582	+	0.817040i	$0.304386\pi$
$608$	−3.09313	−	5.35746i	−0.125443	−	0.217274i
$609$	18.9253	−	10.9265i	0.766893	−	0.442766i
$610$	4.38245			0.177440
$611$	20.5609	−	24.3786i	0.831806	−	0.986252i
$612$	−6.34237			−0.256375
$613$	6.12746	−	3.53769i	0.247486	−	0.142886i	−0.371127	−	0.928582i	$-0.621028\pi$
$613$	6.12746	−	3.53769i	0.247486	−	0.142886i	0.618612	+	0.785696i	$0.287695\pi$
$614$	2.34390	+	4.05976i	0.0945921	+	0.163838i
$615$	9.14794	−	15.8447i	0.368881	−	0.638920i
$616$		−	14.1926i		−	0.571838i
$617$	27.2749	+	15.7472i	1.09805	+	0.633958i	0.935708	−	0.352777i	$-0.114762\pi$
$617$	27.2749	+	15.7472i	1.09805	+	0.633958i	0.162340	+	0.986735i	$0.448096\pi$
$618$	5.78368	+	3.33921i	0.232654	+	0.134323i
$619$			7.05254i			0.283465i	0.989905	+	0.141733i	$0.0452674\pi$
$619$			7.05254i			0.283465i	−0.989905	+	0.141733i	$0.954733\pi$
$620$	−7.69569	+	13.3293i	−0.309067	+	0.535319i
$621$	1.23550	+	2.13996i	0.0495791	+	0.0858735i
$622$	−3.41433	+	1.97127i	−0.136902	+	0.0790405i
$623$	15.9248			0.638012
$624$	−0.148131	+	0.0534932i	−0.00592999	+	0.00214144i
$625$	−14.2230			−0.568920
$626$	8.98119	−	5.18529i	0.358960	−	0.207246i
$627$	−0.548686	−	0.950353i	−0.0219124	−	0.0379534i
$628$	9.49965	−	16.4539i	0.379077	−	0.656581i
$629$		−	9.68556i		−	0.386188i
$630$	12.9901	+	7.49987i	0.517540	+	0.298802i
$631$	23.2779	+	13.4395i	0.926678	+	0.535018i	0.885759	−	0.464145i	$-0.153638\pi$
$631$	23.2779	+	13.4395i	0.926678	+	0.535018i	0.0409183	+	0.999162i	$0.486972\pi$
$632$			36.6583i			1.45819i
$633$	−13.8203	+	23.9375i	−0.549308	+	0.951429i
$634$	10.6776	+	18.4942i	0.424062	+	0.734497i
$635$	−14.1933	+	8.19452i	−0.563245	+	0.325190i
$636$	3.48650			0.138249
$637$	−11.4379	+	63.9259i	−0.453187	+	2.53284i
$638$	3.84358			0.152169
$639$	10.7542	−	6.20896i	0.425431	−	0.245622i
$640$	−11.6547	−	20.1865i	−0.460692	−	0.797943i
$641$	4.20087	−	7.27613i	0.165925	−	0.287390i	−0.771059	−	0.636764i	$-0.780273\pi$
$641$	4.20087	−	7.27613i	0.165925	−	0.287390i	0.936983	+	0.349374i	$0.113606\pi$
$642$		−	12.7467i		−	0.503072i
$643$	−2.80805	−	1.62123i	−0.110739	−	0.0639350i	0.443608	−	0.896221i	$-0.353698\pi$
$643$	−2.80805	−	1.62123i	−0.110739	−	0.0639350i	−0.554346	+	0.832286i	$0.687032\pi$
$644$	13.1239	+	7.57709i	0.517155	+	0.298579i
$645$			19.2372i			0.757463i
$646$	2.49620	−	4.32354i	0.0982115	−	0.170107i
$647$	0.0398702	+	0.0690572i	0.00156746	+	0.00271492i	0.866808	−	0.498642i	$-0.166168\pi$
$647$	0.0398702	+	0.0690572i	0.00156746	+	0.00271492i	−0.865241	+	0.501357i	$0.832834\pi$
$648$	−2.45768	+	1.41894i	−0.0965467	+	0.0557412i
$649$	1.42990			0.0561285
$650$	20.6870	+	3.70142i	0.811410	+	0.145182i
$651$	18.4092			0.721514
$652$	8.36258	−	4.82814i	0.327504	−	0.189085i
$653$	−10.9185	−	18.9114i	−0.427273	−	0.740059i	0.569356	−	0.822091i	$-0.307192\pi$
$653$	−10.9185	−	18.9114i	−0.427273	−	0.740059i	−0.996630	+	0.0820317i	$0.973859\pi$
$654$	−8.46596	+	14.6635i	−0.331045	+	0.573387i
$655$			68.5251i			2.67750i
$656$	−0.202981	−	0.117191i	−0.00792506	−	0.00457553i
$657$	10.5459	+	6.08868i	0.411435	+	0.237542i
$658$			38.9103i			1.51688i
$659$	4.66914	−	8.08719i	0.181884	−	0.315032i	−0.760638	−	0.649176i	$-0.775114\pi$
$659$	4.66914	−	8.08719i	0.181884	−	0.315032i	0.942522	+	0.334144i	$0.108447\pi$
$660$	−2.09065	−	3.62111i	−0.0813785	−	0.140952i
$661$	−29.2852	+	16.9078i	−1.13906	+	0.657637i	−0.946198	−	0.323588i	$-0.895111\pi$
$661$	−29.2852	+	16.9078i	−1.13906	+	0.657637i	−0.192863	+	0.981226i	$0.561777\pi$
$662$	−6.78775			−0.263813
$663$	14.2550	+	12.0227i	0.553619	+	0.466922i
$664$	9.35334			0.362980
$665$	16.2060	−	9.35655i	0.628442	−	0.362831i
$666$	−0.823616	−	1.42654i	−0.0319145	−	0.0552775i
$667$	−5.39868	+	9.35079i	−0.209038	+	0.362064i
$668$			9.53022i			0.368735i
$669$	−5.58549	−	3.22478i	−0.215947	−	0.124677i
$670$	−25.8288	−	14.9122i	−0.997852	−	0.576110i
$671$			1.46118i			0.0564081i
$672$	−14.0966	+	24.4160i	−0.543787	+	0.941866i
$673$	−4.72135	−	8.17761i	−0.181994	−	0.315224i	0.760565	−	0.649262i	$-0.224922\pi$
$673$	−4.72135	−	8.17761i	−0.181994	−	0.315224i	−0.942560	+	0.334038i	$0.891589\pi$
$674$	0.931395	−	0.537741i	0.0358760	−	0.0207130i
$675$	6.62638			0.255049
$676$	−14.9526	−	5.52774i	−0.575099	−	0.212606i
$677$	−29.7238			−1.14238			−0.571189	−	0.820819i	$-0.693518\pi$
$677$	−29.7238			−1.14238			−0.571189	+	0.820819i	$0.693518\pi$
$678$	5.43423	−	3.13745i	0.208700	−	0.120493i
$679$	44.7836	+	77.5674i	1.71863	+	2.97676i
$680$	25.0235	−	43.3420i	0.959608	−	1.66209i
$681$			5.36217i			0.205479i
$682$	2.80407	+	1.61893i	0.107373	+	0.0619921i
$683$	−12.5667	−	7.25537i	−0.480851	−	0.277619i	0.239920	−	0.970793i	$-0.422879\pi$
$683$	−12.5667	−	7.25537i	−0.480851	−	0.277619i	−0.720771	+	0.693173i	$0.756212\pi$
$684$			1.34569i			0.0514536i
$685$	19.3121	−	33.4496i	0.737879	−	1.27804i
$686$	−24.2200	−	41.9503i	−0.924725	−	1.60167i
$687$	21.1422	−	12.2065i	0.806625	−	0.465705i
$688$	0.246440			0.00939544
$689$	−7.83621	−	6.60906i	−0.298536	−	0.251785i
$690$	−7.41120			−0.282140
$691$	−8.36584	+	4.83002i	−0.318252	+	0.183743i	−0.650613	−	0.759409i	$-0.725488\pi$
$691$	−8.36584	+	4.83002i	−0.318252	+	0.183743i	0.332361	+	0.943152i	$0.392155\pi$
$692$	−13.9883	−	24.2285i	−0.531756	−	0.921028i
$693$	−2.50057	+	4.33112i	−0.0949888	+	0.164525i
$694$		−	1.85884i		−	0.0705606i
$695$	−19.8438	−	11.4568i	−0.752719	−	0.434582i
$696$	−10.7391	−	6.20023i	−0.407065	−	0.235019i
$697$			27.7519i			1.05118i
$698$	−5.77359	+	10.0002i	−0.218534	+	0.378511i
$699$	−9.09760	−	15.7575i	−0.344103	−	0.596003i
$700$	35.1937	−	20.3191i	1.33020	−	0.767990i
$701$	−10.5810			−0.399639			−0.199820	−	0.979833i	$-0.564036\pi$
$701$	−10.5810			−0.399639			−0.199820	+	0.979833i	$0.564036\pi$
$702$	3.12191	+	0.558588i	0.117829	+	0.0210826i
$703$	−2.05502			−0.0775066
$704$	−4.37000	+	2.52302i	−0.164701	+	0.0950900i
$705$	15.0798	+	26.1190i	0.567938	+	0.983697i
$706$	5.05129	−	8.74910i	0.190108	−	0.329277i
$707$		−	28.4380i		−	1.06952i
$708$	−1.51854	−	0.876729i	−0.0570702	−	0.0329495i
$709$	−28.2728	−	16.3233i	−1.06181	−	0.613034i	−0.135874	−	0.990726i	$-0.543384\pi$
$709$	−28.2728	−	16.3233i	−1.06181	−	0.613034i	−0.925931	+	0.377692i	$0.876718\pi$
$710$			37.2446i			1.39776i
$711$	6.45875	−	11.1869i	0.242222	−	0.419541i
$712$	−4.51823	−	7.82580i	−0.169328	−	0.293284i
$713$	−7.87719	+	4.54789i	−0.295003	+	0.170320i
$714$	−22.7522			−0.851480
$715$	−2.16532	+	12.1018i	−0.0809783	+	0.452583i
$716$	−23.0725			−0.862258
$717$	−7.27960	+	4.20288i	−0.271862	+	0.156959i
$718$	9.77541	+	16.9315i	0.364815	+	0.631878i
$719$	−1.58519	+	2.74564i	−0.0591177	+	0.102395i	−0.894070	−	0.447928i	$-0.852162\pi$
$719$	−1.58519	+	2.74564i	−0.0591177	+	0.102395i	0.834952	+	0.550323i	$0.185495\pi$
$720$		−	0.148941i		−	0.00555071i
$721$	−32.8837	−	18.9854i	−1.22465	−	0.707055i
$722$	13.5563	+	7.82671i	0.504511	+	0.291280i
$723$		−	10.6339i		−	0.395478i
$724$	12.1660	−	21.0721i	0.452146	−	0.783139i
$725$	14.4774	+	25.0755i	0.537676	+	0.931282i
$726$	−0.761768	+	0.439807i	−0.0282719	+	0.0163228i
$727$	−35.0881			−1.30135			−0.650673	−	0.759358i	$-0.725513\pi$
$727$	−35.0881			−1.30135			−0.650673	+	0.759358i	$0.725513\pi$
$728$	48.1302	−	17.3808i	1.78382	−	0.644175i
$729$	1.00000			0.0370370
$730$	−31.6299	+	18.2615i	−1.17068	+	0.675890i
$731$	−14.5899	−	25.2704i	−0.539626	−	0.934659i
$732$	0.895906	−	1.55175i	0.0331136	−	0.0573545i
$733$			4.71216i			0.174048i	0.996206	+	0.0870238i	$0.0277356\pi$
$733$			4.71216i			0.174048i	−0.996206	+	0.0870238i	$0.972264\pi$
$734$	10.2795	+	5.93487i	0.379423	+	0.219060i
$735$	−53.1864	−	30.7072i	−1.96181	−	1.13265i
$736$		−	13.9299i		−	0.513463i
$737$	4.97197	−	8.61171i	0.183145	−	0.317216i
$738$	2.35990	+	4.08747i	0.0868691	+	0.150462i
$739$	30.9356	−	17.8607i	1.13799	−	0.657016i	0.192055	−	0.981384i	$-0.438485\pi$
$739$	30.9356	−	17.8607i	1.13799	−	0.657016i	0.945931	+	0.324368i	$0.105152\pi$
$740$	−7.83022			−0.287845
$741$	2.55090	−	3.02454i	0.0937097	−	0.111109i
$742$	12.5072			0.459155
$743$	18.0597	−	10.4268i	0.662545	−	0.382521i	−0.130701	−	0.991422i	$-0.541723\pi$
$743$	18.0597	−	10.4268i	0.662545	−	0.382521i	0.793246	+	0.608901i	$0.208389\pi$
$744$	−5.22312	−	9.04672i	−0.191489	−	0.331669i
$745$	−12.7048	+	22.0054i	−0.465469	+	0.806215i
$746$		−	13.3516i		−	0.488838i
$747$	−2.85432	−	1.64794i	−0.104434	−	0.0602951i
$748$	5.49265	+	3.17118i	0.200831	+	0.115950i
$749$			72.4728i			2.64810i
$750$	−2.43897	+	4.22441i	−0.0890584	+	0.154254i
$751$	−12.9831	−	22.4874i	−0.473759	−	0.820575i	0.525789	−	0.850615i	$-0.323770\pi$
$751$	−12.9831	−	22.4874i	−0.473759	−	0.820575i	−0.999549	+	0.0300395i	$0.990437\pi$
$752$	0.334600	−	0.193182i	0.0122016	−	0.00704460i
$753$	7.10872			0.259056
$754$	4.70698	+	13.0344i	0.171418	+	0.474683i
$755$	−20.2698			−0.737695
$756$	5.31116	−	3.06640i	0.193165	−	0.111524i
$757$	7.99047	+	13.8399i	0.290419	+	0.503020i	0.973909	−	0.226940i	$-0.0728721\pi$
$757$	7.99047	+	13.8399i	0.290419	+	0.503020i	−0.683490	+	0.729960i	$0.739539\pi$
$758$	2.06169	−	3.57095i	0.0748839	−	0.129703i
$759$		−	2.47101i		−	0.0896919i
$760$	−9.19605	−	5.30934i	−0.333576	−	0.192590i
$761$	21.7052	+	12.5315i	0.786812	+	0.454266i	0.838839	−	0.544380i	$-0.183235\pi$
$761$	21.7052	+	12.5315i	0.786812	+	0.454266i	−0.0520273	+	0.998646i	$0.516568\pi$
$762$		−	4.22789i		−	0.153160i
$763$	48.1342	−	83.3708i	1.74257	−	3.01823i
$764$	−5.33139	−	9.23424i	−0.192883	−	0.334083i
$765$	−15.2727	+	8.81768i	−0.552185	+	0.318804i
$766$	−11.7401			−0.424188
$767$	1.75111	+	4.84909i	0.0632288	+	0.175090i
$768$	16.1052			0.581147
$769$	−3.29742	+	1.90377i	−0.118908	+	0.0686516i	−0.558274	−	0.829656i	$-0.688536\pi$
$769$	−3.29742	+	1.90377i	−0.118908	+	0.0686516i	0.439366	+	0.898308i	$0.355203\pi$
$770$	−7.49987	−	12.9901i	−0.270276	−	0.468132i
$771$	10.3643	−	17.9515i	0.373261	−	0.646507i
$772$		−	33.9080i		−	1.22038i
$773$	−17.0616	−	9.85055i	−0.613665	−	0.354300i	0.160734	−	0.986998i	$-0.448614\pi$
$773$	−17.0616	−	9.85055i	−0.613665	−	0.354300i	−0.774398	+	0.632698i	$0.781947\pi$
$774$	−4.29776	−	2.48131i	−0.154480	−	0.0891889i
$775$			24.3917i			0.876176i
$776$	25.4123	−	44.0153i	0.912247	−	1.58006i
$777$	4.68276	+	8.11077i	0.167993	+	0.290972i
$778$	3.41705	−	1.97283i	0.122507	−	0.0707295i
$779$	5.88824			0.210968
$780$	9.71966	−	11.5244i	0.348020	−	0.412639i
$781$	−12.4179			−0.444348
$782$	9.73552	−	5.62080i	0.348141	−	0.201000i
$783$	2.18481	+	3.78420i	0.0780787	+	0.135236i
$784$	−0.393378	+	0.681351i	−0.0140492	+	0.0243340i
$785$		−	52.8288i		−	1.88554i
$786$	−15.3091	−	8.83872i	−0.546058	−	0.315267i
$787$	16.2942	+	9.40744i	0.580824	+	0.335339i	0.761461	−	0.648211i	$-0.224483\pi$
$787$	16.2942	+	9.40744i	0.580824	+	0.335339i	−0.180637	+	0.983550i	$0.557816\pi$
$788$		−	23.5653i		−	0.839478i
$789$	−11.5968	+	20.0863i	−0.412858	+	0.715091i
$790$	19.3715	+	33.5524i	0.689206	+	1.19374i
$791$	−30.8969	+	17.8383i	−1.09857	+	0.634258i
$792$	2.83788			0.100840
$793$	−4.95515	+	1.78941i	−0.175963	+	0.0635437i
$794$	−23.4061			−0.830652
$795$	8.39563	−	4.84722i	0.297762	−	0.171913i
$796$	3.81876	+	6.61429i	0.135352	+	0.234437i
$797$	−22.8122	+	39.5118i	−0.808049	+	1.39958i	0.106165	+	0.994349i	$0.466143\pi$
$797$	−22.8122	+	39.5118i	−0.808049	+	1.39958i	−0.914214	+	0.405233i	$0.867190\pi$
$798$			4.82743i			0.170889i
$799$	−39.6183	−	22.8736i	−1.40160	−	0.809211i
$800$	−32.3505	−	18.6776i	−1.14376	−	0.660352i
$801$			3.18423i			0.112509i
$802$	6.52197	−	11.2964i	0.230299	−	0.398889i
$803$	−6.08868	−	10.5459i	−0.214865	−	0.372157i
$804$	−10.5604	+	6.09702i	−0.372435	+	0.215025i
$805$	42.1372			1.48514
$806$	−2.05617	+	11.4918i	−0.0724253	+	0.404781i
$807$	15.5931			0.548903
$808$	−13.9751	+	8.06854i	−0.491643	+	0.283850i
$809$	18.7931	+	32.5505i	0.660729	+	1.14442i	0.980424	+	0.196896i	$0.0630860\pi$
$809$	18.7931	+	32.5505i	0.660729	+	1.14442i	−0.319696	+	0.947520i	$0.603581\pi$
$810$	−1.49963	+	2.59744i	−0.0526917	+	0.0912646i
$811$		−	4.17585i		−	0.146634i	−0.997309	−	0.0733170i	$-0.976642\pi$
$811$		−	4.17585i		−	0.146634i	0.997309	−	0.0733170i	$-0.0233585\pi$
$812$	23.2077	+	13.3990i	0.814431	+	0.470212i
$813$	−0.267146	−	0.154237i	−0.00936923	−	0.00540933i
$814$			1.64723i			0.0577354i
$815$	13.4250	−	23.2527i	0.470256	−	0.814507i
$816$	0.112960	+	0.195652i	0.00395439	+	0.00684920i
$817$	−5.36172	+	3.09559i	−0.187583	+	0.108301i
$818$	14.8427			0.518964
$819$	−17.7500	−	3.17592i	−0.620235	−	0.110975i
$820$	22.4359			0.783494
$821$	17.9262	−	10.3497i	0.625627	−	0.361206i	−0.153430	−	0.988160i	$-0.549032\pi$
$821$	17.9262	−	10.3497i	0.625627	−	0.361206i	0.779057	+	0.626954i	$0.215698\pi$
$822$	4.98196	+	8.62900i	0.173766	+	0.300971i
$823$	−11.5897	+	20.0739i	−0.403991	+	0.699733i	−0.994203	−	0.107515i	$-0.965711\pi$
$823$	−11.5897	+	20.0739i	−0.403991	+	0.699733i	0.590213	+	0.807248i	$0.299044\pi$
$824$			21.5464i			0.750606i
$825$	−5.73861	−	3.31319i	−0.199793	−	0.115350i
$826$	−5.44751	−	3.14512i	−0.189543	−	0.109433i
$827$			33.5362i			1.16617i	0.812412	+	0.583084i	$0.198154\pi$
$827$			33.5362i			1.16617i	−0.812412	+	0.583084i	$0.801846\pi$
$828$	−1.51507	+	2.62418i	−0.0526524	+	0.0911967i
$829$	15.9173	+	27.5696i	0.552831	+	0.957531i	0.998069	+	0.0621189i	$0.0197858\pi$
$829$	15.9173	+	27.5696i	0.552831	+	0.957531i	−0.445238	+	0.895412i	$0.646881\pi$
$830$	8.56086	−	4.94262i	0.297152	−	0.171561i
$831$	4.96056			0.172080
$832$	−13.9077	−	11.7298i	−0.482164	−	0.406657i
$833$	93.1558			3.22766
$834$	5.11912	−	2.95552i	0.177260	−	0.102341i
$835$	13.2497	+	22.9491i	0.458524	+	0.794187i
$836$	0.672843	−	1.16540i	0.0232708	−	0.0403061i
$837$			3.68100i			0.127234i
$838$	7.28896	+	4.20828i	0.251793	+	0.145373i
$839$	−35.5949	−	20.5507i	−1.22887	−	0.709490i	−0.262078	−	0.965047i	$-0.584408\pi$
$839$	−35.5949	−	20.5507i	−1.22887	−	0.709490i	−0.966794	+	0.255557i	$0.917741\pi$
$840$			48.3933i			1.66973i
$841$	4.95322	−	8.57923i	0.170801	−	0.295836i
$842$	−12.4707	−	21.5999i	−0.429768	−	0.744381i
$843$	−9.82810	+	5.67426i	−0.338498	+	0.195432i
$844$	−33.8951			−1.16672
$845$	−43.6915	+	7.47728i	−1.50303	+	0.257226i
$846$	−7.78028			−0.267492
$847$	4.33112	−	2.50057i	0.148819	−	0.0859206i
$848$	−0.0620959	−	0.107553i	−0.00213238	−	0.00369339i
$849$	5.54097	−	9.59724i	0.190166	−	0.329376i
$850$		−	30.1461i		−	1.03400i
$851$	−4.00744	−	2.31370i	−0.137373	−	0.0793125i
$852$	13.1877	+	7.61391i	0.451803	+	0.260848i
$853$		−	22.3933i		−	0.766732i	−0.923596	−	0.383366i	$-0.874765\pi$
$853$		−	22.3933i		−	0.766732i	0.923596	−	0.383366i	$-0.125235\pi$
$854$	3.21391	−	5.56666i	0.109978	−	0.190487i
$855$	1.87088	+	3.24046i	0.0639828	+	0.110822i
$856$	35.6148	−	20.5622i	1.21729	−	0.702802i
$857$	21.9883			0.751106			0.375553	−	0.926801i	$-0.377453\pi$
$857$	21.9883			0.751106			0.375553	+	0.926801i	$0.377453\pi$
$858$	−2.42436	−	2.04471i	−0.0827664	−	0.0698052i
$859$	52.9507			1.80665			0.903327	−	0.428953i	$-0.141118\pi$
$859$	52.9507			1.80665			0.903327	+	0.428953i	$0.141118\pi$
$860$	−20.4297	+	11.7951i	−0.696646	+	0.402209i
$861$	−13.4175	−	23.2397i	−0.457266	−	0.792008i
$862$	−11.0411	+	19.1238i	−0.376062	+	0.651359i
$863$			27.7222i			0.943675i	0.881686	+	0.471837i	$0.156409\pi$
$863$			27.7222i			0.943675i	−0.881686	+	0.471837i	$0.843591\pi$
$864$	−4.88208	−	2.81867i	−0.166092	−	0.0958931i
$865$	−67.3688	−	38.8954i	−2.29061	−	1.32248i
$866$			1.56996i			0.0533493i
$867$	4.87502	−	8.44378i	0.165564	−	0.286766i
$868$	11.2874	+	19.5504i	0.383120	+	0.663583i
$869$	−11.1869	+	6.45875i	−0.379489	+	0.219098i
$870$	−13.1056			−0.444322
$871$	35.2929	+	6.31478i	1.19585	+	0.213968i
$872$	−54.6271			−1.84991
$873$	−15.5099	+	8.95467i	−0.524932	+	0.303070i
$874$	−1.19259	−	2.06562i	−0.0403399	−	0.0698708i
$875$	13.8670	−	24.0184i	0.468790	−	0.811969i
$876$			14.9328i			0.504534i
$877$	23.7542	+	13.7145i	0.802123	+	0.463106i	0.844213	−	0.536008i	$-0.180068\pi$
$877$	23.7542	+	13.7145i	0.802123	+	0.463106i	−0.0420901	+	0.999114i	$0.513402\pi$
$878$	−11.4089	−	6.58696i	−0.385033	−	0.222299i
$879$			16.0101i			0.540007i
$880$	−0.0744706	+	0.128987i	−0.00251040	+	0.00434814i
$881$	18.7393	+	32.4574i	0.631342	+	1.09352i	0.987278	+	0.159006i	$0.0508289\pi$
$881$	18.7393	+	32.4574i	0.631342	+	1.09352i	−0.355936	+	0.934510i	$0.615838\pi$
$882$	13.7205	−	7.92155i	0.461994	−	0.266732i
$883$	51.9652			1.74877			0.874384	−	0.485235i	$-0.161266\pi$
$883$	51.9652			1.74877			0.874384	+	0.485235i	$0.161266\pi$
$884$	−4.02765	+	22.5103i	−0.135464	+	0.757102i
$885$	−4.87560			−0.163892
$886$	10.4468	−	6.03144i	0.350966	−	0.202630i
$887$	10.1536	+	17.5866i	0.340926	+	0.590501i	0.984605	−	0.174795i	$-0.0559261\pi$
$887$	10.1536	+	17.5866i	0.340926	+	0.590501i	−0.643679	+	0.765296i	$0.722593\pi$
$888$	2.65721	−	4.60243i	0.0891703	−	0.154447i
$889$			24.0381i			0.806213i
$890$	−8.27083	−	4.77516i	−0.277239	−	0.160064i
$891$	−0.866025	−	0.500000i	−0.0290129	−	0.0167506i
$892$		−	7.90896i		−	0.264812i
$893$	−4.85319	+	8.40597i	−0.162406	+	0.281295i
$894$	−3.27747	−	5.67674i	−0.109615	−	0.189859i
$895$	−55.5594	+	32.0772i	−1.85715	+	1.07222i
$896$	−34.1883			−1.14215
$897$	8.37970	−	3.02608i	0.279790	−	0.101038i
$898$	15.2656			0.509419
$899$	−13.9297	+	8.04229i	−0.464580	+	0.268225i
$900$	4.06289	+	7.03714i	0.135430	+	0.234571i
$901$	−7.35246	+	12.7348i	−0.244946	+	0.424259i
$902$		−	4.71980i		−	0.157152i
$903$	24.4354	+	14.1078i	0.813158	+	0.469477i
$904$	17.5323	+	10.1223i	0.583117	+	0.336663i
$905$		−	67.6567i		−	2.24898i
$906$	2.61451	−	4.52847i	0.0868613	−	0.150448i
$907$	−1.86812	−	3.23568i	−0.0620300	−	0.107439i	0.833343	−	0.552757i	$-0.186424\pi$
$907$	−1.86812	−	3.23568i	−0.0620300	−	0.107439i	−0.895373	+	0.445318i	$0.853091\pi$
$908$	−5.69457	+	3.28776i	−0.188981	+	0.109108i
$909$	5.68631			0.188603
$910$	34.8677	−	41.3418i	1.15585	−	1.37047i
$911$	41.9387			1.38949			0.694745	−	0.719256i	$-0.255517\pi$
$911$	41.9387			1.38949			0.694745	+	0.719256i	$0.255517\pi$
$912$	0.0415123	−	0.0239672i	0.00137461	−	0.000793632i
$913$	1.64794	+	2.85432i	0.0545390	+	0.0944643i
$914$	−11.2161	+	19.4268i	−0.370994	+	0.642581i
$915$		−	4.98224i		−	0.164708i
$916$	25.9262	+	14.9685i	0.856627	+	0.494574i
$917$	87.0417	+	50.2535i	2.87437	+	1.65952i
$918$		−	4.54940i		−	0.150153i
$919$	−22.0292	+	38.1556i	−0.726675	+	1.25864i	0.231606	+	0.972810i	$0.425602\pi$
$919$	−22.0292	+	38.1556i	−0.726675	+	1.25864i	−0.958281	+	0.285828i	$0.907731\pi$
$920$	−11.9553	−	20.7072i	−0.394155	−	0.682696i
$921$	4.61538	−	2.66469i	0.152082	−	0.0878046i
$922$	−23.5379			−0.775179
$923$	−15.2074	−	42.1117i	−0.500558	−	1.38612i
$924$	−6.13280			−0.201754
$925$	−10.7466	+	6.20453i	−0.353344	+	0.204004i
$926$	17.7664	+	30.7723i	0.583839	+	1.01124i
$927$	3.79622	−	6.57525i	0.124684	−	0.215959i
$928$		−	24.6330i		−	0.808618i
$929$	15.6925	+	9.06006i	0.514853	+	0.297251i	0.734826	−	0.678255i	$-0.237264\pi$
$929$	15.6925	+	9.06006i	0.514853	+	0.297251i	−0.219973	+	0.975506i	$0.570597\pi$
$930$	−9.56117	−	5.52015i	−0.313523	−	0.181013i
$931$		−	19.7652i		−	0.647780i
$932$	11.1562	−	19.3231i	0.365433	−	0.632949i
$933$	2.24106	+	3.88162i	0.0733689	+	0.127079i
$934$	−4.17242	+	2.40895i	−0.136526	+	0.0788231i
$935$	17.6354			0.576738
$936$	3.47537	+	9.62383i	0.113596	+	0.314565i
$937$	−0.807168			−0.0263690			−0.0131845	−	0.999913i	$-0.504197\pi$
$937$	−0.807168			−0.0263690			−0.0131845	+	0.999913i	$0.504197\pi$
$938$	−37.8835	+	21.8721i	−1.23694	+	0.714148i
$939$	−5.89496	−	10.2104i	−0.192375	−	0.333203i
$940$	−18.4920	+	32.0291i	−0.603144	+	1.04468i
$941$		−	42.9518i		−	1.40019i	−0.714050	−	0.700095i	$-0.753141\pi$
$941$		−	42.9518i		−	1.40019i	0.714050	−	0.700095i	$-0.246859\pi$
$942$	11.8024	+	6.81413i	0.384544	+	0.222016i
$943$	11.4825	+	6.62942i	0.373921	+	0.215884i
$944$			0.0624595i			0.00203288i
$945$	8.52631	−	14.7680i	0.277361	−	0.480403i
$946$	2.48131	+	4.29776i	0.0806744	+	0.139732i
$947$	44.9426	−	25.9476i	1.46044	−	0.843184i	0.461406	−	0.887189i	$-0.347345\pi$
$947$	44.9426	−	25.9476i	1.46044	−	0.843184i	0.999031	+	0.0440047i	$0.0140117\pi$
$948$	15.8405			0.514474
$949$	28.3069	−	33.5628i	0.918881	−	1.08950i
$950$	−6.39621			−0.207520
$951$	21.0253	−	12.1390i	0.681793	−	0.393633i
$952$	−36.7025	−	63.5706i	−1.18953	−	2.06033i
$953$	−8.36653	+	14.4913i	−0.271019	+	0.469418i	−0.969123	−	0.246578i	$-0.920694\pi$
$953$	−8.36653	+	14.4913i	−0.271019	+	0.469418i	0.698104	+	0.715996i	$0.254027\pi$
$954$			2.50088i			0.0809689i
$955$	−25.6764	−	14.8243i	−0.830869	−	0.479702i
$956$	−8.92683	−	5.15391i	−0.288714	−	0.166689i
$957$		−	4.36962i		−	0.141250i
$958$	0.472747	−	0.818821i	0.0152738	−	0.0264549i
$959$	−28.3255	−	49.0611i	−0.914677	−	1.58427i
$960$	14.9006	−	8.60287i	0.480915	−	0.277656i
$961$	17.4502			0.562910
$962$	−5.58610	+	2.01726i	−0.180103	+	0.0650389i
$963$	−14.4912			−0.466974
$964$	11.2931	−	6.52005i	0.363725	−	0.209997i
$965$	−47.1417	−	81.6519i	−1.51755	−	2.62847i
$966$	−5.43507	+	9.41382i	−0.174871	+	0.302885i
$967$		−	15.1832i		−	0.488260i	−0.969743	−	0.244130i	$-0.921498\pi$
$967$		−	15.1832i		−	0.488260i	0.969743	−	0.244130i	$-0.0785023\pi$
$968$	−2.45768	−	1.41894i	−0.0789927	−	0.0456065i
$969$	−4.91527	−	2.83783i	−0.157901	−	0.0911642i
$970$		−	53.7148i		−	1.72468i
$971$	−20.2304	+	35.0400i	−0.649223	+	1.12449i	0.334086	+	0.942543i	$0.391572\pi$
$971$	−20.2304	+	35.0400i	−0.649223	+	1.12449i	−0.983309	+	0.181945i	$0.941761\pi$
$972$	0.613140	+	1.06199i	0.0196665	+	0.0340633i
$973$	−29.1053	+	16.8039i	−0.933073	+	0.538710i
$974$	−1.25804			−0.0403101
$975$	4.20800	−	23.5183i	0.134764	−	0.753187i
$976$	−0.0638257			−0.00204301
$977$	−15.5681	+	8.98827i	−0.498069	+	0.287560i	−0.727916	−	0.685667i	$-0.759511\pi$
$977$	−15.5681	+	8.98827i	−0.498069	+	0.287560i	0.229847	+	0.973227i	$0.426177\pi$
$978$	3.46324	+	5.99851i	0.110742	+	0.191811i
$979$	1.59211	−	2.75762i	0.0508841	−	0.0881339i
$980$		−	75.3112i		−	2.40573i
$981$	16.6704	+	9.62463i	0.532243	+	0.307291i
$982$	−5.33844	−	3.08215i	−0.170356	−	0.0983553i
$983$		−	36.0525i		−	1.14990i	−0.818190	−	0.574948i	$-0.805022\pi$
$983$		−	36.0525i		−	1.14990i	0.818190	−	0.574948i	$-0.194978\pi$
$984$	−7.61369	+	13.1873i	−0.242716	+	0.420396i
$985$	−32.7624	−	56.7461i	−1.04390	−	1.80808i
$986$	17.2158	−	9.93957i	0.548264	−	0.316540i
$987$	44.2356			1.40804
$988$	4.77609	+	0.854561i	0.151948	+	0.0271872i
$989$	−13.9410			−0.443297
$990$	2.59744	−	1.49963i	0.0825520	−	0.0476614i
$991$	−21.0183	−	36.4048i	−0.667668	−	1.15644i	−0.978554	−	0.205988i	$-0.933959\pi$
$991$	−21.0183	−	36.4048i	−0.667668	−	1.15644i	0.310886	−	0.950447i	$-0.399374\pi$
$992$	10.3755	−	17.9709i	0.329423	−	0.570578i
$993$			7.71674i			0.244883i
$994$	47.3086	+	27.3137i	1.50054	+	0.866337i
$995$	18.3915	+	10.6183i	0.583048	+	0.336623i
$996$		−	4.04168i		−	0.128066i
$997$	9.30317	−	16.1136i	0.294634	−	0.510322i	−0.680265	−	0.732966i	$-0.738135\pi$
$997$	9.30317	−	16.1136i	0.294634	−	0.510322i	0.974900	+	0.222644i	$0.0714688\pi$
$998$	−18.7695	−	32.5097i	−0.594137	−	1.02908i
$999$	−1.62178	+	0.936337i	−0.0513110	+	0.0296244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.a.166.5	✓	24
13.2	odd	12		5577.2.a.be.1.5		12
13.4	even	6	inner	429.2.s.a.199.5	yes	24
13.11	odd	12		5577.2.a.z.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.a.166.5	✓	24	1.1	even	1	trivial
429.2.s.a.199.5	yes	24	13.4	even	6	inner
5577.2.a.z.1.8		12	13.11	odd	12
5577.2.a.be.1.5		12	13.2	odd	12

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.761768 + 0.439807i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.613140 + 1.06199i) q^{4} +3.40975i q^{5} +(-0.761768 - 0.439807i) q^{6} +(4.33112 + 2.50057i) q^{7} -2.83788i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.761768 + 0.439807i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.613140 + 1.06199i) q^{4} +3.40975i q^{5} +(-0.761768 - 0.439807i) q^{6} +(4.33112 + 2.50057i) q^{7} -2.83788i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.49963 - 2.59744i) q^{10} +(0.866025 - 0.500000i) q^{11} -1.22628 q^{12} +(2.75617 + 2.32455i) q^{13} -4.39907 q^{14} +(-2.95293 + 1.70487i) q^{15} +(0.0218405 + 0.0378288i) q^{16} +(2.58602 - 4.47912i) q^{17} -0.879614i q^{18} +(-0.950353 - 0.548686i) q^{19} +(-3.62111 - 2.09065i) q^{20} +5.00114i q^{21} +(-0.439807 + 0.761768i) q^{22} +(-1.23550 - 2.13996i) q^{23} +(2.45768 - 1.41894i) q^{24} -6.62638 q^{25} +(-3.12191 - 0.558588i) q^{26} -1.00000 q^{27} +(-5.31116 + 3.06640i) q^{28} +(-2.18481 - 3.78420i) q^{29} +(1.49963 - 2.59744i) q^{30} -3.68100i q^{31} +(4.88208 + 2.81867i) q^{32} +(0.866025 + 0.500000i) q^{33} +4.54940i q^{34} +(-8.52631 + 14.7680i) q^{35} +(-0.613140 - 1.06199i) q^{36} +(1.62178 - 0.936337i) q^{37} +0.965265 q^{38} +(-0.635038 + 3.54919i) q^{39} +9.67646 q^{40} +(-4.64689 + 2.68288i) q^{41} +(-2.19954 - 3.80971i) q^{42} +(2.82091 - 4.88596i) q^{43} +1.22628i q^{44} +(-2.95293 - 1.70487i) q^{45} +(1.88234 + 1.08677i) q^{46} -8.84511i q^{47} +(-0.0218405 + 0.0378288i) q^{48} +(9.00571 + 15.5983i) q^{49} +(5.04776 - 2.91433i) q^{50} +5.17204 q^{51} +(-4.15856 + 1.50174i) q^{52} -2.84315 q^{53} +(0.761768 - 0.439807i) q^{54} +(1.70487 + 2.95293i) q^{55} +(7.09632 - 12.2912i) q^{56} -1.09737i q^{57} +(3.32863 + 1.92179i) q^{58} +(1.23833 + 0.714950i) q^{59} -4.18130i q^{60} +(-0.730589 + 1.26542i) q^{61} +(1.61893 + 2.80407i) q^{62} +(-4.33112 + 2.50057i) q^{63} -5.04604 q^{64} +(-7.92614 + 9.39783i) q^{65} -0.879614 q^{66} +(8.61171 - 4.97197i) q^{67} +(3.17118 + 5.49265i) q^{68} +(1.23550 - 2.13996i) q^{69} -14.9997i q^{70} +(-10.7542 - 6.20896i) q^{71} +(2.45768 + 1.41894i) q^{72} -12.1774i q^{73} +(-0.823616 + 1.42654i) q^{74} +(-3.31319 - 5.73861i) q^{75} +(1.16540 - 0.672843i) q^{76} +5.00114 q^{77} +(-1.07721 - 2.98295i) q^{78} -12.9175 q^{79} +(-0.128987 + 0.0744706i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.35990 - 4.08747i) q^{82} +3.29589i q^{83} +(-5.31116 - 3.06640i) q^{84} +(15.2727 + 8.81768i) q^{85} +4.96262i q^{86} +(2.18481 - 3.78420i) q^{87} +(-1.41894 - 2.45768i) q^{88} +(2.75762 - 1.59211i) q^{89} +2.99926 q^{90} +(6.12457 + 16.9599i) q^{91} +3.03015 q^{92} +(3.18784 - 1.84050i) q^{93} +(3.89014 + 6.73792i) q^{94} +(1.87088 - 3.24046i) q^{95} +5.63734i q^{96} +(15.5099 + 8.95467i) q^{97} +(-13.7205 - 7.92155i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Introduction

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