LMFDB - Embedded newform 403.2.k.d.66.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.5
Character	$\chi$	$=$	403.66
Dual form			403.2.k.d.287.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.288777 - 0.888765i) q^{2} +(0.813772 - 2.50453i) q^{3} +(0.911523 - 0.662261i) q^{4} +1.99869 q^{5} -2.46094 q^{6} +(0.592448 - 0.430438i) q^{7} +(-2.36388 - 1.71746i) q^{8} +(-3.18340 - 2.31288i) q^{9} +O(q^{10})$	\(q+(-0.288777 - 0.888765i) q^{2} +(0.813772 - 2.50453i) q^{3} +(0.911523 - 0.662261i) q^{4} +1.99869 q^{5} -2.46094 q^{6} +(0.592448 - 0.430438i) q^{7} +(-2.36388 - 1.71746i) q^{8} +(-3.18340 - 2.31288i) q^{9} +(-0.577176 - 1.77636i) q^{10} +(-2.80736 + 2.03966i) q^{11} +(-0.916881 - 2.82187i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.553644 - 0.402246i) q^{14} +(1.62648 - 5.00578i) q^{15} +(-0.147440 + 0.453774i) q^{16} +(5.84144 + 4.24405i) q^{17} +(-1.13631 + 3.49720i) q^{18} +(0.108430 + 0.333713i) q^{19} +(1.82185 - 1.32365i) q^{20} +(-0.595929 - 1.83408i) q^{21} +(2.62348 + 1.90607i) q^{22} +(4.42476 + 3.21478i) q^{23} +(-6.22508 + 4.52279i) q^{24} -1.00524 q^{25} +0.934503 q^{26} +(-1.99180 + 1.44712i) q^{27} +(0.254967 - 0.784709i) q^{28} +(0.974968 + 3.00064i) q^{29} -4.91865 q^{30} +(-3.84182 - 4.02994i) q^{31} -5.39795 q^{32} +(2.82386 + 8.69094i) q^{33} +(2.08509 - 6.41725i) q^{34} +(1.18412 - 0.860312i) q^{35} -4.43348 q^{36} -5.79303 q^{37} +(0.265280 - 0.192737i) q^{38} +(2.13048 + 1.54789i) q^{39} +(-4.72466 - 3.43266i) q^{40} +(-0.429558 - 1.32204i) q^{41} +(-1.45798 + 1.05928i) q^{42} +(0.794693 + 2.44581i) q^{43} +(-1.20818 + 3.71840i) q^{44} +(-6.36263 - 4.62272i) q^{45} +(1.57941 - 4.86093i) q^{46} +(-1.59219 + 4.90024i) q^{47} +(1.01651 + 0.738537i) q^{48} +(-1.99740 + 6.14737i) q^{49} +(0.290291 + 0.893425i) q^{50} +(15.3830 - 11.1764i) q^{51} +(0.348171 + 1.07156i) q^{52} +(-1.69699 - 1.23294i) q^{53} +(1.86134 + 1.35234i) q^{54} +(-5.61103 + 4.07666i) q^{55} -2.13973 q^{56} +0.924032 q^{57} +(2.38532 - 1.73303i) q^{58} +(2.17839 - 6.70438i) q^{59} +(-1.83256 - 5.64004i) q^{60} +4.26458 q^{61} +(-2.47224 + 4.57823i) q^{62} -2.88155 q^{63} +(1.85369 + 5.70506i) q^{64} +(-0.617629 + 1.90087i) q^{65} +(6.90873 - 5.01949i) q^{66} -5.16548 q^{67} +8.13528 q^{68} +(11.6523 - 8.46587i) q^{69} +(-1.10656 - 0.803964i) q^{70} +(3.45052 + 2.50695i) q^{71} +(3.55291 + 10.9347i) q^{72} +(10.0319 - 7.28863i) q^{73} +(1.67289 + 5.14864i) q^{74} +(-0.818038 + 2.51766i) q^{75} +(0.319842 + 0.232378i) q^{76} +(-0.785262 + 2.41679i) q^{77} +(0.760472 - 2.34049i) q^{78} +(-9.24965 - 6.72026i) q^{79} +(-0.294687 + 0.906953i) q^{80} +(-1.64435 - 5.06080i) q^{81} +(-1.05094 + 0.763551i) q^{82} +(-1.81060 - 5.57246i) q^{83} +(-1.75784 - 1.27715i) q^{84} +(11.6752 + 8.48254i) q^{85} +(1.94426 - 1.41259i) q^{86} +8.30860 q^{87} +10.1393 q^{88} +(7.28335 - 5.29166i) q^{89} +(-2.27113 + 6.98982i) q^{90} +(0.226295 + 0.696464i) q^{91} +6.16230 q^{92} +(-13.2195 + 6.34249i) q^{93} +4.81495 q^{94} +(0.216718 + 0.666989i) q^{95} +(-4.39270 + 13.5193i) q^{96} +(-10.5211 + 7.64399i) q^{97} +6.04037 q^{98} +13.6545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.288777	−	0.888765i	−0.204196	−	0.628452i	−0.999745	−	0.0225625i	$-0.992818\pi$
$2$	−0.288777	−	0.888765i	−0.204196	−	0.628452i	0.795549	−	0.605889i	$-0.207182\pi$
$3$	0.813772	−	2.50453i	0.469831	−	1.44599i	−0.382972	−	0.923760i	$-0.625099\pi$
$3$	0.813772	−	2.50453i	0.469831	−	1.44599i	0.852803	−	0.522232i	$-0.174901\pi$
$4$	0.911523	−	0.662261i	0.455762	−	0.331130i
$5$	1.99869			0.893841			0.446920	−	0.894574i	$-0.352521\pi$
$5$	1.99869			0.893841			0.446920	+	0.894574i	$0.352521\pi$
$6$	−2.46094			−1.00467
$7$	0.592448	−	0.430438i	0.223924	−	0.162690i	−0.470167	−	0.882577i	$-0.655806\pi$
$7$	0.592448	−	0.430438i	0.223924	−	0.162690i	0.694091	+	0.719887i	$0.255806\pi$
$8$	−2.36388	−	1.71746i	−0.835757	−	0.607213i
$9$	−3.18340	−	2.31288i	−1.06113	−	0.770959i
$10$	−0.577176	−	1.77636i	−0.182519	−	0.561736i
$11$	−2.80736	+	2.03966i	−0.846450	+	0.614982i	−0.924165	−	0.381994i	$-0.875238\pi$
$11$	−2.80736	+	2.03966i	−0.846450	+	0.614982i	0.0777147	+	0.996976i	$0.475238\pi$
$12$	−0.916881	−	2.82187i	−0.264681	−	0.814603i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−0.553644	−	0.402246i	−0.147968	−	0.107505i
$15$	1.62648	−	5.00578i	0.419954	−	1.29249i
$16$	−0.147440	+	0.453774i	−0.0368600	+	0.113444i
$17$	5.84144	+	4.24405i	1.41676	+	1.02933i	0.992296	+	0.123888i	$0.0395362\pi$
$17$	5.84144	+	4.24405i	1.41676	+	1.02933i	0.424460	+	0.905446i	$0.360464\pi$
$18$	−1.13631	+	3.49720i	−0.267831	+	0.824299i
$19$	0.108430	+	0.333713i	0.0248755	+	0.0765590i	0.962724	−	0.270487i	$-0.0871847\pi$
$19$	0.108430	+	0.333713i	0.0248755	+	0.0765590i	−0.937848	+	0.347046i	$0.887185\pi$
$20$	1.82185	−	1.32365i	0.407378	−	0.295978i
$21$	−0.595929	−	1.83408i	−0.130042	−	0.400230i
$22$	2.62348	+	1.90607i	0.559329	+	0.406376i
$23$	4.42476	+	3.21478i	0.922627	+	0.670328i	0.944177	−	0.329440i	$-0.106860\pi$
$23$	4.42476	+	3.21478i	0.922627	+	0.670328i	−0.0215493	+	0.999768i	$0.506860\pi$
$24$	−6.22508	+	4.52279i	−1.27069	+	0.923210i
$25$	−1.00524			−0.201049
$26$	0.934503			0.183271
$27$	−1.99180	+	1.44712i	−0.383321	+	0.278499i
$28$	0.254967	−	0.784709i	0.0481843	−	0.148296i
$29$	0.974968	+	3.00064i	0.181047	+	0.557205i	0.999858	−	0.0168580i	$-0.00536633\pi$
$29$	0.974968	+	3.00064i	0.181047	+	0.557205i	−0.818811	+	0.574063i	$0.805366\pi$
$30$	−4.91865			−0.898018
$31$	−3.84182	−	4.02994i	−0.690010	−	0.723799i
$31$	−3.84182	−	4.02994i	−0.690010	−	0.723799i
$32$	−5.39795			−0.954232
$33$	2.82386	+	8.69094i	0.491570	+	1.51290i
$34$	2.08509	−	6.41725i	0.357590	−	1.10055i
$35$	1.18412	−	0.860312i	0.200153	−	0.145419i
$36$	−4.43348			−0.738913
$37$	−5.79303			−0.952368			−0.476184	−	0.879346i	$-0.657980\pi$
$37$	−5.79303			−0.952368			−0.476184	+	0.879346i	$0.657980\pi$
$38$	0.265280	−	0.192737i	0.0430342	−	0.0312661i
$39$	2.13048	+	1.54789i	0.341150	+	0.247860i
$40$	−4.72466	−	3.43266i	−0.747034	−	0.542752i
$41$	−0.429558	−	1.32204i	−0.0670856	−	0.206468i	0.911894	−	0.410425i	$-0.134620\pi$
$41$	−0.429558	−	1.32204i	−0.0670856	−	0.206468i	−0.978980	+	0.203957i	$0.934620\pi$
$42$	−1.45798	+	1.05928i	−0.224971	+	0.163451i
$43$	0.794693	+	2.44581i	0.121189	+	0.372983i	0.993188	−	0.116526i	$-0.0371759\pi$
$43$	0.794693	+	2.44581i	0.121189	+	0.372983i	−0.871998	+	0.489509i	$0.837176\pi$
$44$	−1.20818	+	3.71840i	−0.182140	+	0.560571i
$45$	−6.36263	−	4.62272i	−0.948485	−	0.689115i
$46$	1.57941	−	4.86093i	0.232872	−	0.716705i
$47$	−1.59219	+	4.90024i	−0.232244	+	0.714774i	0.765231	+	0.643756i	$0.222625\pi$
$47$	−1.59219	+	4.90024i	−0.232244	+	0.714774i	−0.997475	+	0.0710181i	$0.977375\pi$
$48$	1.01651	+	0.738537i	0.146720	+	0.106599i
$49$	−1.99740	+	6.14737i	−0.285343	+	0.878196i
$50$	0.290291	+	0.893425i	0.0410534	+	0.126349i
$51$	15.3830	−	11.1764i	2.15405	−	1.56501i
$52$	0.348171	+	1.07156i	0.0482826	+	0.148599i
$53$	−1.69699	−	1.23294i	−0.233100	−	0.169357i	0.465104	−	0.885256i	$-0.346017\pi$
$53$	−1.69699	−	1.23294i	−0.233100	−	0.169357i	−0.698204	+	0.715899i	$0.746017\pi$
$54$	1.86134	+	1.35234i	0.253296	+	0.184030i
$55$	−5.61103	+	4.07666i	−0.756592	+	0.549696i
$56$	−2.13973			−0.285934
$57$	0.924032			0.122391
$58$	2.38532	−	1.73303i	0.313207	−	0.227559i
$59$	2.17839	−	6.70438i	0.283602	−	0.872836i	−0.703213	−	0.710980i	$-0.748252\pi$
$59$	2.17839	−	6.70438i	0.283602	−	0.872836i	0.986814	−	0.161856i	$-0.0517481\pi$
$60$	−1.83256	−	5.64004i	−0.236582	−	0.728126i
$61$	4.26458			0.546023			0.273012	−	0.962011i	$-0.411980\pi$
$61$	4.26458			0.546023			0.273012	+	0.962011i	$0.411980\pi$
$62$	−2.47224	+	4.57823i	−0.313975	+	0.581435i
$63$	−2.88155			−0.363041
$64$	1.85369	+	5.70506i	0.231711	+	0.713132i
$65$	−0.617629	+	1.90087i	−0.0766074	+	0.235773i
$66$	6.90873	−	5.01949i	0.850406	−	0.617856i
$67$	−5.16548			−0.631064			−0.315532	−	0.948915i	$-0.602183\pi$
$67$	−5.16548			−0.631064			−0.315532	+	0.948915i	$0.602183\pi$
$68$	8.13528			0.986547
$69$	11.6523	−	8.46587i	1.40277	−	1.01917i
$70$	−1.10656	−	0.803964i	−0.132259	−	0.0960921i
$71$	3.45052	+	2.50695i	0.409501	+	0.297520i	0.773400	−	0.633918i	$-0.218555\pi$
$71$	3.45052	+	2.50695i	0.409501	+	0.297520i	−0.363899	+	0.931439i	$0.618555\pi$
$72$	3.55291	+	10.9347i	0.418714	+	1.28867i
$73$	10.0319	−	7.28863i	1.17415	−	0.853070i	0.182650	−	0.983178i	$-0.441532\pi$
$73$	10.0319	−	7.28863i	1.17415	−	0.853070i	0.991500	+	0.130108i	$0.0415324\pi$
$74$	1.67289	+	5.14864i	0.194470	+	0.598517i
$75$	−0.818038	+	2.51766i	−0.0944589	+	0.290715i
$76$	0.319842	+	0.232378i	0.0366883	+	0.0266556i
$77$	−0.785262	+	2.41679i	−0.0894889	+	0.275419i
$78$	0.760472	−	2.34049i	0.0861065	−	0.265008i
$79$	−9.24965	−	6.72026i	−1.04067	−	0.756089i	−0.0702513	−	0.997529i	$-0.522380\pi$
$79$	−9.24965	−	6.72026i	−1.04067	−	0.756089i	−0.970416	+	0.241441i	$0.922380\pi$
$80$	−0.294687	+	0.906953i	−0.0329470	+	0.101400i
$81$	−1.64435	−	5.06080i	−0.182706	−	0.562312i
$82$	−1.05094	+	0.763551i	−0.116057	+	0.0843201i
$83$	−1.81060	−	5.57246i	−0.198739	−	0.611657i	−0.999913	−	0.0132243i	$-0.995790\pi$
$83$	−1.81060	−	5.57246i	−0.198739	−	0.611657i	0.801173	−	0.598433i	$-0.204210\pi$
$84$	−1.75784	−	1.27715i	−0.191796	−	0.139348i
$85$	11.6752	+	8.48254i	1.26635	+	0.920061i
$86$	1.94426	−	1.41259i	0.209655	−	0.152323i
$87$	8.30860			0.890776
$88$	10.1393			1.08085
$89$	7.28335	−	5.29166i	0.772033	−	0.560915i	−0.130544	−	0.991443i	$-0.541672\pi$
$89$	7.28335	−	5.29166i	0.772033	−	0.560915i	0.902578	+	0.430527i	$0.141672\pi$
$90$	−2.27113	+	6.98982i	−0.239398	+	0.736792i
$91$	0.226295	+	0.696464i	0.0237221	+	0.0730092i
$92$	6.16230			0.642464
$93$	−13.2195	+	6.34249i	−1.37080	+	0.657686i
$94$	4.81495			0.496624
$95$	0.216718	+	0.666989i	0.0222348	+	0.0684316i
$96$	−4.39270	+	13.5193i	−0.448328	+	1.37981i
$97$	−10.5211	+	7.64399i	−1.06825	+	0.776130i	−0.975597	−	0.219568i	$-0.929535\pi$
$97$	−10.5211	+	7.64399i	−1.06825	+	0.776130i	−0.0926543	+	0.995698i	$0.529535\pi$
$98$	6.04037			0.610170
$99$	13.6545			1.37232
$100$	−0.916303	+	0.665733i	−0.0916303	+	0.0665733i
$101$	14.8579	+	10.7949i	1.47842	+	1.07413i	0.978063	+	0.208311i	$0.0667967\pi$
$101$	14.8579	+	10.7949i	1.47842	+	1.07413i	0.500354	+	0.865821i	$0.333203\pi$
$102$	−14.3754	−	10.4444i	−1.42338	−	1.03414i
$103$	−3.20705	−	9.87029i	−0.316000	−	0.972549i	−0.975341	−	0.220704i	$-0.929164\pi$
$103$	−3.20705	−	9.87029i	−0.316000	−	0.972549i	0.659341	−	0.751844i	$-0.270836\pi$
$104$	2.36388	−	1.71746i	0.231797	−	0.168411i
$105$	−1.19108	−	3.66576i	−0.116237	−	0.357741i
$106$	−0.605738	+	1.86427i	−0.0588345	+	0.181074i
$107$	−5.41410	−	3.93358i	−0.523401	−	0.380273i	0.294483	−	0.955657i	$-0.404853\pi$
$107$	−5.41410	−	3.93358i	−0.523401	−	0.380273i	−0.817884	+	0.575384i	$0.804853\pi$
$108$	−0.857195	+	2.63817i	−0.0824836	+	0.253858i
$109$	−2.49877	+	7.69042i	−0.239339	+	0.736609i	0.757177	+	0.653209i	$0.226578\pi$
$109$	−2.49877	+	7.69042i	−0.239339	+	0.736609i	−0.996516	+	0.0833996i	$0.973422\pi$
$110$	5.24353	+	3.80965i	0.499951	+	0.363235i
$111$	−4.71420	+	14.5088i	−0.447452	+	1.37712i
$112$	0.107971	+	0.332301i	0.0102023	+	0.0313995i
$113$	−5.31354	+	3.86051i	−0.499856	+	0.363166i	−0.808962	−	0.587861i	$-0.799970\pi$
$113$	−5.31354	+	3.86051i	−0.499856	+	0.363166i	0.309106	+	0.951028i	$0.399970\pi$
$114$	−0.266839	−	0.821247i	−0.0249918	−	0.0769169i
$115$	8.84373	+	6.42534i	0.824682	+	0.599166i
$116$	2.87591	+	2.08947i	0.267022	+	0.194003i
$117$	3.18340	−	2.31288i	0.294306	−	0.213826i
$118$	−6.58768			−0.606446
$119$	5.28755			0.484709
$120$	−12.4420	+	9.03965i	−1.13579	+	0.825203i
$121$	0.321838	−	0.990517i	0.0292580	−	0.0900470i
$122$	−1.23151	−	3.79021i	−0.111496	−	0.343149i
$123$	−3.66066			−0.330070
$124$	−6.17078	−	1.12911i	−0.554152	−	0.101397i
$125$	−12.0026			−1.07355
$126$	0.832126	+	2.56102i	0.0741317	+	0.228154i
$127$	3.91701	−	12.0553i	0.347579	−	1.06974i	−0.612610	−	0.790385i	$-0.709880\pi$
$127$	3.91701	−	12.0553i	0.347579	−	1.06974i	0.960189	−	0.279352i	$-0.0901197\pi$
$128$	−4.19892	+	3.05069i	−0.371135	+	0.269646i
$129$	6.77231			0.596269
$130$	1.86778			0.163815
$131$	14.2046	−	10.3202i	1.24106	−	0.901683i	0.243392	−	0.969928i	$-0.421740\pi$
$131$	14.2046	−	10.3202i	1.24106	−	0.901683i	0.997669	+	0.0682448i	$0.0217399\pi$
$132$	8.32968	+	6.05186i	0.725005	+	0.526747i
$133$	0.207882	+	0.151035i	0.0180257	+	0.0130964i
$134$	1.49167	+	4.59090i	0.128861	+	0.396593i
$135$	−3.98098	+	2.89235i	−0.342628	+	0.248934i
$136$	−6.51946	−	20.0648i	−0.559039	−	1.72055i
$137$	−6.00304	+	18.4754i	−0.512874	+	1.57846i	0.274243	+	0.961660i	$0.411573\pi$
$137$	−6.00304	+	18.4754i	−0.512874	+	1.57846i	−0.787117	+	0.616803i	$0.788427\pi$
$138$	−10.8891	−	7.91137i	−0.926939	−	0.673461i
$139$	4.36216	−	13.4253i	0.369993	−	1.13872i	−0.576802	−	0.816884i	$-0.695699\pi$
$139$	4.36216	−	13.4253i	0.369993	−	1.13872i	0.946795	−	0.321838i	$-0.104301\pi$
$140$	0.509601	−	1.56839i	0.0430691	−	0.132553i
$141$	10.9771	+	7.97536i	0.924442	+	0.671646i
$142$	1.23166	−	3.79065i	0.103358	−	0.318104i
$143$	−1.07232	−	3.30025i	−0.0896715	−	0.275981i
$144$	1.51889	−	1.10353i	0.126574	−	0.0919612i
$145$	1.94866	+	5.99735i	0.161827	+	0.498053i
$146$	−9.37488	−	6.81125i	−0.775870	−	0.563703i
$147$	13.7709	+	10.0051i	1.13580	+	0.825208i
$148$	−5.28048	+	3.83650i	−0.434053	+	0.315358i
$149$	−6.70925			−0.549643			−0.274822	−	0.961495i	$-0.588619\pi$
$149$	−6.70925			−0.549643			−0.274822	+	0.961495i	$0.588619\pi$
$150$	2.47384			0.201988
$151$	12.5828	−	9.14195i	1.02398	−	0.743962i	0.0568812	−	0.998381i	$-0.481884\pi$
$151$	12.5828	−	9.14195i	1.02398	−	0.743962i	0.967094	+	0.254419i	$0.0818844\pi$
$152$	0.316823	−	0.975081i	0.0256977	−	0.0790895i
$153$	−8.77968	−	27.0211i	−0.709795	−	2.18452i
$154$	2.37472			0.191361
$155$	−7.67859	−	8.05461i	−0.616759	−	0.646961i
$156$	2.96709			0.237557
$157$	1.02538	+	3.15578i	0.0818338	+	0.251859i	0.983599	−	0.180367i	$-0.0577285\pi$
$157$	1.02538	+	3.15578i	0.0818338	+	0.251859i	−0.901766	+	0.432225i	$0.857728\pi$
$158$	−3.30165	+	10.1614i	−0.262665	+	0.808399i
$159$	−4.46889	+	3.24684i	−0.354406	+	0.257491i
$160$	−10.7888			−0.852932
$161$	4.00521			0.315654
$162$	−4.02301	+	2.92289i	−0.316078	+	0.229644i
$163$	−10.5653	−	7.67611i	−0.827534	−	0.601239i	0.0913263	−	0.995821i	$-0.470889\pi$
$163$	−10.5653	−	7.67611i	−0.827534	−	0.601239i	−0.918861	+	0.394582i	$0.870889\pi$
$164$	−1.26709	−	0.920593i	−0.0989429	−	0.0718863i
$165$	5.64401	+	17.3705i	0.439386	+	1.35229i
$166$	−4.42974	+	3.21840i	−0.343815	+	0.249796i
$167$	5.67873	+	17.4773i	0.439434	+	1.35244i	0.888474	+	0.458926i	$0.151766\pi$
$167$	5.67873	+	17.4773i	0.439434	+	1.35244i	−0.449041	+	0.893511i	$0.648234\pi$
$168$	−1.74125	+	5.35903i	−0.134341	+	0.413458i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	4.16745	−	12.8261i	0.319629	−	0.983716i
$171$	0.426662	−	1.31313i	0.0326276	−	0.100417i
$172$	2.34415	+	1.70312i	0.178739	+	0.129862i
$173$	−4.09538	+	12.6043i	−0.311366	+	0.958287i	0.665858	+	0.746078i	$0.268066\pi$
$173$	−4.09538	+	12.6043i	−0.311366	+	0.958287i	−0.977224	+	0.212209i	$0.931934\pi$
$174$	−2.39934	−	7.38440i	−0.181893	−	0.559810i
$175$	−0.595554	+	0.432695i	−0.0450196	+	0.0327087i
$176$	−0.511630	−	1.57463i	−0.0385655	−	0.118693i
$177$	−15.0186	−	10.9117i	−1.12887	−	0.820171i
$178$	−6.80631	−	4.94507i	−0.510154	−	0.370649i
$179$	−3.58816	+	2.60695i	−0.268191	+	0.194852i	−0.713750	−	0.700400i	$-0.753005\pi$
$179$	−3.58816	+	2.60695i	−0.268191	+	0.194852i	0.445559	+	0.895253i	$0.353005\pi$
$180$	−8.86114			−0.660470
$181$	−2.84226			−0.211263			−0.105632	−	0.994405i	$-0.533686\pi$
$181$	−2.84226			−0.211263			−0.105632	+	0.994405i	$0.533686\pi$
$182$	0.553644	−	0.402246i	0.0410388	−	0.0298164i
$183$	3.47039	−	10.6808i	0.256539	−	0.789545i
$184$	−4.93835	−	15.1987i	−0.364060	−	1.12046i
$185$	−11.5785			−0.851266
$186$	9.45447	+	9.91745i	0.693235	+	0.727182i
$187$	−25.0555			−1.83224
$188$	1.79392	+	5.52113i	0.130835	+	0.402670i
$189$	−0.557137	+	1.71469i	−0.0405257	+	0.124725i
$190$	0.530213	−	0.385222i	0.0384657	−	0.0279470i
$191$	−3.04331			−0.220206			−0.110103	−	0.993920i	$-0.535118\pi$
$191$	−3.04331			−0.220206			−0.110103	+	0.993920i	$0.535118\pi$
$192$	15.7970			1.14005
$193$	21.3271	−	15.4951i	1.53516	−	1.11536i	0.581881	−	0.813274i	$-0.302317\pi$
$193$	21.3271	−	15.4951i	1.53516	−	1.11536i	0.953281	−	0.302086i	$-0.0976831\pi$
$194$	9.83195	+	7.14333i	0.705893	+	0.512861i
$195$	4.25817	+	3.09374i	0.304934	+	0.221547i
$196$	2.25048	+	6.92627i	0.160749	+	0.494734i
$197$	8.41352	−	6.11278i	0.599439	−	0.435518i	−0.246241	−	0.969209i	$-0.579195\pi$
$197$	8.41352	−	6.11278i	0.599439	−	0.435518i	0.845680	+	0.533691i	$0.179195\pi$
$198$	−3.94309	−	12.1356i	−0.280223	−	0.862439i
$199$	0.852268	−	2.62301i	0.0604157	−	0.185940i	−0.916294	−	0.400507i	$-0.868834\pi$
$199$	0.852268	−	2.62301i	0.0604157	−	0.185940i	0.976709	+	0.214567i	$0.0688340\pi$
$200$	2.37627	+	1.72646i	0.168028	+	0.122079i
$201$	−4.20352	+	12.9371i	−0.296494	+	0.912514i
$202$	5.30350	−	16.3225i	0.373153	−	1.14845i
$203$	1.86921	+	1.35806i	0.131193	+	0.0953171i
$204$	6.62026	−	20.3751i	0.463511	−	1.42654i
$205$	−0.858552	−	2.64235i	−0.0599639	−	0.184550i
$206$	−7.84624	+	5.70063i	−0.546674	+	0.397182i
$207$	−6.65042	−	20.4679i	−0.462236	−	1.42262i
$208$	−0.386003	−	0.280448i	−0.0267645	−	0.0194456i
$209$	−0.985065	−	0.715691i	−0.0681384	−	0.0495054i
$210$	−2.91404	+	2.11718i	−0.201088	+	0.146099i
$211$	−25.2047			−1.73516			−0.867582	−	0.497295i	$-0.834327\pi$
$211$	−25.2047			−1.73516			−0.867582	+	0.497295i	$0.834327\pi$
$212$	−2.36337			−0.162317
$213$	9.08667	−	6.60185i	0.622608	−	0.452351i
$214$	−1.93255	+	5.94779i	−0.132107	+	0.406583i
$215$	1.58834	+	4.88842i	0.108324	+	0.333387i
$216$	7.19374			0.489472
$217$	−4.01072	−	0.733866i	−0.272265	−	0.0498181i
$218$	7.55656			0.511795
$219$	−10.0909	−	31.0566i	−0.681880	−	2.09861i
$220$	−2.41478	+	7.43193i	−0.162805	+	0.501061i
$221$	−5.84144	+	4.24405i	−0.392938	+	0.285486i
$222$	14.2563			0.956820
$223$	7.07525			0.473794			0.236897	−	0.971535i	$-0.423870\pi$
$223$	7.07525			0.473794			0.236897	+	0.971535i	$0.423870\pi$
$224$	−3.19800	+	2.32349i	−0.213676	+	0.155244i
$225$	3.20009	+	2.32500i	0.213340	+	0.155000i
$226$	4.96552	+	3.60766i	0.330301	+	0.239978i
$227$	7.87755	+	24.2446i	0.522851	+	1.60917i	0.768526	+	0.639818i	$0.220990\pi$
$227$	7.87755	+	24.2446i	0.522851	+	1.60917i	−0.245675	+	0.969352i	$0.579010\pi$
$228$	0.842277	−	0.611950i	0.0557812	−	0.0405274i
$229$	−0.999687	−	3.07672i	−0.0660612	−	0.203315i	0.912577	−	0.408904i	$-0.134089\pi$
$229$	−0.999687	−	3.07672i	−0.0660612	−	0.203315i	−0.978638	+	0.205589i	$0.934089\pi$
$230$	3.15675	−	9.71549i	0.208150	−	0.640620i
$231$	5.41390	+	3.93343i	0.356208	+	0.258801i
$232$	2.84877	−	8.76762i	0.187031	−	0.575622i
$233$	−0.333946	+	1.02778i	−0.0218775	+	0.0673321i	−0.961399	−	0.275157i	$-0.911270\pi$
$233$	−0.333946	+	1.02778i	−0.0218775	+	0.0673321i	0.939522	+	0.342489i	$0.111270\pi$
$234$	−2.97490	−	2.16139i	−0.194475	−	0.141295i
$235$	−3.18228	+	9.79406i	−0.207589	+	0.638894i
$236$	−2.45440	−	7.55386i	−0.159768	−	0.491714i
$237$	−24.3582	+	17.6973i	−1.58224	+	1.14956i
$238$	−1.52692	−	4.69939i	−0.0989757	−	0.304616i
$239$	−0.816208	−	0.593010i	−0.0527961	−	0.0383586i	0.561074	−	0.827766i	$-0.310388\pi$
$239$	−0.816208	−	0.593010i	−0.0527961	−	0.0383586i	−0.613870	+	0.789407i	$0.710388\pi$
$240$	2.03168	+	1.47611i	0.131145	+	0.0952822i
$241$	−3.18021	+	2.31056i	−0.204856	+	0.148836i	−0.685483	−	0.728089i	$-0.740409\pi$
$241$	−3.18021	+	2.31056i	−0.204856	+	0.148836i	0.480627	+	0.876925i	$0.340409\pi$
$242$	−0.973276			−0.0625646
$243$	−21.3991			−1.37275
$244$	3.88726	−	2.82426i	0.248856	−	0.180805i
$245$	−3.99219	+	12.2867i	−0.255051	+	0.784967i
$246$	1.05711	+	3.25346i	0.0673992	+	0.207433i
$247$	−0.350887			−0.0223264
$248$	2.16032	+	16.1245i	0.137181	+	1.02390i
$249$	−15.4298			−0.977825
$250$	3.46608	+	10.6675i	0.219214	+	0.674672i
$251$	5.94509	−	18.2971i	0.375250	−	1.15490i	−0.568059	−	0.822988i	$-0.692305\pi$
$251$	5.94509	−	18.2971i	0.375250	−	1.15490i	0.943310	−	0.331914i	$-0.107695\pi$
$252$	−2.62660	+	1.90834i	−0.165460	+	0.120214i
$253$	−18.9790			−1.19320
$254$	−11.8455			−0.743253
$255$	30.7458	−	22.3381i	1.92537	−	1.39887i
$256$	13.6299	+	9.90272i	0.851870	+	0.618920i
$257$	−22.3358	−	16.2279i	−1.39327	−	1.01227i	−0.995498	−	0.0947850i	$-0.969784\pi$
$257$	−22.3358	−	16.2279i	−1.39327	−	1.01227i	−0.397772	−	0.917484i	$-0.630216\pi$
$258$	−1.95569	−	6.01899i	−0.121756	−	0.374726i
$259$	−3.43207	+	2.49354i	−0.213258	+	0.154941i
$260$	0.695885	+	2.14172i	0.0431570	+	0.132824i
$261$	3.83640	−	11.8072i	0.237467	−	0.730850i
$262$	−13.2742	−	9.64429i	−0.820084	−	0.595826i
$263$	−5.44831	+	16.7682i	−0.335957	+	1.03397i	0.630291	+	0.776359i	$0.282936\pi$
$263$	−5.44831	+	16.7682i	−0.335957	+	1.03397i	−0.966249	+	0.257612i	$0.917064\pi$
$264$	8.25107	−	25.3942i	0.507818	−	1.56290i
$265$	−3.39176	−	2.46426i	−0.208354	−	0.151378i
$266$	0.0742031	−	0.228374i	0.00454968	−	0.0140025i
$267$	−7.32615	−	22.5476i	−0.448353	−	1.37989i
$268$	−4.70846	+	3.42089i	−0.287615	+	0.208964i
$269$	−5.71505	−	17.5891i	−0.348453	−	1.07243i	−0.959709	−	0.280995i	$-0.909336\pi$
$269$	−5.71505	−	17.5891i	−0.348453	−	1.07243i	0.611256	−	0.791433i	$-0.290664\pi$
$270$	3.72024	+	2.70291i	0.226406	+	0.164494i
$271$	9.29133	+	6.75055i	0.564408	+	0.410067i	0.833070	−	0.553168i	$-0.186581\pi$
$271$	9.29133	+	6.75055i	0.564408	+	0.410067i	−0.268661	+	0.963235i	$0.586581\pi$
$272$	−2.78710	+	2.02495i	−0.168993	+	0.122781i
$273$	1.92847			0.116716
$274$	18.1539			1.09672
$275$	2.82208	−	2.05036i	0.170178	−	0.123641i
$276$	5.01470	−	15.4337i	0.301850	−	0.928998i
$277$	3.23408	+	9.95348i	0.194317	+	0.598047i	0.999984	+	0.00567763i	$0.00180725\pi$
$277$	3.23408	+	9.95348i	0.194317	+	0.598047i	−0.805667	+	0.592369i	$0.798193\pi$
$278$	−13.1917			−0.791183
$279$	2.90928	+	21.7146i	0.174174	+	1.30002i
$280$	−4.27666			−0.255579
$281$	7.50727	+	23.1050i	0.447846	+	1.37833i	0.879332	+	0.476209i	$0.157990\pi$
$281$	7.50727	+	23.1050i	0.447846	+	1.37833i	−0.431486	+	0.902120i	$0.642010\pi$
$282$	3.91827	−	12.0592i	0.233330	−	0.718115i
$283$	−24.3015	+	17.6561i	−1.44458	+	1.04955i	−0.457515	+	0.889202i	$0.651260\pi$
$283$	−24.3015	+	17.6561i	−1.44458	+	1.04955i	−0.987061	+	0.160344i	$0.948740\pi$
$284$	4.80548			0.285153
$285$	1.84685			0.109398
$286$	−2.62348	+	1.90607i	−0.155130	+	0.112708i
$287$	−0.823548	−	0.598343i	−0.0486125	−	0.0353190i
$288$	17.1839	+	12.4848i	1.01257	+	0.735674i
$289$	10.8571	+	33.4148i	0.638654	+	1.96558i
$290$	4.76751	−	3.46380i	0.279958	−	0.203401i
$291$	10.5829	+	32.5708i	0.620380	+	1.90933i
$292$	4.31738	−	13.2875i	0.252655	−	0.777593i
$293$	−12.1173	−	8.80374i	−0.707901	−	0.514320i	0.174595	−	0.984640i	$-0.444138\pi$
$293$	−12.1173	−	8.80374i	−0.707901	−	0.514320i	−0.882496	+	0.470320i	$0.844138\pi$
$294$	4.91548	−	15.1283i	0.286677	−	0.882300i
$295$	4.35391	−	13.4000i	0.253495	−	0.780176i
$296$	13.6940	+	9.94929i	0.795949	+	0.578290i
$297$	2.64003	−	8.12519i	0.153190	−	0.471471i
$298$	1.93748	+	5.96295i	0.112235	+	0.345424i
$299$	−4.42476	+	3.21478i	−0.255891	+	0.185916i
$300$	0.921688	+	2.83666i	0.0532137	+	0.163775i
$301$	1.52359	+	1.10695i	0.0878180	+	0.0638035i
$302$	−11.7587	−	8.54318i	−0.676636	−	0.491605i
$303$	39.1271	−	28.4275i	2.24779	−	1.63312i
$304$	−0.167417			−0.00960204
$305$	8.52356			0.488058
$306$	−21.4800	+	15.6061i	−1.22793	+	0.892143i
$307$	−6.07054	+	18.6832i	−0.346464	+	1.06631i	0.614331	+	0.789048i	$0.289426\pi$
$307$	−6.07054	+	18.6832i	−0.346464	+	1.06631i	−0.960795	+	0.277259i	$0.910574\pi$
$308$	0.884759	+	2.72301i	0.0504138	+	0.155158i
$309$	−27.3303			−1.55476
$310$	−4.94125	+	9.15045i	−0.280644	+	0.519711i
$311$	28.1319			1.59521			0.797607	−	0.603178i	$-0.206099\pi$
$311$	28.1319			1.59521			0.797607	+	0.603178i	$0.206099\pi$
$312$	−2.37777	−	7.31803i	−0.134615	−	0.414302i
$313$	−2.78430	+	8.56919i	−0.157378	+	0.484359i	−0.998394	−	0.0566508i	$-0.981958\pi$
$313$	−2.78430	+	8.56919i	−0.157378	+	0.484359i	0.841016	+	0.541010i	$0.181958\pi$
$314$	2.50864	−	1.82263i	0.141571	−	0.102857i
$315$	−5.75932			−0.324501
$316$	−12.8818			−0.724660
$317$	−9.42214	+	6.84559i	−0.529200	+	0.384487i	−0.820059	−	0.572280i	$-0.806059\pi$
$317$	−9.42214	+	6.84559i	−0.529200	+	0.384487i	0.290858	+	0.956766i	$0.406059\pi$
$318$	4.17619	+	3.03418i	0.234189	+	0.170148i
$319$	−8.85739	−	6.43527i	−0.495919	−	0.360306i
$320$	3.70494	+	11.4026i	0.207112	+	0.637427i
$321$	−14.2576	+	10.3588i	−0.795782	+	0.578170i
$322$	−1.15661	−	3.55969i	−0.0644555	−	0.198374i
$323$	−0.782909	+	2.40955i	−0.0435622	+	0.134071i
$324$	−4.85044	−	3.52405i	−0.269469	−	0.195781i
$325$	0.310637	−	0.956043i	0.0172311	−	0.0530317i
$326$	−3.77125	+	11.6067i	−0.208870	+	0.642836i
$327$	17.2275	+	12.5165i	0.952682	+	0.692164i
$328$	−1.25513	+	3.86289i	−0.0693030	+	0.213293i
$329$	1.16597	+	3.58848i	0.0642818	+	0.197839i
$330$	13.8084	−	10.0324i	0.760128	−	0.552265i
$331$	−2.45514	−	7.55614i	−0.134947	−	0.415323i	0.860635	−	0.509222i	$-0.170067\pi$
$331$	−2.45514	−	7.55614i	−0.134947	−	0.415323i	−0.995582	+	0.0938991i	$0.970067\pi$
$332$	−5.34083	−	3.88034i	−0.293116	−	0.212961i
$333$	18.4416	+	13.3986i	1.01059	+	0.734237i
$334$	13.8934	−	10.0941i	0.760211	−	0.552326i
$335$	−10.3242			−0.564071
$336$	0.920123			0.0501968
$337$	−6.22469	+	4.52250i	−0.339080	+	0.246356i	−0.744274	−	0.667875i	$-0.767204\pi$
$337$	−6.22469	+	4.52250i	−0.339080	+	0.246356i	0.405193	+	0.914231i	$0.367204\pi$
$338$	−0.288777	+	0.888765i	−0.0157074	+	0.0483424i
$339$	5.34477	+	16.4495i	0.290288	+	0.893414i
$340$	16.2599			0.881816
$341$	19.0051	+	3.47748i	1.02918	+	0.188316i
$342$	−1.29027			−0.0697700
$343$	3.04677	+	9.37700i	0.164510	+	0.506310i
$344$	2.32202	−	7.14645i	0.125195	−	0.385311i
$345$	23.2893	−	16.9206i	1.25385	−	0.910976i
$346$	12.3849			0.665817
$347$	−16.3056			−0.875328			−0.437664	−	0.899139i	$-0.644194\pi$
$347$	−16.3056			−0.875328			−0.437664	+	0.899139i	$0.644194\pi$
$348$	7.57349	−	5.50246i	0.405982	−	0.294963i
$349$	−0.546587	−	0.397119i	−0.0292581	−	0.0212573i	0.573060	−	0.819513i	$-0.305756\pi$
$349$	−0.546587	−	0.397119i	−0.0292581	−	0.0212573i	−0.602318	+	0.798256i	$0.705756\pi$
$350$	0.556547	+	0.404355i	0.0297487	+	0.0216137i
$351$	−0.760798	−	2.34150i	−0.0406084	−	0.124980i
$352$	15.1540	−	11.0100i	0.807710	−	0.586836i
$353$	−0.449757	−	1.38421i	−0.0239382	−	0.0736741i	0.938374	−	0.345622i	$-0.112332\pi$
$353$	−0.449757	−	1.38421i	−0.0239382	−	0.0736741i	−0.962312	+	0.271948i	$0.912332\pi$
$354$	−5.36087	+	16.4991i	−0.284927	+	0.876915i
$355$	6.89652	+	5.01061i	0.366029	+	0.265936i
$356$	3.13448	−	9.64695i	0.166127	−	0.511287i
$357$	4.30286	−	13.2428i	0.227731	−	0.700885i
$358$	3.35314	+	2.43620i	0.177219	+	0.128757i
$359$	7.96739	−	24.5211i	0.420503	−	1.29418i	−0.486732	−	0.873551i	$-0.661811\pi$
$359$	7.96739	−	24.5211i	0.420503	−	1.29418i	0.907235	−	0.420624i	$-0.138189\pi$
$360$	7.10116	+	21.8551i	0.374264	+	1.15187i
$361$	15.2717	−	11.0956i	0.803774	−	0.583976i
$362$	0.820779	+	2.52610i	0.0431392	+	0.132769i
$363$	−2.21888	−	1.61211i	−0.116461	−	0.0846138i
$364$	0.667514	+	0.484977i	0.0349872	+	0.0254197i
$365$	20.0507	−	14.5677i	1.04950	−	0.762509i
$366$	−10.4949			−0.548575
$367$	21.6203			1.12857			0.564285	−	0.825580i	$-0.309152\pi$
$367$	21.6203			1.12857			0.564285	+	0.825580i	$0.309152\pi$
$368$	−2.11117	+	1.53386i	−0.110052	+	0.0799578i
$369$	−1.69027	+	5.20211i	−0.0879918	+	0.270811i
$370$	3.34360	+	10.2905i	0.173825	+	0.534979i
$371$	−1.53608			−0.0797494
$372$	−7.84949	+	14.5361i	−0.406977	+	0.753660i
$373$	33.1073			1.71423			0.857115	−	0.515125i	$-0.172254\pi$
$373$	33.1073			1.71423			0.857115	+	0.515125i	$0.172254\pi$
$374$	7.23544	+	22.2684i	0.374136	+	1.15147i
$375$	−9.76739	+	30.0609i	−0.504386	+	1.55234i
$376$	12.1797	−	8.84907i	0.628120	−	0.456356i
$377$	−3.15506			−0.162494
$378$	1.68484			0.0866591
$379$	3.80266	−	2.76279i	0.195329	−	0.141915i	−0.485822	−	0.874058i	$-0.661480\pi$
$379$	3.80266	−	2.76279i	0.195329	−	0.141915i	0.681151	+	0.732143i	$0.261480\pi$
$380$	0.639264	+	0.464452i	0.0327935	+	0.0238259i
$381$	−27.0054	−	19.6206i	−1.38353	−	1.00519i
$382$	0.878839	+	2.70479i	0.0449653	+	0.138389i
$383$	−27.9839	+	20.3315i	−1.42991	+	1.03889i	−0.439875	+	0.898059i	$0.644977\pi$
$383$	−27.9839	+	20.3315i	−1.42991	+	1.03889i	−0.990034	+	0.140830i	$0.955023\pi$
$384$	4.22360	+	12.9989i	0.215534	+	0.663347i
$385$	−1.56949	+	4.83041i	−0.0799889	+	0.246180i
$386$	−19.9303	−	14.4802i	−1.01442	−	0.737022i
$387$	3.12704	−	9.62404i	0.158956	−	0.489217i
$388$	−4.52787	+	13.9354i	−0.229868	+	0.707461i
$389$	−23.8335	−	17.3161i	−1.20841	−	0.877960i	−0.213322	−	0.976982i	$-0.568428\pi$
$389$	−23.8335	−	17.3161i	−1.20841	−	0.877960i	−0.995085	+	0.0990223i	$0.968428\pi$
$390$	1.51995	−	4.67791i	0.0769655	−	0.236875i
$391$	12.2033	+	37.5579i	0.617147	+	1.89938i
$392$	15.2795	−	11.1012i	0.771730	−	0.560694i
$393$	−14.2881	−	43.9742i	−0.720738	−	2.21820i
$394$	−7.86246	−	5.71241i	−0.396105	−	0.287787i
$395$	−18.4872	−	13.4317i	−0.930191	−	0.675823i
$396$	12.4464	−	9.04280i	0.625453	−	0.454418i
$397$	−11.4657			−0.575448			−0.287724	−	0.957713i	$-0.592899\pi$
$397$	−11.4657			−0.575448			−0.287724	+	0.957713i	$0.592899\pi$
$398$	−2.57736			−0.129191
$399$	0.547441	−	0.397739i	0.0274063	−	0.0199119i
$400$	0.148213	−	0.456153i	0.00741066	−	0.0228077i
$401$	4.08872	+	12.5838i	0.204181	+	0.628404i	0.999746	+	0.0225362i	$0.00717412\pi$
$401$	4.08872	+	12.5838i	0.204181	+	0.628404i	−0.795565	+	0.605868i	$0.792826\pi$
$402$	12.7119			0.634014
$403$	5.01989	−	2.40846i	0.250059	−	0.119974i
$404$	20.6924			1.02948
$405$	−3.28655	−	10.1150i	−0.163310	−	0.502617i
$406$	0.667211	−	2.05346i	0.0331131	−	0.101912i
$407$	16.2631	−	11.8158i	0.806132	−	0.585689i
$408$	−55.5584			−2.75055
$409$	−30.5694			−1.51156			−0.755780	−	0.654825i	$-0.772742\pi$
$409$	−30.5694			−1.51156			−0.755780	+	0.654825i	$0.772742\pi$
$410$	−2.10050	+	1.52610i	−0.103736	+	0.0753688i
$411$	41.3872	+	30.0696i	2.04148	+	1.48322i
$412$	−9.46001	−	6.87310i	−0.466061	−	0.338613i
$413$	−1.59524	−	4.90965i	−0.0784968	−	0.241588i
$414$	−16.2706	+	11.8213i	−0.799659	+	0.580986i
$415$	−3.61883	−	11.1376i	−0.177641	−	0.546724i
$416$	1.66806	−	5.13376i	0.0817833	−	0.251703i
$417$	−30.0744	−	21.8503i	−1.47275	−	1.07001i
$418$	−0.351617	+	1.08217i	−0.0171982	+	0.0529305i
$419$	−6.84572	+	21.0690i	−0.334435	+	1.02929i	0.632564	+	0.774508i	$0.282002\pi$
$419$	−6.84572	+	21.0690i	−0.334435	+	1.02929i	−0.967000	+	0.254778i	$0.917998\pi$
$420$	−3.51338	−	2.55262i	−0.171436	−	0.124555i
$421$	2.95861	−	9.10565i	0.144194	−	0.443782i	−0.852713	−	0.522380i	$-0.825044\pi$
$421$	2.95861	−	9.10565i	0.144194	−	0.443782i	0.996906	+	0.0785976i	$0.0250442\pi$
$422$	7.27854	+	22.4011i	0.354314	+	1.09047i
$423$	16.4022	−	11.9169i	0.797504	−	0.579421i
$424$	1.89396	+	5.82902i	0.0919790	+	0.283082i
$425$	−5.87206	−	4.26630i	−0.284837	−	0.206946i
$426$	−8.49152	−	6.16945i	−0.411415	−	0.298911i
$427$	2.52654	−	1.83564i	0.122268	−	0.0888327i
$428$	−7.54013			−0.364466
$429$	−9.13819			−0.441196
$430$	3.88598	−	2.82333i	0.187398	−	0.136153i
$431$	−0.380166	+	1.17003i	−0.0183119	+	0.0563584i	−0.959795	−	0.280702i	$-0.909433\pi$
$431$	−0.380166	+	1.17003i	−0.0183119	+	0.0563584i	0.941483	+	0.337061i	$0.109433\pi$
$432$	−0.362997	−	1.11719i	−0.0174647	−	0.0537508i
$433$	−0.202852			−0.00974843			−0.00487422	−	0.999988i	$-0.501552\pi$
$433$	−0.202852			−0.00974843			−0.00487422	+	0.999988i	$0.501552\pi$
$434$	0.505969	+	3.77651i	0.0242873	+	0.181278i
$435$	16.6063			0.796212
$436$	2.81538	+	8.66484i	0.134832	+	0.414970i
$437$	−0.593037	+	1.82518i	−0.0283688	+	0.0873102i
$438$	−24.6880	+	17.9369i	−1.17964	+	0.857057i
$439$	−22.9868			−1.09710			−0.548549	−	0.836118i	$-0.684820\pi$
$439$	−22.9868			−1.09710			−0.548549	+	0.836118i	$0.684820\pi$
$440$	20.2653			0.966110
$441$	20.5767	−	14.9498i	0.979841	−	0.711896i
$442$	5.45884	+	3.96608i	0.259650	+	0.188647i
$443$	18.2095	+	13.2300i	0.865161	+	0.628577i	0.929284	−	0.369366i	$-0.120425\pi$
$443$	18.2095	+	13.2300i	0.865161	+	0.628577i	−0.0641229	+	0.997942i	$0.520425\pi$
$444$	5.31152	+	16.3472i	0.252073	+	0.775802i
$445$	14.5571	−	10.5764i	0.690075	−	0.501369i
$446$	−2.04317	−	6.28823i	−0.0967470	−	0.297757i
$447$	−5.45980	+	16.8035i	−0.258240	+	0.794780i
$448$	3.55389	+	2.58205i	0.167905	+	0.121990i
$449$	5.50337	−	16.9376i	0.259720	−	0.799336i	−0.733143	−	0.680075i	$-0.761947\pi$
$449$	5.50337	−	16.9376i	0.259720	−	0.799336i	0.992863	−	0.119262i	$-0.0380527\pi$
$450$	1.14227	−	3.51554i	0.0538470	−	0.165724i
$451$	3.90244	+	2.83529i	0.183759	+	0.133509i
$452$	−2.28675	+	7.03789i	−0.107560	+	0.331035i
$453$	−12.6568	−	38.9535i	−0.594667	−	1.83020i
$454$	19.2729	−	14.0026i	0.904521	−	0.657173i
$455$	0.452293	+	1.39201i	0.0212038	+	0.0652586i
$456$	−2.18430	−	1.58699i	−0.102289	−	0.0743175i
$457$	−9.05625	−	6.57975i	−0.423633	−	0.307788i	0.355465	−	0.934690i	$-0.384323\pi$
$457$	−9.05625	−	6.57975i	−0.423633	−	0.307788i	−0.779098	+	0.626902i	$0.784323\pi$
$458$	−2.44579	+	1.77697i	−0.114284	+	0.0830325i
$459$	−17.7766			−0.829742
$460$	12.3165			0.574261
$461$	24.5147	−	17.8110i	1.14176	−	0.829540i	0.154400	−	0.988008i	$-0.450655\pi$
$461$	24.5147	−	17.8110i	1.14176	−	0.829540i	0.987364	+	0.158468i	$0.0506555\pi$
$462$	1.93248	−	5.94757i	0.0899072	−	0.276706i
$463$	1.83288	+	5.64103i	0.0851812	+	0.262161i	0.984571	−	0.174987i	$-0.0559885\pi$
$463$	1.83288	+	5.64103i	0.0851812	+	0.262161i	−0.899389	+	0.437148i	$0.855988\pi$
$464$	−1.50536			−0.0698847
$465$	−26.4216	+	12.6767i	−1.22527	+	0.587867i
$466$	1.00989			0.0467823
$467$	−6.69430	−	20.6029i	−0.309775	−	0.953390i	−0.977852	−	0.209298i	$-0.932882\pi$
$467$	−6.69430	−	20.6029i	−0.309775	−	0.953390i	0.668077	−	0.744092i	$-0.267118\pi$
$468$	1.37002	−	4.21649i	0.0633292	−	0.194907i
$469$	−3.06028	+	2.22342i	−0.141310	+	0.102668i
$470$	9.62359			0.443903
$471$	8.73817			0.402634
$472$	−16.6639	+	12.1071i	−0.767019	+	0.557272i
$473$	−7.21962	−	5.24536i	−0.331959	−	0.241182i
$474$	22.7628	+	16.5382i	1.04553	+	0.759623i
$475$	−0.108998	−	0.335463i	−0.00500119	−	0.0153921i
$476$	4.81972	−	3.50173i	0.220912	−	0.160502i
$477$	2.55058	+	7.84987i	0.116783	+	0.359421i
$478$	−0.291344	+	0.896664i	−0.0133258	+	0.0410125i
$479$	4.06304	+	2.95197i	0.185645	+	0.134879i	0.676726	−	0.736235i	$-0.263398\pi$
$479$	4.06304	+	2.95197i	0.185645	+	0.134879i	−0.491081	+	0.871114i	$0.663398\pi$
$480$	−8.77964	+	27.0210i	−0.400734	+	1.23333i
$481$	1.79014	−	5.50950i	0.0816236	−	0.251212i
$482$	2.97192	+	2.15923i	0.135367	+	0.0983500i
$483$	3.25932	−	10.0312i	0.148304	−	0.456434i
$484$	−0.362617	−	1.11602i	−0.0164826	−	0.0507282i
$485$	−21.0283	+	15.2780i	−0.954847	+	0.693737i
$486$	6.17956	+	19.0187i	0.280311	+	0.862707i
$487$	31.4082	+	22.8194i	1.42324	+	1.03404i	0.991226	+	0.132177i	$0.0421966\pi$
$487$	31.4082	+	22.8194i	1.42324	+	1.03404i	0.432013	+	0.901867i	$0.357803\pi$
$488$	−10.0809	−	7.32423i	−0.456343	−	0.331552i
$489$	−27.8228	+	20.2144i	−1.25819	+	0.914127i
$490$	12.0728			0.545395
$491$	−24.7693			−1.11782			−0.558911	−	0.829228i	$-0.688781\pi$
$491$	−24.7693			−1.11782			−0.558911	+	0.829228i	$0.688781\pi$
$492$	−3.33678	+	2.42431i	−0.150433	+	0.109296i
$493$	−7.03967	+	21.6659i	−0.317051	+	0.975782i
$494$	0.101328	+	0.311856i	0.00455897	+	0.0140311i
$495$	27.2910			1.22664
$496$	2.39512	−	1.14914i	0.107544	−	0.0515979i
$497$	3.12334			0.140101
$498$	4.45578	+	13.7135i	0.199668	+	0.614516i
$499$	4.16013	−	12.8036i	0.186233	−	0.573167i	−0.813734	−	0.581237i	$-0.802569\pi$
$499$	4.16013	−	12.8036i	0.186233	−	0.573167i	0.999967	+	0.00807025i	$0.00256887\pi$
$500$	−10.9407	+	7.94886i	−0.489281	+	0.355484i
$501$	48.3938			2.16207
$502$	−17.9786			−0.802425
$503$	−20.6854	+	15.0288i	−0.922315	+	0.670101i	−0.944099	−	0.329662i	$-0.893065\pi$
$503$	−20.6854	+	15.0288i	−0.922315	+	0.670101i	0.0217845	+	0.999763i	$0.493065\pi$
$504$	6.81164	+	4.94894i	0.303414	+	0.220443i
$505$	29.6963	+	21.5756i	1.32147	+	0.960103i
$506$	5.48069	+	16.8678i	0.243647	+	0.749867i
$507$	−2.13048	+	1.54789i	−0.0946180	+	0.0687440i
$508$	−4.41332	−	13.5828i	−0.195809	−	0.602639i
$509$	−3.15528	+	9.71096i	−0.139855	+	0.430431i	−0.996314	−	0.0857857i	$-0.972660\pi$
$509$	−3.15528	+	9.71096i	−0.139855	+	0.430431i	0.856458	+	0.516216i	$0.172660\pi$
$510$	−28.7320	−	20.8750i	−1.27227	−	0.924361i
$511$	2.80609	−	8.63627i	0.124134	−	0.382046i
$512$	1.65749	−	5.10123i	0.0732514	−	0.225445i
$513$	−0.698895	−	0.507777i	−0.0308570	−	0.0224189i
$514$	−7.97273	+	24.5375i	−0.351662	+	1.08230i
$515$	−6.40990	−	19.7276i	−0.282454	−	0.869304i
$516$	6.17312	−	4.48504i	0.271757	−	0.197443i
$517$	−5.52502	−	17.0043i	−0.242990	−	0.747847i
$518$	3.20727	+	2.33022i	0.140920	+	0.102384i
$519$	28.2352	+	20.5140i	1.23939	+	0.900467i
$520$	4.72466	−	3.43266i	0.207190	−	0.150532i
$521$	−10.2434			−0.448769			−0.224385	−	0.974501i	$-0.572037\pi$
$521$	−10.2434			−0.448769			−0.224385	+	0.974501i	$0.572037\pi$
$522$	−11.6017			−0.507794
$523$	−5.02956	+	3.65419i	−0.219927	+	0.159787i	−0.692294	−	0.721616i	$-0.743400\pi$
$523$	−5.02956	+	3.65419i	−0.219927	+	0.159787i	0.472367	+	0.881402i	$0.343400\pi$
$524$	6.11313	−	18.8143i	0.267053	−	0.821905i
$525$	0.599054	+	1.84370i	0.0261449	+	0.0804656i
$526$	16.4763			0.718402
$527$	−5.33843	−	39.8455i	−0.232545	−	1.73570i
$528$	−4.36007			−0.189748
$529$	2.13634	+	6.57499i	0.0928845	+	0.285869i
$530$	−1.21068	+	3.72610i	−0.0525887	+	0.161851i
$531$	−22.4411	+	16.3044i	−0.973861	+	0.707551i
$532$	0.289514			0.0125520
$533$	1.39008			0.0602109
$534$	−17.9239	+	13.0225i	−0.775642	+	0.563537i
$535$	−10.8211	−	7.86199i	−0.467837	−	0.339904i
$536$	12.2106	+	8.87150i	0.527416	+	0.383190i
$537$	3.60924	+	11.1081i	0.155750	+	0.479350i
$538$	−13.9822	+	10.1587i	−0.602816	+	0.437971i
$539$	−6.93116	−	21.3319i	−0.298546	−	0.918830i
$540$	−1.71327	+	5.27289i	−0.0737272	+	0.226909i
$541$	−6.43165	−	4.67287i	−0.276518	−	0.200902i	0.440879	−	0.897567i	$-0.354667\pi$
$541$	−6.43165	−	4.67287i	−0.276518	−	0.200902i	−0.717397	+	0.696664i	$0.754667\pi$
$542$	3.31652	−	10.2072i	0.142457	−	0.438437i
$543$	−2.31295	+	7.11852i	−0.0992581	+	0.305485i
$544$	−31.5318	−	22.9092i	−1.35191	−	0.982224i
$545$	−4.99426	+	15.3708i	−0.213931	+	0.658411i
$546$	−0.556898	−	1.71395i	−0.0238330	−	0.0733505i
$547$	20.9554	−	15.2250i	0.895988	−	0.650973i	−0.0414445	−	0.999141i	$-0.513196\pi$
$547$	20.9554	−	15.2250i	0.895988	−	0.650973i	0.937432	+	0.348168i	$0.113196\pi$
$548$	6.76365	+	20.8164i	0.288929	+	0.889231i
$549$	−13.5759	−	9.86345i	−0.579404	−	0.420962i
$550$	−2.63724	−	1.91607i	−0.112452	−	0.0817013i
$551$	−0.895638	+	0.650719i	−0.0381555	+	0.0277216i
$552$	−42.0843			−1.79123
$553$	−8.37259			−0.356039
$554$	7.91237	−	5.74868i	0.336165	−	0.244238i
$555$	−9.42223	+	28.9986i	−0.399951	+	1.23092i
$556$	−4.91486	−	15.1264i	−0.208437	−	0.641502i
$557$	−33.3262			−1.41208			−0.706038	−	0.708174i	$-0.749519\pi$
$557$	−33.3262			−1.41208			−0.706038	+	0.708174i	$0.749519\pi$
$558$	18.4590	−	8.85634i	0.781433	−	0.374919i
$559$	−2.57168			−0.108770
$560$	0.215801	+	0.664167i	0.00911925	+	0.0280662i
$561$	−20.3894	+	62.7522i	−0.860842	+	2.64940i
$562$	18.3670	−	13.3444i	0.774765	−	0.562899i
$563$	−15.2947			−0.644594			−0.322297	−	0.946639i	$-0.604455\pi$
$563$	−15.2947			−0.644594			−0.322297	+	0.946639i	$0.604455\pi$
$564$	15.2877			0.643728
$565$	−10.6201	+	7.71596i	−0.446791	+	0.324613i
$566$	22.7098	+	16.4997i	0.954566	+	0.693533i
$567$	−3.15256	−	2.29047i	−0.132395	−	0.0961906i
$568$	−3.85103	−	11.8522i	−0.161586	−	0.497309i
$569$	6.04545	−	4.39228i	0.253439	−	0.184134i	−0.453811	−	0.891098i	$-0.649936\pi$
$569$	6.04545	−	4.39228i	0.253439	−	0.184134i	0.707249	+	0.706964i	$0.249936\pi$
$570$	−0.533329	−	1.64142i	−0.0223387	−	0.0687514i
$571$	7.69679	−	23.6883i	0.322101	−	0.991324i	−0.650632	−	0.759393i	$-0.725496\pi$
$571$	7.69679	−	23.6883i	0.322101	−	0.991324i	0.972732	−	0.231930i	$-0.0745041\pi$
$572$	−3.16306	−	2.29810i	−0.132254	−	0.0960884i
$573$	−2.47656	+	7.62207i	−0.103460	+	0.318417i
$574$	−0.293964	+	0.904728i	−0.0122698	+	0.0377626i
$575$	−4.44796	−	3.23163i	−0.185493	−	0.134768i
$576$	7.29407	−	22.4489i	0.303920	−	0.935369i
$577$	−7.63428	−	23.4959i	−0.317819	−	0.978147i	−0.974578	−	0.224046i	$-0.928073\pi$
$577$	−7.63428	−	23.4959i	−0.317819	−	0.978147i	0.656759	−	0.754100i	$-0.271927\pi$
$578$	26.5626	−	19.2989i	1.10486	−	0.802726i
$579$	−21.4525	−	66.0240i	−0.891535	−	2.74386i
$580$	5.74805	+	4.17621i	0.238675	+	0.173408i
$581$	−3.47129	−	2.52204i	−0.144013	−	0.104632i
$582$	25.8917	−	18.8114i	1.07324	−	0.779758i
$583$	7.27884			0.301459
$584$	−36.2322			−1.49930
$585$	6.36263	−	4.62272i	0.263063	−	0.191126i
$586$	−4.32525	+	13.3118i	−0.178675	+	0.549904i
$587$	4.48768	+	13.8117i	0.185227	+	0.570069i	0.999952	−	0.00977788i	$-0.00311245\pi$
$587$	4.48768	+	13.8117i	0.185227	+	0.570069i	−0.814726	+	0.579847i	$0.803112\pi$
$588$	19.1785			0.790906
$589$	0.928278	−	1.71903i	0.0382490	−	0.0708314i
$590$	−13.1667			−0.542066
$591$	−8.46297	−	26.0463i	−0.348120	−	1.07140i
$592$	0.854125	−	2.62873i	0.0351043	−	0.108040i
$593$	26.4258	−	19.1995i	1.08518	−	0.788428i	0.106599	−	0.994302i	$-0.466004\pi$
$593$	26.4258	−	19.1995i	1.08518	−	0.788428i	0.978578	+	0.205874i	$0.0660038\pi$
$594$	−7.98376			−0.327578
$595$	10.5682			0.433252
$596$	−6.11564	+	4.44327i	−0.250506	+	0.182004i
$597$	−5.87586	−	4.26906i	−0.240483	−	0.174721i
$598$	4.13495	+	3.00422i	0.169091	+	0.122852i
$599$	−11.6344	−	35.8069i	−0.475367	−	1.46303i	−0.845462	−	0.534035i	$-0.820675\pi$
$599$	−11.6344	−	35.8069i	−0.475367	−	1.46303i	0.370095	−	0.928994i	$-0.379325\pi$
$600$	6.25772	−	4.54650i	0.255470	−	0.185610i
$601$	12.3321	+	37.9543i	0.503037	+	1.54819i	0.804046	+	0.594567i	$0.202677\pi$
$601$	12.3321	+	37.9543i	0.503037	+	1.54819i	−0.301009	+	0.953621i	$0.597323\pi$
$602$	0.543841	−	1.67377i	0.0221653	−	0.0682178i
$603$	16.4438	+	11.9471i	0.669644	+	0.486525i
$604$	5.41518	−	16.6662i	0.220341	−	0.678138i
$605$	0.643255	−	1.97974i	0.0261520	−	0.0804877i
$606$	−36.5644	−	26.5656i	−1.48533	−	1.07915i
$607$	11.9461	−	36.7662i	0.484876	−	1.49230i	−0.347284	−	0.937760i	$-0.612896\pi$
$607$	11.9461	−	36.7662i	0.484876	−	1.49230i	0.832160	−	0.554536i	$-0.187104\pi$
$608$	−0.585300	−	1.80137i	−0.0237370	−	0.0730551i
$609$	4.92241	−	3.57634i	0.199466	−	0.144921i
$610$	−2.46141	−	7.57544i	−0.0996596	−	0.306721i
$611$	−4.16840	−	3.02852i	−0.168635	−	0.122521i
$612$	−25.8979	−	18.8159i	−1.04686	−	0.760588i
$613$	11.8559	−	8.61379i	0.478854	−	0.347908i	−0.322028	−	0.946730i	$-0.604364\pi$
$613$	11.8559	−	8.61379i	0.478854	−	0.347908i	0.800882	+	0.598822i	$0.204364\pi$
$614$	18.3580			0.740869
$615$	−7.31652			−0.295030
$616$	6.00700	−	4.36434i	0.242029	−	0.175844i
$617$	5.24166	−	16.1322i	0.211021	−	0.649456i	−0.788391	−	0.615174i	$-0.789086\pi$
$617$	5.24166	−	16.1322i	0.211021	−	0.649456i	0.999412	−	0.0342820i	$-0.0109144\pi$
$618$	7.89236	+	24.2902i	0.317477	+	0.977094i
$619$	10.1382			0.407488			0.203744	−	0.979024i	$-0.434689\pi$
$619$	10.1382			0.407488			0.203744	+	0.979024i	$0.434689\pi$
$620$	−12.3335	−	2.25673i	−0.495324	−	0.0906326i
$621$	−13.4654			−0.540348
$622$	−8.12385	−	25.0026i	−0.325737	−	1.00251i
$623$	2.03727	−	6.27006i	0.0816214	−	0.251205i
$624$	−1.01651	+	0.738537i	−0.0406929	+	0.0295651i
$625$	−18.9633			−0.758531
$626$	8.42003			0.336532
$627$	−2.59409	+	1.88472i	−0.103598	+	0.0752683i
$628$	3.02460	+	2.19750i	0.120695	+	0.0876899i
$629$	−33.8396	−	24.5859i	−1.34927	−	0.980305i
$630$	1.66316	+	5.11868i	0.0662619	+	0.203933i
$631$	−10.6947	+	7.77017i	−0.425750	+	0.309325i	−0.779947	−	0.625845i	$-0.784754\pi$
$631$	−10.6947	+	7.77017i	−0.425750	+	0.309325i	0.354197	+	0.935171i	$0.384754\pi$
$632$	10.3233	+	31.7718i	0.410638	+	1.26381i
$633$	−20.5109	+	63.1260i	−0.815234	+	2.50903i
$634$	8.80502	+	6.39722i	0.349692	+	0.254066i
$635$	7.82889	−	24.0949i	0.310680	−	0.956175i
$636$	−1.92325	+	5.91914i	−0.0762616	+	0.234709i
$637$	−5.22927	−	3.79928i	−0.207191	−	0.150533i
$638$	−3.16163	+	9.73049i	−0.125170	+	0.385234i
$639$	−5.18613	−	15.9613i	−0.205160	−	0.631418i
$640$	−8.39233	+	6.09738i	−0.331736	+	0.241020i
$641$	11.8521	+	36.4770i	0.468130	+	1.44076i	0.855003	+	0.518623i	$0.173555\pi$
$641$	11.8521	+	36.4770i	0.468130	+	1.44076i	−0.386873	+	0.922133i	$0.626445\pi$
$642$	13.3238	+	9.68029i	0.525847	+	0.382050i
$643$	−12.4265	−	9.02836i	−0.490052	−	0.356044i	0.315152	−	0.949041i	$-0.397944\pi$
$643$	−12.4265	−	9.02836i	−0.490052	−	0.356044i	−0.805204	+	0.592997i	$0.797944\pi$
$644$	3.65084	−	2.65249i	0.143863	−	0.104523i
$645$	13.5357			0.532970
$646$	2.36761			0.0931522
$647$	33.7597	−	24.5278i	1.32723	−	0.964289i	0.327418	−	0.944880i	$-0.393822\pi$
$647$	33.7597	−	24.5278i	1.32723	−	0.964289i	0.999812	−	0.0194091i	$-0.00617849\pi$
$648$	−4.80466	+	14.7872i	−0.188745	+	0.580897i
$649$	7.55918	+	23.2648i	0.296724	+	0.913222i
$650$	−0.939402			−0.0368464
$651$	−5.10180	+	9.44777i	−0.199955	+	0.370287i
$652$	−14.7141			−0.576247
$653$	−10.6730	−	32.8481i	−0.417667	−	1.28545i	−0.909844	−	0.414951i	$-0.863799\pi$
$653$	−10.6730	−	32.8481i	−0.417667	−	1.28545i	0.492177	−	0.870495i	$-0.336201\pi$
$654$	6.14932	−	18.9257i	0.240457	−	0.740052i
$655$	28.3905	−	20.6269i	1.10931	−	0.805961i
$656$	0.663242			0.0258953
$657$	−48.7934			−1.90361
$658$	2.85261	−	2.07254i	0.111206	−	0.0807960i
$659$	−26.4829	−	19.2410i	−1.03163	−	0.749522i	−0.0629943	−	0.998014i	$-0.520065\pi$
$659$	−26.4829	−	19.2410i	−1.03163	−	0.749522i	−0.968634	+	0.248492i	$0.920065\pi$
$660$	16.6484	+	12.0958i	0.648039	+	0.470828i
$661$	−4.36606	−	13.4373i	−0.169820	−	0.522652i	0.829539	−	0.558449i	$-0.188603\pi$
$661$	−4.36606	−	13.4373i	−0.169820	−	0.522652i	−0.999359	+	0.0357965i	$0.988603\pi$
$662$	−6.00664	+	4.36408i	−0.233455	+	0.169615i
$663$	5.87577	+	18.0838i	0.228196	+	0.702315i
$664$	−5.29042	+	16.2822i	−0.205308	+	0.631874i
$665$	0.415491	+	0.301872i	0.0161121	+	0.0117061i
$666$	6.58268	−	20.2594i	0.255074	−	0.785036i
$667$	−5.33240	+	16.4114i	−0.206471	+	0.635454i
$668$	16.7509	+	12.1702i	0.648110	+	0.470880i
$669$	5.75764	−	17.7202i	0.222603	−	0.685102i
$670$	2.98139	+	9.17578i	0.115181	+	0.354491i
$671$	−11.9722	+	8.69831i	−0.462182	+	0.335795i
$672$	3.21680	+	9.90029i	0.124091	+	0.381912i
$673$	30.6689	+	22.2823i	1.18220	+	0.858918i	0.992418	−	0.122909i	$-0.0392222\pi$
$673$	30.6689	+	22.2823i	1.18220	+	0.858918i	0.189781	+	0.981826i	$0.439222\pi$
$674$	5.81698	+	4.22629i	0.224062	+	0.162790i
$675$	2.00224	−	1.45471i	0.0770662	−	0.0559919i
$676$	−1.12670			−0.0433348
$677$	16.2427			0.624256			0.312128	−	0.950040i	$-0.398958\pi$
$677$	16.2427			0.624256			0.312128	+	0.950040i	$0.398958\pi$
$678$	13.0763	−	9.50048i	0.502192	−	0.364864i
$679$	−2.94291	+	9.05733i	−0.112938	+	0.347588i
$680$	−13.0304	−	40.1034i	−0.499692	−	1.53789i
$681$	67.1319			2.57250
$682$	−2.39757	−	17.8953i	−0.0918078	−	0.685245i
$683$	16.6240			0.636099			0.318050	−	0.948074i	$-0.396972\pi$
$683$	16.6240			0.636099			0.318050	+	0.948074i	$0.396972\pi$
$684$	−0.480722	−	1.47951i	−0.0183809	−	0.0565704i
$685$	−11.9982	+	36.9267i	−0.458428	+	1.41090i
$686$	7.45411	−	5.41573i	0.284599	−	0.206773i
$687$	−8.51926			−0.325030
$688$	−1.22702			−0.0467795
$689$	1.69699	−	1.23294i	0.0646502	−	0.0469711i
$690$	−21.7639	−	15.8124i	−0.828536	−	0.601967i
$691$	−24.1757	−	17.5647i	−0.919688	−	0.668192i	0.0237585	−	0.999718i	$-0.492437\pi$
$691$	−24.1757	−	17.5647i	−0.919688	−	0.668192i	−0.943446	+	0.331525i	$0.892437\pi$
$692$	4.61429	+	14.2013i	0.175409	+	0.539853i
$693$	8.08955	−	5.87740i	0.307296	−	0.223264i
$694$	4.70867	+	14.4918i	0.178739	+	0.550101i
$695$	8.71859	−	26.8331i	0.330715	−	1.01784i
$696$	−19.6405	−	14.2697i	−0.744472	−	0.540891i
$697$	3.10158	−	9.54569i	0.117481	−	0.361569i
$698$	−0.195103	+	0.600466i	−0.00738476	+	0.0227280i
$699$	2.30235	+	1.67276i	0.0870829	+	0.0632694i
$700$	−0.256304	+	0.788823i	−0.00968739	+	0.0298147i
$701$	7.25444	+	22.3269i	0.273996	+	0.843274i	0.989483	+	0.144648i	$0.0462049\pi$
$701$	7.25444	+	22.3269i	0.273996	+	0.843274i	−0.715487	+	0.698626i	$0.753795\pi$
$702$	−1.86134	+	1.35234i	−0.0702517	+	0.0510408i
$703$	−0.628138	−	1.93321i	−0.0236907	−	0.0729124i
$704$	−16.8404	−	12.2352i	−0.634695	−	0.461133i
$705$	21.9399	+	15.9403i	0.826304	+	0.600345i
$706$	−1.10036	+	0.799456i	−0.0414125	+	0.0300879i
$707$	13.4491			0.505804
$708$	−20.9162			−0.786079
$709$	5.90971	−	4.29366i	0.221944	−	0.161252i	−0.471257	−	0.881996i	$-0.656200\pi$
$709$	5.90971	−	4.29366i	0.221944	−	0.161252i	0.693201	+	0.720744i	$0.256200\pi$
$710$	2.46170	−	7.57633i	0.0923859	−	0.284335i
$711$	13.9022	+	42.7866i	0.521374	+	1.60462i
$712$	−26.3052			−0.985827
$713$	−4.04374	−	30.1821i	−0.151439	−	1.13033i
$714$	−13.0123			−0.486974
$715$	−2.14322	−	6.59617i	−0.0801521	−	0.246683i
$716$	−1.54421	+	4.75259i	−0.0577098	+	0.177613i
$717$	−2.14942	+	1.56164i	−0.0802715	+	0.0583207i
$718$	−24.0943			−0.899192
$719$	44.0024			1.64101			0.820507	−	0.571636i	$-0.193691\pi$
$719$	44.0024			1.64101			0.820507	+	0.571636i	$0.193691\pi$
$720$	3.03578	−	2.20562i	0.113137	−	0.0821987i
$721$	−6.14856	−	4.46719i	−0.228984	−	0.166367i
$722$	−14.2715	−	10.3688i	−0.531129	−	0.385888i
$723$	3.19890	+	9.84522i	0.118969	+	0.366148i
$724$	−2.59078	+	1.88231i	−0.0962857	+	0.0699557i
$725$	−0.980080	−	3.01637i	−0.0363992	−	0.112025i
$726$	−0.792025	+	2.43760i	−0.0293948	+	0.0904679i
$727$	33.0611	+	24.0203i	1.22617	+	0.890862i	0.996597	−	0.0824297i	$-0.0262680\pi$
$727$	33.0611	+	24.0203i	1.22617	+	0.890862i	0.229570	+	0.973292i	$0.426268\pi$
$728$	0.661214	−	2.03501i	0.0245062	−	0.0754224i
$729$	−12.4809	+	38.4122i	−0.462255	+	1.42267i
$730$	−18.7375	−	13.6136i	−0.693505	−	0.503861i
$731$	−5.73801	+	17.6598i	−0.212228	+	0.653171i
$732$	−3.91011	−	12.0341i	−0.144522	−	0.444792i
$733$	42.2016	−	30.6613i	1.55875	−	1.13250i	0.621730	−	0.783232i	$-0.286430\pi$
$733$	42.2016	−	30.6613i	1.55875	−	1.13250i	0.937023	−	0.349269i	$-0.113570\pi$
$734$	−6.24345	−	19.2154i	−0.230450	−	0.709252i
$735$	27.5237	+	19.9971i	1.01523	+	0.737604i
$736$	−23.8847	−	17.3532i	−0.880401	−	0.639648i
$737$	14.5014	−	10.5359i	0.534164	−	0.388093i
$738$	5.11156			0.188159
$739$	13.7818			0.506973			0.253486	−	0.967339i	$-0.418423\pi$
$739$	13.7818			0.506973			0.253486	+	0.967339i	$0.418423\pi$
$740$	−10.5540	+	7.66796i	−0.387974	+	0.281880i
$741$	−0.285542	+	0.878807i	−0.0104896	+	0.0322838i
$742$	0.443585	+	1.36521i	0.0162845	+	0.0501186i
$743$	13.7435			0.504199			0.252099	−	0.967701i	$-0.418879\pi$
$743$	13.7435			0.504199			0.252099	+	0.967701i	$0.418879\pi$
$744$	42.1422	+	7.71103i	1.54501	+	0.282700i
$745$	−13.4097			−0.491294
$746$	−9.56063	−	29.4246i	−0.350039	−	1.07731i
$747$	−7.12454	+	21.9271i	−0.260673	+	0.802270i
$748$	−22.8386	+	16.5932i	−0.835063	+	0.606709i
$749$	−4.90073			−0.179069
$750$	29.5377			1.07856
$751$	24.0097	−	17.4441i	0.876128	−	0.636544i	−0.0560964	−	0.998425i	$-0.517865\pi$
$751$	24.0097	−	17.4441i	0.876128	−	0.636544i	0.932224	+	0.361881i	$0.117865\pi$
$752$	−1.98885	−	1.44499i	−0.0725259	−	0.0526932i
$753$	−40.9877	−	29.7793i	−1.49368	−	1.08522i
$754$	0.911110	+	2.80411i	0.0331807	+	0.102120i
$755$	25.1491	−	18.2719i	0.915271	−	0.664983i
$756$	0.627729	+	1.93195i	0.0228303	+	0.0702643i
$757$	−4.45762	+	13.7191i	−0.162015	+	0.498630i	−0.998804	−	0.0488950i	$-0.984430\pi$
$757$	−4.45762	+	13.7191i	−0.162015	+	0.498630i	0.836789	+	0.547525i	$0.184430\pi$
$758$	−3.55359	−	2.58184i	−0.129072	−	0.0937766i
$759$	−15.4445	+	47.5334i	−0.560602	+	1.72535i
$760$	0.633231	−	1.94888i	0.0229697	−	0.0706934i
$761$	7.67819	+	5.57853i	0.278334	+	0.202222i	0.718191	−	0.695847i	$-0.244971\pi$
$761$	7.67819	+	5.57853i	0.278334	+	0.202222i	−0.439856	+	0.898068i	$0.644971\pi$
$762$	−9.63953	+	29.6674i	−0.349203	+	1.07474i
$763$	1.82986	+	5.63174i	0.0662455	+	0.203883i
$764$	−2.77405	+	2.01547i	−0.100362	+	0.0729170i
$765$	−17.5478	−	54.0067i	−0.634444	−	1.95262i
$766$	26.1510	+	18.9998i	0.944874	+	0.686491i
$767$	5.70309	+	4.14353i	0.205927	+	0.149614i
$768$	35.8933	−	26.0780i	1.29519	−	0.941010i
$769$	−42.3145			−1.52590			−0.762949	−	0.646458i	$-0.776249\pi$
$769$	−42.3145			−1.52590			−0.762949	+	0.646458i	$0.776249\pi$
$770$	4.74633			0.171046
$771$	−58.8196	+	42.7349i	−2.11834	+	1.53906i
$772$	9.17841	−	28.2483i	0.330338	−	1.01668i
$773$	6.19953	+	19.0802i	0.222982	+	0.686267i	0.998490	+	0.0549301i	$0.0174936\pi$
$773$	6.19953	+	19.0802i	0.222982	+	0.686267i	−0.775508	+	0.631337i	$0.782506\pi$
$774$	−9.45652			−0.339908
$775$	3.86196	+	4.05107i	0.138726	+	0.145519i
$776$	37.9987			1.36407
$777$	3.45224	+	10.6249i	0.123848	+	0.381166i
$778$	−8.50733	+	26.1829i	−0.305003	+	0.938702i
$779$	0.394606	−	0.286698i	0.0141382	−	0.0102720i
$780$	5.93029			0.212338
$781$	−14.8002			−0.529592
$782$	29.8561	−	21.6917i	1.06765	−	0.775694i
$783$	−6.28424	−	4.56577i	−0.224580	−	0.163167i
$784$	−2.49502	−	1.81274i	−0.0891079	−	0.0647407i
$785$	2.04941	+	6.30742i	0.0731464	+	0.225122i
$786$	−34.9566	+	25.3975i	−1.24686	+	0.905898i
$787$	−0.349584	−	1.07591i	−0.0124613	−	0.0383520i	0.944633	−	0.328130i	$-0.106418\pi$
$787$	−0.349584	−	1.07591i	−0.0124613	−	0.0383520i	−0.957094	+	0.289778i	$0.906418\pi$
$788$	3.62087	−	11.1439i	0.128988	−	0.396985i
$789$	37.5628	+	27.2910i	1.33727	+	0.971584i
$790$	−6.59896	+	20.3095i	−0.234781	+	0.722580i
$791$	−1.48628	+	4.57430i	−0.0528461	+	0.162643i
$792$	−32.2775	−	23.4509i	−1.14693	−	0.833293i
$793$	−1.31783	+	4.05585i	−0.0467974	+	0.144028i
$794$	3.31104	+	10.1903i	0.117504	+	0.361641i
$795$	−8.93192	+	6.48942i	−0.316783	+	0.230156i
$796$	−0.960254	−	2.95536i	−0.0340353	−	0.104750i
$797$	−28.3657	−	20.6089i	−1.00476	−	0.730004i	−0.0416594	−	0.999132i	$-0.513264\pi$
$797$	−28.3657	−	20.6089i	−1.00476	−	0.730004i	−0.963104	+	0.269128i	$0.913264\pi$
$798$	−0.511585	−	0.371688i	−0.0181099	−	0.0131576i
$799$	−30.0975	+	21.8671i	−1.06477	+	0.773604i
$800$	5.42625			0.191847
$801$	−35.4248			−1.25167
$802$	10.0033	−	7.26782i	0.353229	−	0.256636i
$803$	−13.2969	+	40.9236i	−0.469237	+	1.44416i
$804$	4.73613	+	14.5763i	0.167030	+	0.514067i
$805$	8.00516			0.282145
$806$	−3.59019	−	3.76599i	−0.126459	−	0.132651i
$807$	−48.7033			−1.71444
$808$	−16.5825	−	51.0356i	−0.583370	−	1.79543i
$809$	−13.0381	+	40.1272i	−0.458396	+	1.41080i	0.408706	+	0.912666i	$0.365980\pi$
$809$	−13.0381	+	40.1272i	−0.458396	+	1.41080i	−0.867102	+	0.498131i	$0.834020\pi$
$810$	−8.04075	+	5.84195i	−0.282523	+	0.205265i
$811$	−46.8266			−1.64430			−0.822152	−	0.569269i	$-0.807226\pi$
$811$	−46.8266			−1.64430			−0.822152	+	0.569269i	$0.807226\pi$
$812$	2.60322			0.0913550
$813$	24.4680	−	17.7770i	0.858130	−	0.623468i
$814$	−15.1979	−	11.0419i	−0.532687	−	0.387020i
$815$	−21.1167	−	15.3421i	−0.739684	−	0.537412i
$816$	2.80348	+	8.62823i	0.0981415	+	0.302049i
$817$	−0.730031	+	0.530399i	−0.0255406	+	0.0185563i
$818$	8.82775	+	27.1690i	0.308655	+	0.949943i
$819$	0.890448	−	2.74052i	0.0311148	−	0.0957615i
$820$	−2.53251	−	1.83998i	−0.0884392	−	0.0642549i
$821$	10.6861	−	32.8884i	0.372947	−	1.14781i	−0.571906	−	0.820319i	$-0.693796\pi$
$821$	10.6861	−	32.8884i	0.372947	−	1.14781i	0.944853	−	0.327494i	$-0.106204\pi$
$822$	14.7731	−	45.4669i	0.515271	−	1.58584i
$823$	11.9819	+	8.70539i	0.417664	+	0.303451i	0.776697	−	0.629874i	$-0.216893\pi$
$823$	11.9819	+	8.70539i	0.417664	+	0.303451i	−0.359033	+	0.933325i	$0.616893\pi$
$824$	−9.37073	+	28.8401i	−0.326445	+	1.00469i
$825$	−2.83866	−	8.73651i	−0.0988296	−	0.304166i
$826$	−3.90286	+	2.83559i	−0.135798	+	0.0986629i
$827$	11.8829	+	36.5717i	0.413208	+	1.27172i	0.913844	+	0.406065i	$0.133099\pi$
$827$	11.8829	+	36.5717i	0.413208	+	1.27172i	−0.500636	+	0.865658i	$0.666901\pi$
$828$	−19.6171	−	14.2526i	−0.681741	−	0.495314i
$829$	38.6824	+	28.1044i	1.34349	+	0.976105i	0.999308	+	0.0372038i	$0.0118451\pi$
$829$	38.6824	+	28.1044i	1.34349	+	0.976105i	0.344186	+	0.938901i	$0.388155\pi$
$830$	−8.85368	+	6.43258i	−0.307316	+	0.223278i
$831$	27.5606			0.956067
$832$	−5.99865			−0.207966
$833$	−37.7575	+	27.4324i	−1.30822	+	0.950477i
$834$	−10.7350	+	33.0389i	−0.371723	+	1.14404i
$835$	11.3500	+	34.9318i	0.392784	+	1.20886i
$836$	−1.37188			−0.0474476
$837$	13.4839	+	2.46724i	0.466073	+	0.0852804i
$838$	20.7022			0.715147
$839$	2.75009	+	8.46390i	0.0949435	+	0.292206i	0.987239	−	0.159246i	$-0.0509062\pi$
$839$	2.75009	+	8.46390i	0.0949435	+	0.292206i	−0.892295	+	0.451452i	$0.850906\pi$
$840$	−3.48023	+	10.7110i	−0.120079	+	0.369566i
$841$	15.4082	−	11.1947i	0.531317	−	0.386025i
$842$	−8.94716			−0.308340
$843$	63.9764			2.20347
$844$	−22.9747	+	16.6921i	−0.790821	+	0.574565i
$845$	−1.61697	−	1.17480i	−0.0556256	−	0.0404143i
$846$	−15.3279	−	11.1364i	−0.526985	−	0.382877i
$847$	−0.235684	−	0.725361i	−0.00809820	−	0.0249237i
$848$	0.809679	−	0.588266i	0.0278045	−	0.0202011i
$849$	24.4444	+	75.2320i	0.838928	+	2.58196i
$850$	−2.09602	+	6.45090i	−0.0718930	+	0.221264i
$851$	−25.6328	−	18.6233i	−0.878681	−	0.638399i
$852$	3.91057	−	12.0355i	0.133974	−	0.412329i
$853$	−5.90337	+	18.1687i	−0.202128	+	0.622085i	0.797692	+	0.603066i	$0.206054\pi$
$853$	−5.90337	+	18.1687i	−0.202128	+	0.622085i	−0.999819	+	0.0190190i	$0.993946\pi$
$854$	−2.36106	−	1.71541i	−0.0807937	−	0.0587001i
$855$	0.852764	−	2.62454i	0.0291639	−	0.0897573i
$856$	6.04253	+	18.5970i	0.206529	+	0.635632i
$857$	7.87583	−	5.72213i	0.269033	−	0.195464i	−0.445087	−	0.895488i	$-0.646827\pi$
$857$	7.87583	−	5.72213i	0.269033	−	0.195464i	0.714120	+	0.700023i	$0.246827\pi$
$858$	2.63890	+	8.12170i	0.0900906	+	0.277270i
$859$	−20.3760	−	14.8040i	−0.695221	−	0.505107i	0.183151	−	0.983085i	$-0.441370\pi$
$859$	−20.3760	−	14.8040i	−0.695221	−	0.505107i	−0.878372	+	0.477977i	$0.841370\pi$
$860$	4.68522	+	3.40401i	0.159765	+	0.116076i
$861$	−2.16875	+	1.57569i	−0.0739107	+	0.0536993i
$862$	1.14966			0.0391577
$863$	−6.96100			−0.236955			−0.118478	−	0.992957i	$-0.537801\pi$
$863$	−6.96100			−0.236955			−0.118478	+	0.992957i	$0.537801\pi$
$864$	10.7516	−	7.81151i	0.365777	−	0.265753i
$865$	−8.18540	+	25.1921i	−0.278312	+	0.856556i
$866$	0.0585789	+	0.180287i	0.00199059	+	0.00612642i
$867$	92.5236			3.14227
$868$	−4.14187	+	1.98720i	−0.140584	+	0.0674501i
$869$	39.6742			1.34585
$870$	−4.79552	−	14.7591i	−0.162584	−	0.500381i
$871$	1.59622	−	4.91267i	0.0540859	−	0.166459i
$872$	19.1148	−	13.8877i	0.647307	−	0.470296i
$873$	51.1724			1.73192
$874$	1.79341			0.0606631
$875$	−7.11092	+	5.16638i	−0.240393	+	0.174656i
$876$	−29.7657	−	21.6260i	−1.00569	−	0.730675i
$877$	22.0289	+	16.0049i	0.743862	+	0.540448i	0.893918	−	0.448230i	$-0.147945\pi$
$877$	22.0289	+	16.0049i	0.743862	+	0.540448i	−0.150056	+	0.988678i	$0.547945\pi$
$878$	6.63805	+	20.4298i	0.224023	+	0.689473i
$879$	−31.9100	+	23.1840i	−1.07630	+	0.781976i
$880$	−1.02259	−	3.14720i	−0.0344715	−	0.106092i
$881$	−6.15305	+	18.9371i	−0.207302	+	0.638009i	0.792309	+	0.610119i	$0.208879\pi$
$881$	−6.15305	+	18.9371i	−0.207302	+	0.638009i	−0.999611	+	0.0278892i	$0.991121\pi$
$882$	−19.2289	−	13.9706i	−0.647472	−	0.470416i
$883$	−10.1865	+	31.3507i	−0.342802	+	1.05504i	0.619948	+	0.784643i	$0.287154\pi$
$883$	−10.1865	+	31.3507i	−0.342802	+	1.05504i	−0.962750	+	0.270393i	$0.912846\pi$
$884$	−2.51394	+	7.73711i	−0.0845529	+	0.260227i
$885$	−30.0176	−	21.8090i	−1.00903	−	0.733103i
$886$	6.49986	−	20.0045i	0.218367	−	0.672065i
$887$	−5.92718	−	18.2420i	−0.199015	−	0.612506i	−0.999906	−	0.0136956i	$-0.995640\pi$
$887$	−5.92718	−	18.2420i	−0.199015	−	0.612506i	0.800891	−	0.598810i	$-0.204360\pi$
$888$	36.0621	−	26.2007i	1.21016	−	0.879236i
$889$	−2.86845	−	8.82818i	−0.0962048	−	0.296088i
$890$	−13.6037	−	9.88366i	−0.455997	−	0.331301i
$891$	14.9386	+	10.8536i	0.500463	+	0.363608i
$892$	6.44926	−	4.68566i	0.215937	−	0.156888i
$893$	−1.80792			−0.0604996
$894$	16.5111			0.552212
$895$	−7.17161	+	5.21048i	−0.239720	+	0.174167i
$896$	−1.17450	+	3.61475i	−0.0392374	+	0.120760i
$897$	4.45077	+	13.6981i	0.148607	+	0.457365i
$898$	−16.6428			−0.555378
$899$	8.34678	−	15.4570i	0.278381	−	0.515519i
$900$	4.45672			0.148557
$901$	−4.68022	−	14.4042i	−0.155921	−	0.479875i
$902$	1.39297	−	4.28712i	0.0463808	−	0.142746i
$903$	4.01224	−	2.91506i	0.133519	−	0.0970072i
$904$	19.1908			0.638277
$905$	−5.68079			−0.188836
$906$	−30.9655	+	22.4978i	−1.02876	+	0.747439i
$907$	14.8246	+	10.7707i	0.492241	+	0.357634i	0.806046	−	0.591853i	$-0.201604\pi$
$907$	14.8246	+	10.7707i	0.492241	+	0.357634i	−0.313804	+	0.949488i	$0.601604\pi$
$908$	23.2368	+	16.8825i	0.771140	+	0.560266i
$909$	−22.3314	−	68.7290i	−0.740686	−	2.27960i
$910$	1.10656	−	0.803964i	0.0366822	−	0.0266511i
$911$	0.352209	+	1.08399i	0.0116692	+	0.0359141i	0.956722	−	0.291005i	$-0.0939896\pi$
$911$	0.352209	+	1.08399i	0.0116692	+	0.0359141i	−0.945052	+	0.326919i	$0.893990\pi$
$912$	−0.136239	+	0.419302i	−0.00451134	+	0.0138845i
$913$	16.4490	+	11.9509i	0.544381	+	0.395516i
$914$	−3.23261	+	9.94896i	−0.106925	+	0.329082i
$915$	6.93624	−	21.3475i	0.229305	−	0.705728i
$916$	−2.94883	−	2.14245i	−0.0974320	−	0.0707885i
$917$	3.97325	−	12.2284i	0.131208	−	0.403817i
$918$	5.13348	+	15.7992i	0.169430	+	0.521452i
$919$	15.4753	−	11.2434i	0.510481	−	0.370886i	−0.302525	−	0.953142i	$-0.597829\pi$
$919$	15.4753	−	11.2434i	0.510481	−	0.370886i	0.813006	+	0.582255i	$0.197829\pi$
$920$	−9.87023	−	30.3775i	−0.325412	−	1.00152i
$921$	41.8527	+	30.4077i	1.37909	+	1.00197i
$922$	−22.9091	−	16.6444i	−0.754470	−	0.548155i
$923$	−3.45052	+	2.50695i	−0.113575	+	0.0825173i
$924$	7.53985			0.248043
$925$	5.82340			0.191472
$926$	4.48425	−	3.25800i	0.147362	−	0.107065i
$927$	−12.6194	+	38.8386i	−0.414477	+	1.27563i
$928$	−5.26283	−	16.1973i	−0.172761	−	0.531703i
$929$	53.6628			1.76062			0.880309	−	0.474401i	$-0.157335\pi$
$929$	53.6628			1.76062			0.880309	+	0.474401i	$0.157335\pi$
$930$	18.8965	+	19.8219i	0.619642	+	0.649985i
$931$	−2.26804			−0.0743319
$932$	0.376258	+	1.15800i	0.0123248	+	0.0379317i
$933$	22.8929	−	70.4572i	0.749481	−	2.30667i
$934$	−16.3780	+	11.8993i	−0.535905	+	0.389357i
$935$	−50.0780			−1.63773
$936$	−11.4974			−0.375806
$937$	−13.0657	+	9.49278i	−0.426837	+	0.310116i	−0.780383	−	0.625302i	$-0.784976\pi$
$937$	−13.0657	+	9.49278i	−0.426837	+	0.310116i	0.353546	+	0.935417i	$0.384976\pi$
$938$	2.85984	+	2.07779i	0.0933770	+	0.0678423i
$939$	19.1960	+	13.9467i	0.626438	+	0.455134i
$940$	3.58549	+	11.0350i	0.116946	+	0.359923i
$941$	43.9769	−	31.9511i	1.43361	−	1.04158i	0.444276	−	0.895890i	$-0.353461\pi$
$941$	43.9769	−	31.9511i	1.43361	−	1.04158i	0.989331	−	0.145687i	$-0.0465391\pi$
$942$	−2.52338	−	7.76618i	−0.0822163	−	0.253036i
$943$	2.34938	−	7.23066i	0.0765064	−	0.235463i
$944$	2.72109	+	1.97699i	0.0885640	+	0.0643455i
$945$	−1.11354	+	3.42713i	−0.0362235	+	0.111485i
$946$	−2.57703	+	7.93129i	−0.0837865	+	0.257868i
$947$	−7.72106	−	5.60968i	−0.250901	−	0.182290i	0.455225	−	0.890376i	$-0.349559\pi$
$947$	−7.72106	−	5.60968i	−0.250901	−	0.182290i	−0.706126	+	0.708086i	$0.749559\pi$
$948$	−10.4829	+	32.2630i	−0.340468	+	1.04785i
$949$	3.83186	+	11.7933i	0.124387	+	0.382825i
$950$	−0.266671	+	0.193748i	−0.00865196	+	0.00628602i
$951$	9.47752	+	29.1688i	0.307330	+	0.945863i
$952$	−12.4991	−	9.08114i	−0.405099	−	0.294321i
$953$	8.41825	+	6.11621i	0.272694	+	0.198124i	0.715724	−	0.698383i	$-0.246097\pi$
$953$	8.41825	+	6.11621i	0.272694	+	0.198124i	−0.443031	+	0.896506i	$0.646097\pi$
$954$	6.24014	−	4.53373i	0.202032	−	0.146785i
$955$	−6.08264			−0.196829
$956$	−1.13672			−0.0367641
$957$	−23.3252	+	16.9468i	−0.753997	+	0.547811i
$958$	1.45029	−	4.46355i	0.0468569	−	0.144211i
$959$	4.39606	+	13.5297i	0.141956	+	0.436896i
$960$	31.5732			1.01902
$961$	−1.48091	+	30.9646i	−0.0477713	+	0.998858i
$962$	−5.41360			−0.174542
$963$	8.13739	+	25.0443i	0.262224	+	0.807042i
$964$	−1.36865	+	4.21226i	−0.0440811	+	0.135668i
$965$	42.6263	−	30.9698i	1.37219	−	0.996954i
$966$	−9.85656			−0.317130
$967$	53.3532			1.71572			0.857861	−	0.513881i	$-0.171793\pi$
$967$	53.3532			1.71572			0.857861	+	0.513881i	$0.171793\pi$
$968$	−2.46196	+	1.78872i	−0.0791303	+	0.0574915i
$969$	5.39768	+	3.92164i	0.173398	+	0.125981i
$970$	19.6510	+	14.2773i	0.630956	+	0.458416i
$971$	−9.28910	−	28.5889i	−0.298101	−	0.917462i	−0.982162	−	0.188037i	$-0.939788\pi$
$971$	−9.28910	−	28.5889i	−0.298101	−	0.917462i	0.684061	−	0.729425i	$-0.260212\pi$
$972$	−19.5057	+	14.1718i	−0.625647	+	0.454559i
$973$	−3.19443	−	9.83145i	−0.102409	−	0.315182i
$974$	11.2111	−	34.5042i	0.359226	−	1.10559i
$975$	−2.14165	−	1.55600i	−0.0685878	−	0.0498319i
$976$	−0.628770	+	1.93515i	−0.0201264	+	0.0619428i
$977$	14.0496	−	43.2403i	0.449488	−	1.38338i	−0.427998	−	0.903779i	$-0.640781\pi$
$977$	14.0496	−	43.2403i	0.449488	−	1.38338i	0.877486	−	0.479602i	$-0.159219\pi$
$978$	26.0004	+	18.8904i	0.831402	+	0.604049i
$979$	−9.65375	+	29.7112i	−0.308535	+	0.949573i
$980$	4.49801	+	13.8435i	0.143684	+	0.442213i
$981$	25.7416	−	18.7024i	0.821866	−	0.597121i
$982$	7.15280	+	22.0141i	0.228255	+	0.702497i
$983$	−31.4408	−	22.8431i	−1.00281	−	0.728582i	−0.0401188	−	0.999195i	$-0.512774\pi$
$983$	−31.4408	−	22.8431i	−1.00281	−	0.728582i	−0.962688	+	0.270613i	$0.912774\pi$
$984$	8.65335	+	6.28703i	0.275859	+	0.200423i
$985$	16.8160	−	12.2175i	0.535803	−	0.389283i
$986$	21.2888			0.677972
$987$	9.93628			0.316275
$988$	−0.319842	+	0.232378i	−0.0101755	+	0.00739294i
$989$	−4.34642	+	13.3769i	−0.138208	+	0.425361i
$990$	−7.88102	−	24.2553i	−0.250475	−	0.770883i
$991$	−38.5746			−1.22536			−0.612682	−	0.790330i	$-0.709909\pi$
$991$	−38.5746			−1.22536			−0.612682	+	0.790330i	$0.709909\pi$
$992$	20.7379	+	21.7534i	0.658430	+	0.690673i
$993$	−20.9225			−0.663956
$994$	−0.901949	−	2.77591i	−0.0286081	−	0.0880466i
$995$	1.70342	−	5.24258i	0.0540020	−	0.166201i
$996$	−14.0646	+	10.2186i	−0.445655	+	0.323787i
$997$	17.7919			0.563476			0.281738	−	0.959491i	$-0.409089\pi$
$997$	17.7919			0.563476			0.281738	+	0.959491i	$0.409089\pi$
$998$	−12.5807			−0.398236
$999$	11.5385	−	8.38323i	0.365063	−	0.265234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.66.5	✓	48
31.8	even	5	inner	403.2.k.d.287.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.66.5	✓	48	1.1	even	1	trivial
403.2.k.d.287.5	yes	48	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.288777 - 0.888765i) q^{2} +(0.813772 - 2.50453i) q^{3} +(0.911523 - 0.662261i) q^{4} +1.99869 q^{5} -2.46094 q^{6} +(0.592448 - 0.430438i) q^{7} +(-2.36388 - 1.71746i) q^{8} +(-3.18340 - 2.31288i) q^{9} +O(q^{10})\)	\(q+(-0.288777 - 0.888765i) q^{2} +(0.813772 - 2.50453i) q^{3} +(0.911523 - 0.662261i) q^{4} +1.99869 q^{5} -2.46094 q^{6} +(0.592448 - 0.430438i) q^{7} +(-2.36388 - 1.71746i) q^{8} +(-3.18340 - 2.31288i) q^{9} +(-0.577176 - 1.77636i) q^{10} +(-2.80736 + 2.03966i) q^{11} +(-0.916881 - 2.82187i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.553644 - 0.402246i) q^{14} +(1.62648 - 5.00578i) q^{15} +(-0.147440 + 0.453774i) q^{16} +(5.84144 + 4.24405i) q^{17} +(-1.13631 + 3.49720i) q^{18} +(0.108430 + 0.333713i) q^{19} +(1.82185 - 1.32365i) q^{20} +(-0.595929 - 1.83408i) q^{21} +(2.62348 + 1.90607i) q^{22} +(4.42476 + 3.21478i) q^{23} +(-6.22508 + 4.52279i) q^{24} -1.00524 q^{25} +0.934503 q^{26} +(-1.99180 + 1.44712i) q^{27} +(0.254967 - 0.784709i) q^{28} +(0.974968 + 3.00064i) q^{29} -4.91865 q^{30} +(-3.84182 - 4.02994i) q^{31} -5.39795 q^{32} +(2.82386 + 8.69094i) q^{33} +(2.08509 - 6.41725i) q^{34} +(1.18412 - 0.860312i) q^{35} -4.43348 q^{36} -5.79303 q^{37} +(0.265280 - 0.192737i) q^{38} +(2.13048 + 1.54789i) q^{39} +(-4.72466 - 3.43266i) q^{40} +(-0.429558 - 1.32204i) q^{41} +(-1.45798 + 1.05928i) q^{42} +(0.794693 + 2.44581i) q^{43} +(-1.20818 + 3.71840i) q^{44} +(-6.36263 - 4.62272i) q^{45} +(1.57941 - 4.86093i) q^{46} +(-1.59219 + 4.90024i) q^{47} +(1.01651 + 0.738537i) q^{48} +(-1.99740 + 6.14737i) q^{49} +(0.290291 + 0.893425i) q^{50} +(15.3830 - 11.1764i) q^{51} +(0.348171 + 1.07156i) q^{52} +(-1.69699 - 1.23294i) q^{53} +(1.86134 + 1.35234i) q^{54} +(-5.61103 + 4.07666i) q^{55} -2.13973 q^{56} +0.924032 q^{57} +(2.38532 - 1.73303i) q^{58} +(2.17839 - 6.70438i) q^{59} +(-1.83256 - 5.64004i) q^{60} +4.26458 q^{61} +(-2.47224 + 4.57823i) q^{62} -2.88155 q^{63} +(1.85369 + 5.70506i) q^{64} +(-0.617629 + 1.90087i) q^{65} +(6.90873 - 5.01949i) q^{66} -5.16548 q^{67} +8.13528 q^{68} +(11.6523 - 8.46587i) q^{69} +(-1.10656 - 0.803964i) q^{70} +(3.45052 + 2.50695i) q^{71} +(3.55291 + 10.9347i) q^{72} +(10.0319 - 7.28863i) q^{73} +(1.67289 + 5.14864i) q^{74} +(-0.818038 + 2.51766i) q^{75} +(0.319842 + 0.232378i) q^{76} +(-0.785262 + 2.41679i) q^{77} +(0.760472 - 2.34049i) q^{78} +(-9.24965 - 6.72026i) q^{79} +(-0.294687 + 0.906953i) q^{80} +(-1.64435 - 5.06080i) q^{81} +(-1.05094 + 0.763551i) q^{82} +(-1.81060 - 5.57246i) q^{83} +(-1.75784 - 1.27715i) q^{84} +(11.6752 + 8.48254i) q^{85} +(1.94426 - 1.41259i) q^{86} +8.30860 q^{87} +10.1393 q^{88} +(7.28335 - 5.29166i) q^{89} +(-2.27113 + 6.98982i) q^{90} +(0.226295 + 0.696464i) q^{91} +6.16230 q^{92} +(-13.2195 + 6.34249i) q^{93} +4.81495 q^{94} +(0.216718 + 0.666989i) q^{95} +(-4.39270 + 13.5193i) q^{96} +(-10.5211 + 7.64399i) q^{97} +6.04037 q^{98} +13.6545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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