LMFDB - Embedded newform 285.2.v.a.197.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(68,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("285.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.v (of order $12$, 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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.25
Character	$\chi$	$=$	285.197
Dual form			285.2.v.a.68.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01730 + 0.272584i) q^{2} +(-1.49607 + 0.872801i) q^{3} +(-0.771457 - 0.445401i) q^{4} +(-1.26772 - 1.84198i) q^{5} +(-1.75986 + 0.480094i) q^{6} +(1.17470 + 1.17470i) q^{7} +(-2.15282 - 2.15282i) q^{8} +(1.47644 - 2.61154i) q^{9} +O(q^{10})$	\(q+(1.01730 + 0.272584i) q^{2} +(-1.49607 + 0.872801i) q^{3} +(-0.771457 - 0.445401i) q^{4} +(-1.26772 - 1.84198i) q^{5} +(-1.75986 + 0.480094i) q^{6} +(1.17470 + 1.17470i) q^{7} +(-2.15282 - 2.15282i) q^{8} +(1.47644 - 2.61154i) q^{9} +(-0.787559 - 2.21940i) q^{10} -3.18549i q^{11} +(1.54290 - 0.00697821i) q^{12} +(-1.15900 - 4.32544i) q^{13} +(0.874812 + 1.51522i) q^{14} +(3.50428 + 1.64925i) q^{15} +(-0.712434 - 1.23397i) q^{16} +(-3.91722 - 1.04962i) q^{17} +(2.21384 - 2.25426i) q^{18} +(4.35819 - 0.0784366i) q^{19} +(0.157576 + 1.98565i) q^{20} +(-2.78270 - 0.732149i) q^{21} +(0.868315 - 3.24060i) q^{22} +(-5.98254 + 1.60302i) q^{23} +(5.09975 + 1.34178i) q^{24} +(-1.78576 + 4.67023i) q^{25} -4.71619i q^{26} +(0.0705008 + 5.19567i) q^{27} +(-0.383017 - 1.42944i) q^{28} +(1.01594 - 1.75966i) q^{29} +(3.11534 + 2.63299i) q^{30} -3.68027 q^{31} +(1.18758 + 4.43210i) q^{32} +(2.78030 + 4.76571i) q^{33} +(-3.69887 - 2.13555i) q^{34} +(0.674573 - 3.65295i) q^{35} +(-2.30219 + 1.35708i) q^{36} +(0.612918 + 0.612918i) q^{37} +(4.45496 + 1.10818i) q^{38} +(5.50919 + 5.45958i) q^{39} +(-1.23627 + 6.69463i) q^{40} +(4.82698 - 2.78686i) q^{41} +(-2.63126 - 1.50333i) q^{42} +(10.4383 + 2.79692i) q^{43} +(-1.41882 + 2.45747i) q^{44} +(-6.68211 + 0.591143i) q^{45} -6.52299 q^{46} +(-0.290142 - 1.08283i) q^{47} +(2.14286 + 1.22429i) q^{48} -4.24018i q^{49} +(-3.08968 + 4.26425i) q^{50} +(6.77654 - 1.84866i) q^{51} +(-1.03244 + 3.85311i) q^{52} +(-0.0565928 + 0.0151640i) q^{53} +(-1.34454 + 5.30477i) q^{54} +(-5.86760 + 4.03832i) q^{55} -5.05782i q^{56} +(-6.45169 + 3.92118i) q^{57} +(1.51317 - 1.51317i) q^{58} +(-6.45911 - 11.1875i) q^{59} +(-1.96882 - 2.83314i) q^{60} +(-5.26233 + 9.11463i) q^{61} +(-3.74393 - 1.00318i) q^{62} +(4.80213 - 1.33340i) q^{63} +7.68222i q^{64} +(-6.49807 + 7.61831i) q^{65} +(1.52934 + 5.60602i) q^{66} +(8.21169 - 2.20032i) q^{67} +(2.55447 + 2.55447i) q^{68} +(7.55118 - 7.61979i) q^{69} +(1.68198 - 3.53226i) q^{70} +(2.39262 - 1.38138i) q^{71} +(-8.80068 + 2.44367i) q^{72} +(-13.6069 - 3.64595i) q^{73} +(0.456449 + 0.790593i) q^{74} +(-1.40457 - 8.54559i) q^{75} +(-3.39709 - 1.88063i) q^{76} +(3.74198 - 3.74198i) q^{77} +(4.11629 + 7.05573i) q^{78} +(13.2657 - 7.65897i) q^{79} +(-1.36978 + 2.87662i) q^{80} +(-4.64026 - 7.71155i) q^{81} +(5.67013 - 1.51931i) q^{82} +(6.32843 + 6.32843i) q^{83} +(1.82063 + 1.80424i) q^{84} +(3.03258 + 8.54606i) q^{85} +(9.85642 + 5.69061i) q^{86} +(0.0159170 + 3.51929i) q^{87} +(-6.85780 + 6.85780i) q^{88} +(1.42916 - 2.47537i) q^{89} +(-6.95883 - 1.22007i) q^{90} +(3.71960 - 6.44254i) q^{91} +(5.32926 + 1.42797i) q^{92} +(5.50594 - 3.21214i) q^{93} -1.18064i q^{94} +(-5.66946 - 7.92825i) q^{95} +(-5.64504 - 5.59420i) q^{96} +(-0.574239 + 2.14309i) q^{97} +(1.15581 - 4.31353i) q^{98} +(-8.31904 - 4.70318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 2 q^{3} - 4 q^{6} - 16 q^{7}+O(q^{10}) $ 144 * q - 2 * q^3 - 4 * q^6 - 16 * q^7	$ 144 q - 2 q^{3} - 4 q^{6} - 16 q^{7} - 4 q^{10} - 28 q^{12} + 4 q^{13} - 8 q^{15} + 36 q^{16} - 60 q^{18} - 4 q^{21} + 12 q^{22} - 12 q^{25} - 20 q^{27} + 28 q^{28} - 28 q^{30} - 64 q^{31} - 8 q^{33} - 20 q^{36} - 36 q^{40} + 22 q^{42} + 16 q^{43} + 24 q^{45} - 80 q^{46} + 24 q^{48} + 12 q^{51} - 60 q^{52} + 8 q^{55} + 72 q^{57} - 96 q^{58} + 30 q^{60} + 16 q^{61} - 28 q^{63} - 4 q^{66} - 4 q^{67} - 52 q^{70} - 94 q^{72} - 52 q^{73} + 116 q^{75} + 96 q^{76} + 8 q^{78} - 12 q^{81} - 68 q^{82} - 28 q^{85} + 84 q^{87} - 34 q^{90} - 112 q^{91} - 4 q^{93} + 168 q^{96} + 4 q^{97}+O(q^{100}) $ 144 * q - 2 * q^3 - 4 * q^6 - 16 * q^7 - 4 * q^10 - 28 * q^12 + 4 * q^13 - 8 * q^15 + 36 * q^16 - 60 * q^18 - 4 * q^21 + 12 * q^22 - 12 * q^25 - 20 * q^27 + 28 * q^28 - 28 * q^30 - 64 * q^31 - 8 * q^33 - 20 * q^36 - 36 * q^40 + 22 * q^42 + 16 * q^43 + 24 * q^45 - 80 * q^46 + 24 * q^48 + 12 * q^51 - 60 * q^52 + 8 * q^55 + 72 * q^57 - 96 * q^58 + 30 * q^60 + 16 * q^61 - 28 * q^63 - 4 * q^66 - 4 * q^67 - 52 * q^70 - 94 * q^72 - 52 * q^73 + 116 * q^75 + 96 * q^76 + 8 * q^78 - 12 * q^81 - 68 * q^82 - 28 * q^85 + 84 * q^87 - 34 * q^90 - 112 * q^91 - 4 * q^93 + 168 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.01730	+	0.272584i	0.719339	+	0.192746i	0.599877	−	0.800093i	$-0.295216\pi$
$2$	1.01730	+	0.272584i	0.719339	+	0.192746i	0.119462	+	0.992839i	$0.461883\pi$
$3$	−1.49607	+	0.872801i	−0.863755	+	0.503912i
$3$	−1.49607	+	0.872801i	−0.863755	+	0.503912i
$4$	−0.771457	−	0.445401i	−0.385729	−	0.222700i
$5$	−1.26772	−	1.84198i	−0.566943	−	0.823757i
$5$	−1.26772	−	1.84198i	−0.566943	−	0.823757i
$6$	−1.75986	+	0.480094i	−0.718459	+	0.195998i
$7$	1.17470	+	1.17470i	0.443993	+	0.443993i	0.893352	−	0.449358i	$-0.148347\pi$
$7$	1.17470	+	1.17470i	0.443993	+	0.443993i	−0.449358	+	0.893352i	$0.648347\pi$
$8$	−2.15282	−	2.15282i	−0.761137	−	0.761137i
$9$	1.47644	−	2.61154i	0.492146	−	0.870513i
$10$	−0.787559	−	2.21940i	−0.249048	−	0.701836i
$11$		−	3.18549i		−	0.960462i	−0.877142	−	0.480231i	$-0.840553\pi$
$11$		−	3.18549i		−	0.960462i	0.877142	−	0.480231i	$-0.159447\pi$
$12$	1.54290	−	0.00697821i	0.445396	−	0.00201444i
$13$	−1.15900	−	4.32544i	−0.321448	−	1.19966i	−0.917834	−	0.396963i	$-0.870064\pi$
$13$	−1.15900	−	4.32544i	−0.321448	−	1.19966i	0.596386	−	0.802698i	$-0.296603\pi$
$14$	0.874812	+	1.51522i	0.233803	+	0.404959i
$15$	3.50428	+	1.64925i	0.904801	+	0.425835i
$16$	−0.712434	−	1.23397i	−0.178109	−	0.308493i
$17$	−3.91722	−	1.04962i	−0.950066	−	0.254569i	−0.249676	−	0.968330i	$-0.580324\pi$
$17$	−3.91722	−	1.04962i	−0.950066	−	0.254569i	−0.700390	+	0.713760i	$0.746991\pi$
$18$	2.21384	−	2.25426i	0.521808	−	0.531334i
$19$	4.35819	−	0.0784366i	0.999838	−	0.0179946i
$19$	4.35819	−	0.0784366i	0.999838	−	0.0179946i
$20$	0.157576	+	1.98565i	0.0352350	+	0.444005i
$21$	−2.78270	−	0.732149i	−0.607235	−	0.159768i
$22$	0.868315	−	3.24060i	0.185125	−	0.690898i
$23$	−5.98254	+	1.60302i	−1.24745	+	0.334252i	−0.821350	−	0.570425i	$-0.806778\pi$
$23$	−5.98254	+	1.60302i	−1.24745	+	0.334252i	−0.426097	+	0.904677i	$0.640112\pi$
$24$	5.09975	+	1.34178i	1.04098	+	0.273890i
$25$	−1.78576	+	4.67023i	−0.357151	+	0.934047i
$26$		−	4.71619i		−	0.924920i
$27$	0.0705008	+	5.19567i	0.0135679	+	0.999908i
$28$	−0.383017	−	1.42944i	−0.0723834	−	0.270138i
$29$	1.01594	−	1.75966i	0.188656	−	0.326761i	−0.756147	−	0.654402i	$-0.772920\pi$
$29$	1.01594	−	1.75966i	0.188656	−	0.326761i	0.944802	+	0.327641i	$0.106254\pi$
$30$	3.11534	+	2.63299i	0.568780	+	0.480717i
$31$	−3.68027			−0.660996			−0.330498	−	0.943807i	$-0.607217\pi$
$31$	−3.68027			−0.660996			−0.330498	+	0.943807i	$0.607217\pi$
$32$	1.18758	+	4.43210i	0.209936	+	0.783492i
$33$	2.78030	+	4.76571i	0.483988	+	0.829604i
$34$	−3.69887	−	2.13555i	−0.634352	−	0.366243i
$35$	0.674573	−	3.65295i	0.114024	−	0.617461i
$36$	−2.30219	+	1.35708i	−0.383698	+	0.226180i
$37$	0.612918	+	0.612918i	0.100763	+	0.100763i	0.755691	−	0.654928i	$-0.227301\pi$
$37$	0.612918	+	0.612918i	0.100763	+	0.100763i	−0.654928	+	0.755691i	$0.727301\pi$
$38$	4.45496	+	1.10818i	0.722690	+	0.179771i
$39$	5.50919	+	5.45958i	0.882176	+	0.874232i
$40$	−1.23627	+	6.69463i	−0.195471	+	1.05851i
$41$	4.82698	−	2.78686i	0.753847	−	0.435234i	−0.0732351	−	0.997315i	$-0.523332\pi$
$41$	4.82698	−	2.78686i	0.753847	−	0.435234i	0.827082	+	0.562081i	$0.189999\pi$
$42$	−2.63126	−	1.50333i	−0.406013	−	0.231970i
$43$	10.4383	+	2.79692i	1.59182	+	0.426526i	0.942559	−	0.334040i	$-0.108412\pi$
$43$	10.4383	+	2.79692i	1.59182	+	0.426526i	0.649260	+	0.760567i	$0.275079\pi$
$44$	−1.41882	+	2.45747i	−0.213895	+	0.370478i
$45$	−6.68211	+	0.591143i	−0.996110	+	0.0881223i
$46$	−6.52299			−0.961762
$47$	−0.290142	−	1.08283i	−0.0423216	−	0.157946i	0.941531	−	0.336926i	$-0.109387\pi$
$47$	−0.290142	−	1.08283i	−0.0423216	−	0.157946i	−0.983853	+	0.178979i	$0.942720\pi$
$48$	2.14286	+	1.22429i	0.309295	+	0.176711i
$49$		−	4.24018i		−	0.605740i
$50$	−3.08968	+	4.26425i	−0.436947	+	0.603056i
$51$	6.77654	−	1.84866i	0.948905	−	0.258864i
$52$	−1.03244	+	3.85311i	−0.143173	+	0.534330i
$53$	−0.0565928	+	0.0151640i	−0.00777362	+	0.00208294i	−0.262704	−	0.964877i	$-0.584614\pi$
$53$	−0.0565928	+	0.0151640i	−0.00777362	+	0.00208294i	0.254930	+	0.966959i	$0.417948\pi$
$54$	−1.34454	+	5.30477i	−0.182969	+	0.721888i
$55$	−5.86760	+	4.03832i	−0.791187	+	0.544527i
$56$		−	5.05782i		−	0.675880i
$57$	−6.45169	+	3.92118i	−0.854548	+	0.519373i
$58$	1.51317	−	1.51317i	0.198689	−	0.198689i
$59$	−6.45911	−	11.1875i	−0.840905	−	1.45649i	−0.889131	−	0.457653i	$-0.848690\pi$
$59$	−6.45911	−	11.1875i	−0.840905	−	1.45649i	0.0482259	−	0.998836i	$-0.484643\pi$
$60$	−1.96882	−	2.83314i	−0.254174	−	0.365756i
$61$	−5.26233	+	9.11463i	−0.673773	+	1.16701i	0.303053	+	0.952974i	$0.401994\pi$
$61$	−5.26233	+	9.11463i	−0.673773	+	1.16701i	−0.976826	+	0.214035i	$0.931339\pi$
$62$	−3.74393	−	1.00318i	−0.475480	−	0.127404i
$63$	4.80213	−	1.33340i	0.605011	−	0.167992i
$64$			7.68222i			0.960277i
$65$	−6.49807	+	7.61831i	−0.805986	+	0.944935i
$66$	1.52934	+	5.60602i	0.188248	+	0.690053i
$67$	8.21169	−	2.20032i	1.00322	−	0.268811i	0.280425	−	0.959876i	$-0.409525\pi$
$67$	8.21169	−	2.20032i	1.00322	−	0.268811i	0.722793	+	0.691065i	$0.242858\pi$
$68$	2.55447	+	2.55447i	0.309775	+	0.309775i
$69$	7.55118	−	7.61979i	0.909055	−	0.917315i
$70$	1.68198	−	3.53226i	0.201035	−	0.422186i
$71$	2.39262	−	1.38138i	0.283952	−	0.163940i	−0.351259	−	0.936278i	$-0.614246\pi$
$71$	2.39262	−	1.38138i	0.283952	−	0.163940i	0.635211	+	0.772338i	$0.280913\pi$
$72$	−8.80068	+	2.44367i	−1.03717	+	0.287989i
$73$	−13.6069	−	3.64595i	−1.59256	−	0.426726i	−0.649778	−	0.760124i	$-0.725138\pi$
$73$	−13.6069	−	3.64595i	−1.59256	−	0.426726i	−0.942786	+	0.333398i	$0.891805\pi$
$74$	0.456449	+	0.790593i	0.0530611	+	0.0919046i
$75$	−1.40457	−	8.54559i	−0.162186	−	0.986760i
$76$	−3.39709	−	1.88063i	−0.389673	−	0.215723i
$77$	3.74198	−	3.74198i	0.426439	−	0.426439i
$78$	4.11629	+	7.05573i	0.466078	+	0.798905i
$79$	13.2657	−	7.65897i	1.49251	−	0.861702i	0.492548	−	0.870285i	$-0.336065\pi$
$79$	13.2657	−	7.65897i	1.49251	−	0.861702i	0.999963	+	0.00858312i	$0.00273213\pi$
$80$	−1.36978	+	2.87662i	−0.153146	+	0.321616i
$81$	−4.64026	−	7.71155i	−0.515585	−	0.856839i
$82$	5.67013	−	1.51931i	0.626161	−	0.167779i
$83$	6.32843	+	6.32843i	0.694636	+	0.694636i	0.963248	−	0.268613i	$-0.0865652\pi$
$83$	6.32843	+	6.32843i	0.694636	+	0.694636i	−0.268613	+	0.963248i	$0.586565\pi$
$84$	1.82063	+	1.80424i	0.198647	+	0.196859i
$85$	3.03258	+	8.54606i	0.328930	+	0.926950i
$86$	9.85642	+	5.69061i	1.06285	+	0.613634i
$87$	0.0159170	+	3.51929i	0.00170649	+	0.377308i
$88$	−6.85780	+	6.85780i	−0.731043	+	0.731043i
$89$	1.42916	−	2.47537i	0.151490	−	0.262389i	−0.780285	−	0.625424i	$-0.784926\pi$
$89$	1.42916	−	2.47537i	0.151490	−	0.262389i	0.931776	+	0.363035i	$0.118259\pi$
$90$	−6.95883	−	1.22007i	−0.733525	−	0.128607i
$91$	3.71960	−	6.44254i	0.389921	−	0.675362i
$92$	5.32926	+	1.42797i	0.555614	+	0.148876i
$93$	5.50594	−	3.21214i	0.570939	−	0.333084i
$94$		−	1.18064i		−	0.121774i
$95$	−5.66946	−	7.92825i	−0.581674	−	0.813422i
$96$	−5.64504	−	5.59420i	−0.576144	−	0.570956i
$97$	−0.574239	+	2.14309i	−0.0583051	+	0.217598i	−0.988931	−	0.148373i	$-0.952596\pi$
$97$	−0.574239	+	2.14309i	−0.0583051	+	0.217598i	0.930626	+	0.365971i	$0.119263\pi$
$98$	1.15581	−	4.31353i	0.116754	−	0.435732i
$99$	−8.31904	−	4.70318i	−0.836095	−	0.472688i
$100$	3.45776	−	2.80751i	0.345776	−	0.280751i
$101$	0.580083	+	0.334911i	0.0577204	+	0.0333249i	0.528582	−	0.848882i	$-0.322724\pi$
$101$	0.580083	+	0.334911i	0.0577204	+	0.0333249i	−0.470862	+	0.882207i	$0.656057\pi$
$102$	7.39767	−	0.0334582i	0.732479	−	0.00331285i
$103$	2.52297	−	2.52297i	0.248595	−	0.248595i	−0.571799	−	0.820394i	$-0.693754\pi$
$103$	2.52297	−	2.52297i	0.248595	−	0.248595i	0.820394	+	0.571799i	$0.193754\pi$
$104$	−6.81678	+	11.8070i	−0.668440	+	1.15777i
$105$	2.17909	+	6.05383i	0.212657	+	0.590793i
$106$	−0.0617052			−0.00599334
$107$	10.8551	−	10.8551i	1.04940	−	1.04940i	0.0506902	−	0.998714i	$-0.483858\pi$
$107$	10.8551	−	10.8551i	1.04940	−	1.04940i	0.998714	−	0.0506902i	$-0.0161421\pi$
$108$	2.25977	−	4.03964i	0.217446	−	0.388715i
$109$	3.61611	−	2.08776i	0.346361	−	0.199972i	−0.316720	−	0.948519i	$-0.602582\pi$
$109$	3.61611	−	2.08776i	0.346361	−	0.199972i	0.663081	+	0.748547i	$0.269248\pi$
$110$	−7.06989	+	2.50876i	−0.674087	+	0.239201i
$111$	−1.45192	−	0.382012i	−0.137810	−	0.0362590i
$112$	0.612648	−	2.28644i	0.0578898	−	0.216048i
$113$	6.65597	+	6.65597i	0.626141	+	0.626141i	0.947095	−	0.320954i	$-0.104003\pi$
$113$	6.65597	+	6.65597i	0.626141	+	0.626141i	−0.320954	+	0.947095i	$0.604003\pi$
$114$	−7.63215	+	2.23038i	−0.714816	+	0.208894i
$115$	10.5369	+	8.98752i	0.982574	+	0.838091i
$116$	−1.56751	+	0.905003i	−0.145540	+	0.0840275i
$117$	−13.0072	−	3.35948i	−1.20252	−	0.310584i
$118$	−3.52130	−	13.1417i	−0.324162	−	1.20979i
$119$	−3.36856	−	5.83452i	−0.308796	−	0.534850i
$120$	−3.99354	−	11.0946i	−0.364558	−	1.01280i
$121$	0.852636			0.0775124
$122$	−7.83787	+	7.83787i	−0.709607	+	0.709607i
$123$	−4.78911	+	8.38232i	−0.431820	+	0.755808i
$124$	2.83917	+	1.63920i	0.254965	+	0.147204i
$125$	10.8663	−	2.63124i	0.971912	−	0.235345i
$126$	5.24866	−	0.0474782i	0.467588	−	0.00422970i
$127$	−7.74262	+	2.07463i	−0.687046	+	0.184094i	−0.585421	−	0.810729i	$-0.699071\pi$
$127$	−7.74262	+	2.07463i	−0.687046	+	0.184094i	−0.101625	+	0.994823i	$0.532404\pi$
$128$	0.281103	−	1.04909i	0.0248462	−	0.0927274i
$129$	−18.0575	+	4.92613i	−1.58987	+	0.433722i
$130$	−8.68711	+	5.97882i	−0.761910	+	0.524377i
$131$	−5.99294	+	3.46003i	−0.523606	+	0.302304i	−0.738409	−	0.674353i	$-0.764422\pi$
$131$	−5.99294	+	3.46003i	−0.523606	+	0.302304i	0.214803	+	0.976657i	$0.431089\pi$
$132$	−0.0222291	−	4.91489i	−0.00193479	−	0.427786i
$133$	5.21169	+	5.02741i	0.451911	+	0.435932i
$134$	8.95351			0.773466
$135$	9.48094	−	6.71654i	0.815989	−	0.578067i
$136$	6.17344	+	10.6927i	0.529368	+	0.916893i
$137$	−1.53410	−	5.72535i	−0.131067	−	0.489150i	0.868916	−	0.494960i	$-0.164817\pi$
$137$	−1.53410	−	5.72535i	−0.131067	−	0.489150i	−0.999983	+	0.00581008i	$0.998151\pi$
$138$	9.75883	−	5.69327i	0.830727	−	0.484643i
$139$	−6.62891	−	3.82720i	−0.562257	−	0.324619i	0.191794	−	0.981435i	$-0.438569\pi$
$139$	−6.62891	−	3.82720i	−0.562257	−	0.324619i	−0.754051	+	0.656816i	$0.771903\pi$
$140$	−2.14743	+	2.51764i	−0.181491	+	0.212779i
$141$	1.37916	+	1.36674i	0.116146	+	0.115101i
$142$	2.81055	−	0.753086i	0.235856	−	0.0631975i
$143$	−13.7787	+	3.69198i	−1.15223	+	0.308739i
$144$	−4.27443	+	0.0386655i	−0.356202	+	0.00322213i
$145$	−4.52919	+	0.359424i	−0.376129	+	0.0298486i
$146$	−12.8484	−	7.41804i	−1.06334	−	0.613921i
$147$	3.70083	+	6.34360i	0.305239	+	0.523211i
$148$	−0.199846	−	0.745835i	−0.0164272	−	0.0613072i
$149$	7.61099	+	13.1826i	0.623516	+	1.07996i	0.988826	+	0.149076i	$0.0476299\pi$
$149$	7.61099	+	13.1826i	0.623516	+	1.07996i	−0.365309	+	0.930886i	$0.619037\pi$
$150$	0.900528	−	9.07628i	0.0735278	−	0.741075i
$151$	7.41432			0.603369			0.301684	−	0.953408i	$-0.402451\pi$
$151$	7.41432			0.603369			0.301684	+	0.953408i	$0.402451\pi$
$152$	−9.55127	−	9.21355i	−0.774710	−	0.747318i
$153$	−8.52465	+	8.68028i	−0.689177	+	0.701759i
$154$	4.82672	−	2.78671i	0.388948	−	0.224559i
$155$	4.66556	+	6.77897i	0.374747	+	0.544500i
$156$	−1.81840	−	6.66562i	−0.145588	−	0.533677i
$157$	3.56371	−	13.2999i	0.284415	−	1.06145i	−0.664851	−	0.746976i	$-0.731505\pi$
$157$	3.56371	−	13.2999i	0.284415	−	1.06145i	0.949266	−	0.314474i	$-0.101828\pi$
$158$	15.5829	−	4.17543i	1.23971	−	0.332180i
$159$	0.0714315	−	0.0720806i	0.00566489	−	0.00571637i
$160$	6.65831	−	7.80617i	0.526385	−	0.617132i
$161$	−8.91073	−	5.14461i	−0.702264	−	0.405452i
$162$	−2.61848	−	9.10981i	−0.205728	−	0.715734i
$163$	0.536149	−	0.536149i	0.0419945	−	0.0419945i	−0.685798	−	0.727792i	$-0.740547\pi$
$163$	0.536149	−	0.536149i	0.0419945	−	0.0419945i	0.727792	+	0.685798i	$0.240547\pi$
$164$	−4.96507			−0.387707
$165$	5.25368	−	11.1629i	0.408999	−	0.869027i
$166$	4.71287	+	8.16293i	0.365790	+	0.633567i
$167$	5.70856	+	21.3046i	0.441741	+	1.64860i	0.724400	+	0.689380i	$0.242117\pi$
$167$	5.70856	+	21.3046i	0.441741	+	1.64860i	−0.282658	+	0.959221i	$0.591216\pi$
$168$	4.41447	+	7.56684i	0.340584	+	0.583794i
$169$	−6.10781	+	3.52635i	−0.469832	+	0.271258i
$170$	0.755522	+	9.52052i	0.0579459	+	0.730191i
$171$	6.22976	−	11.4974i	0.476402	−	0.879228i
$172$	−6.80691	−	6.80691i	−0.519022	−	0.519022i
$173$	−0.872016	+	3.25441i	−0.0662982	+	0.247428i	−0.991120	−	0.132973i	$-0.957548\pi$
$173$	−0.872016	+	3.25441i	−0.0662982	+	0.247428i	0.924821	+	0.380401i	$0.124214\pi$
$174$	−0.943111	+	3.58451i	−0.0714971	+	0.271741i
$175$	−7.58382	+	3.38838i	−0.573283	+	0.256138i
$176$	−3.93081	+	2.26945i	−0.296296	+	0.171067i
$177$	19.4277	+	11.0998i	1.46028	+	0.834309i
$178$	2.12863	−	2.12863i	0.159547	−	0.159547i
$179$	2.60357			0.194600			0.0973001	−	0.995255i	$-0.468979\pi$
$179$	2.60357			0.194600			0.0973001	+	0.995255i	$0.468979\pi$
$180$	5.41825	+	2.52018i	0.403853	+	0.187843i
$181$	8.81094	−	15.2610i	0.654912	−	1.13434i	−0.327004	−	0.945023i	$-0.606039\pi$
$181$	8.81094	−	15.2610i	0.654912	−	1.13434i	0.981916	−	0.189318i	$-0.0606278\pi$
$182$	5.54008	−	5.54008i	0.410658	−	0.410658i
$183$	−0.0824464	−	18.2291i	−0.00609461	−	1.34753i
$184$	16.3304	+	9.42833i	1.20389	+	0.695066i
$185$	0.351971	−	1.90599i	0.0258774	−	0.140131i
$186$	6.47676	−	1.76688i	0.474899	−	0.129554i
$187$	−3.34355	+	12.4783i	−0.244504	+	0.912502i
$188$	−0.258459	+	0.964583i	−0.0188501	+	0.0703494i
$189$	−6.02052	+	6.18615i	−0.437928	+	0.449976i
$190$	−3.60642	−	9.61081i	−0.261637	−	0.697241i
$191$		−	11.2190i		−	0.811782i	−0.913922	−	0.405891i	$-0.866961\pi$
$191$		−	11.2190i		−	0.811782i	0.913922	−	0.405891i	$-0.133039\pi$
$192$	−6.70505	−	11.4931i	−0.483895	−	0.829445i
$193$	−17.6337	−	4.72494i	−1.26930	−	0.340109i	−0.439540	−	0.898223i	$-0.644858\pi$
$193$	−17.6337	−	4.72494i	−1.26930	−	0.340109i	−0.829764	+	0.558114i	$0.811525\pi$
$194$	−1.16834	+	2.02363i	−0.0838822	+	0.145288i
$195$	3.07229	−	17.0690i	0.220011	−	1.22234i
$196$	−1.88858	+	3.27112i	−0.134899	+	0.233651i
$197$	−9.31584	+	9.31584i	−0.663726	+	0.663726i	−0.956256	−	0.292530i	$-0.905503\pi$
$197$	−9.31584	+	9.31584i	−0.663726	+	0.663726i	0.292530	+	0.956256i	$0.405503\pi$
$198$	−7.18093	−	7.05218i	−0.510326	−	0.501176i
$199$	−17.1894	−	9.92431i	−1.21853	−	0.703516i	−0.253923	−	0.967224i	$-0.581721\pi$
$199$	−17.1894	−	9.92431i	−1.21853	−	0.703516i	−0.964602	+	0.263708i	$0.915054\pi$
$200$	13.8986	−	6.20976i	0.982779	−	0.439096i
$201$	−10.3648	+	10.4590i	−0.731077	+	0.737720i
$202$	0.498826	+	0.498826i	0.0350973	+	0.0350973i
$203$	3.26049	−	0.873646i	0.228842	−	0.0613180i
$204$	−6.05120	−	1.59212i	−0.423669	−	0.111470i
$205$	−11.2526	−	5.35822i	−0.785915	−	0.374234i
$206$	3.25433	−	1.87889i	0.226740	−	0.130908i
$207$	−4.64651	+	17.9904i	−0.322955	+	1.25042i
$208$	−4.51176	+	4.51176i	−0.312834	+	0.312834i
$209$	−0.249859	−	13.8830i	−0.0172831	−	0.960307i
$210$	0.566606	+	6.75254i	0.0390996	+	0.465969i
$211$	−8.41167	−	14.5694i	−0.579083	−	1.00300i	−0.995585	−	0.0938662i	$-0.970077\pi$
$211$	−8.41167	−	14.5694i	−0.579083	−	1.00300i	0.416502	−	0.909135i	$-0.363256\pi$
$212$	0.0504130	+	0.0135081i	0.00346238	+	0.000927741i
$213$	−2.37386	+	4.15492i	−0.162654	+	0.284691i
$214$	14.0018	−	8.08396i	0.957146	−	0.552608i
$215$	−8.08095	−	22.7727i	−0.551116	−	1.55309i
$216$	11.0336	−	11.3371i	0.750740	−	0.771394i
$217$	−4.32320	−	4.32320i	−0.293478	−	0.293478i
$218$	4.24776	−	1.13818i	0.287695	−	0.0770875i
$219$	23.5390	−	6.42150i	1.59062	−	0.433925i
$220$	6.32528	−	0.501956i	0.426450	−	0.0338419i
$221$			18.1602i			1.22159i
$222$	−1.37291	−	0.784392i	−0.0921436	−	0.0526449i
$223$	−15.1970	−	4.07201i	−1.01766	−	0.272682i	−0.288836	−	0.957379i	$-0.593268\pi$
$223$	−15.1970	−	4.07201i	−1.01766	−	0.272682i	−0.728828	+	0.684696i	$0.759935\pi$
$224$	−3.81133	+	6.60141i	−0.254655	+	0.441075i
$225$	9.55993	+	11.5589i	0.637329	+	0.770592i
$226$	4.95679	+	8.58542i	0.329721	+	0.571094i
$227$	10.3632	−	10.3632i	0.687831	−	0.687831i	−0.273921	−	0.961752i	$-0.588321\pi$
$227$	10.3632	−	10.3632i	0.687831	−	0.687831i	0.961752	+	0.273921i	$0.0883207\pi$
$228$	6.72370	−	0.151432i	0.445288	−	0.0100288i
$229$			20.6484i			1.36449i	0.731125	+	0.682243i	$0.238995\pi$
$229$			20.6484i			1.36449i	−0.731125	+	0.682243i	$0.761005\pi$
$230$	8.26934	+	12.0152i	0.545264	+	0.792258i
$231$	−2.33226	+	8.86427i	−0.153451	+	0.583226i
$232$	−5.97538	+	1.60110i	−0.392303	+	0.105117i
$233$	1.38470	−	5.16777i	0.0907146	−	0.338552i	−0.905620	−	0.424089i	$-0.860594\pi$
$233$	1.38470	−	5.16777i	0.0907146	−	0.338552i	0.996335	+	0.0855379i	$0.0272609\pi$
$234$	−12.3165	−	6.96316i	−0.805155	−	0.455196i
$235$	−1.62672	+	1.90716i	−0.106115	+	0.124409i
$236$			11.5076i			0.749080i
$237$	−13.1617	+	23.0367i	−0.854943	+	1.49639i
$238$	−1.83644	−	6.85367i	−0.119038	−	0.444257i
$239$	6.77356			0.438145			0.219073	−	0.975709i	$-0.429697\pi$
$239$	6.77356			0.438145			0.219073	+	0.975709i	$0.429697\pi$
$240$	−0.461436	−	5.49917i	−0.0297855	−	0.354970i
$241$	−6.61102	+	11.4506i	−0.425853	+	0.737599i	−0.996500	−	0.0835967i	$-0.973359\pi$
$241$	−6.61102	+	11.4506i	−0.425853	+	0.737599i	0.570647	+	0.821196i	$0.306693\pi$
$242$	0.867385	+	0.232415i	0.0557576	+	0.0149402i
$243$	13.6728	+	7.48698i	0.877110	+	0.480290i
$244$	8.11933	−	4.68770i	0.519787	−	0.300099i
$245$	−7.81031	+	5.37537i	−0.498983	+	0.343420i
$246$	−7.15685	+	7.22188i	−0.456304	+	0.460450i
$247$	−5.39041	−	18.7602i	−0.342984	−	1.19368i
$248$	7.92296	+	7.92296i	0.503109	+	0.503109i
$249$	−14.9912	−	3.94430i	−0.950030	−	0.249960i
$250$	11.7715	+	0.285228i	0.744496	+	0.0180394i
$251$	18.5860	+	10.7306i	1.17314	+	0.677312i	0.954417	−	0.298476i	$-0.0964781\pi$
$251$	18.5860	+	10.7306i	1.17314	+	0.677312i	0.218721	+	0.975787i	$0.429811\pi$
$252$	−4.29853	−	1.11021i	−0.270782	−	0.0699369i
$253$	5.10640	+	19.0573i	0.321037	+	1.19813i
$254$	−8.44207			−0.529702
$255$	−11.9960	−	10.1386i	−0.751216	−	0.634906i
$256$	8.25415	−	14.2966i	0.515884	−	0.893538i
$257$	3.53497	+	13.1927i	0.220506	+	0.822938i	0.984156	+	0.177307i	$0.0567387\pi$
$257$	3.53497	+	13.1927i	0.220506	+	0.822938i	−0.763650	+	0.645630i	$0.776595\pi$
$258$	−19.7126	+	0.0891562i	−1.22726	+	0.00555063i
$259$			1.43999i			0.0894763i
$260$	8.40618	−	2.98295i	0.521329	−	0.184995i
$261$	−3.09545	−	5.25121i	−0.191604	−	0.325042i
$262$	−7.03976	+	1.88630i	−0.434918	+	0.116536i
$263$	−4.35006	+	16.2346i	−0.268236	+	1.00107i	0.692004	+	0.721894i	$0.256728\pi$
$263$	−4.35006	+	16.2346i	−0.268236	+	1.00107i	−0.960240	+	0.279176i	$0.909939\pi$
$264$	4.27424	−	16.2452i	0.263061	−	0.999824i
$265$	0.0996758	+	0.0850189i	0.00612303	+	0.00522267i
$266$	3.93145	+	6.53500i	0.241053	+	0.400687i
$267$	0.0223910	+	4.95069i	0.00137031	+	0.302977i
$268$	−7.31499	−	1.96005i	−0.446834	−	0.119729i
$269$	−4.07112	−	7.05139i	−0.248221	−	0.429931i	0.714811	−	0.699317i	$-0.246513\pi$
$269$	−4.07112	−	7.05139i	−0.248221	−	0.429931i	−0.963032	+	0.269386i	$0.913179\pi$
$270$	11.4758	−	4.24837i	0.698393	−	0.258547i
$271$	13.3075	+	23.0493i	0.808374	+	1.40015i	0.913989	+	0.405738i	$0.132986\pi$
$271$	13.3075	+	23.0493i	0.808374	+	1.40015i	−0.105615	+	0.994407i	$0.533681\pi$
$272$	1.49557	+	5.58153i	0.0906820	+	0.338430i
$273$	0.0582760	+	12.8850i	0.00352703	+	0.779833i
$274$		−	6.24256i		−	0.377127i
$275$	14.8770	+	5.68851i	0.897116	+	0.343030i
$276$	−9.21927	+	2.51504i	−0.554935	+	0.151388i
$277$	11.1812	+	11.1812i	0.671815	+	0.671815i	0.958134	−	0.286319i	$-0.0924317\pi$
$277$	11.1812	+	11.1812i	0.671815	+	0.671815i	−0.286319	+	0.958134i	$0.592432\pi$
$278$	−5.70034	−	5.70034i	−0.341884	−	0.341884i
$279$	−5.43369	+	9.61117i	−0.325307	+	0.575406i
$280$	−9.31639	+	6.41191i	−0.556761	+	0.383185i
$281$	−10.9955	−	6.34827i	−0.655938	−	0.378706i	0.134790	−	0.990874i	$-0.456964\pi$
$281$	−10.9955	−	6.34827i	−0.655938	−	0.378706i	−0.790727	+	0.612168i	$0.790297\pi$
$282$	1.03047	+	1.76632i	0.0613634	+	0.105183i
$283$	1.88327	+	0.504621i	0.111949	+	0.0299966i	0.314358	−	0.949304i	$-0.398211\pi$
$283$	1.88327	+	0.504621i	0.111949	+	0.0299966i	−0.202410	+	0.979301i	$0.564877\pi$
$284$	−2.46107			−0.146038
$285$	15.4017	+	6.91290i	0.912317	+	0.409485i
$286$	−15.0234			−0.888351
$287$	8.94394	+	2.39652i	0.527944	+	0.141462i
$288$	13.3280	+	3.44232i	0.785359	+	0.202840i
$289$	−0.479496	−	0.276837i	−0.0282057	−	0.0162845i
$290$	−4.70551	−	0.868945i	−0.276317	−	0.0510262i
$291$	−1.01139	−	3.70740i	−0.0592886	−	0.217332i
$292$	8.87321	+	8.87321i	0.519265	+	0.519265i
$293$	−23.2378	−	23.2378i	−1.35757	−	1.35757i	−0.876904	−	0.480665i	$-0.840395\pi$
$293$	−23.2378	−	23.2378i	−1.35757	−	1.35757i	−0.480665	−	0.876904i	$-0.659605\pi$
$294$	2.03569	+	7.46212i	0.118724	+	0.435200i
$295$	−12.4188	+	26.0802i	−0.723049	+	1.51845i
$296$		−	2.63901i		−	0.153389i
$297$	16.5508	−	0.224580i	0.960374	−	0.0130314i
$298$	4.14927	+	15.4853i	0.240361	+	0.897039i
$299$	13.8675	+	24.0192i	0.801979	+	1.38907i
$300$	−2.72265	+	7.21816i	−0.157192	+	0.416740i
$301$	8.97624	+	15.5473i	0.517382	+	0.896132i
$302$	7.54257	+	2.02103i	0.434026	+	0.116297i
$303$	−1.16015	+	0.00524714i	−0.0666491	+	0.000301440i
$304$	−3.20171	−	5.32201i	−0.183631	−	0.305238i
$305$	23.4601	−	1.86173i	1.34332	−	0.106602i
$306$	−11.0382	+	6.50675i	−0.631013	+	0.371966i
$307$	2.61109	−	9.74473i	0.149023	−	0.556161i	−0.850520	−	0.525942i	$-0.823713\pi$
$307$	2.61109	−	9.74473i	0.149023	−	0.556161i	0.999543	−	0.0302191i	$-0.00962052\pi$
$308$	−4.55346	+	1.22010i	−0.259458	+	0.0695215i
$309$	−1.57248	+	5.97657i	−0.0894554	+	0.339995i
$310$	2.89843	+	8.16800i	0.164620	+	0.463911i
$311$			25.9114i			1.46930i	0.678445	+	0.734652i	$0.262654\pi$
$311$			25.9114i			1.46930i	−0.678445	+	0.734652i	$0.737346\pi$
$312$	−0.106800	−	23.6138i	−0.00604638	−	1.33687i
$313$	−8.19581	−	30.5872i	−0.463254	−	1.72889i	−0.662613	−	0.748962i	$-0.730552\pi$
$313$	−8.19581	−	30.5872i	−0.463254	−	1.72889i	0.199358	−	0.979927i	$-0.436114\pi$
$314$	7.25070	−	12.5586i	0.409181	−	0.708722i
$315$	−8.54386	−	7.15503i	−0.481392	−	0.403140i
$316$	−13.6453			−0.767606
$317$	−0.617775	−	2.30557i	−0.0346977	−	0.129494i	0.946405	−	0.322984i	$-0.104686\pi$
$317$	−0.617775	−	2.30557i	−0.0346977	−	0.129494i	−0.981102	+	0.193490i	$0.938019\pi$
$318$	0.0923152	−	0.0538564i	0.00517678	−	0.00302012i
$319$	−5.60540	−	3.23628i	−0.313842	−	0.181197i
$320$	14.1505	−	9.73893i	0.791035	−	0.544423i
$321$	−6.76564	+	25.7144i	−0.377621	+	1.43524i
$322$	−7.66253	−	7.66253i	−0.427016	−	0.427016i
$323$	−17.1543	−	4.26718i	−0.954493	−	0.237432i
$324$	0.145032	+	8.01590i	0.00805734	+	0.445328i
$325$	22.2705	+	2.31139i	1.23534	+	0.128213i
$326$	0.691570	−	0.399278i	0.0383025	−	0.0221140i
$327$	−3.58775	+	6.27959i	−0.198403	+	0.347262i
$328$	−16.3912	−	4.39201i	−0.905054	−	0.242508i
$329$	0.931161	−	1.61282i	0.0513366	−	0.0889176i
$330$	8.38738	−	9.92388i	0.461710	−	0.546292i
$331$	6.06581			0.333407			0.166704	−	0.986007i	$-0.446688\pi$
$331$	6.06581			0.333407			0.166704	+	0.986007i	$0.446688\pi$
$332$	−2.06342	−	7.70080i	−0.113245	−	0.422636i
$333$	2.50560	−	0.695724i	0.137306	−	0.0381254i
$334$			23.2292i			1.27105i
$335$	−14.4631	−	12.3364i	−0.790203	−	0.674007i
$336$	1.07904	+	3.95538i	0.0588664	+	0.215784i
$337$	4.36353	−	16.2849i	0.237696	−	0.887095i	−0.739218	−	0.673466i	$-0.764805\pi$
$337$	4.36353	−	16.2849i	0.237696	−	0.887095i	0.976915	−	0.213629i	$-0.0685284\pi$
$338$	−7.17470	+	1.92245i	−0.390252	+	0.104568i
$339$	−15.7671	−	4.14845i	−0.856352	−	0.225313i
$340$	1.46691	−	7.94363i	0.0795545	−	0.430804i
$341$			11.7235i			0.634862i
$342$	9.47154	−	9.99814i	0.512162	−	0.540638i
$343$	13.2038	−	13.2038i	0.712938	−	0.712938i
$344$	−16.4504	−	28.4930i	−0.886947	−	1.53624i
$345$	−23.6083	−	4.24931i	−1.27103	−	0.228775i
$346$	−1.77420	+	3.07301i	−0.0953817	+	0.165206i
$347$	−25.7532	−	6.90054i	−1.38250	−	0.370440i	−0.510473	−	0.859894i	$-0.670530\pi$
$347$	−25.7532	−	6.90054i	−1.38250	−	0.370440i	−0.872029	+	0.489454i	$0.837196\pi$
$348$	1.55522	−	2.72207i	0.0833684	−	0.145918i
$349$		−	2.13852i		−	0.114473i	−0.998361	−	0.0572363i	$-0.981771\pi$
$349$		−	2.13852i		−	0.114473i	0.998361	−	0.0572363i	$-0.0182288\pi$
$350$	−8.63863	+	1.37976i	−0.461754	+	0.0737515i
$351$	22.3919	−	6.32672i	1.19519	−	0.337695i
$352$	14.1184	−	3.78302i	0.752514	−	0.201636i
$353$	−0.491067	−	0.491067i	−0.0261369	−	0.0261369i	0.693918	−	0.720054i	$-0.255883\pi$
$353$	−0.491067	−	0.491067i	−0.0261369	−	0.0261369i	−0.720054	+	0.693918i	$0.755883\pi$
$354$	16.7382	+	16.5875i	0.889625	+	0.881614i
$355$	−5.57766	−	2.65595i	−0.296031	−	0.140963i
$356$	−2.20507	+	1.27310i	−0.116868	+	0.0674739i
$357$	10.1320	+	5.78876i	0.536241	+	0.306374i
$358$	2.64861	+	0.709693i	0.139983	+	0.0375084i
$359$	8.37493	+	14.5058i	0.442012	+	0.765588i	0.997839	−	0.0657108i	$-0.0209315\pi$
$359$	8.37493	+	14.5058i	0.442012	+	0.765588i	−0.555827	+	0.831298i	$0.687598\pi$
$360$	15.6580	+	13.1128i	0.825249	+	0.691103i
$361$	18.9877	−	0.683684i	0.999352	−	0.0359833i
$362$	13.1233	−	13.1233i	0.689744	−	0.689744i
$363$	−1.27560	+	0.744181i	−0.0669517	+	0.0390594i
$364$	−5.73903	+	3.31343i	−0.300807	+	0.173671i
$365$	10.5340	+	29.6856i	0.551374	+	1.55382i
$366$	4.88509	−	18.5669i	0.255348	−	0.970507i
$367$	9.96637	−	2.67048i	0.520240	−	0.139398i	0.0108625	−	0.999941i	$-0.496542\pi$
$367$	9.96637	−	2.67048i	0.520240	−	0.139398i	0.509378	+	0.860543i	$0.329876\pi$
$368$	6.24025	+	6.24025i	0.325295	+	0.325295i
$369$	−0.151250	−	16.7205i	−0.00787374	−	0.870432i
$370$	0.877603	−	1.84302i	0.0456244	−	0.0958141i
$371$	−0.0842924	−	0.0486663i	−0.00437624	−	0.00252663i
$372$	−5.67828	+	0.0256817i	−0.294405	+	0.00133154i
$373$	−12.0320	+	12.0320i	−0.622994	+	0.622994i	−0.946296	−	0.323302i	$-0.895207\pi$
$373$	−12.0320	+	12.0320i	−0.622994	+	0.622994i	0.323302	+	0.946296i	$0.395207\pi$
$374$	−6.80277	+	11.7827i	−0.351763	+	0.609271i
$375$	−13.9602	+	13.4206i	−0.720901	+	0.693038i
$376$	−1.70650	+	2.95575i	−0.0880062	+	0.152431i
$377$	−8.78879	−	2.35495i	−0.452646	−	0.121286i
$378$	−7.81091	+	4.65206i	−0.401750	+	0.239276i
$379$			22.9049i			1.17655i	0.808662	+	0.588273i	$0.200192\pi$
$379$			22.9049i			1.17655i	−0.808662	+	0.588273i	$0.799808\pi$
$380$	0.842493	+	8.64149i	0.0432190	+	0.443299i
$381$	9.77275	−	9.86155i	0.500673	−	0.505222i
$382$	3.05814	−	11.4131i	0.156468	−	0.583946i
$383$	4.23700	−	15.8127i	0.216500	−	0.807991i	−0.769132	−	0.639089i	$-0.779311\pi$
$383$	4.23700	−	15.8127i	0.216500	−	0.807991i	0.985633	−	0.168901i	$-0.0540219\pi$
$384$	0.495098	+	1.81486i	0.0252654	+	0.0926141i
$385$	−11.6364	−	2.14885i	−0.593048	−	0.109515i
$386$	−16.6508	−	9.61336i	−0.847504	−	0.489307i
$387$	22.7157	−	23.1304i	1.15470	−	1.17578i
$388$	1.39753	−	1.39753i	0.0709490	−	0.0709490i
$389$	11.8638	−	20.5487i	0.601519	−	1.04186i	−0.391073	−	0.920360i	$-0.627896\pi$
$389$	11.8638	−	20.5487i	0.601519	−	1.04186i	0.992591	−	0.121501i	$-0.0387708\pi$
$390$	7.77818	−	16.5268i	0.393864	−	0.836869i
$391$	25.1175			1.27025
$392$	−9.12835	+	9.12835i	−0.461051	+	0.461051i
$393$	5.94594	−	10.4071i	0.299933	−	0.524968i
$394$	−12.0163	+	6.93764i	−0.605374	+	0.349513i
$395$	−30.9249	−	14.7257i	−1.55600	−	0.740931i
$396$	4.32298	+	7.33361i	0.217238	+	0.368528i
$397$	7.43185	−	27.7361i	0.372994	−	1.39203i	−0.483260	−	0.875477i	$-0.660547\pi$
$397$	7.43185	−	27.7361i	0.372994	−	1.39203i	0.856254	−	0.516556i	$-0.172786\pi$
$398$	−14.7816	−	14.7816i	−0.740932	−	0.740932i
$399$	−12.1850	−	2.97258i	−0.610012	−	0.148815i
$400$	7.03517	−	1.12366i	0.351759	−	0.0561830i
$401$	22.8392	−	13.1862i	1.14053	−	0.658488i	0.193971	−	0.981007i	$-0.437863\pi$
$401$	22.8392	−	13.1862i	1.14053	−	0.658488i	0.946563	+	0.322520i	$0.104530\pi$
$402$	−13.3951	+	7.81463i	−0.668085	+	0.389758i
$403$	4.26543	+	15.9188i	0.212476	+	0.792971i
$404$	−0.298339	−	0.516739i	−0.0148429	−	0.0257087i
$405$	−8.32192	+	18.3234i	−0.413520	+	0.910495i
$406$	3.55504			0.176433
$407$	1.95245	−	1.95245i	0.0967792	−	0.0967792i
$408$	−18.5685	−	10.6088i	−0.919278	−	0.525216i
$409$	4.19713	+	2.42322i	0.207535	+	0.119820i	0.600165	−	0.799876i	$-0.295101\pi$
$409$	4.19713	+	2.42322i	0.207535	+	0.119820i	−0.392630	+	0.919696i	$0.628435\pi$
$410$	−9.98668	−	8.51819i	−0.493207	−	0.420683i
$411$	7.29221	+	7.22655i	0.359698	+	0.356459i
$412$	−3.07009	+	0.822628i	−0.151253	+	0.0405280i
$413$	5.55443	−	20.7294i	0.273316	−	1.02003i
$414$	−9.63079	+	17.0350i	−0.473327	+	0.837226i
$415$	3.63413	−	19.6795i	0.178392	−	0.966030i
$416$	17.7944	−	10.2736i	0.872441	−	0.503704i
$417$	13.2577	−	0.0599618i	0.649231	−	0.00293634i
$418$	3.53010	−	14.1913i	0.172663	−	0.694117i
$419$	−11.3217			−0.553104			−0.276552	−	0.960999i	$-0.589192\pi$
$419$	−11.3217			−0.553104			−0.276552	+	0.960999i	$0.589192\pi$
$420$	1.01531	−	5.64084i	0.0495419	−	0.275245i
$421$	−7.22437	−	12.5130i	−0.352094	−	0.609845i	0.634522	−	0.772905i	$-0.281197\pi$
$421$	−7.22437	−	12.5130i	−0.352094	−	0.609845i	−0.986616	+	0.163060i	$0.947864\pi$
$422$	−4.58578	−	17.1143i	−0.223232	−	0.833113i
$423$	−3.25622	−	0.841007i	−0.158323	−	0.0408912i
$424$	0.154480	+	0.0891888i	0.00750219	+	0.00433139i
$425$	11.8972	−	16.4200i	0.577097	−	0.796486i
$426$	−3.54749	+	3.57972i	−0.171876	+	0.173438i
$427$	−16.8886	+	4.52528i	−0.817295	+	0.218993i
$428$	−13.2091	+	3.53938i	−0.638488	+	0.171082i
$429$	17.3914	−	17.5495i	0.839667	−	0.847296i
$430$	−2.01325	−	25.3694i	−0.0970873	−	1.22342i
$431$	−3.58543	−	2.07005i	−0.172704	−	0.0997107i	0.411156	−	0.911565i	$-0.365125\pi$
$431$	−3.58543	−	2.07005i	−0.172704	−	0.0997107i	−0.583860	+	0.811854i	$0.698458\pi$
$432$	6.36109	−	3.78857i	0.306048	−	0.182278i
$433$	−6.32636	−	23.6103i	−0.304026	−	1.13464i	−0.933781	−	0.357845i	$-0.883511\pi$
$433$	−6.32636	−	23.6103i	−0.304026	−	1.13464i	0.629755	−	0.776794i	$-0.283155\pi$
$434$	−3.21955	−	5.57642i	−0.154543	−	0.267677i
$435$	6.46227	−	4.49081i	0.309842	−	0.215318i
$436$	−3.71957			−0.178135
$437$	−25.9473	+	7.45551i	−1.24123	+	0.356645i
$438$	25.6966	−	0.116220i	1.22783	−	0.00555322i
$439$	−2.20262	+	1.27168i	−0.105125	+	0.0606941i	−0.551641	−	0.834082i	$-0.685998\pi$
$439$	−2.20262	+	1.27168i	−0.105125	+	0.0606941i	0.446516	+	0.894776i	$0.352665\pi$
$440$	21.3257	+	3.93811i	1.01666	+	0.187742i
$441$	−11.0734	−	6.26036i	−0.527304	−	0.298112i
$442$	−4.95019	+	18.4744i	−0.235456	+	0.878735i
$443$	3.64821	−	0.977535i	0.173332	−	0.0464441i	−0.171109	−	0.985252i	$-0.554735\pi$
$443$	3.64821	−	0.977535i	0.173332	−	0.0464441i	0.344441	+	0.938808i	$0.388068\pi$
$444$	0.949948	+	0.941394i	0.0450825	+	0.0446766i
$445$	−6.37135	+	0.505613i	−0.302031	+	0.0239683i
$446$	−14.3499	−	8.28491i	−0.679486	−	0.392302i
$447$	−22.8924	−	13.0792i	−1.08277	−	0.618626i
$448$	−9.02427	+	9.02427i	−0.426357	+	0.426357i
$449$	−3.32977			−0.157141			−0.0785707	−	0.996909i	$-0.525036\pi$
$449$	−3.32977			−0.157141			−0.0785707	+	0.996909i	$0.525036\pi$
$450$	6.57453	+	14.3647i	0.309927	+	0.677159i
$451$	−8.87751	−	15.3763i	−0.418026	−	0.724042i
$452$	−2.17022	−	8.09937i	−0.102079	−	0.380962i
$453$	−11.0923	+	6.47122i	−0.521163	+	0.304044i
$454$	13.3673	−	7.71764i	0.627360	−	0.362207i
$455$	−16.5824	+	1.31594i	−0.777397	+	0.0616921i
$456$	22.3309	+	5.44774i	1.04574	+	0.255114i
$457$	8.69902	+	8.69902i	0.406923	+	0.406923i	0.880664	−	0.473741i	$-0.157097\pi$
$457$	8.69902	+	8.69902i	0.406923	+	0.406923i	−0.473741	+	0.880664i	$0.657097\pi$
$458$	−5.62844	+	21.0056i	−0.263000	+	0.981528i
$459$	5.17730	−	20.4266i	0.241656	−	0.953432i
$460$	−4.12574	−	11.6266i	−0.192363	−	0.542095i
$461$	−12.1158	+	6.99508i	−0.564291	+	0.325794i	−0.754866	−	0.655879i	$-0.772298\pi$
$461$	−12.1158	+	6.99508i	−0.564291	+	0.325794i	0.190575	+	0.981673i	$0.438965\pi$
$462$	−4.78886	+	8.38187i	−0.222798	+	0.389960i
$463$	4.98382	−	4.98382i	0.231618	−	0.231618i	−0.581750	−	0.813368i	$-0.697632\pi$
$463$	4.98382	−	4.98382i	0.231618	−	0.231618i	0.813368	+	0.581750i	$0.197632\pi$
$464$	−2.89517			−0.134405
$465$	−12.8967	−	6.06970i	−0.598070	−	0.281475i
$466$	2.81730	−	4.87971i	0.130509	−	0.226048i
$467$	21.1184	−	21.1184i	0.977244	−	0.977244i	−0.0225025	−	0.999747i	$-0.507163\pi$
$467$	21.1184	−	21.1184i	0.977244	−	0.977244i	0.999747	+	0.0225025i	$0.00716336\pi$
$468$	8.53821	+	8.38513i	0.394679	+	0.387603i
$469$	12.2309	+	7.06154i	0.564772	+	0.326071i
$470$	−2.17472	+	1.49673i	−0.100312	+	0.0690390i
$471$	6.27664	+	23.0080i	0.289212	+	1.06015i
$472$	−10.1794	+	37.9900i	−0.468545	+	1.74863i
$473$	8.90957	−	33.2510i	0.409663	−	1.52888i
$474$	−19.6688	+	19.8475i	−0.903418	+	0.911627i
$475$	−7.41635	+	20.4938i	−0.340286	+	0.940322i
$476$			6.00145i			0.275076i
$477$	−0.0439544	+	0.170183i	−0.00201253	+	0.00779214i
$478$	6.89073	+	1.84637i	0.315175	+	0.0844508i
$479$	−20.4388	+	35.4011i	−0.933875	+	1.61752i	−0.157246	+	0.987559i	$0.550262\pi$
$479$	−20.4388	+	35.4011i	−0.933875	+	1.61752i	−0.776629	+	0.629959i	$0.783072\pi$
$480$	−3.14805	+	17.4899i	−0.143688	+	0.798302i
$481$	1.94077	−	3.36151i	0.0884915	−	0.153272i
$482$	−9.84663	+	9.84663i	−0.448502	+	0.448502i
$483$	17.8213	−	0.0806020i	0.810896	−	0.00366752i
$484$	−0.657772	−	0.379765i	−0.0298987	−	0.0172620i
$485$	4.67549	−	1.65911i	0.212303	−	0.0753362i
$486$	11.8685	+	11.3435i	0.538365	+	0.514550i
$487$	20.5453	+	20.5453i	0.930997	+	0.930997i	0.997768	−	0.0667713i	$-0.0212698\pi$
$487$	20.5453	+	20.5453i	0.930997	+	0.930997i	−0.0667713	+	0.997768i	$0.521270\pi$
$488$	30.9510	−	8.29330i	1.40109	−	0.375420i
$489$	−0.334164	+	1.27007i	−0.0151114	+	0.0574344i
$490$	−9.41066	+	3.33939i	−0.425130	+	0.150858i
$491$	3.26707	−	1.88624i	0.147441	−	0.0851249i	−0.424465	−	0.905444i	$-0.639538\pi$
$491$	3.26707	−	1.88624i	0.147441	−	0.0851249i	0.571905	+	0.820320i	$0.306204\pi$
$492$	7.42809	−	4.33352i	0.334884	−	0.195370i
$493$	−5.82664	+	5.82664i	−0.262419	+	0.262419i
$494$	−0.369922	−	20.5541i	−0.0166436	−	0.924770i
$495$	1.88308	+	21.2858i	0.0846382	+	0.956726i
$496$	2.62195	+	4.54135i	0.117729	+	0.203913i
$497$	4.43331	+	1.18790i	0.198861	+	0.0532846i
$498$	−14.1754	−	8.09891i	−0.635214	−	0.362921i
$499$	11.0440	−	6.37628i	0.494399	−	0.285442i	−0.231998	−	0.972716i	$-0.574526\pi$
$499$	11.0440	−	6.37628i	0.494399	−	0.285442i	0.726398	+	0.687275i	$0.241193\pi$
$500$	−9.55484	−	2.80997i	−0.427306	−	0.125666i
$501$	−27.1351	−	26.8907i	−1.21231	−	1.20139i
$502$	15.9825	+	15.9825i	0.713335	+	0.713335i
$503$	−18.8401	+	5.04819i	−0.840038	+	0.225088i	−0.653088	−	0.757282i	$-0.726527\pi$
$503$	−18.8401	+	5.04819i	−0.840038	+	0.225088i	−0.186950	+	0.982369i	$0.559860\pi$
$504$	−13.2087	−	7.46756i	−0.588362	−	0.332631i
$505$	−0.118486	−	1.49307i	−0.00527257	−	0.0664409i
$506$			20.7789i			0.923736i
$507$	6.05991	−	10.6066i	0.269130	−	0.471054i
$508$	6.89714	+	1.84808i	0.306011	+	0.0819954i
$509$	13.1468	−	22.7709i	0.582722	−	1.00930i	−0.412434	−	0.910988i	$-0.635321\pi$
$509$	13.1468	−	22.7709i	0.582722	−	1.00930i	0.995155	−	0.0983159i	$-0.0313456\pi$
$510$	−9.43983	−	13.5839i	−0.418003	−	0.601506i
$511$	−11.7011	−	20.2668i	−0.517624	−	0.896551i
$512$	10.7580	−	10.7580i	0.475440	−	0.475440i
$513$	0.714787	+	22.6382i	0.0315586	+	0.999502i
$514$			14.3845i			0.634472i
$515$	−7.84567	−	1.44882i	−0.345721	−	0.0638427i
$516$	16.1247	+	4.24252i	0.709849	+	0.186767i
$517$	−3.44933	+	0.924246i	−0.151701	+	0.0406483i
$518$	−0.392517	+	1.46489i	−0.0172462	+	0.0643638i
$519$	−1.53585	−	5.62991i	−0.0674165	−	0.247126i
$520$	30.3900	−	2.41167i	1.33269	−	0.105759i
$521$			24.4146i			1.06962i	0.844972	+	0.534810i	$0.179617\pi$
$521$			24.4146i			1.06962i	−0.844972	+	0.534810i	$0.820383\pi$
$522$	−1.71760	−	6.18582i	−0.0751774	−	0.270746i
$523$	9.26653	+	34.5832i	0.405197	+	1.51222i	0.803692	+	0.595046i	$0.202866\pi$
$523$	9.26653	+	34.5832i	0.405197	+	1.51222i	−0.398494	+	0.917171i	$0.630467\pi$
$524$	6.16440			0.269293
$525$	8.38853	−	11.6884i	0.366106	−	0.510124i
$526$	−8.85061	+	15.3297i	−0.385905	+	0.668407i
$527$	14.4164	+	3.86287i	0.627990	+	0.168269i
$528$	3.89998	−	6.82607i	0.169725	−	0.297067i
$529$	13.3026	−	7.68025i	0.578373	−	0.333924i
$530$	0.0782252	+	0.113660i	0.00339788	+	0.00493706i
$531$	−38.7531	+	0.350552i	−1.68174	+	0.0152127i
$532$	−1.78138	−	6.19972i	−0.0772327	−	0.268792i
$533$	−17.6488	−	17.6488i	−0.764456	−	0.764456i
$534$	−1.32670	+	5.04243i	−0.0574120	+	0.218208i
$535$	−33.7562	−	6.23360i	−1.45941	−	0.269502i
$536$	−22.4152	−	12.9414i	−0.968189	−	0.558984i
$537$	−3.89512	+	2.27240i	−0.168087	+	0.0980613i
$538$	−2.21945	−	8.28310i	−0.0956872	−	0.357110i
$539$	−13.5071			−0.581790
$540$	−10.3057	+	0.958702i	−0.443486	+	0.0412560i
$541$	−13.8903	+	24.0587i	−0.597191	+	1.03436i	0.396043	+	0.918232i	$0.370383\pi$
$541$	−13.8903	+	24.0587i	−0.597191	+	1.03436i	−0.993234	+	0.116133i	$0.962950\pi$
$542$	7.25484	+	27.0754i	0.311622	+	1.16299i
$543$	0.138043	+	30.5217i	0.00592401	+	1.30981i
$544$		−	18.6080i		−	0.797812i
$545$	−8.42985	−	4.01409i	−0.361095	−	0.171945i
$546$	−3.45295	+	13.1237i	−0.147773	+	0.561644i
$547$	23.6364	−	6.33336i	1.01062	−	0.270795i	0.284732	−	0.958607i	$-0.408095\pi$
$547$	23.6364	−	6.33336i	1.01062	−	0.270795i	0.725889	+	0.687812i	$0.241429\pi$
$548$	−1.36658	+	5.10015i	−0.0583775	+	0.217868i
$549$	16.0337	+	27.2000i	0.684301	+	1.16087i
$550$	13.5837	+	9.84215i	0.579213	+	0.419671i
$551$	4.28965	−	7.74864i	0.182745	−	0.330103i
$552$	−32.6604	+	0.147716i	−1.39012	+	0.00628722i
$553$	24.5802	+	6.58624i	1.04525	+	0.280075i
$554$	8.32682	+	14.4225i	0.353773	+	0.612752i
$555$	1.13698	+	3.15869i	0.0482621	+	0.134079i
$556$	3.40928	+	5.90504i	0.144586	+	0.250430i
$557$	−3.37300	−	12.5882i	−0.142918	−	0.533379i	−0.999839	−	0.0179309i	$-0.994292\pi$
$557$	−3.37300	−	12.5882i	−0.142918	−	0.533379i	0.856921	−	0.515448i	$-0.172375\pi$
$558$	−8.14754	+	8.29629i	−0.344913	+	0.351210i
$559$		−	48.3916i		−	2.04675i
$560$	−4.98823	+	1.77008i	−0.210791	+	0.0747996i
$561$	−5.88888	−	21.5866i	−0.248629	−	0.911387i
$562$	−9.45529	−	9.45529i	−0.398847	−	0.398847i
$563$	18.7080	+	18.7080i	0.788447	+	0.788447i	0.981239	−	0.192793i	$-0.0617546\pi$
$563$	18.7080	+	18.7080i	0.788447	+	0.788447i	−0.192793	+	0.981239i	$0.561755\pi$
$564$	−0.455216	−	1.66866i	−0.0191680	−	0.0702634i
$565$	3.82221	−	20.6981i	0.160802	−	0.870774i
$566$	1.77830	+	1.02670i	0.0747473	+	0.0431554i
$567$	3.60783	−	14.5096i	0.151514	−	0.609347i
$568$	−8.12475	−	2.17702i	−0.340907	−	0.0913458i
$569$	6.29706			0.263986			0.131993	−	0.991251i	$-0.457862\pi$
$569$	6.29706			0.263986			0.131993	+	0.991251i	$0.457862\pi$
$570$	13.7838	+	11.2307i	0.577338	+	0.470404i
$571$	32.2657			1.35028			0.675138	−	0.737691i	$-0.264084\pi$
$571$	32.2657			1.35028			0.675138	+	0.737691i	$0.264084\pi$
$572$	12.2741	+	3.28882i	0.513204	+	0.137513i
$573$	9.79199	+	16.7845i	0.409066	+	0.701181i
$574$	8.44540	+	4.87595i	0.352504	+	0.203518i
$575$	3.19690	−	30.8025i	0.133320	−	1.28455i
$576$	20.0624	+	11.3423i	0.835934	+	0.472597i
$577$	−28.6204	−	28.6204i	−1.19148	−	1.19148i	−0.976650	−	0.214834i	$-0.931079\pi$
$577$	−28.6204	−	28.6204i	−1.19148	−	1.19148i	−0.214834	−	0.976650i	$-0.568921\pi$
$578$	−0.412329	−	0.412329i	−0.0171506	−	0.0171506i
$579$	30.5052	−	8.32190i	1.26775	−	0.345846i
$580$	3.65417	+	1.74003i	0.151731	+	0.0722507i
$581$			14.8680i			0.616827i
$582$	−0.0183048	−	4.04722i	−0.000758757	−	0.167763i
$583$	0.0483048	+	0.180276i	0.00200058	+	0.00746627i
$584$	21.4441	+	37.1422i	0.887362	+	1.53696i
$585$	10.3015	+	28.2179i	0.425915	+	1.16667i
$586$	−17.3056	−	29.9741i	−0.714886	−	1.23822i
$587$	−14.0613	−	3.76770i	−0.580371	−	0.155510i	−0.0433220	−	0.999061i	$-0.513794\pi$
$587$	−14.0613	−	3.76770i	−0.580371	−	0.155510i	−0.537049	+	0.843551i	$0.680461\pi$
$588$	−0.0295889	−	6.54217i	−0.00122023	−	0.269794i
$589$	−16.0393	+	0.288668i	−0.660889	+	0.0118944i
$590$	−19.7426	+	23.1462i	−0.812792	+	0.952913i
$591$	5.80626	−	22.0680i	0.238837	−	0.907756i
$592$	0.319660	−	1.19299i	0.0131380	−	0.0490315i
$593$	27.8162	−	7.45333i	1.14228	−	0.306072i	0.362410	−	0.932019i	$-0.381954\pi$
$593$	27.8162	−	7.45333i	1.14228	−	0.306072i	0.779865	+	0.625947i	$0.215287\pi$
$594$	16.8983	+	4.28302i	0.693346	+	0.175734i
$595$	−6.47665	+	13.6014i	−0.265517	+	0.557602i
$596$		−	13.5598i		−	0.555430i
$597$	34.3785	−	0.155487i	1.40702	−	0.00636365i
$598$	7.56013	+	28.2148i	0.309157	+	1.15379i
$599$	−8.34533	+	14.4545i	−0.340981	+	0.590596i	−0.984615	−	0.174737i	$-0.944092\pi$
$599$	−8.34533	+	14.4545i	−0.340981	+	0.590596i	0.643634	+	0.765333i	$0.277426\pi$
$600$	−15.3733	+	21.4209i	−0.627614	+	0.874505i
$601$	6.40147			0.261122			0.130561	−	0.991440i	$-0.458322\pi$
$601$	6.40147			0.261122			0.130561	+	0.991440i	$0.458322\pi$
$602$	4.89356	+	18.2630i	0.199447	+	0.744345i
$603$	6.37784	−	24.6938i	0.259726	−	1.00561i
$604$	−5.71983	−	3.30234i	−0.232736	−	0.134370i
$605$	−1.08091	−	1.57054i	−0.0439451	−	0.0638513i
$606$	−1.18165	−	0.310902i	−0.0480014	−	0.0126295i
$607$	−20.1985	−	20.1985i	−0.819832	−	0.819832i	0.166252	−	0.986083i	$-0.446834\pi$
$607$	−20.1985	−	20.1985i	−0.819832	−	0.819832i	−0.986083	+	0.166252i	$0.946834\pi$
$608$	5.52333	+	19.2228i	0.224001	+	0.779587i
$609$	−4.11540	+	4.15279i	−0.166764	+	0.168280i
$610$	24.3734	+	4.50093i	0.986851	+	0.182237i
$611$	−4.34742	+	2.50998i	−0.175878	+	0.101543i
$612$	10.4426	−	2.89958i	0.422117	−	0.117208i
$613$	−0.542741	−	0.145427i	−0.0219211	−	0.00587374i	0.247842	−	0.968801i	$-0.420279\pi$
$613$	−0.542741	−	0.145427i	−0.0219211	−	0.00587374i	−0.269763	+	0.962927i	$0.586945\pi$
$614$	5.31252	−	9.20156i	0.214396	−	0.371345i
$615$	21.5113	−	1.80502i	0.867419	−	0.0727853i
$616$	−16.1116			−0.649157
$617$	11.5449	+	43.0860i	0.464778	+	1.73458i	0.657623	+	0.753347i	$0.271562\pi$
$617$	11.5449	+	43.0860i	0.464778	+	1.73458i	−0.192845	+	0.981229i	$0.561771\pi$
$618$	−3.22880	+	5.65133i	−0.129882	+	0.227330i
$619$			8.36631i			0.336270i	0.985764	+	0.168135i	$0.0537745\pi$
$619$			8.36631i			0.336270i	−0.985764	+	0.168135i	$0.946226\pi$
$620$	−0.579921	−	7.30773i	−0.0232902	−	0.293486i
$621$	−8.75053	−	30.9703i	−0.351147	−	1.24280i
$622$	−7.06305	+	26.3597i	−0.283203	+	1.05693i
$623$	4.58663	−	1.22898i	0.183760	−	0.0492382i
$624$	2.81203	−	10.6878i	0.112571	−	0.427853i
$625$	−18.6221	−	16.6798i	−0.744886	−	0.667192i
$626$		−	33.3503i		−	1.33295i
$627$	12.4909	+	20.5518i	0.498838	+	0.820761i
$628$	−8.67305	+	8.67305i	−0.346092	+	0.346092i
$629$	−1.75761	−	3.04427i	−0.0700804	−	0.121383i
$630$	−6.74130	−	9.60772i	−0.268580	−	0.382781i
$631$	−7.99072	+	13.8403i	−0.318106	+	0.550975i	−0.980093	−	0.198540i	$-0.936380\pi$
$631$	−7.99072	+	13.8403i	−0.318106	+	0.550975i	0.661987	+	0.749515i	$0.269713\pi$
$632$	−45.0471	−	12.0703i	−1.79188	−	0.480133i
$633$	25.3006	+	14.4552i	1.00561	+	0.574541i
$634$		−	2.51385i		−	0.0998376i
$635$	13.6369	+	11.6317i	0.541165	+	0.461589i
$636$	−0.0872111	+	0.0237914i	−0.00345815	+	0.000943391i
$637$	−18.3406	+	4.91436i	−0.726683	+	0.194714i
$638$	−4.82020	−	4.82020i	−0.190834	−	0.190834i
$639$	−0.0749709	−	8.28795i	−0.00296580	−	0.327866i
$640$	−2.28876	+	0.812171i	−0.0904712	+	0.0321039i
$641$	0.126211	−	0.0728677i	0.00498502	−	0.00287810i	−0.497505	−	0.867461i	$-0.665751\pi$
$641$	0.126211	−	0.0728677i	0.00498502	−	0.00287810i	0.502490	+	0.864583i	$0.332417\pi$
$642$	−13.8920	+	24.3150i	−0.548274	+	0.959635i
$643$	4.92252	+	1.31899i	0.194125	+	0.0520157i	0.354572	−	0.935029i	$-0.384627\pi$
$643$	4.92252	+	1.31899i	0.194125	+	0.0520157i	−0.160446	+	0.987045i	$0.551293\pi$
$644$	4.58283	+	7.93769i	0.180589	+	0.312789i
$645$	31.9657	+	27.0165i	1.25865	+	1.06377i
$646$	−16.2879	−	9.01700i	−0.640839	−	0.354769i
$647$	−9.22011	+	9.22011i	−0.362480	+	0.362480i	−0.864725	−	0.502245i	$-0.832507\pi$
$647$	−9.22011	+	9.22011i	−0.362480	+	0.362480i	0.502245	+	0.864725i	$0.332507\pi$
$648$	−6.61193	+	26.5912i	−0.259741	+	1.04460i
$649$	−35.6377	+	20.5755i	−1.39890	+	0.807657i
$650$	22.0257	+	8.42196i	0.863919	+	0.330336i
$651$	10.2411	+	2.69451i	0.401380	+	0.105606i
$652$	−0.652418	+	0.174815i	−0.0255506	+	0.00684627i
$653$	9.07320	+	9.07320i	0.355062	+	0.355062i	0.861989	−	0.506927i	$-0.169219\pi$
$653$	9.07320	+	9.07320i	0.355062	+	0.355062i	−0.506927	+	0.861989i	$0.669219\pi$
$654$	−5.36153	+	5.41025i	−0.209652	+	0.211557i
$655$	13.9707	+	6.65251i	0.545880	+	0.259935i
$656$	−6.87781	−	3.97090i	−0.268533	−	0.155038i
$657$	−29.6112	+	30.1518i	−1.15524	+	1.17634i
$658$	1.38690	−	1.38690i	0.0540669	−	0.0540669i
$659$	−0.558310	+	0.967021i	−0.0217487	+	0.0376698i	−0.876695	−	0.481047i	$-0.840257\pi$
$659$	−0.558310	+	0.967021i	−0.0217487	+	0.0376698i	0.854946	+	0.518717i	$0.173590\pi$
$660$	−9.02494	+	6.27167i	−0.351295	+	0.244124i
$661$	−18.0167	+	31.2058i	−0.700767	+	1.21376i	0.267430	+	0.963577i	$0.413825\pi$
$661$	−18.0167	+	31.2058i	−0.700767	+	1.21376i	−0.968198	+	0.250187i	$0.919508\pi$
$662$	6.17074	+	1.65345i	0.239833	+	0.0642630i
$663$	−15.8502	−	27.1689i	−0.615572	−	1.05515i
$664$		−	27.2480i		−	1.05743i
$665$	2.65340	−	15.9732i	0.102894	−	0.619413i
$666$	2.73858	−	0.0247726i	0.106118	−	0.000959919i
$667$	−3.25715	+	12.1558i	−0.126117	+	0.470676i
$668$	5.08519	−	18.9782i	0.196752	−	0.734288i
$669$	26.2897	−	7.17191i	1.01642	−	0.277282i
$670$	−11.3506	−	16.4922i	−0.438511	−	0.637148i
$671$	29.0346	+	16.7631i	1.12087	+	0.647133i
$672$	−0.0597131	−	13.2027i	−0.00230348	−	0.509305i
$673$	0.860357	−	0.860357i	0.0331643	−	0.0331643i	−0.690330	−	0.723494i	$-0.742535\pi$
$673$	0.860357	−	0.860357i	0.0331643	−	0.0331643i	0.723494	+	0.690330i	$0.242535\pi$
$674$	8.87801	−	15.3772i	0.341968	−	0.592307i
$675$	−24.3909	−	8.94895i	−0.938806	−	0.344445i
$676$	6.28256			0.241637
$677$	−25.8492	+	25.8492i	−0.993466	+	0.993466i	−0.999979	−	0.00651274i	$-0.997927\pi$
$677$	−25.8492	+	25.8492i	−0.993466	+	0.993466i	0.00651274	+	0.999979i	$0.497927\pi$
$678$	−14.9091	−	8.51808i	−0.572579	−	0.327135i
$679$	−3.19203	+	1.84292i	−0.122499	+	0.0707248i
$680$	11.8695	−	24.9267i	0.455175	−	0.955897i
$681$	−6.45906	+	24.5491i	−0.247512	+	0.940724i
$682$	−3.19564	+	11.9263i	−0.122367	+	0.456681i
$683$	21.6600	+	21.6600i	0.828796	+	0.828796i	0.987350	−	0.158554i	$-0.0506831\pi$
$683$	21.6600	+	21.6600i	0.828796	+	0.828796i	−0.158554	+	0.987350i	$0.550683\pi$
$684$	−9.92694	+	6.09500i	−0.379566	+	0.233048i
$685$	−8.60115	+	10.0839i	−0.328633	+	0.385288i
$686$	17.0313	−	9.83305i	0.650260	−	0.375428i
$687$	−18.0220	−	30.8914i	−0.687581	−	1.17858i
$688$	−3.98524	−	14.8731i	−0.151936	−	0.567033i
$689$	0.131182	+	0.227214i	0.00499763	+	0.00865615i
$690$	−22.8584	−	10.7581i	−0.870203	−	0.409552i
$691$	−31.5310			−1.19949			−0.599747	−	0.800190i	$-0.704732\pi$
$691$	−31.5310			−1.19949			−0.599747	+	0.800190i	$0.704732\pi$
$692$	2.12224	−	2.12224i	0.0806755	−	0.0806755i
$693$	−4.24753	−	15.2971i	−0.161350	−	0.581090i
$694$	−24.3177	−	14.0398i	−0.923086	−	0.532944i
$695$	1.35400	+	17.0621i	0.0513603	+	0.647203i
$696$	7.54214	−	7.61067i	0.285884	−	0.288482i
$697$	−21.8335	+	5.85026i	−0.827002	+	0.221594i
$698$	0.582928	−	2.17552i	0.0220642	−	0.0823445i
$699$	2.43883	+	8.93989i	0.0922449	+	0.338138i
$700$	7.35978	+	0.763851i	0.278174	+	0.0288708i
$701$	35.4512	−	20.4677i	1.33897	−	0.773056i	0.352317	−	0.935881i	$-0.385394\pi$
$701$	35.4512	−	20.4677i	1.33897	−	0.773056i	0.986655	+	0.162825i	$0.0520605\pi$
$702$	24.5038	−	0.332495i	0.924835	−	0.0125492i
$703$	2.71929	+	2.62314i	0.102560	+	0.0989337i
$704$	24.4717			0.922310
$705$	0.769113	−	4.27304i	0.0289665	−	0.160932i
$706$	−0.365705	−	0.633419i	−0.0137635	−	0.0238390i
$707$	0.288002	+	1.07484i	0.0108314	+	0.0404235i
$708$	−10.0438	−	17.2161i	−0.377470	−	0.647021i
$709$	−28.0586	−	16.1997i	−1.05376	−	0.608391i	−0.130064	−	0.991506i	$-0.541518\pi$
$709$	−28.0586	−	16.1997i	−1.05376	−	0.608391i	−0.923701	+	0.383115i	$0.874851\pi$
$710$	−4.95017	−	4.22227i	−0.185777	−	0.158459i
$711$	−0.415671	−	45.9520i	−0.0155889	−	1.72333i
$712$	−8.40575	+	2.25231i	−0.315019	+	0.0844090i
$713$	22.0174	−	5.89954i	0.824557	−	0.220939i
$714$	8.72932	+	8.65071i	0.326687	+	0.323745i
$715$	24.2681	+	20.6996i	0.907574	+	0.774119i
$716$	−2.00855	−	1.15963i	−0.0750629	−	0.0433376i
$717$	−10.1337	+	5.91197i	−0.378450	+	0.220787i
$718$	4.56575	+	17.0396i	0.170392	+	0.635913i
$719$	5.00582	+	8.67033i	0.186686	+	0.323349i	0.944143	−	0.329535i	$-0.106892\pi$
$719$	5.00582	+	8.67033i	0.186686	+	0.323349i	−0.757458	+	0.652884i	$0.773559\pi$
$720$	5.49001	+	7.82438i	0.204601	+	0.291598i
$721$	5.92743			0.220749
$722$	19.5025	+	4.48024i	0.725808	+	0.166737i
$723$	−0.103577	−	22.9010i	−0.00385205	−	0.851697i
$724$	−13.5945	+	7.84880i	−0.505237	+	0.291699i
$725$	6.40381	+	7.88702i	0.237832	+	0.292916i
$726$	−1.50052	+	0.409345i	−0.0556895	+	0.0151922i
$727$	−3.19003	+	11.9053i	−0.118311	+	0.441544i	−0.999513	−	0.0311958i	$-0.990068\pi$
$727$	−3.19003	+	11.9053i	−0.118311	+	0.441544i	0.881202	+	0.472740i	$0.156735\pi$
$728$	−21.8773	+	5.86200i	−0.810826	+	0.217260i
$729$	−26.9901	+	0.732598i	−0.999632	+	0.0271333i
$730$	2.62438	+	33.0705i	0.0971328	+	1.22399i
$731$	−37.9533	−	21.9123i	−1.40375	−	0.810457i
$732$	−8.05564	+	14.0997i	−0.297745	+	0.521139i
$733$	30.5495	−	30.5495i	1.12837	−	1.12837i	0.137929	−	0.990442i	$-0.455955\pi$
$733$	30.5495	−	30.5495i	1.12837	−	1.12837i	0.990442	−	0.137929i	$-0.0440446\pi$
$734$	10.8667			0.401097
$735$	6.99313	−	14.8588i	0.257945	−	0.548074i
$736$	−14.2095	−	24.6115i	−0.523768	−	0.907193i
$737$	−7.00909	−	26.1583i	−0.258183	−	0.963553i
$738$	4.40387	−	17.0509i	0.162109	−	0.627653i
$739$	−1.43662	+	0.829432i	−0.0528468	+	0.0305111i	−0.526191	−	0.850367i	$-0.676380\pi$
$739$	−1.43662	+	0.829432i	−0.0528468	+	0.0305111i	0.473344	+	0.880878i	$0.343047\pi$
$740$	−1.12046	+	1.31362i	−0.0411890	+	0.0482897i
$741$	24.4383	+	23.3618i	0.897764	+	0.858216i
$742$	−0.0724849	−	0.0724849i	−0.00266100	−	0.00266100i
$743$	−11.0355	+	41.1849i	−0.404852	+	1.51093i	0.399476	+	0.916744i	$0.369192\pi$
$743$	−11.0355	+	41.1849i	−0.404852	+	1.51093i	−0.804328	+	0.594185i	$0.797475\pi$
$744$	−18.7685	−	4.93812i	−0.688085	−	0.181040i
$745$	14.6334	−	30.7312i	0.536128	−	1.12590i
$746$	−15.5199	+	8.96041i	−0.568223	+	0.328064i
$747$	25.8705	−	7.18340i	0.946551	−	0.262827i
$748$	8.13724	−	8.13724i	0.297527	−	0.297527i
$749$	25.5029			0.931857
$750$	−17.8599	+	9.84746i	−0.652152	+	0.359578i
$751$	0.0163649	−	0.0283448i	0.000597164	−	0.00103432i	−0.865727	−	0.500517i	$-0.833143\pi$
$751$	0.0163649	−	0.0283448i	0.000597164	−	0.00103432i	0.866324	+	0.499483i	$0.166477\pi$
$752$	−1.12947	+	1.12947i	−0.0411875	+	0.0411875i
$753$	−37.1716	+	0.168120i	−1.35461	+	0.00612662i
$754$	−8.29890	−	4.79137i	−0.302228	−	0.174492i
$755$	−9.39930	−	13.6570i	−0.342076	−	0.497029i
$756$	7.39989	−	2.09081i	0.269131	−	0.0760419i
$757$	0.778037	−	2.90367i	0.0282782	−	0.105536i	−0.950344	−	0.311200i	$-0.899269\pi$
$757$	0.778037	−	2.90367i	0.0282782	−	0.105536i	0.978623	+	0.205665i	$0.0659356\pi$
$758$	−6.24352	+	23.3011i	−0.226775	+	0.846335i
$759$	−24.2728	−	24.0542i	−0.881046	−	0.873113i
$760$	−4.86278	+	29.2734i	−0.176392	+	1.06186i
$761$		−	43.0173i		−	1.55938i	−0.626169	−	0.779688i	$-0.715378\pi$
$761$		−	43.0173i		−	1.55938i	0.626169	−	0.779688i	$-0.284622\pi$
$762$	12.6299	−	7.36824i	0.457533	−	0.266923i
$763$	6.70032	+	1.79535i	0.242568	+	0.0649959i
$764$	−4.99697	+	8.65501i	−0.180784	+	0.313127i
$765$	26.7958	+	4.69801i	0.968803	+	0.169857i
$766$	8.62058	−	14.9313i	0.311474	−	0.539489i
$767$	−40.9048	+	40.9048i	−1.47699	+	1.47699i
$768$	0.129320	+	28.5929i	0.00466643	+	1.03176i
$769$	32.5777	+	18.8088i	1.17478	+	0.678261i	0.954802	−	0.297243i	$-0.0960671\pi$
$769$	32.5777	+	18.8088i	1.17478	+	0.678261i	0.219981	+	0.975504i	$0.429400\pi$
$770$	−11.2520	−	5.35793i	−0.405494	−	0.193087i
$771$	−16.8032	−	16.6518i	−0.605151	−	0.599701i
$772$	11.4992	+	11.4992i	0.413864	+	0.413864i
$773$	−17.1691	+	4.60045i	−0.617530	+	0.165467i	−0.554005	−	0.832513i	$-0.686901\pi$
$773$	−17.1691	+	4.60045i	−0.617530	+	0.165467i	−0.0635255	+	0.997980i	$0.520234\pi$
$774$	29.4136	−	17.3386i	1.05725	−	0.623223i
$775$	6.57207	−	17.1877i	0.236076	−	0.617401i
$776$	5.84992	−	3.37745i	0.210000	−	0.121243i
$777$	−1.25682	−	2.15432i	−0.0450882	−	0.0772857i
$778$	17.6703	−	17.6703i	0.633510	−	0.633510i
$779$	20.8183	−	12.5243i	0.745893	−	0.448729i
$780$	−9.97270	+	11.7996i	−0.357080	+	0.422494i
$781$	−4.40038	−	7.62168i	−0.157458	−	0.272725i
$782$	25.5520	+	6.84664i	0.913738	+	0.244835i
$783$	9.21426	+	5.15445i	0.329291	+	0.184205i
$784$	−5.23226	+	3.02085i	−0.186867	+	0.107887i
$785$	−29.0160	+	10.2964i	−1.03562	+	0.367493i
$786$	8.88560	−	8.96634i	0.316939	−	0.319819i
$787$	−7.63596	−	7.63596i	−0.272193	−	0.272193i	0.557790	−	0.829982i	$-0.311650\pi$
$787$	−7.63596	−	7.63596i	−0.272193	−	0.272193i	−0.829982	+	0.557790i	$0.811650\pi$
$788$	11.3361	−	3.03749i	0.403830	−	0.108206i
$789$	−7.66162	−	28.0848i	−0.272761	−	0.999847i
$790$	−27.4459	−	23.4101i	−0.976481	−	0.832894i
$791$			15.6375i			0.556005i
$792$	7.78428	+	28.0345i	0.276602	+	0.996163i
$793$	45.5238	+	12.1981i	1.61660	+	0.433166i
$794$	15.1208	−	26.1900i	0.536618	−	0.929450i
$795$	−0.223326	−	0.0401970i	−0.00792057	−	0.00142564i
$796$	8.84060	+	15.3124i	0.313347	+	0.542732i
$797$	22.8307	−	22.8307i	0.808705	−	0.808705i	−0.175733	−	0.984438i	$-0.556230\pi$
$797$	22.8307	−	22.8307i	0.808705	−	0.808705i	0.984438	+	0.175733i	$0.0562296\pi$
$798$	−11.5855	−	6.34543i	−0.410121	−	0.224626i
$799$			4.54620i			0.160833i
$800$	−22.8197	−	2.36839i	−0.806797	−	0.0837351i
$801$	−4.35447	−	7.38703i	−0.153858	−	0.261008i
$802$	26.8286	−	7.18870i	0.947351	−	0.253842i
$803$	−11.6141	+	43.3446i	−0.409854	+	1.52960i
$804$	12.6545	−	3.45217i	0.446288	−	0.121749i
$805$	1.82008	+	22.9353i	0.0641494	+	0.808363i
$806$			17.3568i			0.611369i
$807$	12.2451	+	6.99608i	0.431049	+	0.246274i
$808$	−0.527811	−	1.96982i	−0.0185683	−	0.0692980i
$809$	−36.4626			−1.28196			−0.640979	−	0.767559i	$-0.721471\pi$
$809$	−36.4626			−1.28196			−0.640979	+	0.767559i	$0.721471\pi$
$810$	−13.4605	+	16.3719i	−0.472955	+	0.575250i
$811$	21.3472	−	36.9744i	0.749601	−	1.29835i	−0.198413	−	0.980119i	$-0.563579\pi$
$811$	21.3472	−	36.9744i	0.749601	−	1.29835i	0.948014	−	0.318229i	$-0.103088\pi$
$812$	−2.90445	−	0.778246i	−0.101926	−	0.0273111i
$813$	−40.0264	−	22.8685i	−1.40379	−	0.802034i
$814$	2.51843	−	1.45401i	0.0882709	−	0.0509632i
$815$	−1.66726	−	0.307886i	−0.0584017	−	0.0107848i
$816$	−7.10903	−	7.04501i	−0.248866	−	0.246625i
$817$	45.7113	+	11.3708i	1.59924	+	0.397813i
$818$	3.60921	+	3.60921i	0.126193	+	0.126193i
$819$	−11.3332	−	19.2259i	−0.396014	−	0.671808i
$820$	6.29434	+	9.14555i	0.219808	+	0.319376i
$821$	−11.4360	−	6.60257i	−0.399118	−	0.230431i	0.286985	−	0.957935i	$-0.407347\pi$
$821$	−11.4360	−	6.60257i	−0.399118	−	0.230431i	−0.686104	+	0.727504i	$0.740680\pi$
$822$	5.44851	+	9.33930i	0.190039	+	0.325745i
$823$	1.29471	+	4.83192i	0.0451307	+	0.168430i	0.984813	−	0.173618i	$-0.0555459\pi$
$823$	1.29471	+	4.83192i	0.0451307	+	0.168430i	−0.939682	+	0.342049i	$0.888879\pi$
$824$	−10.8630			−0.378430
$825$	−27.2219	+	4.47425i	−0.947746	+	0.155773i
$826$	11.3010	−	19.5739i	0.393213	−	0.681065i
$827$	1.20112	+	4.48264i	0.0417670	+	0.155877i	0.983660	−	0.180037i	$-0.0576217\pi$
$827$	1.20112	+	4.48264i	0.0417670	+	0.155877i	−0.941893	+	0.335914i	$0.890955\pi$
$828$	11.5975	−	11.8093i	0.403042	−	0.410400i
$829$		−	43.8472i		−	1.52288i	−0.648238	−	0.761438i	$-0.724494\pi$
$829$		−	43.8472i		−	1.52288i	0.648238	−	0.761438i	$-0.275506\pi$
$830$	9.06132	−	19.0293i	0.314523	−	0.660518i
$831$	−26.4869	−	6.96890i	−0.918819	−	0.241748i
$832$	33.2290	−	8.90368i	1.15201	−	0.308679i
$833$	−4.45056	+	16.6097i	−0.154203	+	0.575493i
$834$	13.5034	+	3.55284i	0.467583	+	0.123025i
$835$	32.0057	−	37.5234i	1.10760	−	1.29855i
$836$	−5.99074	+	10.8214i	−0.207194	+	0.374267i
$837$	−0.259462	−	19.1215i	−0.00896832	−	0.660935i
$838$	−11.5176	−	3.08613i	−0.397869	−	0.106609i
$839$	27.0157	+	46.7926i	0.932686	+	1.61546i	0.778710	+	0.627384i	$0.215875\pi$
$839$	27.0157	+	46.7926i	0.932686	+	1.61546i	0.153976	+	0.988075i	$0.450792\pi$
$840$	8.34162	−	17.7240i	0.287813	−	0.611536i
$841$	12.4357	+	21.5393i	0.428818	+	0.742735i
$842$	−3.93850	−	14.6987i	−0.135730	−	0.506550i
$843$	21.9908	−	0.0994600i	0.757404	−	0.00342558i
$844$			14.9863i			0.515848i
$845$	14.2385	+	6.78002i	0.489818	+	0.233240i
$846$	−3.08330	−	1.74315i	−0.106006	−	0.0599307i
$847$	1.00159	+	1.00159i	0.0344150	+	0.0344150i
$848$	0.0590306	+	0.0590306i	0.00202712	+	0.00202712i
$849$	−3.25793	+	0.888772i	−0.111812	+	0.0305026i
$850$	16.5788	−	13.4610i	0.568648	−	0.461710i
$851$	−4.64933	−	2.68429i	−0.159377	−	0.0920163i
$852$	3.68193	−	2.14803i	0.126141	−	0.0735902i
$853$	12.9713	+	3.47566i	0.444130	+	0.119004i	0.473951	−	0.880551i	$-0.342827\pi$
$853$	12.9713	+	3.47566i	0.444130	+	0.119004i	−0.0298216	+	0.999555i	$0.509494\pi$
$854$	−18.4142			−0.630122
$855$	−29.0755	+	3.10044i	−0.994363	+	0.106033i
$856$	−46.7383			−1.59748
$857$	40.6508	+	10.8924i	1.38861	+	0.372076i	0.874240	−	0.485495i	$-0.161360\pi$
$857$	40.6508	+	10.8924i	1.38861	+	0.372076i	0.514366	+	0.857570i	$0.328027\pi$
$858$	22.4760	−	13.1124i	0.767318	−	0.447650i
$859$	41.0099	+	23.6771i	1.39924	+	0.807851i	0.994313	−	0.106498i	$-0.0339638\pi$
$859$	41.0099	+	23.6771i	1.39924	+	0.807851i	0.404926	+	0.914349i	$0.367297\pi$
$860$	−3.90889	+	21.1675i	−0.133292	+	0.721804i
$861$	−15.4724	+	4.22092i	−0.527299	+	0.143848i
$862$	−3.08319	−	3.08319i	−0.105014	−	0.105014i
$863$	2.13213	+	2.13213i	0.0725785	+	0.0725785i	0.742464	−	0.669886i	$-0.233657\pi$
$863$	2.13213	+	2.13213i	0.0725785	+	0.0725785i	−0.669886	+	0.742464i	$0.733657\pi$
$864$	−22.9440	+	6.48273i	−0.780571	+	0.220547i
$865$	7.10002	−	2.51946i	0.241408	−	0.0856641i
$866$		−	25.7432i		−	0.874789i
$867$	0.958983	−	0.00433728i	0.0325688	−	0.000147302i
$868$	1.40961	+	5.26072i	0.0478451	+	0.178560i
$869$	−24.3976	−	42.2579i	−0.827632	−	1.43350i
$870$	7.79818	−	2.80697i	0.264383	−	0.0951654i
$871$	−19.0347	−	32.9690i	−0.644965	−	1.11711i
$872$	−12.2794	−	3.29026i	−0.415834	−	0.111422i
$873$	4.74893	+	4.66378i	0.160727	+	0.157845i
$874$	−28.4284	+	0.511641i	−0.961607	+	0.0173065i
$875$	15.8555	+	9.67370i	0.536014	+	0.327031i
$876$	−21.0195	−	5.53038i	−0.710182	−	0.186854i
$877$	−1.86234	+	6.95034i	−0.0628866	+	0.234696i	−0.990214	−	0.139554i	$-0.955433\pi$
$877$	−1.86234	+	6.95034i	−0.0628866	+	0.234696i	0.927328	+	0.374250i	$0.122100\pi$
$878$	−2.58736	+	0.693281i	−0.0873191	+	0.0233971i
$879$	55.0474	+	14.4834i	1.85670	+	0.488512i
$880$	9.16346	+	4.36342i	0.308900	+	0.147091i
$881$			4.58873i			0.154598i	0.997008	+	0.0772992i	$0.0246297\pi$
$881$			4.58873i			0.154598i	−0.997008	+	0.0772992i	$0.975370\pi$
$882$	−9.55847	−	9.38709i	−0.321850	−	0.316080i
$883$	4.99486	+	18.6411i	0.168090	+	0.627321i	0.997626	+	0.0688675i	$0.0219386\pi$
$883$	4.99486	+	18.6411i	0.168090	+	0.627321i	−0.829536	+	0.558454i	$0.811395\pi$
$884$	8.08857	−	14.0098i	0.272048	−	0.471201i
$885$	−4.18350	−	49.8569i	−0.140627	−	1.67592i
$886$	3.97778			0.133636
$887$	−7.84089	−	29.2626i	−0.263271	−	0.982542i	−0.963300	−	0.268427i	$-0.913496\pi$
$887$	−7.84089	−	29.2626i	−0.263271	−	0.982542i	0.700029	−	0.714115i	$-0.253170\pi$
$888$	2.30333	+	3.94813i	0.0772946	+	0.132491i
$889$	−11.5323	−	6.65817i	−0.386780	−	0.223308i
$890$	−6.61939	−	1.22237i	−0.221882	−	0.0409740i
$891$	−24.5651	+	14.7815i	−0.822961	+	0.495200i
$892$	9.91013	+	9.91013i	0.331816	+	0.331816i
$893$	−1.34943	−	4.69640i	−0.0451569	−	0.157159i
$894$	−19.7232	−	19.5456i	−0.659641	−	0.653701i
$895$	−3.30061	−	4.79572i	−0.110327	−	0.160303i
$896$	1.56257	−	0.902152i	0.0522019	−	0.0301388i
$897$	−41.7107	−	23.8308i	−1.39268	−	0.795688i
$898$	−3.38737	−	0.907642i	−0.113038	−	0.0302884i
$899$	−3.73894	+	6.47604i	−0.124701	+	0.215988i
$900$	−2.22674	−	13.1752i	−0.0742247	−	0.439173i
$901$	0.237603			0.00791570
$902$	−4.83974	−	18.0622i	−0.161146	−	0.601404i
$903$	−26.9988	−	15.4254i	−0.898462	−	0.513324i
$904$		−	28.6582i		−	0.953158i
$905$	−39.2802	+	3.11717i	−1.30572	+	0.103618i
$906$	−13.0482	+	3.55957i	−0.433496	+	0.118259i
$907$	−4.83721	+	18.0527i	−0.160617	+	0.599430i	0.837942	+	0.545759i	$0.183759\pi$
$907$	−4.83721	+	18.0527i	−0.160617	+	0.599430i	−0.998559	+	0.0536706i	$0.982908\pi$
$908$	−12.6106	+	3.37899i	−0.418496	+	0.112136i
$909$	1.73109	−	1.02043i	0.0574166	−	0.0338456i
$910$	−17.2280	−	3.18141i	−0.571103	−	0.105463i
$911$			4.02070i			0.133212i	0.997779	+	0.0666059i	$0.0212170\pi$
$911$			4.02070i			0.133212i	−0.997779	+	0.0666059i	$0.978783\pi$
$912$	9.43503	+	5.16763i	0.312425	+	0.171117i
$913$	20.1592	−	20.1592i	0.667171	−	0.667171i
$914$	6.47828	+	11.2207i	0.214283	+	0.371148i
$915$	−33.4730	+	23.2613i	−1.10658	+	0.768994i
$916$	9.19683	−	15.9294i	0.303872	−	0.526321i
$917$	−11.1044	−	2.97541i	−0.366699	−	0.0982566i
$918$	10.8348	−	19.3687i	0.357603	−	0.639263i
$919$			35.4814i			1.17042i	0.810880	+	0.585212i	$0.198989\pi$
$919$			35.4814i			1.17042i	−0.810880	+	0.585212i	$0.801011\pi$
$920$	−3.33559	−	42.0326i	−0.109971	−	1.38578i
$921$	4.59884	+	16.8577i	0.151537	+	0.555482i
$922$	−14.2322	+	3.81350i	−0.468712	+	0.125591i
$923$	−8.74812	−	8.74812i	−0.287948	−	0.287948i
$924$	5.74739	−	5.79961i	0.189075	−	0.190793i
$925$	−3.95699	+	1.76795i	−0.130105	+	0.0581298i
$926$	6.42854	−	3.71152i	0.211255	−	0.121968i
$927$	−2.86382	−	10.3138i	−0.0940601	−	0.338750i
$928$	9.00552	+	2.41302i	0.295621	+	0.0792113i
$929$	16.7779	+	29.0601i	0.550464	+	0.953431i	0.998241	+	0.0592859i	$0.0188823\pi$
$929$	16.7779	+	29.0601i	0.550464	+	0.953431i	−0.447777	+	0.894145i	$0.647784\pi$
$930$	−11.4653	−	9.69013i	−0.375961	−	0.317752i
$931$	−0.332585	−	18.4795i	−0.0109000	−	0.605642i
$932$	−3.36996	+	3.36996i	−0.110387	+	0.110387i
$933$	−22.6155	−	38.7653i	−0.740399	−	1.26912i
$934$	27.2403	−	15.7272i	0.891330	−	0.514609i
$935$	27.2234	−	9.66027i	0.890300	−	0.315925i
$936$	20.7699	+	35.2346i	0.678885	+	1.15168i
$937$	−21.9474	+	5.88080i	−0.716992	+	0.192117i	−0.598829	−	0.800877i	$-0.704367\pi$
$937$	−21.9474	+	5.88080i	−0.716992	+	0.192117i	−0.118163	+	0.992994i	$0.537700\pi$
$938$	10.5177	+	10.5177i	0.343414	+	0.343414i
$939$	38.9580	+	38.6072i	1.27135	+	1.25990i
$940$	2.10439	−	0.746748i	0.0686377	−	0.0243562i
$941$	39.3929	+	22.7435i	1.28417	+	0.741417i	0.977608	−	0.210433i	$-0.0674875\pi$
$941$	39.3929	+	22.7435i	1.28417	+	0.741417i	0.306564	+	0.951850i	$0.400821\pi$
$942$	0.113599	+	25.1169i	0.00370125	+	0.818353i
$943$	−24.4102	+	24.4102i	−0.794906	+	0.794906i
$944$	−9.20338	+	15.9407i	−0.299545	+	0.518827i
$945$	19.0271	+	3.24733i	0.618952	+	0.105636i
$946$	18.1274	−	31.3976i	0.589372	−	1.02082i
$947$	−30.6847	−	8.22193i	−0.997118	−	0.267177i	−0.276880	−	0.960904i	$-0.589301\pi$
$947$	−30.6847	−	8.22193i	−0.997118	−	0.267177i	−0.720238	+	0.693727i	$0.755967\pi$
$948$	20.4142	−	11.9096i	0.663023	−	0.386806i
$949$			63.0813i			2.04771i
$950$	−13.1309	+	18.8268i	−0.426024	+	0.610821i
$951$	2.93653	+	2.91009i	0.0952237	+	0.0943662i
$952$	−5.30877	+	19.8126i	−0.172058	+	0.642130i
$953$	−1.90289	+	7.10168i	−0.0616407	+	0.230046i	−0.989873	−	0.141954i	$-0.954661\pi$
$953$	−1.90289	+	7.10168i	−0.0616407	+	0.230046i	0.928233	+	0.372001i	$0.121328\pi$
$954$	−0.0911040	+	0.161146i	−0.00294960	+	0.00521728i
$955$	−20.6652	+	14.2226i	−0.668711	+	0.460234i
$956$	−5.22551	−	3.01695i	−0.169005	−	0.0975752i
$957$	11.2107	−	0.0507036i	0.362390	−	0.00163901i
$958$	−30.4422	+	30.4422i	−0.983542	+	0.983542i
$959$	4.92344	−	8.52765i	0.158986	−	0.275372i
$960$	−12.6699	+	26.9206i	−0.408920	+	0.868860i
$961$	−17.4556			−0.563084
$962$	2.89064	−	2.89064i	0.0931979	−	0.0931979i
$963$	−12.3217	−	44.3755i	−0.397060	−	1.42998i
$964$	10.2002	−	5.88911i	0.328527	−	0.189675i
$965$	13.6515	+	38.4708i	0.439456	+	1.23842i
$966$	18.1515	+	4.77580i	0.584016	+	0.153659i
$967$	−4.97506	+	18.5672i	−0.159987	+	0.597080i	0.838640	+	0.544687i	$0.183351\pi$
$967$	−4.97506	+	18.5672i	−0.159987	+	0.597080i	−0.998627	+	0.0523929i	$0.983315\pi$
$968$	−1.83557	−	1.83557i	−0.0589975	−	0.0589975i
$969$	29.3885	−	8.58833i	0.944093	−	0.275897i
$970$	5.20862	−	0.413341i	0.167239	−	0.0132716i
$971$	43.2283	−	24.9579i	1.38726	−	0.800937i	0.394257	−	0.919000i	$-0.371002\pi$
$971$	43.2283	−	24.9579i	1.38726	−	0.800937i	0.993006	+	0.118064i	$0.0376686\pi$
$972$	−7.21327	−	11.8658i	−0.231366	−	0.380594i
$973$	−3.29115	−	12.2827i	−0.105510	−	0.393767i
$974$	15.3004	+	26.5010i	0.490256	+	0.849148i
$975$	−35.3356	+	15.9797i	−1.13164	+	0.511760i
$976$	14.9963			0.480019
$977$	25.0796	−	25.0796i	0.802367	−	0.802367i	−0.181098	−	0.983465i	$-0.557965\pi$
$977$	25.0796	−	25.0796i	0.802367	−	0.802367i	0.983465	+	0.181098i	$0.0579652\pi$
$978$	−0.686145	+	1.20095i	−0.0219405	+	0.0384021i
$979$	−7.88528	−	4.55257i	−0.252015	−	0.145501i
$980$	8.41952	−	0.668149i	0.268952	−	0.0213433i
$981$	−0.113308	−	12.5261i	−0.00361765	−	0.399927i
$982$	3.83774	−	1.02832i	0.122467	−	0.0328150i
$983$	0.888484	−	3.31587i	0.0283382	−	0.105760i	−0.950308	−	0.311311i	$-0.899232\pi$
$983$	0.888484	−	3.31587i	0.0283382	−	0.105760i	0.978646	+	0.205551i	$0.0658987\pi$
$984$	28.3557	−	7.73552i	0.903948	−	0.246599i
$985$	28.9695	+	5.34965i	0.923044	+	0.170454i
$986$	−7.51569	+	4.33918i	−0.239348	+	0.138188i
$987$	0.0145888	+	3.22560i	0.000464365	+	0.102672i
$988$	−4.19734	+	16.8736i	−0.133535	+	0.536820i
$989$	−66.9308			−2.12828
$990$	−3.88652	+	22.1673i	−0.123522	+	0.704523i
$991$	5.63087	+	9.75295i	0.178870	+	0.309813i	0.941494	−	0.337030i	$-0.109422\pi$
$991$	5.63087	+	9.75295i	0.178870	+	0.309813i	−0.762623	+	0.646843i	$0.776089\pi$
$992$	−4.37061	−	16.3113i	−0.138767	−	0.517885i
$993$	−9.07487	+	5.29425i	−0.287982	+	0.168008i
$994$	4.18619	+	2.41690i	0.132778	+	0.0766594i
$995$	3.51106	+	44.2438i	0.111308	+	1.40262i
$996$	9.80829	+	9.71997i	0.310788	+	0.307989i
$997$	12.1383	−	3.25245i	0.384424	−	0.103006i	−0.0614307	−	0.998111i	$-0.519566\pi$
$997$	12.1383	−	3.25245i	0.384424	−	0.103006i	0.445855	+	0.895105i	$0.352900\pi$
$998$	12.9732	−	3.47615i	0.410658	−	0.110036i
$999$	−3.14131	+	3.22774i	−0.0993868	+	0.102121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.v.a.197.25	yes	144
3.2	odd	2	inner	285.2.v.a.197.12	yes	144
5.3	odd	4	inner	285.2.v.a.83.25	yes	144
15.8	even	4	inner	285.2.v.a.83.12	yes	144
19.11	even	3	inner	285.2.v.a.182.12	yes	144
57.11	odd	6	inner	285.2.v.a.182.25	yes	144
95.68	odd	12	inner	285.2.v.a.68.12	✓	144
285.68	even	12	inner	285.2.v.a.68.25	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.v.a.68.12	✓	144	95.68	odd	12	inner
285.2.v.a.68.25	yes	144	285.68	even	12	inner
285.2.v.a.83.12	yes	144	15.8	even	4	inner
285.2.v.a.83.25	yes	144	5.3	odd	4	inner
285.2.v.a.182.12	yes	144	19.11	even	3	inner
285.2.v.a.182.25	yes	144	57.11	odd	6	inner
285.2.v.a.197.12	yes	144	3.2	odd	2	inner
285.2.v.a.197.25	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01730 + 0.272584i) q^{2} +(-1.49607 + 0.872801i) q^{3} +(-0.771457 - 0.445401i) q^{4} +(-1.26772 - 1.84198i) q^{5} +(-1.75986 + 0.480094i) q^{6} +(1.17470 + 1.17470i) q^{7} +(-2.15282 - 2.15282i) q^{8} +(1.47644 - 2.61154i) q^{9} +O(q^{10})\)	\(q+(1.01730 + 0.272584i) q^{2} +(-1.49607 + 0.872801i) q^{3} +(-0.771457 - 0.445401i) q^{4} +(-1.26772 - 1.84198i) q^{5} +(-1.75986 + 0.480094i) q^{6} +(1.17470 + 1.17470i) q^{7} +(-2.15282 - 2.15282i) q^{8} +(1.47644 - 2.61154i) q^{9} +(-0.787559 - 2.21940i) q^{10} -3.18549i q^{11} +(1.54290 - 0.00697821i) q^{12} +(-1.15900 - 4.32544i) q^{13} +(0.874812 + 1.51522i) q^{14} +(3.50428 + 1.64925i) q^{15} +(-0.712434 - 1.23397i) q^{16} +(-3.91722 - 1.04962i) q^{17} +(2.21384 - 2.25426i) q^{18} +(4.35819 - 0.0784366i) q^{19} +(0.157576 + 1.98565i) q^{20} +(-2.78270 - 0.732149i) q^{21} +(0.868315 - 3.24060i) q^{22} +(-5.98254 + 1.60302i) q^{23} +(5.09975 + 1.34178i) q^{24} +(-1.78576 + 4.67023i) q^{25} -4.71619i q^{26} +(0.0705008 + 5.19567i) q^{27} +(-0.383017 - 1.42944i) q^{28} +(1.01594 - 1.75966i) q^{29} +(3.11534 + 2.63299i) q^{30} -3.68027 q^{31} +(1.18758 + 4.43210i) q^{32} +(2.78030 + 4.76571i) q^{33} +(-3.69887 - 2.13555i) q^{34} +(0.674573 - 3.65295i) q^{35} +(-2.30219 + 1.35708i) q^{36} +(0.612918 + 0.612918i) q^{37} +(4.45496 + 1.10818i) q^{38} +(5.50919 + 5.45958i) q^{39} +(-1.23627 + 6.69463i) q^{40} +(4.82698 - 2.78686i) q^{41} +(-2.63126 - 1.50333i) q^{42} +(10.4383 + 2.79692i) q^{43} +(-1.41882 + 2.45747i) q^{44} +(-6.68211 + 0.591143i) q^{45} -6.52299 q^{46} +(-0.290142 - 1.08283i) q^{47} +(2.14286 + 1.22429i) q^{48} -4.24018i q^{49} +(-3.08968 + 4.26425i) q^{50} +(6.77654 - 1.84866i) q^{51} +(-1.03244 + 3.85311i) q^{52} +(-0.0565928 + 0.0151640i) q^{53} +(-1.34454 + 5.30477i) q^{54} +(-5.86760 + 4.03832i) q^{55} -5.05782i q^{56} +(-6.45169 + 3.92118i) q^{57} +(1.51317 - 1.51317i) q^{58} +(-6.45911 - 11.1875i) q^{59} +(-1.96882 - 2.83314i) q^{60} +(-5.26233 + 9.11463i) q^{61} +(-3.74393 - 1.00318i) q^{62} +(4.80213 - 1.33340i) q^{63} +7.68222i q^{64} +(-6.49807 + 7.61831i) q^{65} +(1.52934 + 5.60602i) q^{66} +(8.21169 - 2.20032i) q^{67} +(2.55447 + 2.55447i) q^{68} +(7.55118 - 7.61979i) q^{69} +(1.68198 - 3.53226i) q^{70} +(2.39262 - 1.38138i) q^{71} +(-8.80068 + 2.44367i) q^{72} +(-13.6069 - 3.64595i) q^{73} +(0.456449 + 0.790593i) q^{74} +(-1.40457 - 8.54559i) q^{75} +(-3.39709 - 1.88063i) q^{76} +(3.74198 - 3.74198i) q^{77} +(4.11629 + 7.05573i) q^{78} +(13.2657 - 7.65897i) q^{79} +(-1.36978 + 2.87662i) q^{80} +(-4.64026 - 7.71155i) q^{81} +(5.67013 - 1.51931i) q^{82} +(6.32843 + 6.32843i) q^{83} +(1.82063 + 1.80424i) q^{84} +(3.03258 + 8.54606i) q^{85} +(9.85642 + 5.69061i) q^{86} +(0.0159170 + 3.51929i) q^{87} +(-6.85780 + 6.85780i) q^{88} +(1.42916 - 2.47537i) q^{89} +(-6.95883 - 1.22007i) q^{90} +(3.71960 - 6.44254i) q^{91} +(5.32926 + 1.42797i) q^{92} +(5.50594 - 3.21214i) q^{93} -1.18064i q^{94} +(-5.66946 - 7.92825i) q^{95} +(-5.64504 - 5.59420i) q^{96} +(-0.574239 + 2.14309i) q^{97} +(1.15581 - 4.31353i) q^{98} +(-8.31904 - 4.70318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 2 q^{3} - 4 q^{6} - 16 q^{7}+O(q^{10}) \) 144 * q - 2 * q^3 - 4 * q^6 - 16 * q^7	\( 144 q - 2 q^{3} - 4 q^{6} - 16 q^{7} - 4 q^{10} - 28 q^{12} + 4 q^{13} - 8 q^{15} + 36 q^{16} - 60 q^{18} - 4 q^{21} + 12 q^{22} - 12 q^{25} - 20 q^{27} + 28 q^{28} - 28 q^{30} - 64 q^{31} - 8 q^{33} - 20 q^{36} - 36 q^{40} + 22 q^{42} + 16 q^{43} + 24 q^{45} - 80 q^{46} + 24 q^{48} + 12 q^{51} - 60 q^{52} + 8 q^{55} + 72 q^{57} - 96 q^{58} + 30 q^{60} + 16 q^{61} - 28 q^{63} - 4 q^{66} - 4 q^{67} - 52 q^{70} - 94 q^{72} - 52 q^{73} + 116 q^{75} + 96 q^{76} + 8 q^{78} - 12 q^{81} - 68 q^{82} - 28 q^{85} + 84 q^{87} - 34 q^{90} - 112 q^{91} - 4 q^{93} + 168 q^{96} + 4 q^{97}+O(q^{100}) \) 144 * q - 2 * q^3 - 4 * q^6 - 16 * q^7 - 4 * q^10 - 28 * q^12 + 4 * q^13 - 8 * q^15 + 36 * q^16 - 60 * q^18 - 4 * q^21 + 12 * q^22 - 12 * q^25 - 20 * q^27 + 28 * q^28 - 28 * q^30 - 64 * q^31 - 8 * q^33 - 20 * q^36 - 36 * q^40 + 22 * q^42 + 16 * q^43 + 24 * q^45 - 80 * q^46 + 24 * q^48 + 12 * q^51 - 60 * q^52 + 8 * q^55 + 72 * q^57 - 96 * q^58 + 30 * q^60 + 16 * q^61 - 28 * q^63 - 4 * q^66 - 4 * q^67 - 52 * q^70 - 94 * q^72 - 52 * q^73 + 116 * q^75 + 96 * q^76 + 8 * q^78 - 12 * q^81 - 68 * q^82 - 28 * q^85 + 84 * q^87 - 34 * q^90 - 112 * q^91 - 4 * q^93 + 168 * q^96 + 4 * q^97

Introduction

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