LMFDB - Embedded newform 16.3.f.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,3,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	16.f (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:	$0.435968422976$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.3
Root			$0.264658 + 1.38923i$ of defining polynomial
Character	$\chi$	$=$	16.11
Dual form			16.3.f.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12457 + 1.65389i) q^{2} +(-3.24914 - 3.24914i) q^{3} +(-1.47068 + 3.71982i) q^{4} +(-0.0586332 - 0.0586332i) q^{5} +(1.71982 - 9.02760i) q^{6} +4.61555 q^{7} +(-7.80605 + 1.75086i) q^{8} +12.1138i q^{9} +O(q^{10})$	\(q+(1.12457 + 1.65389i) q^{2} +(-3.24914 - 3.24914i) q^{3} +(-1.47068 + 3.71982i) q^{4} +(-0.0586332 - 0.0586332i) q^{5} +(1.71982 - 9.02760i) q^{6} +4.61555 q^{7} +(-7.80605 + 1.75086i) q^{8} +12.1138i q^{9} +(0.0310355 - 0.162910i) q^{10} +(-5.36641 + 5.36641i) q^{11} +(16.8647 - 7.30777i) q^{12} +(11.0552 - 11.0552i) q^{13} +(5.19051 + 7.63359i) q^{14} +0.381015i q^{15} +(-11.6742 - 10.9414i) q^{16} -12.8793 q^{17} +(-20.0349 + 13.6229i) q^{18} +(2.63359 + 2.63359i) q^{19} +(0.304336 - 0.131874i) q^{20} +(-14.9966 - 14.9966i) q^{21} +(-14.9103 - 2.84053i) q^{22} +16.3810 q^{23} +(31.0518 + 19.6742i) q^{24} -24.9931i q^{25} +(30.7164 + 5.85170i) q^{26} +(10.1173 - 10.1173i) q^{27} +(-6.78801 + 17.1690i) q^{28} +(-26.0518 + 26.0518i) q^{29} +(-0.630155 + 0.428478i) q^{30} +20.2345i q^{31} +(4.96735 - 31.6121i) q^{32} +34.8724 q^{33} +(-14.4837 - 21.3009i) q^{34} +(-0.270624 - 0.270624i) q^{35} +(-45.0613 - 17.8156i) q^{36} +(41.2829 + 41.2829i) q^{37} +(-1.39400 + 7.31733i) q^{38} -71.8398 q^{39} +(0.560352 + 0.355035i) q^{40} +3.29640i q^{41} +(7.93793 - 41.6673i) q^{42} +(-0.786951 + 0.786951i) q^{43} +(-12.0698 - 27.8544i) q^{44} +(0.710272 - 0.710272i) q^{45} +(18.4216 + 27.0923i) q^{46} -79.7517i q^{47} +(2.38101 + 73.4811i) q^{48} -27.6967 q^{49} +(41.3358 - 28.1065i) q^{50} +(41.8466 + 41.8466i) q^{51} +(24.8647 + 57.3821i) q^{52} +(1.06207 + 1.06207i) q^{53} +(28.1104 + 5.35524i) q^{54} +0.629299 q^{55} +(-36.0292 + 8.08117i) q^{56} -17.1138i q^{57} +(-72.3837 - 13.7896i) q^{58} +(32.5163 - 32.5163i) q^{59} +(-1.41731 - 0.560352i) q^{60} +(15.2897 - 15.2897i) q^{61} +(-33.4656 + 22.7552i) q^{62} +55.9119i q^{63} +(57.8690 - 27.3346i) q^{64} -1.29640 q^{65} +(39.2165 + 57.6750i) q^{66} +(-60.0631 - 60.0631i) q^{67} +(18.9414 - 47.9087i) q^{68} +(-53.2242 - 53.2242i) q^{69} +(0.143246 - 0.751918i) q^{70} +56.3535 q^{71} +(-21.2096 - 94.5612i) q^{72} -9.70663i q^{73} +(-21.8517 + 114.703i) q^{74} +(-81.2062 + 81.2062i) q^{75} +(-13.6697 + 5.92332i) q^{76} +(-24.7689 + 24.7689i) q^{77} +(-80.7889 - 118.815i) q^{78} +84.4278i q^{79} +(0.0429672 + 1.32602i) q^{80} +43.2796 q^{81} +(-5.45188 + 3.70704i) q^{82} +(26.7577 + 26.7577i) q^{83} +(77.8398 - 33.7294i) q^{84} +(0.755154 + 0.755154i) q^{85} +(-2.18651 - 0.416546i) q^{86} +169.292 q^{87} +(32.4946 - 51.2863i) q^{88} +115.555i q^{89} +(1.97346 + 0.375959i) q^{90} +(51.0258 - 51.0258i) q^{91} +(-24.0913 + 60.9345i) q^{92} +(65.7448 - 65.7448i) q^{93} +(131.900 - 89.6864i) q^{94} -0.308832i q^{95} +(-118.852 + 86.5726i) q^{96} -146.245 q^{97} +(-31.1469 - 45.8072i) q^{98} +(-65.0077 - 65.0077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21} - 52 q^{22} + 60 q^{23} + 48 q^{24} + 96 q^{26} + 64 q^{27} + 56 q^{28} - 18 q^{29} + 52 q^{30} + 8 q^{32} - 4 q^{33} - 76 q^{34} - 100 q^{35} - 52 q^{36} + 46 q^{37} + 40 q^{38} - 196 q^{39} + 40 q^{40} - 24 q^{42} - 114 q^{43} + 20 q^{44} + 66 q^{45} + 28 q^{46} - 24 q^{48} - 46 q^{49} + 46 q^{50} + 156 q^{51} + 100 q^{52} + 78 q^{53} + 32 q^{54} + 252 q^{55} - 168 q^{56} - 176 q^{58} + 206 q^{59} - 160 q^{60} + 30 q^{61} - 144 q^{62} + 64 q^{64} + 12 q^{65} + 196 q^{66} - 226 q^{67} + 112 q^{68} - 116 q^{69} - 16 q^{70} - 260 q^{71} + 52 q^{72} - 92 q^{74} - 238 q^{75} - 188 q^{76} - 212 q^{77} - 84 q^{78} + 232 q^{80} + 86 q^{81} + 304 q^{82} + 318 q^{83} + 232 q^{84} - 212 q^{85} + 268 q^{86} + 444 q^{87} - 8 q^{88} - 160 q^{90} + 188 q^{91} - 168 q^{92} - 32 q^{93} + 48 q^{94} - 80 q^{96} - 4 q^{97} + 10 q^{98} - 226 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8 + 36 * q^10 - 18 * q^11 + 52 * q^12 - 2 * q^13 + 12 * q^14 - 40 * q^16 - 4 * q^17 - 74 * q^18 + 30 * q^19 - 84 * q^20 - 20 * q^21 - 52 * q^22 + 60 * q^23 + 48 * q^24 + 96 * q^26 + 64 * q^27 + 56 * q^28 - 18 * q^29 + 52 * q^30 + 8 * q^32 - 4 * q^33 - 76 * q^34 - 100 * q^35 - 52 * q^36 + 46 * q^37 + 40 * q^38 - 196 * q^39 + 40 * q^40 - 24 * q^42 - 114 * q^43 + 20 * q^44 + 66 * q^45 + 28 * q^46 - 24 * q^48 - 46 * q^49 + 46 * q^50 + 156 * q^51 + 100 * q^52 + 78 * q^53 + 32 * q^54 + 252 * q^55 - 168 * q^56 - 176 * q^58 + 206 * q^59 - 160 * q^60 + 30 * q^61 - 144 * q^62 + 64 * q^64 + 12 * q^65 + 196 * q^66 - 226 * q^67 + 112 * q^68 - 116 * q^69 - 16 * q^70 - 260 * q^71 + 52 * q^72 - 92 * q^74 - 238 * q^75 - 188 * q^76 - 212 * q^77 - 84 * q^78 + 232 * q^80 + 86 * q^81 + 304 * q^82 + 318 * q^83 + 232 * q^84 - 212 * q^85 + 268 * q^86 + 444 * q^87 - 8 * q^88 - 160 * q^90 + 188 * q^91 - 168 * q^92 - 32 * q^93 + 48 * q^94 - 80 * q^96 - 4 * q^97 + 10 * q^98 - 226 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.12457	+	1.65389i	0.562285	+	0.826943i
$2$	1.12457	+	1.65389i	0.562285	+	0.826943i
$3$	−3.24914	−	3.24914i	−1.08305	−	1.08305i	−0.996224	−	0.0868231i	$-0.972329\pi$
$3$	−3.24914	−	3.24914i	−1.08305	−	1.08305i	−0.0868231	−	0.996224i	$-0.527671\pi$
$4$	−1.47068	+	3.71982i	−0.367671	+	0.929956i
$5$	−0.0586332	−	0.0586332i	−0.0117266	−	0.0117266i	0.701219	−	0.712946i	$-0.252639\pi$
$5$	−0.0586332	−	0.0586332i	−0.0117266	−	0.0117266i	−0.712946	+	0.701219i	$0.752639\pi$
$6$	1.71982	−	9.02760i	0.286637	−	1.50460i
$7$	4.61555			0.659364			0.329682	−	0.944092i	$-0.393058\pi$
$7$	4.61555			0.659364			0.329682	+	0.944092i	$0.393058\pi$
$8$	−7.80605	+	1.75086i	−0.975757	+	0.218857i
$9$			12.1138i			1.34598i
$10$	0.0310355	−	0.162910i	0.00310355	−	0.0162910i
$11$	−5.36641	+	5.36641i	−0.487855	+	0.487855i	−0.907629	−	0.419774i	$-0.862109\pi$
$11$	−5.36641	+	5.36641i	−0.487855	+	0.487855i	0.419774	+	0.907629i	$0.362109\pi$
$12$	16.8647	−	7.30777i	1.40539	−	0.608981i
$13$	11.0552	−	11.0552i	0.850400	−	0.850400i	−0.139783	−	0.990182i	$-0.544640\pi$
$13$	11.0552	−	11.0552i	0.850400	−	0.850400i	0.990182	+	0.139783i	$0.0446404\pi$
$14$	5.19051	+	7.63359i	0.370751	+	0.545257i
$15$			0.381015i			0.0254010i
$16$	−11.6742	−	10.9414i	−0.729636	−	0.683835i
$17$	−12.8793			−0.757606			−0.378803	−	0.925477i	$-0.623664\pi$
$17$	−12.8793			−0.757606			−0.378803	+	0.925477i	$0.623664\pi$
$18$	−20.0349	+	13.6229i	−1.11305	+	0.756825i
$19$	2.63359	+	2.63359i	0.138610	+	0.138610i	0.773007	−	0.634397i	$-0.218752\pi$
$19$	2.63359	+	2.63359i	0.138610	+	0.138610i	−0.634397	+	0.773007i	$0.718752\pi$
$20$	0.304336	−	0.131874i	0.0152168	−	0.00659371i
$21$	−14.9966	−	14.9966i	−0.714122	−	0.714122i
$22$	−14.9103	−	2.84053i	−0.677742	−	0.129115i
$23$	16.3810			0.712218			0.356109	−	0.934444i	$-0.384103\pi$
$23$	16.3810			0.712218			0.356109	+	0.934444i	$0.384103\pi$
$24$	31.0518	+	19.6742i	1.29382	+	0.819758i
$25$		−	24.9931i		−	0.999725i
$26$	30.7164	+	5.85170i	1.18140	+	0.225065i
$27$	10.1173	−	10.1173i	0.374714	−	0.374714i
$28$	−6.78801	+	17.1690i	−0.242429	+	0.613179i
$29$	−26.0518	+	26.0518i	−0.898336	+	0.898336i	−0.995289	−	0.0969525i	$-0.969090\pi$
$29$	−26.0518	+	26.0518i	−0.898336	+	0.898336i	0.0969525	+	0.995289i	$0.469090\pi$
$30$	−0.630155	+	0.428478i	−0.0210052	+	0.0142826i
$31$			20.2345i			0.652727i	0.945244	+	0.326363i	$0.105823\pi$
$31$			20.2345i			0.652727i	−0.945244	+	0.326363i	$0.894177\pi$
$32$	4.96735	−	31.6121i	0.155230	−	0.987878i
$33$	34.8724			1.05674
$34$	−14.4837	−	21.3009i	−0.425990	−	0.626497i
$35$	−0.270624	−	0.270624i	−0.00773212	−	0.00773212i
$36$	−45.0613	−	17.8156i	−1.25170	−	0.494878i
$37$	41.2829	+	41.2829i	1.11575	+	1.11575i	0.992358	+	0.123395i	$0.0393783\pi$
$37$	41.2829	+	41.2829i	1.11575	+	1.11575i	0.123395	+	0.992358i	$0.460622\pi$
$38$	−1.39400	+	7.31733i	−0.0366843	+	0.192561i
$39$	−71.8398			−1.84205
$40$	0.560352	+	0.355035i	0.0140088	+	0.00887588i
$41$			3.29640i			0.0804001i	0.999192	+	0.0402000i	$0.0127995\pi$
$41$			3.29640i			0.0804001i	−0.999192	+	0.0402000i	$0.987200\pi$
$42$	7.93793	−	41.6673i	0.188998	−	0.992079i
$43$	−0.786951	+	0.786951i	−0.0183012	+	0.0183012i	−0.716198	−	0.697897i	$-0.754119\pi$
$43$	−0.786951	+	0.786951i	−0.0183012	+	0.0183012i	0.697897	+	0.716198i	$0.254119\pi$
$44$	−12.0698	−	27.8544i	−0.274314	−	0.633054i
$45$	0.710272	−	0.710272i	0.0157838	−	0.0157838i
$46$	18.4216	+	27.0923i	0.400470	+	0.588964i
$47$		−	79.7517i		−	1.69685i	−0.529320	−	0.848423i	$-0.677553\pi$
$47$		−	79.7517i		−	1.69685i	0.529320	−	0.848423i	$-0.322447\pi$
$48$	2.38101	+	73.4811i	0.0496045	+	1.53086i
$49$	−27.6967			−0.565239
$50$	41.3358	−	28.1065i	0.826716	−	0.562130i
$51$	41.8466	+	41.8466i	0.820522	+	0.820522i
$52$	24.8647	+	57.3821i	0.478167	+	1.10350i
$53$	1.06207	+	1.06207i	0.0200391	+	0.0200391i	0.717055	−	0.697016i	$-0.245489\pi$
$53$	1.06207	+	1.06207i	0.0200391	+	0.0200391i	−0.697016	+	0.717055i	$0.745489\pi$
$54$	28.1104	+	5.35524i	0.520563	+	0.0991711i
$55$	0.629299			0.0114418
$56$	−36.0292	+	8.08117i	−0.643379	+	0.144307i
$57$		−	17.1138i		−	0.300243i
$58$	−72.3837	−	13.7896i	−1.24799	−	0.237752i
$59$	32.5163	−	32.5163i	0.551124	−	0.551124i	−0.375641	−	0.926765i	$-0.622577\pi$
$59$	32.5163	−	32.5163i	0.551124	−	0.551124i	0.926765	+	0.375641i	$0.122577\pi$
$60$	−1.41731	−	0.560352i	−0.0236218	−	0.00933920i
$61$	15.2897	−	15.2897i	0.250651	−	0.250651i	−0.570586	−	0.821238i	$-0.693284\pi$
$61$	15.2897	−	15.2897i	0.250651	−	0.250651i	0.821238	+	0.570586i	$0.193284\pi$
$62$	−33.4656	+	22.7552i	−0.539768	+	0.367019i
$63$			55.9119i			0.887491i
$64$	57.8690	−	27.3346i	0.904203	−	0.427103i
$65$	−1.29640			−0.0199446
$66$	39.2165	+	57.6750i	0.594189	+	0.873864i
$67$	−60.0631	−	60.0631i	−0.896465	−	0.896465i	0.0986569	−	0.995122i	$-0.468545\pi$
$67$	−60.0631	−	60.0631i	−0.896465	−	0.896465i	−0.995122	+	0.0986569i	$0.968545\pi$
$68$	18.9414	−	47.9087i	0.278550	−	0.704540i
$69$	−53.2242	−	53.2242i	−0.771365	−	0.771365i
$70$	0.143246	−	0.751918i	0.00204637	−	0.0107417i
$71$	56.3535			0.793711			0.396856	−	0.917881i	$-0.370101\pi$
$71$	56.3535			0.793711			0.396856	+	0.917881i	$0.370101\pi$
$72$	−21.2096	−	94.5612i	−0.294578	−	1.31335i
$73$		−	9.70663i		−	0.132968i	−0.997788	−	0.0664838i	$-0.978822\pi$
$73$		−	9.70663i		−	0.132968i	0.997788	−	0.0664838i	$-0.0211781\pi$
$74$	−21.8517	+	114.703i	−0.295293	+	1.55004i
$75$	−81.2062	+	81.2062i	−1.08275	+	1.08275i
$76$	−13.6697	+	5.92332i	−0.179864	+	0.0779384i
$77$	−24.7689	+	24.7689i	−0.321674	+	0.321674i
$78$	−80.7889	−	118.815i	−1.03575	−	1.52327i
$79$			84.4278i			1.06871i	0.845261	+	0.534353i	$0.179445\pi$
$79$			84.4278i			1.06871i	−0.845261	+	0.534353i	$0.820555\pi$
$80$	0.0429672	+	1.32602i	0.000537090	+	0.0165753i
$81$	43.2796			0.534316
$82$	−5.45188	+	3.70704i	−0.0664863	+	0.0452078i
$83$	26.7577	+	26.7577i	0.322382	+	0.322382i	0.849680	−	0.527298i	$-0.176795\pi$
$83$	26.7577	+	26.7577i	0.322382	+	0.322382i	−0.527298	+	0.849680i	$0.676795\pi$
$84$	77.8398	−	33.7294i	0.926664	−	0.401540i
$85$	0.755154	+	0.755154i	0.00888416	+	0.00888416i
$86$	−2.18651	−	0.416546i	−0.0254245	−	0.00484356i
$87$	169.292			1.94588
$88$	32.4946	−	51.2863i	0.369257	−	0.582799i
$89$			115.555i			1.29838i	0.760628	+	0.649188i	$0.224891\pi$
$89$			115.555i			1.29838i	−0.760628	+	0.649188i	$0.775109\pi$
$90$	1.97346	+	0.375959i	0.0219273	+	0.00417732i
$91$	51.0258	−	51.0258i	0.560723	−	0.560723i
$92$	−24.0913	+	60.9345i	−0.261862	+	0.662331i
$93$	65.7448	−	65.7448i	0.706934	−	0.706934i
$94$	131.900	−	89.6864i	1.40319	−	0.954111i
$95$		−	0.308832i		−	0.00325086i
$96$	−118.852	+	86.5726i	−1.23804	+	0.901798i
$97$	−146.245			−1.50768			−0.753841	−	0.657056i	$-0.771801\pi$
$97$	−146.245			−1.50768			−0.753841	+	0.657056i	$0.771801\pi$
$98$	−31.1469	−	45.8072i	−0.317826	−	0.467421i
$99$	−65.0077	−	65.0077i	−0.656644	−	0.656644i
$100$	92.9700	+	36.7570i	0.929700	+	0.367570i
$101$	−53.8554	−	53.8554i	−0.533222	−	0.533222i	0.388308	−	0.921530i	$-0.373060\pi$
$101$	−53.8554	−	53.8554i	−0.533222	−	0.533222i	−0.921530	+	0.388308i	$0.873060\pi$
$102$	−22.1501	+	116.269i	−0.217158	+	1.13989i
$103$	−158.184			−1.53577			−0.767885	−	0.640588i	$-0.778691\pi$
$103$	−158.184			−1.53577			−0.767885	+	0.640588i	$0.778691\pi$
$104$	−66.9414	+	105.654i	−0.643667	+	1.01590i
$105$			1.75859i			0.0167485i
$106$	−0.562172	+	2.95092i	−0.00530351	+	0.0278389i
$107$	−57.6009	+	57.6009i	−0.538327	+	0.538327i	−0.923037	−	0.384711i	$-0.874301\pi$
$107$	−57.6009	+	57.6009i	−0.538327	+	0.538327i	0.384711	+	0.923037i	$0.374301\pi$
$108$	22.7552	+	52.5137i	0.210696	+	0.486238i
$109$	56.8795	−	56.8795i	0.521830	−	0.521830i	−0.396294	−	0.918124i	$-0.629704\pi$
$109$	56.8795	−	56.8795i	0.521830	−	0.521830i	0.918124	+	0.396294i	$0.129704\pi$
$110$	0.707691	+	1.04079i	0.00643355	+	0.00946172i
$111$		−	268.268i		−	2.41683i
$112$	−53.8827	−	50.5004i	−0.481096	−	0.450896i
$113$	135.731			1.20116			0.600580	−	0.799565i	$-0.294936\pi$
$113$	135.731			1.20116			0.600580	+	0.799565i	$0.294936\pi$
$114$	28.3043	−	19.2457i	0.248284	−	0.168822i
$115$	−0.960471	−	0.960471i	−0.00835192	−	0.00835192i
$116$	−58.5941	−	135.222i	−0.505121	−	1.16571i
$117$	133.921	+	133.921i	1.14462	+	1.14462i
$118$	90.3452	+	17.2114i	0.765637	+	0.145860i
$119$	−59.4450			−0.499538
$120$	−0.667103	−	2.97422i	−0.00555919	−	0.0247852i
$121$			63.4034i			0.523995i
$122$	42.4819	+	8.09311i	0.348212	+	0.0663369i
$123$	10.7105	−	10.7105i	0.0870770	−	0.0870770i
$124$	−75.2689	−	29.7586i	−0.607007	−	0.239989i
$125$	−2.93125	+	2.93125i	−0.0234500	+	0.0234500i
$126$	−92.4720	+	62.8769i	−0.733905	+	0.499023i
$127$			166.552i			1.31144i	0.755006	+	0.655718i	$0.227634\pi$
$127$			166.552i			1.31144i	−0.755006	+	0.655718i	$0.772366\pi$
$128$	110.286	+	64.9691i	0.861610	+	0.507571i
$129$	5.11383			0.0396421
$130$	−1.45790	−	2.14410i	−0.0112146	−	0.0164931i
$131$	22.2547	+	22.2547i	0.169883	+	0.169883i	0.786928	−	0.617045i	$-0.211670\pi$
$131$	22.2547	+	22.2547i	0.169883	+	0.169883i	−0.617045	+	0.786928i	$0.711670\pi$
$132$	−51.2863	+	129.719i	−0.388533	+	0.982722i
$133$	12.1555	+	12.1555i	0.0913945	+	0.0913945i
$134$	31.7924	−	166.883i	0.237257	−	1.24539i
$135$	−1.18641			−0.00878826
$136$	100.536	−	22.5498i	0.739239	−	0.165808i
$137$		−	174.890i		−	1.27657i	−0.769800	−	0.638285i	$-0.779644\pi$
$137$		−	174.890i		−	1.27657i	0.769800	−	0.638285i	$-0.220356\pi$
$138$	28.1725	−	147.881i	0.204148	−	1.07160i
$139$	99.8891	−	99.8891i	0.718627	−	0.718627i	−0.249697	−	0.968324i	$-0.580331\pi$
$139$	99.8891	−	99.8891i	0.718627	−	0.718627i	0.968324	+	0.249697i	$0.0803310\pi$
$140$	1.40468	−	0.608672i	0.0100334	−	0.00434766i
$141$	−259.125	+	259.125i	−1.83776	+	1.83776i
$142$	63.3735	+	93.2023i	0.446292	+	0.656354i
$143$			118.653i			0.829744i
$144$	132.542	−	141.419i	0.920429	−	0.982077i
$145$	3.05499			0.0210689
$146$	16.0537	−	10.9158i	0.109957	−	0.0747657i
$147$	89.9905	+	89.9905i	0.612181	+	0.612181i
$148$	−214.279	+	92.8509i	−1.44783	+	0.627371i
$149$	−74.8860	−	74.8860i	−0.502590	−	0.502590i	0.409652	−	0.912242i	$-0.365650\pi$
$149$	−74.8860	−	74.8860i	−0.502590	−	0.502590i	−0.912242	+	0.409652i	$0.865650\pi$
$150$	−225.628	−	42.9838i	−1.50419	−	0.286558i
$151$	70.0357			0.463813			0.231906	−	0.972738i	$-0.425504\pi$
$151$	70.0357			0.463813			0.231906	+	0.972738i	$0.425504\pi$
$152$	−25.1690	−	15.9469i	−0.165586	−	0.104914i
$153$		−	156.018i		−	1.01972i
$154$	−68.8193	−	13.1106i	−0.446879	−	0.0851337i
$155$	1.18641	−	1.18641i	0.00765429	−	0.00765429i
$156$	105.654	−	267.231i	0.677266	−	1.71302i
$157$	−29.5307	+	29.5307i	−0.188094	+	0.188094i	−0.794872	−	0.606778i	$-0.792462\pi$
$157$	−29.5307	+	29.5307i	−0.188094	+	0.188094i	0.606778	+	0.794872i	$0.292462\pi$
$158$	−139.634	+	94.9450i	−0.883760	+	0.600918i
$159$		−	6.90164i		−	0.0434065i
$160$	−2.14477	+	1.56227i	−0.0134048	+	0.00976417i
$161$	75.6074			0.469611
$162$	48.6710	+	71.5796i	0.300438	+	0.441849i
$163$	47.7990	+	47.7990i	0.293245	+	0.293245i	0.838361	−	0.545116i	$-0.183514\pi$
$163$	47.7990	+	47.7990i	0.293245	+	0.293245i	−0.545116	+	0.838361i	$0.683514\pi$
$164$	−12.2620	−	4.84796i	−0.0747685	−	0.0295608i
$165$	−2.04468	−	2.04468i	−0.0123920	−	0.0123920i
$166$	−14.1633	+	74.3452i	−0.0853212	+	0.447863i
$167$	−156.268			−0.935734			−0.467867	−	0.883799i	$-0.654977\pi$
$167$	−156.268			−0.935734			−0.467867	+	0.883799i	$0.654977\pi$
$168$	143.321	+	90.8071i	0.853100	+	0.540519i
$169$		−	75.4347i		−	0.446359i
$170$	−0.399715	+	2.09816i	−0.00235127	+	0.0123421i
$171$	−31.9029	+	31.9029i	−0.186567	+	0.186567i
$172$	−1.76996	−	4.08467i	−0.0102905	−	0.0237481i
$173$	190.103	−	190.103i	1.09886	−	1.09886i	0.104319	−	0.994544i	$-0.466734\pi$
$173$	190.103	−	190.103i	1.09886	−	1.09886i	0.994544	−	0.104319i	$-0.0332664\pi$
$174$	190.380	+	279.989i	1.09414	+	1.60913i
$175$		−	115.357i		−	0.659183i
$176$	121.364	−	3.93258i	0.689569	−	0.0223442i
$177$	−211.300			−1.19379
$178$	−191.116	+	129.950i	−1.07368	+	0.730057i
$179$	54.2749	+	54.2749i	0.303212	+	0.303212i	0.842269	−	0.539057i	$-0.181219\pi$
$179$	54.2749	+	54.2749i	0.303212	+	0.303212i	−0.539057	+	0.842269i	$0.681219\pi$
$180$	1.59750	+	3.68667i	0.00887501	+	0.0204815i
$181$	19.7343	+	19.7343i	0.109029	+	0.109029i	0.759517	−	0.650487i	$-0.225435\pi$
$181$	19.7343	+	19.7343i	0.109029	+	0.109029i	−0.650487	+	0.759517i	$0.725435\pi$
$182$	141.773	+	27.0088i	0.778972	+	0.148400i
$183$	−99.3569			−0.542934
$184$	−127.871	+	28.6809i	−0.694952	+	0.155874i
$185$		−	4.84109i		−	0.0261680i
$186$	182.669	+	34.7998i	0.982093	+	0.187096i
$187$	69.1155	−	69.1155i	0.369602	−	0.369602i
$188$	296.662	+	117.290i	1.57799	+	0.623880i
$189$	46.6967	−	46.6967i	0.247073	−	0.247073i
$190$	0.510773	−	0.347303i	0.00268828	−	0.00182791i
$191$		−	166.552i		−	0.872002i	−0.899946	−	0.436001i	$-0.856394\pi$
$191$		−	166.552i		−	0.872002i	0.899946	−	0.436001i	$-0.143606\pi$
$192$	−276.838	−	99.2105i	−1.44187	−	0.516721i
$193$	2.18257			0.0113087			0.00565434	−	0.999984i	$-0.498200\pi$
$193$	2.18257			0.0113087			0.00565434	+	0.999984i	$0.498200\pi$
$194$	−164.463	−	241.873i	−0.847748	−	1.24677i
$195$	4.21219	+	4.21219i	0.0216010	+	0.0216010i
$196$	40.7331	−	103.027i	0.207822	−	0.525648i
$197$	67.4310	+	67.4310i	0.342290	+	0.342290i	0.857227	−	0.514938i	$-0.172185\pi$
$197$	67.4310	+	67.4310i	0.342290	+	0.342290i	−0.514938	+	0.857227i	$0.672185\pi$
$198$	34.4097	−	180.621i	0.173786	−	0.912228i
$199$	222.906			1.12013			0.560065	−	0.828449i	$-0.310776\pi$
$199$	222.906			1.12013			0.560065	+	0.828449i	$0.310776\pi$
$200$	43.7594	+	195.098i	0.218797	+	0.975488i
$201$			390.307i			1.94183i
$202$	28.5066	−	149.635i	0.141122	−	0.740767i
$203$	−120.243	+	120.243i	−0.592331	+	0.592331i
$204$	−217.205	+	94.1190i	−1.06473	+	0.461368i
$205$	0.193278	−	0.193278i	0.000942822	−	0.000942822i
$206$	−177.889	−	261.619i	−0.863541	−	1.26999i
$207$			198.437i			0.958632i
$208$	−250.019	+	8.10140i	−1.20202	+	0.0389490i
$209$	−28.2659			−0.135243
$210$	−2.90851	+	1.97766i	−0.0138501	+	0.00941743i
$211$	−147.118	−	147.118i	−0.697240	−	0.697240i	0.266574	−	0.963814i	$-0.414108\pi$
$211$	−147.118	−	147.118i	−0.697240	−	0.697240i	−0.963814	+	0.266574i	$0.914108\pi$
$212$	−5.51269	+	2.38875i	−0.0260032	+	0.0112677i
$213$	−183.100	−	183.100i	−0.859627	−	0.859627i
$214$	−160.042	−	30.4891i	−0.747859	−	0.142473i
$215$	0.0922828			0.000429223
$216$	−61.2620	+	96.6898i	−0.283620	+	0.447638i
$217$			93.3934i			0.430385i
$218$	158.037	+	30.1073i	0.724941	+	0.138107i
$219$	−31.5382	+	31.5382i	−0.144010	+	0.144010i
$220$	−0.925499	+	2.34088i	−0.00420681	+	0.0106404i
$221$	−142.383	+	142.383i	−0.644268	+	0.644268i
$222$	443.684	−	301.686i	1.99858	−	1.35894i
$223$		−	60.7036i		−	0.272213i	−0.990694	−	0.136107i	$-0.956541\pi$
$223$		−	60.7036i		−	0.272213i	0.990694	−	0.136107i	$-0.0434590\pi$
$224$	22.9270	−	145.907i	0.102353	−	0.651371i
$225$	302.762			1.34561
$226$	152.639	+	224.484i	0.675394	+	0.993291i
$227$	−225.526	−	225.526i	−0.993505	−	0.993505i	0.00647371	−	0.999979i	$-0.497939\pi$
$227$	−225.526	−	225.526i	−0.993505	−	0.993505i	−0.999979	+	0.00647371i	$0.997939\pi$
$228$	63.6604	+	25.1690i	0.279212	+	0.110390i
$229$	227.796	+	227.796i	0.994743	+	0.994743i	0.999986	−	0.00524305i	$-0.00166892\pi$
$229$	227.796	+	227.796i	0.994743	+	0.994743i	−0.00524305	+	0.999986i	$0.501669\pi$
$230$	0.508393	−	2.66863i	0.00221040	−	0.0116027i
$231$	160.955			0.696776
$232$	157.748	−	248.974i	0.679950	−	1.07317i
$233$			121.053i			0.519540i	0.965671	+	0.259770i	$0.0836467\pi$
$233$			121.053i			0.519540i	−0.965671	+	0.259770i	$0.916353\pi$
$234$	−70.8865	+	372.093i	−0.302934	+	1.59014i
$235$	−4.67610	+	4.67610i	−0.0198983	+	0.0198983i
$236$	73.1338	+	168.776i	0.309889	+	0.715154i
$237$	274.318	−	274.318i	1.15746	−	1.15746i
$238$	−66.8501	−	98.3153i	−0.280883	−	0.413090i
$239$			221.393i			0.926332i	0.886271	+	0.463166i	$0.153287\pi$
$239$			221.393i			0.926332i	−0.886271	+	0.463166i	$0.846713\pi$
$240$	4.16882	−	4.44804i	0.0173701	−	0.0185335i
$241$	84.2667			0.349654			0.174827	−	0.984599i	$-0.444063\pi$
$241$	84.2667			0.349654			0.174827	+	0.984599i	$0.444063\pi$
$242$	−104.862	+	71.3015i	−0.433314	+	0.294634i
$243$	−231.677	−	231.677i	−0.953403	−	0.953403i
$244$	34.3887	+	79.3614i	0.140937	+	0.325252i
$245$	1.62395	+	1.62395i	0.00662835	+	0.00662835i
$246$	29.7586	+	5.66923i	0.120970	+	0.0230457i
$247$	58.2298			0.235748
$248$	−35.4278	−	157.952i	−0.142854	−	0.636903i
$249$		−	173.879i		−	0.698310i
$250$	−8.14437	−	1.55156i	−0.0325775	−	0.00620625i
$251$	−176.615	+	176.615i	−0.703646	+	0.703646i	−0.965191	−	0.261545i	$-0.915768\pi$
$251$	−176.615	+	176.615i	−0.703646	+	0.703646i	0.261545	+	0.965191i	$0.415768\pi$
$252$	−207.983	−	82.2288i	−0.825328	−	0.326305i
$253$	−87.9072	+	87.9072i	−0.347459	+	0.347459i
$254$	−275.459	+	187.300i	−1.08448	+	0.737401i
$255$		−	4.90720i		−	0.0192439i
$256$	16.5730	+	255.463i	0.0647382	+	0.997902i
$257$	−163.001			−0.634244			−0.317122	−	0.948385i	$-0.602717\pi$
$257$	−163.001			−0.634244			−0.317122	+	0.948385i	$0.602717\pi$
$258$	5.75086	+	8.45769i	0.0222902	+	0.0327818i
$259$	190.543	+	190.543i	0.735687	+	0.735687i
$260$	1.90660	−	4.82239i	0.00733307	−	0.0185476i
$261$	−315.587	−	315.587i	−1.20914	−	1.20914i
$262$	−11.7798	+	61.8337i	−0.0449610	+	0.236007i
$263$	175.001			0.665404			0.332702	−	0.943032i	$-0.392040\pi$
$263$	175.001			0.665404			0.332702	+	0.943032i	$0.392040\pi$
$264$	−272.216	+	61.0567i	−1.03112	+	0.231275i
$265$		−	0.124545i		−	0.000469982i
$266$	−6.43409	+	33.7735i	−0.0241883	+	0.126968i
$267$	375.456	−	375.456i	1.40620	−	1.40620i
$268$	311.758	−	135.090i	1.16328	−	0.504069i
$269$	29.7489	−	29.7489i	0.110591	−	0.110591i	−0.649646	−	0.760237i	$-0.725083\pi$
$269$	29.7489	−	29.7489i	0.110591	−	0.110591i	0.760237	+	0.649646i	$0.225083\pi$
$270$	−1.33421	−	1.96220i	−0.00494151	−	0.00726739i
$271$		−	275.891i		−	1.01805i	−0.860753	−	0.509024i	$-0.830007\pi$
$271$		−	275.891i		−	1.01805i	0.860753	−	0.509024i	$-0.169993\pi$
$272$	150.355	+	140.917i	0.552777	+	0.518078i
$273$	−331.580			−1.21458
$274$	289.248	−	196.676i	1.05565	−	0.717796i
$275$	134.123	+	134.123i	0.487721	+	0.487721i
$276$	276.261	−	119.709i	1.00094	−	0.433727i
$277$	−278.337	−	278.337i	−1.00483	−	1.00483i	−0.999988	−	0.00484003i	$-0.998459\pi$
$277$	−278.337	−	278.337i	−1.00483	−	1.00483i	−0.00484003	−	0.999988i	$-0.501541\pi$
$278$	277.538	+	52.8730i	0.998337	+	0.190191i
$279$	−245.118			−0.878558
$280$	2.58633	+	1.63868i	0.00923690	+	0.00585244i
$281$		−	202.356i		−	0.720128i	−0.932928	−	0.360064i	$-0.882755\pi$
$281$		−	202.356i		−	0.720128i	0.932928	−	0.360064i	$-0.117245\pi$
$282$	−719.966	−	137.159i	−2.55307	−	0.486379i
$283$	−292.256	+	292.256i	−1.03271	+	1.03271i	−0.0332615	+	0.999447i	$0.510589\pi$
$283$	−292.256	+	292.256i	−1.03271	+	1.03271i	−0.999447	+	0.0332615i	$0.989411\pi$
$284$	−82.8782	+	209.625i	−0.291825	+	0.738117i
$285$	−1.00344	+	1.00344i	−0.00352083	+	0.00352083i
$286$	−196.239	+	133.434i	−0.686151	+	0.466553i
$287$			15.2147i			0.0530129i
$288$	382.944	+	60.1736i	1.32967	+	0.208936i
$289$	−123.124			−0.426034
$290$	3.43556	+	5.05261i	0.0118467	+	0.0174228i
$291$	475.171	+	475.171i	1.63289	+	1.63289i
$292$	36.1070	+	14.2754i	0.123654	+	0.0488883i
$293$	331.170	+	331.170i	1.13027	+	1.13027i	0.990132	+	0.140141i	$0.0447555\pi$
$293$	331.170	+	331.170i	1.13027	+	1.13027i	0.140141	+	0.990132i	$0.455244\pi$
$294$	−47.6335	+	250.035i	−0.162019	+	0.850459i
$295$	−3.81307			−0.0129257
$296$	−394.537	−	249.976i	−1.33289	−	0.844513i
$297$			108.587i			0.365612i
$298$	39.6384	−	208.067i	0.133015	−	0.698213i
$299$	181.095	−	181.095i	0.605670	−	0.605670i
$300$	−182.644	−	421.501i	−0.608814	−	1.40500i
$301$	−3.63221	+	3.63221i	−0.0120671	+	0.0120671i
$302$	78.7601	+	115.831i	0.260795	+	0.383547i
$303$			349.968i			1.15501i
$304$	−1.92993	−	59.5602i	−0.00634846	−	0.195922i
$305$	−1.79297			−0.00587859
$306$	258.035	−	175.453i	0.843253	−	0.573375i
$307$	23.7513	+	23.7513i	0.0773656	+	0.0773656i	0.744731	−	0.667365i	$-0.232578\pi$
$307$	23.7513	+	23.7513i	0.0773656	+	0.0773656i	−0.667365	+	0.744731i	$0.732578\pi$
$308$	−55.7087	−	128.563i	−0.180873	−	0.417413i
$309$	513.963	+	513.963i	1.66331	+	1.66331i
$310$	3.29640	+	0.627989i	0.0106336	+	0.00202577i
$311$	−157.757			−0.507258			−0.253629	−	0.967302i	$-0.581624\pi$
$311$	−157.757			−0.507258			−0.253629	+	0.967302i	$0.581624\pi$
$312$	560.785	−	125.781i	1.79739	−	0.403145i
$313$		−	58.5936i		−	0.187200i	−0.995610	−	0.0936000i	$-0.970163\pi$
$313$		−	58.5936i		−	0.187200i	0.995610	−	0.0936000i	$-0.0298375\pi$
$314$	−82.0499	−	15.6311i	−0.261305	−	0.0497806i
$315$	3.27829	−	3.27829i	0.0104073	−	0.0104073i
$316$	−314.057	−	124.167i	−0.993850	−	0.392932i
$317$	27.0040	−	27.0040i	0.0851863	−	0.0851863i	−0.663230	−	0.748416i	$-0.730815\pi$
$317$	27.0040	−	27.0040i	0.0851863	−	0.0851863i	0.748416	+	0.663230i	$0.230815\pi$
$318$	11.4145	−	7.76137i	0.0358947	−	0.0244068i
$319$		−	279.609i		−	0.876516i
$320$	−4.99576	−	1.79033i	−0.0156117	−	0.00559477i
$321$	374.307			1.16607
$322$	85.0258	+	125.046i	0.264055	+	0.388342i
$323$	−33.9188	−	33.9188i	−0.105012	−	0.105012i
$324$	−63.6506	+	160.993i	−0.196453	+	0.496891i
$325$	−276.304	−	276.304i	−0.850166	−	0.850166i
$326$	−25.3008	+	132.807i	−0.0776098	+	0.407385i
$327$	−369.619			−1.13033
$328$	−5.77154	−	25.7319i	−0.0175961	−	0.0784509i
$329$		−	368.098i		−	1.11884i
$330$	1.08228	−	5.68106i	0.00327965	−	0.0172153i
$331$	−182.195	+	182.195i	−0.550437	+	0.550437i	−0.926567	−	0.376130i	$-0.877255\pi$
$331$	−182.195	+	182.195i	−0.550437	+	0.550437i	0.376130	+	0.926567i	$0.377255\pi$
$332$	−138.886	+	60.1819i	−0.418332	+	0.181271i
$333$	−500.093	+	500.093i	−1.50178	+	1.50178i
$334$	−175.734	−	258.449i	−0.526149	−	0.773799i
$335$			7.04338i			0.0210250i
$336$	10.9897	+	339.155i	0.0327074	+	1.00939i
$337$	510.137			1.51376			0.756881	−	0.653553i	$-0.226722\pi$
$337$	510.137			1.51376			0.756881	+	0.653553i	$0.226722\pi$
$338$	124.760	−	84.8316i	0.369114	−	0.250981i
$339$	−441.009	−	441.009i	−1.30091	−	1.30091i
$340$	−3.91963	+	1.69845i	−0.0115283	+	0.00499543i
$341$	−108.587	−	108.587i	−0.318436	−	0.318436i
$342$	−88.6408	−	16.8867i	−0.259184	−	0.0493764i
$343$	−353.997			−1.03206
$344$	4.76514	−	7.52082i	0.0138522	−	0.0218629i
$345$			6.24141i			0.0180910i
$346$	528.194	+	100.625i	1.52657	+	0.290823i
$347$	432.614	−	432.614i	1.24673	−	1.24673i	0.289570	−	0.957157i	$-0.406488\pi$
$347$	432.614	−	432.614i	1.24673	−	1.24673i	0.957157	−	0.289570i	$-0.0935122\pi$
$348$	−248.974	+	629.735i	−0.715444	+	1.80958i
$349$	−148.839	+	148.839i	−0.426472	+	0.426472i	−0.887425	−	0.460953i	$-0.847508\pi$
$349$	−148.839	+	148.839i	−0.426472	+	0.426472i	0.460953	+	0.887425i	$0.347508\pi$
$350$	190.787	−	129.727i	0.545107	−	0.370649i
$351$		−	223.697i		−	0.637313i
$352$	142.987	+	196.300i	0.406212	+	0.557671i
$353$	−268.587			−0.760869			−0.380434	−	0.924808i	$-0.624226\pi$
$353$	−268.587			−0.760869			−0.380434	+	0.924808i	$0.624226\pi$
$354$	−237.622	−	349.467i	−0.671248	−	0.987194i
$355$	−3.30418	−	3.30418i	−0.00930756	−	0.00930756i
$356$	−429.846	−	169.945i	−1.20743	−	0.477375i
$357$	193.145	+	193.145i	0.541023	+	0.541023i
$358$	−28.7286	+	150.801i	−0.0802475	+	0.421231i
$359$	628.520			1.75075			0.875376	−	0.483442i	$-0.160614\pi$
$359$	628.520			1.75075			0.875376	+	0.483442i	$0.160614\pi$
$360$	−4.30084	+	6.78801i	−0.0119468	+	0.0188556i
$361$		−	347.128i		−	0.961574i
$362$	−10.4457	+	54.8310i	−0.0288556	+	0.151467i
$363$	206.006	−	206.006i	0.567511	−	0.567511i
$364$	114.764	+	264.850i	0.315286	+	0.727609i
$365$	−0.569131	+	0.569131i	−0.00155926	+	0.00155926i
$366$	−111.734	−	164.325i	−0.305284	−	0.448976i
$367$			396.386i			1.08007i	0.841643	+	0.540035i	$0.181589\pi$
$367$			396.386i			1.08007i	−0.841643	+	0.540035i	$0.818411\pi$
$368$	−191.235	−	179.231i	−0.519660	−	0.487040i
$369$	−39.9320			−0.108217
$370$	8.00661	−	5.44414i	0.0216395	−	0.0147139i
$371$	4.90204	+	4.90204i	0.0132130	+	0.0132130i
$372$	147.869	+	341.249i	0.397498	+	0.917336i
$373$	134.275	+	134.275i	0.359987	+	0.359987i	0.863808	−	0.503821i	$-0.168073\pi$
$373$	134.275	+	134.275i	0.359987	+	0.359987i	−0.503821	+	0.863808i	$0.668073\pi$
$374$	192.035	+	36.5840i	0.513461	+	0.0978182i
$375$	19.0481			0.0507950
$376$	139.634	+	622.546i	0.371367	+	1.65571i
$377$			576.015i			1.52789i
$378$	129.745	+	24.7173i	0.343240	+	0.0653898i
$379$	−350.491	+	350.491i	−0.924777	+	0.924777i	−0.997362	−	0.0725851i	$-0.976875\pi$
$379$	−350.491	+	350.491i	−0.924777	+	0.924777i	0.0725851	+	0.997362i	$0.476875\pi$
$380$	1.14880	+	0.454194i	0.00302316	+	0.00119525i
$381$	541.152	−	541.152i	1.42035	−	1.42035i
$382$	275.459	−	187.300i	0.721096	−	0.490314i
$383$		−	403.778i		−	1.05425i	−0.849787	−	0.527126i	$-0.823270\pi$
$383$		−	403.778i		−	1.05425i	0.849787	−	0.527126i	$-0.176730\pi$
$384$	−147.241	−	569.429i	−0.383441	−	1.48289i
$385$	2.90456			0.00754431
$386$	2.45446	+	3.60973i	0.00635870	+	0.00935163i
$387$	−9.53299	−	9.53299i	−0.0246330	−	0.0246330i
$388$	215.080	−	544.007i	0.554331	−	1.40208i
$389$	−125.310	−	125.310i	−0.322134	−	0.322134i	0.527452	−	0.849585i	$-0.323148\pi$
$389$	−125.310	−	125.310i	−0.322134	−	0.322134i	−0.849585	+	0.527452i	$0.823148\pi$
$390$	−2.22958	+	11.7034i	−0.00571688	+	0.0300087i
$391$	−210.976			−0.539580
$392$	216.202	−	48.4931i	0.551536	−	0.123707i
$393$		−	144.617i		−	0.367983i
$394$	−35.6924	+	187.354i	−0.0905898	+	0.475518i
$395$	4.95027	−	4.95027i	0.0125323	−	0.0125323i
$396$	337.423	−	146.212i	0.852079	−	0.369221i
$397$	−69.8722	+	69.8722i	−0.176001	+	0.176001i	−0.789610	−	0.613609i	$-0.789717\pi$
$397$	−69.8722	+	69.8722i	−0.176001	+	0.176001i	0.613609	+	0.789610i	$0.289717\pi$
$398$	250.673	+	368.661i	0.629832	+	0.926284i
$399$		−	78.9897i		−	0.197969i
$400$	−273.459	+	291.774i	−0.683647	+	0.729436i
$401$	11.3010			0.0281821			0.0140911	−	0.999901i	$-0.495515\pi$
$401$	11.3010			0.0281821			0.0140911	+	0.999901i	$0.495515\pi$
$402$	−645.524	+	438.928i	−1.60578	+	1.09186i
$403$	223.697	+	223.697i	0.555079	+	0.555079i
$404$	279.537	−	121.128i	0.691923	−	0.299823i
$405$	−2.53762	−	2.53762i	−0.00626573	−	0.00626573i
$406$	−334.090	−	63.6467i	−0.822883	−	0.156765i
$407$	−443.081			−1.08865
$408$	−399.925	−	253.390i	−0.980208	−	0.621053i
$409$			614.595i			1.50268i	0.659917	+	0.751339i	$0.270592\pi$
$409$			614.595i			1.50268i	−0.659917	+	0.751339i	$0.729408\pi$
$410$	0.537016	+	0.102305i	0.00130979	+	0.000249526i
$411$	−568.242	+	568.242i	−1.38258	+	1.38258i
$412$	232.639	−	588.418i	0.564658	−	1.42820i
$413$	150.081	−	150.081i	0.363391	−	0.363391i
$414$	−328.192	+	223.156i	−0.792734	+	0.539024i
$415$		−	3.13778i		−	0.00756092i
$416$	−294.563	−	404.393i	−0.708084	−	0.972099i
$417$	−649.108			−1.55661
$418$	−31.7870	−	46.7485i	−0.0760453	−	0.111839i
$419$	78.7092	+	78.7092i	0.187850	+	0.187850i	0.794766	−	0.606916i	$-0.207594\pi$
$419$	78.7092	+	78.7092i	0.187850	+	0.187850i	−0.606916	+	0.794766i	$0.707594\pi$
$420$	−6.54165	−	2.58633i	−0.0155754	−	0.00615793i
$421$	−374.618	−	374.618i	−0.889829	−	0.889829i	0.104678	−	0.994506i	$-0.466619\pi$
$421$	−374.618	−	374.618i	−0.889829	−	0.889829i	−0.994506	+	0.104678i	$0.966619\pi$
$422$	77.8718	−	408.760i	0.184530	−	0.968626i
$423$	966.099			2.28392
$424$	−10.1501	−	6.43105i	−0.0239390	−	0.0151676i
$425$			321.894i			0.757397i
$426$	96.9181	−	508.737i	0.227507	−	1.19422i
$427$	70.5705	−	70.5705i	0.165270	−	0.165270i
$428$	−129.553	−	298.978i	−0.302693	−	0.698547i
$429$	385.521	−	385.521i	0.898651	−	0.898651i
$430$	0.103779	+	0.152625i	0.000241345	+	0.000354943i
$431$			616.593i			1.43061i	0.698813	+	0.715305i	$0.253712\pi$
$431$			616.593i			1.43061i	−0.698813	+	0.715305i	$0.746288\pi$
$432$	−228.808	+	7.41407i	−0.529647	+	0.0171622i
$433$	219.246			0.506342			0.253171	−	0.967422i	$-0.418526\pi$
$433$	219.246			0.506342			0.253171	+	0.967422i	$0.418526\pi$
$434$	−154.462	+	105.027i	−0.355904	+	0.241999i
$435$	−9.92610	−	9.92610i	−0.0228186	−	0.0228186i
$436$	127.930	+	295.233i	0.293417	+	0.677141i
$437$	43.1409	+	43.1409i	0.0987207	+	0.0987207i
$438$	−87.6276	−	16.6937i	−0.200063	−	0.0381135i
$439$	575.292			1.31046			0.655231	−	0.755429i	$-0.272571\pi$
$439$	575.292			1.31046			0.655231	+	0.755429i	$0.272571\pi$
$440$	−4.91234	+	1.10181i	−0.0111644	+	0.00250412i
$441$		−	335.513i		−	0.760801i
$442$	−395.605	−	75.3658i	−0.895035	−	0.170511i
$443$	371.895	−	371.895i	0.839492	−	0.839492i	−0.149300	−	0.988792i	$-0.547702\pi$
$443$	371.895	−	371.895i	0.839492	−	0.839492i	0.988792	+	0.149300i	$0.0477021\pi$
$444$	997.908	+	394.537i	2.24754	+	0.888596i
$445$	6.77538	−	6.77538i	0.0152256	−	0.0152256i
$446$	100.397	−	68.2655i	0.225105	−	0.153062i
$447$			486.630i			1.08866i
$448$	267.097	−	126.164i	0.596199	−	0.281616i
$449$	−498.135			−1.10943			−0.554716	−	0.832040i	$-0.687173\pi$
$449$	−498.135			−1.10943			−0.554716	+	0.832040i	$0.687173\pi$
$450$	340.478	+	500.735i	0.756617	+	1.11274i
$451$	−17.6898	−	17.6898i	−0.0392236	−	0.0392236i
$452$	−199.617	+	504.896i	−0.441632	+	1.11703i
$453$	−227.556	−	227.556i	−0.502331	−	0.502331i
$454$	119.374	−	626.614i	0.262939	−	1.38021i
$455$	−5.98361			−0.0131508
$456$	29.9639	+	133.591i	0.0657103	+	0.292964i
$457$		−	61.1711i		−	0.133854i	−0.997758	−	0.0669268i	$-0.978681\pi$
$457$		−	61.1711i		−	0.133854i	0.997758	−	0.0669268i	$-0.0213194\pi$
$458$	−120.576	+	632.922i	−0.263267	+	1.38193i
$459$	−130.303	+	130.303i	−0.283885	+	0.283885i
$460$	4.98533	−	2.16023i	0.0108377	−	0.00469616i
$461$	−443.183	+	443.183i	−0.961352	+	0.961352i	−0.999280	−	0.0379287i	$-0.987924\pi$
$461$	−443.183	+	443.183i	−0.961352	+	0.961352i	0.0379287	+	0.999280i	$0.487924\pi$
$462$	181.006	+	266.202i	0.391787	+	0.576195i
$463$		−	706.883i		−	1.52675i	−0.645958	−	0.763373i	$-0.723542\pi$
$463$		−	706.883i		−	1.52675i	0.645958	−	0.763373i	$-0.276458\pi$
$464$	589.175	−	19.0911i	1.26977	−	0.0411446i
$465$	−7.70966			−0.0165799
$466$	−200.208	+	136.132i	−0.429630	+	0.292129i
$467$	−406.857	−	406.857i	−0.871214	−	0.871214i	0.121391	−	0.992605i	$-0.461265\pi$
$467$	−406.857	−	406.857i	−0.871214	−	0.871214i	−0.992605	+	0.121391i	$0.961265\pi$
$468$	−695.117	+	301.207i	−1.48529	+	0.643604i
$469$	−277.224	−	277.224i	−0.591096	−	0.591096i
$470$	−12.9923	−	2.47513i	−0.0276433	−	0.00526624i
$471$	191.899			0.407429
$472$	−196.893	+	310.756i	−0.417146	+	0.658381i
$473$		−	8.44620i		−	0.0178567i
$474$	762.180	+	145.201i	1.60798	+	0.306331i
$475$	65.8217	−	65.8217i	0.138572	−	0.138572i
$476$	87.4248	−	221.125i	0.183665	−	0.464548i
$477$	−12.8657	+	12.8657i	−0.0269722	+	0.0269722i
$478$	−366.160	+	248.972i	−0.766024	+	0.520863i
$479$			133.063i			0.277793i	0.990307	+	0.138896i	$0.0443555\pi$
$479$			133.063i			0.277793i	−0.990307	+	0.138896i	$0.955645\pi$
$480$	12.0447	+	1.89263i	0.0250931	+	0.00394298i
$481$	912.780			1.89767
$482$	94.7638	+	139.368i	0.196605	+	0.289144i
$483$	−245.659	−	245.659i	−0.508611	−	0.508611i
$484$	−235.849	−	93.2463i	−0.487292	−	0.192658i
$485$	8.57482	+	8.57482i	0.0176800	+	0.0176800i
$486$	122.630	−	643.704i	0.252326	−	1.32449i
$487$	−208.075			−0.427259			−0.213629	−	0.976915i	$-0.568529\pi$
$487$	−208.075			−0.427259			−0.213629	+	0.976915i	$0.568529\pi$
$488$	−92.5823	+	146.123i	−0.189718	+	0.299432i
$489$		−	310.611i		−	0.635197i
$490$	−0.859582	+	4.51207i	−0.00175425	+	0.00920830i
$491$	−98.9374	+	98.9374i	−0.201502	+	0.201502i	−0.800643	−	0.599141i	$-0.795509\pi$
$491$	−98.9374	+	98.9374i	−0.201502	+	0.201502i	0.599141	+	0.800643i	$0.295509\pi$
$492$	24.0894	+	55.5928i	0.0489621	+	0.112993i
$493$	335.528	−	335.528i	0.680585	−	0.680585i
$494$	65.4835	+	96.3055i	0.132558	+	0.194950i
$495$			7.62322i			0.0154004i
$496$	221.393	−	236.222i	0.446358	−	0.476253i
$497$	260.102			0.523345
$498$	287.577	−	195.539i	0.577463	−	0.392650i
$499$	−287.076	−	287.076i	−0.575304	−	0.575304i	0.358302	−	0.933606i	$-0.383356\pi$
$499$	−287.076	−	287.076i	−0.575304	−	0.575304i	−0.933606	+	0.358302i	$0.883356\pi$
$500$	−6.59280	−	15.2147i	−0.0131856	−	0.0304294i
$501$	507.735	+	507.735i	1.01344	+	1.01344i
$502$	−490.717	−	93.4853i	−0.977525	−	0.186226i
$503$	−78.7359			−0.156533			−0.0782663	−	0.996932i	$-0.524938\pi$
$503$	−78.7359			−0.156533			−0.0782663	+	0.996932i	$0.524938\pi$
$504$	−97.8940	−	436.452i	−0.194234	−	0.865976i
$505$			6.31543i			0.0125058i
$506$	−244.246	−	46.5307i	−0.482700	−	0.0919580i
$507$	−245.098	+	245.098i	−0.483428	+	0.483428i
$508$	−619.545	−	244.946i	−1.21958	−	0.482177i
$509$	−242.477	+	242.477i	−0.476378	+	0.476378i	−0.903971	−	0.427593i	$-0.859362\pi$
$509$	−242.477	+	242.477i	−0.476378	+	0.476378i	0.427593	+	0.903971i	$0.359362\pi$
$510$	8.11596	−	5.51849i	0.0159136	−	0.0108206i
$511$		−	44.8014i		−	0.0876740i
$512$	−403.869	+	314.696i	−0.788807	+	0.614640i
$513$	53.2895			0.103878
$514$	−183.306	−	269.585i	−0.356626	−	0.524484i
$515$	9.27484	+	9.27484i	0.0180094	+	0.0180094i
$516$	−7.52082	+	19.0225i	−0.0145752	+	0.0368654i
$517$	427.980	+	427.980i	0.827815	+	0.827815i
$518$	−100.858	+	529.415i	−0.194706	+	1.02204i
$519$	−1235.34			−2.38024
$520$	10.1198	−	2.26982i	0.0194611	−	0.00436503i
$521$			561.306i			1.07736i	0.842510	+	0.538681i	$0.181077\pi$
$521$			561.306i			1.07736i	−0.842510	+	0.538681i	$0.818923\pi$
$522$	167.045	−	876.844i	0.320010	−	1.67978i
$523$	396.152	−	396.152i	0.757460	−	0.757460i	−0.218399	−	0.975859i	$-0.570084\pi$
$523$	396.152	−	396.152i	0.757460	−	0.757460i	0.975859	+	0.218399i	$0.0700836\pi$
$524$	−115.513	+	50.0539i	−0.220445	+	0.0955228i
$525$	−374.811	+	374.811i	−0.713926	+	0.713926i
$526$	196.801	+	289.432i	0.374147	+	0.550252i
$527$		−	260.607i		−	0.494510i
$528$	−407.107	−	381.552i	−0.771036	−	0.722636i
$529$	−260.662			−0.492745
$530$	0.205984	−	0.140060i	0.000388648	−	0.000264264i
$531$	393.897	+	393.897i	0.741803	+	0.741803i
$532$	−63.0931	+	27.3394i	−0.118596	+	0.0513898i
$533$	36.4424	+	36.4424i	0.0683722	+	0.0683722i
$534$	1043.19	+	198.735i	1.95353	+	0.372163i
$535$	6.75465			0.0126255
$536$	574.018	+	363.694i	1.07093	+	0.678534i
$537$		−	352.694i		−	0.656785i
$538$	82.6560	+	15.7466i	0.153636	+	0.0292687i
$539$	148.632	−	148.632i	0.275755	−	0.275755i
$540$	1.74484	−	4.41325i	0.00323119	−	0.00817269i
$541$	−22.5728	+	22.5728i	−0.0417242	+	0.0417242i	−0.727661	−	0.685937i	$-0.759393\pi$
$541$	−22.5728	+	22.5728i	−0.0417242	+	0.0417242i	0.685937	+	0.727661i	$0.259393\pi$
$542$	456.292	−	310.259i	0.841867	−	0.572433i
$543$		−	128.239i		−	0.236168i
$544$	−63.9759	+	407.142i	−0.117603	+	0.748422i
$545$	−6.67005			−0.0122386
$546$	−372.885	−	548.396i	−0.682939	−	1.00439i
$547$	601.634	+	601.634i	1.09988	+	1.09988i	0.994424	+	0.105456i	$0.0336302\pi$
$547$	601.634	+	601.634i	1.09988	+	1.09988i	0.105456	+	0.994424i	$0.466370\pi$
$548$	650.560	+	257.208i	1.18715	+	0.469357i
$549$	185.217	+	185.217i	0.337372	+	0.337372i
$550$	−70.9937	+	372.656i	−0.129079	+	0.677556i
$551$	−137.219			−0.249037
$552$	508.659	+	322.283i	0.921484	+	0.583846i
$553$			389.681i			0.704666i
$554$	147.329	−	773.349i	0.265936	−	1.39594i
$555$	−15.7294	+	15.7294i	−0.0283412	+	0.0283412i
$556$	224.665	+	518.475i	0.404073	+	0.932510i
$557$	502.883	−	502.883i	0.902841	−	0.902841i	−0.0928399	−	0.995681i	$-0.529594\pi$
$557$	502.883	−	502.883i	0.902841	−	0.902841i	0.995681	+	0.0928399i	$0.0295945\pi$
$558$	−275.652	−	405.397i	−0.494000	−	0.726518i
$559$			17.3998i			0.0311266i
$560$	0.198317	+	6.12031i	0.000354138	+	0.0109291i
$561$	−449.132			−0.800592
$562$	334.674	−	227.564i	0.595505	−	0.404917i
$563$	655.972	+	655.972i	1.16514	+	1.16514i	0.983335	+	0.181802i	$0.0581929\pi$
$563$	655.972	+	655.972i	1.16514	+	1.16514i	0.181802	+	0.983335i	$0.441807\pi$
$564$	−582.807	−	1344.99i	−1.03335	−	2.38473i
$565$	−7.95834	−	7.95834i	−0.0140856	−	0.0140856i
$566$	−812.022	−	154.696i	−1.43467	−	0.273315i
$567$	199.759			0.352309
$568$	−439.899	+	98.6671i	−0.774469	+	0.173710i
$569$		−	649.911i		−	1.14220i	−0.820881	−	0.571099i	$-0.806517\pi$
$569$		−	649.911i		−	1.14220i	0.820881	−	0.571099i	$-0.193483\pi$
$570$	−2.78801	−	0.531136i	−0.00489124	−	0.000931818i
$571$	269.718	−	269.718i	0.472360	−	0.472360i	−0.430317	−	0.902678i	$-0.641598\pi$
$571$	269.718	−	269.718i	0.472360	−	0.472360i	0.902678	+	0.430317i	$0.141598\pi$
$572$	−441.370	−	174.502i	−0.771625	−	0.305073i
$573$	−541.152	+	541.152i	−0.944419	+	0.944419i
$574$	−25.1634	+	17.1100i	−0.0438387	+	0.0298084i
$575$		−	409.413i		−	0.712022i
$576$	331.127	+	701.015i	0.574873	+	1.21704i
$577$	−142.675			−0.247271			−0.123635	−	0.992328i	$-0.539455\pi$
$577$	−142.675			−0.247271			−0.123635	+	0.992328i	$0.539455\pi$
$578$	−138.461	−	203.633i	−0.239552	−	0.352306i
$579$	−7.09149	−	7.09149i	−0.0122478	−	0.0122478i
$580$	−4.49293	+	11.3640i	−0.00774643	+	0.0195932i
$581$	123.502	+	123.502i	0.212567	+	0.212567i
$582$	−251.516	+	1320.24i	−0.432158	+	2.26846i
$583$	−11.3990			−0.0195523
$584$	16.9949	+	75.7705i	0.0291009	+	0.129744i
$585$		−	15.7044i		−	0.0268451i
$586$	−175.294	+	920.141i	−0.299136	+	1.57021i
$587$	−687.876	+	687.876i	−1.17185	+	1.17185i	−0.190082	+	0.981768i	$0.560875\pi$
$587$	−687.876	+	687.876i	−1.17185	+	1.17185i	−0.981768	+	0.190082i	$0.939125\pi$
$588$	−467.097	+	202.401i	−0.794382	+	0.344220i
$589$	−53.2895	+	53.2895i	−0.0904746	+	0.0904746i
$590$	−4.28807	−	6.30639i	−0.00726791	−	0.0106888i
$591$		−	438.186i		−	0.741431i
$592$	−30.2526	−	933.634i	−0.0511024	−	1.57708i
$593$	−58.8678			−0.0992711			−0.0496355	−	0.998767i	$-0.515806\pi$
$593$	−58.8678			−0.0992711			−0.0496355	+	0.998767i	$0.515806\pi$
$594$	−179.590	+	122.113i	−0.302340	+	0.205578i
$595$	3.48545	+	3.48545i	0.00585790	+	0.00585790i
$596$	388.696	−	168.429i	0.652175	−	0.282599i
$597$	−724.252	−	724.252i	−1.21315	−	1.21315i
$598$	503.166	+	95.8568i	0.841414	+	0.160296i
$599$	−670.449			−1.11928			−0.559641	−	0.828735i	$-0.689061\pi$
$599$	−670.449			−1.11928			−0.559641	+	0.828735i	$0.689061\pi$
$600$	491.719	−	776.080i	0.819532	−	1.29347i
$601$		−	910.721i		−	1.51534i	−0.652636	−	0.757671i	$-0.726337\pi$
$601$		−	910.721i		−	1.51534i	0.652636	−	0.757671i	$-0.273663\pi$
$602$	−10.0919	−	1.92259i	−0.0167640	−	0.00319367i
$603$	727.594	−	727.594i	1.20662	−	1.20662i
$604$	−103.000	+	260.520i	−0.170530	+	0.431325i
$605$	3.71754	−	3.71754i	0.00614469	−	0.00614469i
$606$	−578.807	+	393.563i	−0.955127	+	0.649444i
$607$			761.794i			1.25501i	0.778611	+	0.627507i	$0.215925\pi$
$607$			761.794i			1.25501i	−0.778611	+	0.627507i	$0.784075\pi$
$608$	96.3354	−	70.1715i	0.158446	−	0.115414i
$609$	781.374			1.28304
$610$	−2.01632	−	2.96537i	−0.00330544	−	0.00486126i
$611$	−881.671	−	881.671i	−1.44300	−	1.44300i
$612$	580.358	+	229.452i	0.948297	+	0.374922i
$613$	273.397	+	273.397i	0.445999	+	0.445999i	0.894022	−	0.448023i	$-0.147872\pi$
$613$	273.397	+	273.397i	0.445999	+	0.445999i	−0.448023	+	0.894022i	$0.647872\pi$
$614$	−12.5719	+	65.9918i	−0.0204755	+	0.107479i
$615$	−1.25598			−0.00204224
$616$	149.981	−	236.714i	0.243475	−	0.384276i
$617$		−	1088.68i		−	1.76448i	−0.470804	−	0.882238i	$-0.656036\pi$
$617$		−	1088.68i		−	1.76448i	0.470804	−	0.882238i	$-0.343964\pi$
$618$	−272.049	+	1428.02i	−0.440209	+	2.31072i
$619$	−129.299	+	129.299i	−0.208884	+	0.208884i	−0.803793	−	0.594909i	$-0.797188\pi$
$619$	−129.299	+	129.299i	−0.208884	+	0.208884i	0.594909	+	0.803793i	$0.297188\pi$
$620$	2.66841	+	6.15809i	0.00430389	+	0.00993241i
$621$	165.731	−	165.731i	0.266878	−	0.266878i
$622$	−177.409	−	260.913i	−0.285224	−	0.419474i
$623$			533.351i			0.856102i
$624$	838.670	+	786.025i	1.34402	+	1.25966i
$625$	−624.484			−0.999175
$626$	96.9072	−	65.8926i	0.154804	−	0.105260i
$627$	91.8398	+	91.8398i	0.146475	+	0.146475i
$628$	−66.4188	−	153.279i	−0.105762	−	0.244076i
$629$	−531.694	−	531.694i	−0.845301	−	0.845301i
$630$	9.10860	+	1.73526i	0.0144581	+	0.00275437i
$631$	455.029			0.721123			0.360562	−	0.932735i	$-0.382585\pi$
$631$	455.029			0.721123			0.360562	+	0.932735i	$0.382585\pi$
$632$	−147.821	−	659.048i	−0.233894	−	1.04280i
$633$			956.012i			1.51029i
$634$	75.0296	+	14.2937i	0.118343	+	0.0225452i
$635$	9.76549	−	9.76549i	0.0153787	−	0.0153787i
$636$	25.6729	+	10.1501i	0.0403661	+	0.0159593i
$637$	−306.193	+	306.193i	−0.480679	+	0.480679i
$638$	462.441	−	314.440i	0.724829	−	0.492852i
$639$			682.657i			1.06832i
$640$	−2.65708	−	10.2758i	−0.00415169	−	0.0160559i
$641$	798.626			1.24591			0.622953	−	0.782259i	$-0.285933\pi$
$641$	798.626			1.24591			0.622953	+	0.782259i	$0.285933\pi$
$642$	420.935	+	619.062i	0.655661	+	0.964270i
$643$	−305.718	−	305.718i	−0.475455	−	0.475455i	0.428219	−	0.903675i	$-0.359141\pi$
$643$	−305.718	−	305.718i	−0.475455	−	0.475455i	−0.903675	+	0.428219i	$0.859141\pi$
$644$	−111.194	+	281.246i	−0.172662	+	0.436717i
$645$	−0.299840	−	0.299840i	−0.000464868	−	0.000464868i
$646$	17.9538	−	94.2420i	0.0277923	−	0.145885i
$647$	1161.90			1.79583			0.897916	−	0.440167i	$-0.145081\pi$
$647$	1161.90			1.79583			0.897916	+	0.440167i	$0.145081\pi$
$648$	−337.843	+	75.7765i	−0.521363	+	0.116939i
$649$			348.992i			0.537738i
$650$	146.252	−	767.698i	0.225003	−	1.18107i
$651$	303.448	−	303.448i	0.466127	−	0.466127i
$652$	−248.101	+	107.507i	−0.380523	+	0.164887i
$653$	77.5410	−	77.5410i	0.118746	−	0.118746i	−0.645237	−	0.763983i	$-0.723241\pi$
$653$	77.5410	−	77.5410i	0.118746	−	0.118746i	0.763983	+	0.645237i	$0.223241\pi$
$654$	−415.662	−	611.308i	−0.635570	−	0.934722i
$655$		−	2.60973i		−	0.00398431i
$656$	36.0671	−	38.4828i	0.0549804	−	0.0586628i
$657$	117.584			0.178972
$658$	608.792	−	413.952i	0.925216	−	0.629106i
$659$	836.993	+	836.993i	1.27010	+	1.27010i	0.946037	+	0.324059i	$0.105048\pi$
$659$	836.993	+	836.993i	1.27010	+	1.27010i	0.324059	+	0.946037i	$0.394952\pi$
$660$	10.6129	−	4.59877i	0.0160802	−	0.00696784i
$661$	121.071	+	121.071i	0.183164	+	0.183164i	0.792733	−	0.609569i	$-0.208658\pi$
$661$	121.071	+	121.071i	0.183164	+	0.183164i	−0.609569	+	0.792733i	$0.708658\pi$
$662$	−506.220	−	96.4386i	−0.764682	−	0.145678i
$663$	925.246			1.39554
$664$	−255.721	−	162.023i	−0.385123	−	0.244011i
$665$		−	1.42543i		−	0.00214350i
$666$	−1389.49	−	264.708i	−2.08632	−	0.397459i
$667$	−426.754	+	426.754i	−0.639811	+	0.639811i
$668$	229.820	−	581.288i	0.344042	−	0.870191i
$669$	−197.235	+	197.235i	−0.294820	+	0.294820i
$670$	−11.6490	+	7.92078i	−0.0173865	+	0.0118221i
$671$			164.102i			0.244563i
$672$	−548.566	+	399.580i	−0.816319	+	0.594613i
$673$	−954.371			−1.41808			−0.709042	−	0.705166i	$-0.750872\pi$
$673$	−954.371			−1.41808			−0.709042	+	0.705166i	$0.750872\pi$
$674$	573.685	+	843.710i	0.851165	+	1.25179i
$675$	−252.862	−	252.862i	−0.374611	−	0.374611i
$676$	280.604	+	110.941i	0.415094	+	0.164113i
$677$	245.475	+	245.475i	0.362593	+	0.362593i	0.864767	−	0.502174i	$-0.167466\pi$
$677$	245.475	+	245.475i	0.362593	+	0.362593i	−0.502174	+	0.864767i	$0.667466\pi$
$678$	233.434	−	1225.33i	0.344297	−	1.80726i
$679$	−675.002			−0.994112
$680$	−7.21694	−	4.57260i	−0.0106131	−	0.00672442i
$681$			1465.53i			2.15203i
$682$	57.4768	−	301.704i	0.0842768	−	0.442381i
$683$	−911.271	+	911.271i	−1.33422	+	1.33422i	−0.432663	+	0.901556i	$0.642426\pi$
$683$	−911.271	+	911.271i	−1.33422	+	1.33422i	−0.901556	+	0.432663i	$0.857574\pi$
$684$	−71.7541	−	165.592i	−0.104904	−	0.242094i
$685$	−10.2544	+	10.2544i	−0.0149699	+	0.0149699i
$686$	−398.095	−	585.472i	−0.580313	−	0.853457i
$687$		−	1480.28i		−	2.15471i
$688$	17.7973	−	0.576688i	0.0258682	−	0.000838210i
$689$	23.4828			0.0340824
$690$	−10.3226	+	7.01890i	−0.0149603	+	0.0101723i
$691$	−476.155	−	476.155i	−0.689081	−	0.689081i	0.272947	−	0.962029i	$-0.412001\pi$
$691$	−476.155	−	476.155i	−0.689081	−	0.689081i	−0.962029	+	0.272947i	$0.912001\pi$
$692$	427.569	+	986.733i	0.617874	+	1.42591i
$693$	−300.046	−	300.046i	−0.432967	−	0.432967i
$694$	1202.00	+	228.990i	1.73199	+	0.329957i
$695$	−11.7136			−0.0168541
$696$	−1321.50	+	296.406i	−1.89871	+	0.425871i
$697$		−	42.4553i		−	0.0609115i
$698$	−413.542	−	78.7828i	−0.592467	−	0.112869i
$699$	393.317	−	393.317i	0.562686	−	0.562686i
$700$	429.108	+	169.654i	0.613011	+	0.242362i
$701$	934.966	−	934.966i	1.33376	−	1.33376i	0.431782	−	0.901978i	$-0.357885\pi$
$701$	934.966	−	934.966i	1.33376	−	1.33376i	0.901978	−	0.431782i	$-0.142115\pi$
$702$	369.969	−	251.563i	0.527021	−	0.358351i
$703$			217.444i			0.309309i
$704$	−163.860	+	457.237i	−0.232755	+	0.649485i
$705$	30.3866			0.0431015
$706$	−302.045	−	444.212i	−0.427825	−	0.629196i
$707$	−248.572	−	248.572i	−0.351587	−	0.351587i
$708$	310.756	−	786.000i	0.438921	−	1.11017i
$709$	5.89548	+	5.89548i	0.00831520	+	0.00831520i	0.711252	−	0.702937i	$-0.248128\pi$
$709$	5.89548	+	5.89548i	0.00831520	+	0.00831520i	−0.702937	+	0.711252i	$0.748128\pi$
$710$	1.74896	−	9.18053i	0.00246332	−	0.0129303i
$711$	−1022.74			−1.43846
$712$	−202.321	−	902.032i	−0.284159	−	1.26690i
$713$			331.462i			0.464884i
$714$	−102.235	+	536.646i	−0.143186	+	0.751604i
$715$	6.95702	−	6.95702i	0.00973010	−	0.00973010i
$716$	−281.714	+	122.072i	−0.393456	+	0.170492i
$717$	719.338	−	719.338i	1.00326	−	1.00326i
$718$	706.815	+	1039.50i	0.984422	+	1.44777i
$719$			19.5965i			0.0272552i	0.999907	+	0.0136276i	$0.00433793\pi$
$719$			19.5965i			0.0272552i	−0.999907	+	0.0136276i	$0.995662\pi$
$720$	−16.0632	+	0.520497i	−0.0223100	+	0.000722913i
$721$	−730.107			−1.01263
$722$	574.111	−	390.370i	0.795168	−	0.540679i
$723$	−273.794	−	273.794i	−0.378692	−	0.378692i
$724$	−102.431	+	44.3853i	−0.141480	+	0.0613057i
$725$	651.115	+	651.115i	0.898089	+	0.898089i
$726$	572.380	+	109.043i	0.788402	+	0.150196i
$727$	741.995			1.02063			0.510313	−	0.859989i	$-0.329530\pi$
$727$	741.995			1.02063			0.510313	+	0.859989i	$0.329530\pi$
$728$	−308.971	+	487.649i	−0.424411	+	0.669848i
$729$			1115.99i			1.53084i
$730$	−1.58130	−	0.301250i	−0.00216617	−	0.000412672i
$731$	10.1354	−	10.1354i	0.0138651	−	0.0138651i
$732$	146.123	−	369.590i	0.199621	−	0.504905i
$733$	349.267	−	349.267i	0.476490	−	0.476490i	−0.427517	−	0.904007i	$-0.640612\pi$
$733$	349.267	−	349.267i	0.476490	−	0.476490i	0.904007	+	0.427517i	$0.140612\pi$
$734$	−655.577	+	445.764i	−0.893157	+	0.607307i
$735$		−	10.5529i		−	0.0143576i
$736$	81.3702	−	517.838i	0.110557	−	0.703585i
$737$	644.646			0.874690
$738$	−44.9064	−	66.0431i	−0.0608488	−	0.0894893i
$739$	−358.932	−	358.932i	−0.485700	−	0.485700i	0.421246	−	0.906946i	$-0.361593\pi$
$739$	−358.932	−	358.932i	−0.485700	−	0.485700i	−0.906946	+	0.421246i	$0.861593\pi$
$740$	18.0080	+	7.11971i	0.0243351	+	0.00962123i
$741$	−189.197	−	189.197i	−0.255326	−	0.255326i
$742$	−2.59473	+	13.6201i	−0.00349694	+	0.0183559i
$743$	−856.214			−1.15237			−0.576187	−	0.817318i	$-0.695460\pi$
$743$	−856.214			−1.15237			−0.576187	+	0.817318i	$0.695460\pi$
$744$	−398.098	+	628.318i	−0.535078	+	0.844513i
$745$			8.78160i			0.0117874i
$746$	−71.0741	+	373.078i	−0.0952736	+	0.500104i
$747$	−324.139	+	324.139i	−0.433921	+	0.433921i
$748$	155.451	+	358.745i	0.207822	+	0.479605i
$749$	−265.860	+	265.860i	−0.354953	+	0.354953i
$750$	21.4209	+	31.5034i	0.0285613	+	0.0420046i
$751$		−	442.218i		−	0.588839i	−0.955676	−	0.294420i	$-0.904874\pi$
$751$		−	442.218i		−	0.588839i	0.955676	−	0.294420i	$-0.0951264\pi$
$752$	−872.593	+	931.036i	−1.16036	+	1.23808i
$753$	1147.69			1.52416
$754$	−952.663	+	647.769i	−1.26348	+	0.859110i
$755$	−4.10641	−	4.10641i	−0.00543896	−	0.00543896i
$756$	105.027	+	242.380i	0.138925	+	0.320608i
$757$	489.198	+	489.198i	0.646233	+	0.646233i	0.952080	−	0.305848i	$-0.0989399\pi$
$757$	489.198	+	489.198i	0.646233	+	0.646233i	−0.305848	+	0.952080i	$0.598940\pi$
$758$	−973.823	−	185.520i	−1.28473	−	0.244750i
$759$	571.246			0.752629
$760$	0.540721	+	2.41076i	0.000711475	+	0.00317205i
$761$		−	404.015i		−	0.530899i	−0.964125	−	0.265450i	$-0.914480\pi$
$761$		−	404.015i		−	0.530899i	0.964125	−	0.265450i	$-0.0855204\pi$
$762$	1503.57	+	286.441i	1.97319	+	0.375906i
$763$	262.530	−	262.530i	0.344076	−	0.344076i
$764$	619.545	+	244.946i	0.810923	+	0.320610i
$765$	−9.14780	+	9.14780i	−0.0119579	+	0.0119579i
$766$	667.804	−	454.077i	0.871807	−	0.592790i
$767$		−	718.949i		−	0.937352i
$768$	776.187	−	883.883i	1.01066	−	1.15089i
$769$	−387.336			−0.503688			−0.251844	−	0.967768i	$-0.581037\pi$
$769$	−387.336			−0.503688			−0.251844	+	0.967768i	$0.581037\pi$
$770$	3.26638	+	4.80381i	0.00424205	+	0.00623872i
$771$	529.612	+	529.612i	0.686916	+	0.686916i
$772$	−3.20987	+	8.11879i	−0.00415787	+	0.0105166i
$773$	−960.396	−	960.396i	−1.24243	−	1.24243i	−0.958991	−	0.283436i	$-0.908526\pi$
$773$	−960.396	−	960.396i	−1.24243	−	1.24243i	−0.283436	−	0.958991i	$-0.591474\pi$
$774$	5.04597	−	26.4870i	0.00651934	−	0.0342209i
$775$	505.724			0.652547
$776$	1141.60	−	256.055i	1.47113	−	0.329968i
$777$		−	1238.20i		−	1.59357i
$778$	66.3286	−	348.168i	0.0852553	−	0.447517i
$779$	−8.68138	+	8.68138i	−0.0111443	+	0.0111443i
$780$	−21.8634	+	9.47381i	−0.0280300	+	0.0121459i
$781$	−302.416	+	302.416i	−0.387216	+	0.387216i
$782$	−237.257	−	348.930i	−0.303398	−	0.446202i
$783$			527.145i			0.673238i
$784$	323.337	+	303.040i	0.412419	+	0.386531i
$785$	3.46296			0.00441141
$786$	239.181	−	162.632i	0.304301	−	0.206911i
$787$	−298.374	−	298.374i	−0.379129	−	0.379129i	0.491659	−	0.870788i	$-0.336391\pi$
$787$	−298.374	−	298.374i	−0.379129	−	0.379129i	−0.870788	+	0.491659i	$0.836391\pi$
$788$	−350.001	+	151.662i	−0.444164	+	0.192464i
$789$	−568.604	−	568.604i	−0.720664	−	0.720664i
$790$	13.7541	+	2.62026i	0.0174103	+	0.00331678i
$791$	626.473			0.792002
$792$	621.273	+	393.635i	0.784436	+	0.497013i
$793$		−	338.062i		−	0.426308i
$794$	−194.137	−	36.9845i	−0.244505	−	0.0465800i
$795$	−0.404665	+	0.404665i	−0.000509012	+	0.000509012i
$796$	−327.824	+	829.171i	−0.411839	+	1.04167i
$797$	−870.093	+	870.093i	−1.09171	+	1.09171i	−0.0963642	+	0.995346i	$0.530721\pi$
$797$	−870.093	+	870.093i	−1.09171	+	1.09171i	−0.995346	+	0.0963642i	$0.969279\pi$
$798$	130.640	−	88.8295i	0.163709	−	0.111315i
$799$			1027.15i			1.28554i
$800$	−790.085	−	124.150i	−0.987607	−	0.155187i
$801$	−1399.82			−1.74759
$802$	12.7088	+	18.6906i	0.0158464	+	0.0233050i
$803$	52.0897	+	52.0897i	0.0648689	+	0.0648689i
$804$	−1451.87	−	574.018i	−1.80581	−	0.713953i
$805$	−4.43310	−	4.43310i	−0.00550695	−	0.00550695i
$806$	−118.406	+	621.532i	−0.146906	+	0.771131i
$807$	−193.317			−0.239550
$808$	514.692	+	326.105i	0.636995	+	0.403595i
$809$			107.642i			0.133055i	0.997785	+	0.0665277i	$0.0211921\pi$
$809$			107.642i			0.133055i	−0.997785	+	0.0665277i	$0.978808\pi$
$810$	1.34320	−	7.05067i	0.00165828	−	0.00870453i
$811$	829.739	−	829.739i	1.02311	−	1.02311i	0.0233795	−	0.999727i	$-0.492557\pi$
$811$	829.739	−	829.739i	1.02311	−	1.02311i	0.999727	−	0.0233795i	$-0.00744260\pi$
$812$	−270.444	−	624.123i	−0.333059	−	0.768624i
$813$	−896.408	+	896.408i	−1.10259	+	1.10259i
$814$	−498.276	−	732.806i	−0.612133	−	0.900253i
$815$		−	5.60521i		−	0.00687756i
$816$	−30.6658	−	946.385i	−0.0375806	−	1.15979i
$817$	−4.14502			−0.00507346
$818$	−1016.47	+	691.155i	−1.24263	+	0.844933i
$819$	618.118	+	618.118i	0.754722	+	0.754722i
$820$	0.434710	+	1.00321i	0.000530135	+	0.00122343i
$821$	506.899	+	506.899i	0.617416	+	0.617416i	0.944868	−	0.327452i	$-0.106190\pi$
$821$	506.899	+	506.899i	0.617416	+	0.617416i	−0.327452	+	0.944868i	$0.606190\pi$
$822$	−1578.84	−	300.780i	−1.92073	−	0.365912i
$823$	−927.304			−1.12674			−0.563368	−	0.826206i	$-0.690495\pi$
$823$	−927.304			−1.12674			−0.563368	+	0.826206i	$0.690495\pi$
$824$	1234.80	−	276.958i	1.49854	−	0.336115i
$825$		−	871.571i		−	1.05645i
$826$	416.993	+	79.4402i	0.504834	+	0.0961745i
$827$	−19.4711	+	19.4711i	−0.0235443	+	0.0235443i	−0.718781	−	0.695237i	$-0.755300\pi$
$827$	−19.4711	+	19.4711i	−0.0235443	+	0.0235443i	0.695237	+	0.718781i	$0.255300\pi$
$828$	−738.150	−	291.838i	−0.891485	−	0.352461i
$829$	409.028	−	409.028i	0.493400	−	0.493400i	−0.415976	−	0.909376i	$-0.636560\pi$
$829$	409.028	−	409.028i	0.493400	−	0.493400i	0.909376	+	0.415976i	$0.136560\pi$
$830$	5.18953	−	3.52866i	0.00625245	−	0.00425139i
$831$			1808.71i			2.17655i
$832$	337.563	−	941.942i	0.405725	−	1.13214i
$833$	356.714			0.428228
$834$	−729.967	−	1073.55i	−0.875261	−	1.28723i
$835$	9.16246	+	9.16246i	0.0109730	+	0.0109730i
$836$	41.5701	−	105.144i	0.0497250	−	0.125770i
$837$	204.718	+	204.718i	0.244586	+	0.244586i
$838$	−41.6621	+	218.690i	−0.0497161	+	0.260967i
$839$	634.212			0.755914			0.377957	−	0.925823i	$-0.376627\pi$
$839$	634.212			0.755914			0.377957	+	0.925823i	$0.376627\pi$
$840$	−3.07905	−	13.7277i	−0.00366553	−	0.0163425i
$841$		−	516.388i		−	0.614017i
$842$	198.291	−	1040.86i	0.235501	−	1.23618i
$843$	−657.483	+	657.483i	−0.779933	+	0.779933i
$844$	763.616	−	330.888i	0.904758	−	0.392048i
$845$	−4.42297	+	4.42297i	−0.00523429	+	0.00523429i
$846$	1086.45	+	1597.82i	1.28421	+	1.88867i
$847$			292.641i			0.345503i
$848$	−0.778300	−	24.0193i	−0.000917807	−	0.0283247i
$849$	1899.16			2.23694
$850$	−532.376	+	361.992i	−0.626325	+	0.425873i
$851$	676.255	+	676.255i	0.794659	+	0.794659i
$852$	950.384	−	411.819i	1.11547	−	0.483355i
$853$	687.203	+	687.203i	0.805630	+	0.805630i	0.983969	−	0.178339i	$-0.0570723\pi$
$853$	687.203	+	687.203i	0.805630	+	0.805630i	−0.178339	+	0.983969i	$0.557072\pi$
$854$	196.077	+	37.3541i	0.229598	+	0.0437402i
$855$	3.74114			0.00437560
$856$	348.785	−	550.487i	0.407459	−	0.643093i
$857$			995.675i			1.16181i	0.813970	+	0.580907i	$0.197302\pi$
$857$			995.675i			1.16181i	−0.813970	+	0.580907i	$0.802698\pi$
$858$	1071.15	+	204.063i	1.24843	+	0.237836i
$859$	430.241	−	430.241i	0.500863	−	0.500863i	−0.410843	−	0.911706i	$-0.634766\pi$
$859$	430.241	−	430.241i	0.500863	−	0.500863i	0.911706	+	0.410843i	$0.134766\pi$
$860$	−0.135719	+	0.343276i	−0.000157813	+	0.000399158i
$861$	49.4347	−	49.4347i	0.0574154	−	0.0574154i
$862$	−1019.77	+	693.402i	−1.18303	+	0.804411i
$863$		−	1014.03i		−	1.17501i	−0.809222	−	0.587503i	$-0.800111\pi$
$863$		−	1014.03i		−	1.17501i	0.809222	−	0.587503i	$-0.199889\pi$
$864$	−269.572	−	370.084i	−0.312005	−	0.428338i
$865$	−22.2927			−0.0257719
$866$	246.558	+	362.608i	0.284709	+	0.418716i
$867$	400.046	+	400.046i	0.461414	+	0.461414i
$868$	−347.407	−	137.352i	−0.400239	−	0.158240i
$869$	−453.074	−	453.074i	−0.521374	−	0.521374i
$870$	5.25405	−	27.5793i	0.00603914	−	0.0317003i
$871$	−1328.02			−1.52471
$872$	−344.416	+	543.592i	−0.394973	+	0.623386i
$873$		−	1771.59i		−	2.02931i
$874$	−22.8352	+	119.865i	−0.0261272	+	0.137146i
$875$	−13.5293	+	13.5293i	−0.0154621	+	0.0154621i
$876$	−70.9339	−	163.699i	−0.0809747	−	0.186871i
$877$	−544.315	+	544.315i	−0.620656	+	0.620656i	−0.945699	−	0.325043i	$-0.894621\pi$
$877$	−544.315	+	544.315i	−0.620656	+	0.620656i	0.325043	+	0.945699i	$0.394621\pi$
$878$	646.957	+	951.469i	0.736853	+	1.08368i
$879$		−	2152.03i		−	2.44828i
$880$	−7.34655	−	6.88539i	−0.00834835	−	0.00782431i
$881$	−645.905			−0.733150			−0.366575	−	0.930388i	$-0.619470\pi$
$881$	−645.905			−0.733150			−0.366575	+	0.930388i	$0.619470\pi$
$882$	554.901	−	377.308i	0.629140	−	0.427787i
$883$	586.952	+	586.952i	0.664725	+	0.664725i	0.956490	−	0.291765i	$-0.0942425\pi$
$883$	586.952	+	586.952i	0.664725	+	0.664725i	−0.291765	+	0.956490i	$0.594243\pi$
$884$	−320.240	−	739.041i	−0.362262	−	0.836019i
$885$	12.3892	+	12.3892i	0.0139991	+	0.0139991i
$886$	1033.29	+	196.850i	1.16625	+	0.222178i
$887$	−1221.93			−1.37759			−0.688797	−	0.724955i	$-0.741861\pi$
$887$	−1221.93			−1.37759			−0.688797	+	0.724955i	$0.741861\pi$
$888$	469.699	+	2094.11i	0.528940	+	2.35823i
$889$			768.730i			0.864713i
$890$	18.8251	+	3.58632i	0.0211518	+	0.00402957i
$891$	−232.256	+	232.256i	−0.260669	+	0.260669i
$892$	225.807	+	89.2758i	0.253147	+	0.100085i
$893$	210.034	−	210.034i	0.235200	−	0.235200i
$894$	−804.831	+	547.250i	−0.900258	+	0.612136i
$895$		−	6.36462i		−	0.00711131i
$896$	509.031	+	299.868i	0.568115	+	0.334674i
$897$	−1176.81			−1.31194
$898$	−560.188	−	823.859i	−0.623817	−	0.917438i
$899$	−527.145	−	527.145i	−0.586368	−	0.586368i
$900$	−445.268	+	1126.22i	−0.494742	+	1.25136i
$901$	−13.6787	−	13.6787i	−0.0151817	−	0.0151817i
$902$	9.36352	−	49.1504i	0.0103808	−	0.0544905i
$903$	23.6031			0.0261386
$904$	−1059.52	+	237.646i	−1.17204	+	0.262883i
$905$		−	2.31417i		−	0.00255710i
$906$	120.449	−	632.254i	0.132946	−	0.697852i
$907$	310.014	−	310.014i	0.341801	−	0.341801i	−0.515243	−	0.857044i	$-0.672298\pi$
$907$	310.014	−	310.014i	0.341801	−	0.341801i	0.857044	+	0.515243i	$0.172298\pi$
$908$	1170.59	−	507.239i	1.28920	−	0.558633i
$909$	652.395	−	652.395i	0.717707	−	0.717707i
$910$	−6.72898	−	9.89621i	−0.00739449	−	0.0108750i
$911$			1044.12i			1.14612i	0.819513	+	0.573060i	$0.194244\pi$
$911$			1044.12i			1.14612i	−0.819513	+	0.573060i	$0.805756\pi$
$912$	−187.249	+	199.790i	−0.205317	+	0.219068i
$913$	−287.186			−0.314552
$914$	101.170	−	68.7911i	0.110689	−	0.0752638i
$915$	5.82561	+	5.82561i	0.00636679	+	0.00636679i
$916$	−1182.38	+	512.346i	−1.29081	+	0.559329i
$917$	102.718	+	102.718i	0.112015	+	0.112015i
$918$	−362.042	−	68.9717i	−0.394381	−	0.0751325i
$919$	188.522			0.205138			0.102569	−	0.994726i	$-0.467294\pi$
$919$	188.522			0.205138			0.102569	+	0.994726i	$0.467294\pi$
$920$	9.17914	+	5.81584i	0.00997732	+	0.00632156i
$921$		−	154.342i		−	0.167581i
$922$	−1231.37	−	234.584i	−1.33554	−	0.254430i
$923$	622.999	−	622.999i	0.674972	−	0.674972i
$924$	−236.714	+	598.725i	−0.256184	+	0.647971i
$925$	1031.79	−	1031.79i	1.11545	−	1.11545i
$926$	1169.10	−	794.940i	1.26253	−	0.858466i
$927$		−	1916.22i		−	2.06712i
$928$	694.143	+	952.959i	0.747999	+	1.02690i
$929$	−220.366			−0.237208			−0.118604	−	0.992942i	$-0.537842\pi$
$929$	−220.366			−0.237208			−0.118604	+	0.992942i	$0.537842\pi$
$930$	−8.67005	−	12.7509i	−0.00932263	−	0.0137106i
$931$	−72.9419	−	72.9419i	−0.0783479	−	0.0783479i
$932$	−450.295	−	178.030i	−0.483149	−	0.191020i
$933$	512.576	+	512.576i	0.549384	+	0.549384i
$934$	215.356	−	1130.43i	0.230574	−	1.21032i
$935$	−8.10493			−0.00866837
$936$	−1279.87	−	810.916i	−1.36738	−	0.866363i
$937$			558.321i			0.595860i	0.954588	+	0.297930i	$0.0962962\pi$
$937$			558.321i			0.595860i	−0.954588	+	0.297930i	$0.903704\pi$
$938$	146.739	−	770.256i	0.156439	−	0.821168i
$939$	−190.379	+	190.379i	−0.202746	+	0.202746i
$940$	−10.5172	−	24.2713i	−0.0111885	−	0.0258205i
$941$	−794.760	+	794.760i	−0.844591	+	0.844591i	−0.989452	−	0.144861i	$-0.953726\pi$
$941$	−794.760	+	794.760i	−0.844591	+	0.844591i	0.144861	+	0.989452i	$0.453726\pi$
$942$	215.804	+	317.379i	0.229091	+	0.336921i
$943$			53.9984i			0.0572624i
$944$	−735.375	+	23.8284i	−0.778998	+	0.0252420i
$945$	−5.47595			−0.00579466
$946$	13.9691	−	9.49834i	0.0147664	−	0.0100405i
$947$	−44.9362	−	44.9362i	−0.0474511	−	0.0474511i	0.682983	−	0.730434i	$-0.260682\pi$
$947$	−44.9362	−	44.9362i	−0.0474511	−	0.0474511i	−0.730434	+	0.682983i	$0.760682\pi$
$948$	616.979	+	1423.85i	0.650822	+	1.50195i
$949$	−107.309	−	107.309i	−0.113076	−	0.113076i
$950$	182.883	+	34.8405i	0.192508	+	0.0366742i
$951$	−175.480			−0.184521
$952$	464.031	−	104.080i	0.487427	−	0.109328i
$953$			304.232i			0.319236i	0.987179	+	0.159618i	$0.0510262\pi$
$953$			304.232i			0.319236i	−0.987179	+	0.159618i	$0.948974\pi$
$954$	−35.7469	−	6.81005i	−0.0374706	−	0.00713842i
$955$	−9.76549	+	9.76549i	−0.0102256	+	0.0102256i
$956$	−823.545	−	325.600i	−0.861448	−	0.340585i
$957$	−908.488	+	908.488i	−0.949308	+	0.949308i
$958$	−220.071	+	149.638i	−0.229719	+	0.156199i
$959$		−	807.213i		−	0.841724i
$960$	10.4149	+	22.0489i	0.0108488	+	0.0229676i
$961$	551.564			0.573948
$962$	1026.49	+	1509.63i	1.06703	+	1.56927i
$963$	−697.768	−	697.768i	−0.724577	−	0.724577i
$964$	−123.930	+	313.457i	−0.128558	+	0.325163i
$965$	−0.127971	−	0.127971i	−0.000132613	−	0.000132613i
$966$	130.031	−	682.553i	0.134608	−	0.706576i
$967$	834.409			0.862884			0.431442	−	0.902141i	$-0.358005\pi$
$967$	834.409			0.862884			0.431442	+	0.902141i	$0.358005\pi$
$968$	−111.010	−	494.930i	−0.114680	−	0.511291i
$969$			220.414i			0.227465i
$970$	−4.53879	+	23.8248i	−0.00467917	+	0.0245616i
$971$	211.499	−	211.499i	0.217816	−	0.217816i	−0.589761	−	0.807577i	$-0.700778\pi$
$971$	211.499	−	211.499i	0.217816	−	0.217816i	0.807577	+	0.589761i	$0.200778\pi$
$972$	1202.52	−	521.074i	1.23716	−	0.536084i
$973$	461.043	−	461.043i	0.473837	−	0.473837i
$974$	−233.995	−	344.133i	−0.240241	−	0.353319i
$975$			1795.50i			1.84154i
$976$	−345.786	+	11.2045i	−0.354288	+	0.0114800i
$977$	891.561			0.912549			0.456275	−	0.889839i	$-0.349183\pi$
$977$	891.561			0.912549			0.456275	+	0.889839i	$0.349183\pi$
$978$	513.716	−	349.304i	0.525272	−	0.357162i
$979$	−620.117	−	620.117i	−0.633419	−	0.633419i
$980$	−8.42911	+	3.65248i	−0.00860113	+	0.00372702i
$981$	689.028	+	689.028i	0.702374	+	0.702374i
$982$	−274.893	−	52.3692i	−0.279932	−	0.0533291i
$983$	−181.589			−0.184730			−0.0923648	−	0.995725i	$-0.529443\pi$
$983$	−181.589			−0.184730			−0.0923648	+	0.995725i	$0.529443\pi$
$984$	−64.8540	+	102.359i	−0.0659085	+	0.104023i
$985$		−	7.90739i		−	0.00802781i
$986$	932.251	+	177.601i	0.945488	+	0.180122i
$987$	−1196.00	+	1196.00i	−1.21175	+	1.21175i
$988$	−85.6376	+	216.605i	−0.0866777	+	0.219235i
$989$	−12.8911	+	12.8911i	−0.0130344	+	0.0130344i
$990$	−12.6079	+	8.57284i	−0.0127353	+	0.00865944i
$991$			1140.89i			1.15125i	0.817715	+	0.575624i	$0.195241\pi$
$991$			1140.89i			1.15125i	−0.817715	+	0.575624i	$0.804759\pi$
$992$	639.656	+	100.512i	0.644815	+	0.101323i
$993$	1183.95			1.19230
$994$	292.503	+	430.180i	0.294269	+	0.432776i
$995$	−13.0697	−	13.0697i	−0.0131354	−	0.0131354i
$996$	646.800	+	255.721i	0.649398	+	0.256748i
$997$	−742.946	−	742.946i	−0.745182	−	0.745182i	0.228388	−	0.973570i	$-0.426654\pi$
$997$	−742.946	−	742.946i	−0.745182	−	0.745182i	−0.973570	+	0.228388i	$0.926654\pi$
$998$	151.954	−	797.630i	0.152259	−	0.799228i
$999$	835.339			0.836175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.3.f.a.11.3	yes	6
3.2	odd	2		144.3.m.a.91.1		6
4.3	odd	2		64.3.f.a.15.3		6
5.2	odd	4		400.3.k.c.299.1		6
5.3	odd	4		400.3.k.d.299.3		6
5.4	even	2		400.3.r.c.251.1		6
8.3	odd	2		128.3.f.a.31.1		6
8.5	even	2		128.3.f.b.31.3		6
12.11	even	2		576.3.m.a.271.2		6
16.3	odd	4	inner	16.3.f.a.3.3	✓	6
16.5	even	4		128.3.f.a.95.1		6
16.11	odd	4		128.3.f.b.95.3		6
16.13	even	4		64.3.f.a.47.3		6
24.5	odd	2		1152.3.m.a.415.2		6
24.11	even	2		1152.3.m.b.415.2		6
32.3	odd	8		1024.3.c.j.1023.12		12
32.5	even	8		1024.3.d.k.511.11		12
32.11	odd	8		1024.3.d.k.511.12		12
32.13	even	8		1024.3.c.j.1023.11		12
32.19	odd	8		1024.3.c.j.1023.1		12
32.21	even	8		1024.3.d.k.511.2		12
32.27	odd	8		1024.3.d.k.511.1		12
32.29	even	8		1024.3.c.j.1023.2		12
48.5	odd	4		1152.3.m.b.991.2		6
48.11	even	4		1152.3.m.a.991.2		6
48.29	odd	4		576.3.m.a.559.2		6
48.35	even	4		144.3.m.a.19.1		6
80.3	even	4		400.3.k.c.99.1		6
80.19	odd	4		400.3.r.c.51.1		6
80.67	even	4		400.3.k.d.99.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.3	✓	6	16.3	odd	4	inner
16.3.f.a.11.3	yes	6	1.1	even	1	trivial
64.3.f.a.15.3		6	4.3	odd	2
64.3.f.a.47.3		6	16.13	even	4
128.3.f.a.31.1		6	8.3	odd	2
128.3.f.a.95.1		6	16.5	even	4
128.3.f.b.31.3		6	8.5	even	2
128.3.f.b.95.3		6	16.11	odd	4
144.3.m.a.19.1		6	48.35	even	4
144.3.m.a.91.1		6	3.2	odd	2
400.3.k.c.99.1		6	80.3	even	4
400.3.k.c.299.1		6	5.2	odd	4
400.3.k.d.99.3		6	80.67	even	4
400.3.k.d.299.3		6	5.3	odd	4
400.3.r.c.51.1		6	80.19	odd	4
400.3.r.c.251.1		6	5.4	even	2
576.3.m.a.271.2		6	12.11	even	2
576.3.m.a.559.2		6	48.29	odd	4
1024.3.c.j.1023.1		12	32.19	odd	8
1024.3.c.j.1023.2		12	32.29	even	8
1024.3.c.j.1023.11		12	32.13	even	8
1024.3.c.j.1023.12		12	32.3	odd	8
1024.3.d.k.511.1		12	32.27	odd	8
1024.3.d.k.511.2		12	32.21	even	8
1024.3.d.k.511.11		12	32.5	even	8
1024.3.d.k.511.12		12	32.11	odd	8
1152.3.m.a.415.2		6	24.5	odd	2
1152.3.m.a.991.2		6	48.11	even	4
1152.3.m.b.415.2		6	24.11	even	2
1152.3.m.b.991.2		6	48.5	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12457 + 1.65389i) q^{2} +(-3.24914 - 3.24914i) q^{3} +(-1.47068 + 3.71982i) q^{4} +(-0.0586332 - 0.0586332i) q^{5} +(1.71982 - 9.02760i) q^{6} +4.61555 q^{7} +(-7.80605 + 1.75086i) q^{8} +12.1138i q^{9} +O(q^{10})\)	\(q+(1.12457 + 1.65389i) q^{2} +(-3.24914 - 3.24914i) q^{3} +(-1.47068 + 3.71982i) q^{4} +(-0.0586332 - 0.0586332i) q^{5} +(1.71982 - 9.02760i) q^{6} +4.61555 q^{7} +(-7.80605 + 1.75086i) q^{8} +12.1138i q^{9} +(0.0310355 - 0.162910i) q^{10} +(-5.36641 + 5.36641i) q^{11} +(16.8647 - 7.30777i) q^{12} +(11.0552 - 11.0552i) q^{13} +(5.19051 + 7.63359i) q^{14} +0.381015i q^{15} +(-11.6742 - 10.9414i) q^{16} -12.8793 q^{17} +(-20.0349 + 13.6229i) q^{18} +(2.63359 + 2.63359i) q^{19} +(0.304336 - 0.131874i) q^{20} +(-14.9966 - 14.9966i) q^{21} +(-14.9103 - 2.84053i) q^{22} +16.3810 q^{23} +(31.0518 + 19.6742i) q^{24} -24.9931i q^{25} +(30.7164 + 5.85170i) q^{26} +(10.1173 - 10.1173i) q^{27} +(-6.78801 + 17.1690i) q^{28} +(-26.0518 + 26.0518i) q^{29} +(-0.630155 + 0.428478i) q^{30} +20.2345i q^{31} +(4.96735 - 31.6121i) q^{32} +34.8724 q^{33} +(-14.4837 - 21.3009i) q^{34} +(-0.270624 - 0.270624i) q^{35} +(-45.0613 - 17.8156i) q^{36} +(41.2829 + 41.2829i) q^{37} +(-1.39400 + 7.31733i) q^{38} -71.8398 q^{39} +(0.560352 + 0.355035i) q^{40} +3.29640i q^{41} +(7.93793 - 41.6673i) q^{42} +(-0.786951 + 0.786951i) q^{43} +(-12.0698 - 27.8544i) q^{44} +(0.710272 - 0.710272i) q^{45} +(18.4216 + 27.0923i) q^{46} -79.7517i q^{47} +(2.38101 + 73.4811i) q^{48} -27.6967 q^{49} +(41.3358 - 28.1065i) q^{50} +(41.8466 + 41.8466i) q^{51} +(24.8647 + 57.3821i) q^{52} +(1.06207 + 1.06207i) q^{53} +(28.1104 + 5.35524i) q^{54} +0.629299 q^{55} +(-36.0292 + 8.08117i) q^{56} -17.1138i q^{57} +(-72.3837 - 13.7896i) q^{58} +(32.5163 - 32.5163i) q^{59} +(-1.41731 - 0.560352i) q^{60} +(15.2897 - 15.2897i) q^{61} +(-33.4656 + 22.7552i) q^{62} +55.9119i q^{63} +(57.8690 - 27.3346i) q^{64} -1.29640 q^{65} +(39.2165 + 57.6750i) q^{66} +(-60.0631 - 60.0631i) q^{67} +(18.9414 - 47.9087i) q^{68} +(-53.2242 - 53.2242i) q^{69} +(0.143246 - 0.751918i) q^{70} +56.3535 q^{71} +(-21.2096 - 94.5612i) q^{72} -9.70663i q^{73} +(-21.8517 + 114.703i) q^{74} +(-81.2062 + 81.2062i) q^{75} +(-13.6697 + 5.92332i) q^{76} +(-24.7689 + 24.7689i) q^{77} +(-80.7889 - 118.815i) q^{78} +84.4278i q^{79} +(0.0429672 + 1.32602i) q^{80} +43.2796 q^{81} +(-5.45188 + 3.70704i) q^{82} +(26.7577 + 26.7577i) q^{83} +(77.8398 - 33.7294i) q^{84} +(0.755154 + 0.755154i) q^{85} +(-2.18651 - 0.416546i) q^{86} +169.292 q^{87} +(32.4946 - 51.2863i) q^{88} +115.555i q^{89} +(1.97346 + 0.375959i) q^{90} +(51.0258 - 51.0258i) q^{91} +(-24.0913 + 60.9345i) q^{92} +(65.7448 - 65.7448i) q^{93} +(131.900 - 89.6864i) q^{94} -0.308832i q^{95} +(-118.852 + 86.5726i) q^{96} -146.245 q^{97} +(-31.1469 - 45.8072i) q^{98} +(-65.0077 - 65.0077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21} - 52 q^{22} + 60 q^{23} + 48 q^{24} + 96 q^{26} + 64 q^{27} + 56 q^{28} - 18 q^{29} + 52 q^{30} + 8 q^{32} - 4 q^{33} - 76 q^{34} - 100 q^{35} - 52 q^{36} + 46 q^{37} + 40 q^{38} - 196 q^{39} + 40 q^{40} - 24 q^{42} - 114 q^{43} + 20 q^{44} + 66 q^{45} + 28 q^{46} - 24 q^{48} - 46 q^{49} + 46 q^{50} + 156 q^{51} + 100 q^{52} + 78 q^{53} + 32 q^{54} + 252 q^{55} - 168 q^{56} - 176 q^{58} + 206 q^{59} - 160 q^{60} + 30 q^{61} - 144 q^{62} + 64 q^{64} + 12 q^{65} + 196 q^{66} - 226 q^{67} + 112 q^{68} - 116 q^{69} - 16 q^{70} - 260 q^{71} + 52 q^{72} - 92 q^{74} - 238 q^{75} - 188 q^{76} - 212 q^{77} - 84 q^{78} + 232 q^{80} + 86 q^{81} + 304 q^{82} + 318 q^{83} + 232 q^{84} - 212 q^{85} + 268 q^{86} + 444 q^{87} - 8 q^{88} - 160 q^{90} + 188 q^{91} - 168 q^{92} - 32 q^{93} + 48 q^{94} - 80 q^{96} - 4 q^{97} + 10 q^{98} - 226 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8 + 36 * q^10 - 18 * q^11 + 52 * q^12 - 2 * q^13 + 12 * q^14 - 40 * q^16 - 4 * q^17 - 74 * q^18 + 30 * q^19 - 84 * q^20 - 20 * q^21 - 52 * q^22 + 60 * q^23 + 48 * q^24 + 96 * q^26 + 64 * q^27 + 56 * q^28 - 18 * q^29 + 52 * q^30 + 8 * q^32 - 4 * q^33 - 76 * q^34 - 100 * q^35 - 52 * q^36 + 46 * q^37 + 40 * q^38 - 196 * q^39 + 40 * q^40 - 24 * q^42 - 114 * q^43 + 20 * q^44 + 66 * q^45 + 28 * q^46 - 24 * q^48 - 46 * q^49 + 46 * q^50 + 156 * q^51 + 100 * q^52 + 78 * q^53 + 32 * q^54 + 252 * q^55 - 168 * q^56 - 176 * q^58 + 206 * q^59 - 160 * q^60 + 30 * q^61 - 144 * q^62 + 64 * q^64 + 12 * q^65 + 196 * q^66 - 226 * q^67 + 112 * q^68 - 116 * q^69 - 16 * q^70 - 260 * q^71 + 52 * q^72 - 92 * q^74 - 238 * q^75 - 188 * q^76 - 212 * q^77 - 84 * q^78 + 232 * q^80 + 86 * q^81 + 304 * q^82 + 318 * q^83 + 232 * q^84 - 212 * q^85 + 268 * q^86 + 444 * q^87 - 8 * q^88 - 160 * q^90 + 188 * q^91 - 168 * q^92 - 32 * q^93 + 48 * q^94 - 80 * q^96 - 4 * q^97 + 10 * q^98 - 226 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more