LMFDB - Embedded newform 960.2.cn.a.131.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.17
Character	$\chi$	$=$	960.131
Dual form			960.2.cn.a.491.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31369 + 0.523657i) q^{2} +(0.243225 + 1.71489i) q^{3} +(1.45157 - 1.37585i) q^{4} +(0.555570 - 0.831470i) q^{5} +(-1.21754 - 2.12547i) q^{6} +(-0.799421 - 1.92997i) q^{7} +(-1.18644 + 2.56756i) q^{8} +(-2.88168 + 0.834208i) q^{9} +O(q^{10})$	\(q+(-1.31369 + 0.523657i) q^{2} +(0.243225 + 1.71489i) q^{3} +(1.45157 - 1.37585i) q^{4} +(0.555570 - 0.831470i) q^{5} +(-1.21754 - 2.12547i) q^{6} +(-0.799421 - 1.92997i) q^{7} +(-1.18644 + 2.56756i) q^{8} +(-2.88168 + 0.834208i) q^{9} +(-0.294442 + 1.38322i) q^{10} +(-2.67444 + 0.531979i) q^{11} +(2.71248 + 2.15463i) q^{12} +(-4.23423 + 2.82922i) q^{13} +(2.06084 + 2.11677i) q^{14} +(1.56101 + 0.750507i) q^{15} +(0.214087 - 3.99427i) q^{16} +(0.635098 - 0.635098i) q^{17} +(3.34880 - 2.60491i) q^{18} +(6.79701 - 4.54162i) q^{19} +(-0.337529 - 1.97131i) q^{20} +(3.11525 - 1.84034i) q^{21} +(3.23481 - 2.09935i) q^{22} +(-0.709001 + 1.71168i) q^{23} +(-4.69165 - 1.41011i) q^{24} +(-0.382683 - 0.923880i) q^{25} +(4.08092 - 5.93400i) q^{26} +(-2.13147 - 4.73886i) q^{27} +(-3.81576 - 1.70160i) q^{28} +(0.845332 - 4.24977i) q^{29} +(-2.44369 - 0.168501i) q^{30} -2.99137 q^{31} +(1.81038 + 5.35934i) q^{32} +(-1.56278 - 4.45697i) q^{33} +(-0.501748 + 1.16690i) q^{34} +(-2.04885 - 0.407542i) q^{35} +(-3.03521 + 5.17566i) q^{36} +(1.81389 - 2.71467i) q^{37} +(-6.55092 + 9.52558i) q^{38} +(-5.88167 - 6.57309i) q^{39} +(1.47570 + 2.41295i) q^{40} +(-1.29914 - 0.538123i) q^{41} +(-3.12877 + 4.04896i) q^{42} +(-11.2111 + 2.23003i) q^{43} +(-3.15020 + 4.45182i) q^{44} +(-0.907359 + 2.85949i) q^{45} +(0.0350741 - 2.61989i) q^{46} +(-7.49614 - 7.49614i) q^{47} +(6.90179 - 0.604371i) q^{48} +(1.86402 - 1.86402i) q^{49} +(0.986524 + 1.01330i) q^{50} +(1.24359 + 0.934650i) q^{51} +(-2.25368 + 9.93245i) q^{52} +(-2.51076 - 12.6224i) q^{53} +(5.28163 + 5.10924i) q^{54} +(-1.04351 + 2.51927i) q^{55} +(5.90379 + 0.237226i) q^{56} +(9.44157 + 10.5515i) q^{57} +(1.11492 + 6.02555i) q^{58} +(-7.64390 - 5.10749i) q^{59} +(3.29849 - 1.05830i) q^{60} +(1.87065 - 9.40437i) q^{61} +(3.92974 - 1.56646i) q^{62} +(3.91368 + 4.89469i) q^{63} +(-5.18474 - 6.09249i) q^{64} +5.09246i q^{65} +(4.38693 + 5.03673i) q^{66} +(10.5377 + 2.09608i) q^{67} +(0.0480885 - 1.79568i) q^{68} +(-3.10779 - 0.799534i) q^{69} +(2.90497 - 0.537512i) q^{70} +(-8.81850 + 3.65274i) q^{71} +(1.27705 - 8.38863i) q^{72} +(10.5330 + 4.36291i) q^{73} +(-0.961327 + 4.51610i) q^{74} +(1.49127 - 0.880970i) q^{75} +(3.61773 - 15.9441i) q^{76} +(3.16471 + 4.73632i) q^{77} +(11.1687 + 5.55503i) q^{78} +(-9.58802 - 9.58802i) q^{79} +(-3.20217 - 2.39710i) q^{80} +(7.60820 - 4.80784i) q^{81} +(1.98846 + 0.0266208i) q^{82} +(-3.05217 - 4.56789i) q^{83} +(1.98997 - 6.95748i) q^{84} +(-0.175223 - 0.880906i) q^{85} +(13.5602 - 8.80036i) q^{86} +(7.49349 + 0.415999i) q^{87} +(1.80716 - 7.49795i) q^{88} +(1.06646 - 0.441740i) q^{89} +(-0.305406 - 4.23163i) q^{90} +(8.84525 + 5.91021i) q^{91} +(1.32585 + 3.46009i) q^{92} +(-0.727577 - 5.12987i) q^{93} +(13.7730 + 5.92220i) q^{94} -8.17469i q^{95} +(-8.75034 + 4.40813i) q^{96} +10.3774i q^{97} +(-1.47264 + 3.42486i) q^{98} +(7.26311 - 3.76403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	−1.31369	+	0.523657i	−0.928920	+	0.370282i
$2$	−1.31369	+	0.523657i	−0.928920	+	0.370282i
$3$	0.243225	+	1.71489i	0.140426	+	0.990091i
$3$	0.243225	+	1.71489i	0.140426	+	0.990091i
$4$	1.45157	−	1.37585i	0.725783	−	0.687924i
$5$	0.555570	−	0.831470i	0.248459	−	0.371845i
$5$	0.555570	−	0.831470i	0.248459	−	0.371845i
$6$	−1.21754	−	2.12547i	−0.497057	−	0.867718i
$7$	−0.799421	−	1.92997i	−0.302153	−	0.729462i	−0.999914	−	0.0131309i	$-0.995820\pi$
$7$	−0.799421	−	1.92997i	−0.302153	−	0.729462i	0.697761	−	0.716331i	$-0.254180\pi$
$8$	−1.18644	+	2.56756i	−0.419468	+	0.907770i
$9$	−2.88168	+	0.834208i	−0.960561	+	0.278069i
$10$	−0.294442	+	1.38322i	−0.0931108	+	0.437413i
$11$	−2.67444	+	0.531979i	−0.806374	+	0.160398i	−0.581031	−	0.813882i	$-0.697350\pi$
$11$	−2.67444	+	0.531979i	−0.806374	+	0.160398i	−0.225343	+	0.974279i	$0.572350\pi$
$12$	2.71248	+	2.15463i	0.783026	+	0.621989i
$13$	−4.23423	+	2.82922i	−1.17436	+	0.784685i	−0.980534	−	0.196351i	$-0.937091\pi$
$13$	−4.23423	+	2.82922i	−1.17436	+	0.784685i	−0.193830	+	0.981035i	$0.562091\pi$
$14$	2.06084	+	2.11677i	0.550782	+	0.565729i
$15$	1.56101	+	0.750507i	0.403050	+	0.193780i
$16$	0.214087	−	3.99427i	0.0535217	−	0.998567i
$17$	0.635098	−	0.635098i	0.154034	−	0.154034i	−0.625883	−	0.779917i	$-0.715261\pi$
$17$	0.635098	−	0.635098i	0.154034	−	0.154034i	0.779917	+	0.625883i	$0.215261\pi$
$18$	3.34880	−	2.60491i	0.789320	−	0.613982i
$19$	6.79701	−	4.54162i	1.55934	−	1.04192i	0.586642	−	0.809846i	$-0.300450\pi$
$19$	6.79701	−	4.54162i	1.55934	−	1.04192i	0.972699	−	0.232072i	$-0.0745505\pi$
$20$	−0.337529	−	1.97131i	−0.0754737	−	0.440799i
$21$	3.11525	−	1.84034i	0.679803	−	0.401594i
$22$	3.23481	−	2.09935i	0.689664	−	0.447582i
$23$	−0.709001	+	1.71168i	−0.147837	+	0.356910i	−0.980399	−	0.197022i	$-0.936873\pi$
$23$	−0.709001	+	1.71168i	−0.147837	+	0.356910i	0.832562	+	0.553932i	$0.186873\pi$
$24$	−4.69165	−	1.41011i	−0.957679	−	0.287837i
$25$	−0.382683	−	0.923880i	−0.0765367	−	0.184776i
$26$	4.08092	−	5.93400i	0.800335	−	1.16375i
$27$	−2.13147	−	4.73886i	−0.410202	−	0.911995i
$28$	−3.81576	−	1.70160i	−0.721111	−	0.321573i
$29$	0.845332	−	4.24977i	0.156974	−	0.789162i	−0.819425	−	0.573187i	$-0.805707\pi$
$29$	0.845332	−	4.24977i	0.156974	−	0.789162i	0.976399	−	0.215975i	$-0.0692931\pi$
$30$	−2.44369	−	0.168501i	−0.446154	−	0.0307639i
$31$	−2.99137			−0.537267			−0.268633	−	0.963242i	$-0.586572\pi$
$31$	−2.99137			−0.537267			−0.268633	+	0.963242i	$0.586572\pi$
$32$	1.81038	+	5.35934i	0.320034	+	0.947406i
$33$	−1.56278	−	4.45697i	−0.272044	−	0.775860i
$34$	−0.501748	+	1.16690i	−0.0860491	+	0.200121i
$35$	−2.04885	−	0.407542i	−0.346319	−	0.0688871i
$36$	−3.03521	+	5.17566i	−0.505868	+	0.862611i
$37$	1.81389	−	2.71467i	0.298201	−	0.446290i	−0.651866	−	0.758334i	$-0.726014\pi$
$37$	1.81389	−	2.71467i	0.298201	−	0.446290i	0.950068	+	0.312044i	$0.101014\pi$
$38$	−6.55092	+	9.52558i	−1.06270	+	1.54525i
$39$	−5.88167	−	6.57309i	−0.941820	−	1.05254i
$40$	1.47570	+	2.41295i	0.233329	+	0.381520i
$41$	−1.29914	−	0.538123i	−0.202892	−	0.0840406i	0.278923	−	0.960313i	$-0.410022\pi$
$41$	−1.29914	−	0.538123i	−0.202892	−	0.0840406i	−0.481815	+	0.876273i	$0.660022\pi$
$42$	−3.12877	+	4.04896i	−0.482780	+	0.624768i
$43$	−11.2111	+	2.23003i	−1.70968	+	0.340077i	−0.950481	−	0.310781i	$-0.899409\pi$
$43$	−11.2111	+	2.23003i	−1.70968	+	0.340077i	−0.759200	+	0.650858i	$0.774409\pi$
$44$	−3.15020	+	4.45182i	−0.474911	+	0.671138i
$45$	−0.907359	+	2.85949i	−0.135261	+	0.426268i
$46$	0.0350741	−	2.61989i	0.00517140	−	0.386282i
$47$	−7.49614	−	7.49614i	−1.09342	−	1.09342i	−0.995160	−	0.0982638i	$-0.968671\pi$
$47$	−7.49614	−	7.49614i	−1.09342	−	1.09342i	−0.0982638	−	0.995160i	$-0.531329\pi$
$48$	6.90179	−	0.604371i	0.996188	−	0.0872335i
$49$	1.86402	−	1.86402i	0.266289	−	0.266289i
$50$	0.986524	+	1.01330i	0.139516	+	0.143302i
$51$	1.24359	+	0.934650i	0.174138	+	0.130877i
$52$	−2.25368	+	9.93245i	−0.312530	+	1.37738i
$53$	−2.51076	−	12.6224i	−0.344879	−	1.73383i	−0.631135	−	0.775673i	$-0.717411\pi$
$53$	−2.51076	−	12.6224i	−0.344879	−	1.73383i	0.286256	−	0.958153i	$-0.407589\pi$
$54$	5.28163	+	5.10924i	0.718739	+	0.695280i
$55$	−1.04351	+	2.51927i	−0.140707	+	0.339698i
$56$	5.90379	+	0.237226i	0.788927	+	0.0317007i
$57$	9.44157	+	10.5515i	1.25057	+	1.39758i
$58$	1.11492	+	6.02555i	0.146396	+	0.791193i
$59$	−7.64390	−	5.10749i	−0.995151	−	0.664938i	−0.0524657	−	0.998623i	$-0.516708\pi$
$59$	−7.64390	−	5.10749i	−0.995151	−	0.664938i	−0.942685	+	0.333684i	$0.891708\pi$
$60$	3.29849	−	1.05830i	0.425833	−	0.136626i
$61$	1.87065	−	9.40437i	0.239512	−	1.20411i	−0.654500	−	0.756062i	$-0.727121\pi$
$61$	1.87065	−	9.40437i	0.239512	−	1.20411i	0.894011	−	0.448044i	$-0.147879\pi$
$62$	3.92974	−	1.56646i	0.499078	−	0.198940i
$63$	3.91368	+	4.89469i	0.493077	+	0.616673i
$64$	−5.18474	−	6.09249i	−0.648093	−	0.761561i
$65$			5.09246i			0.631642i
$66$	4.38693	+	5.03673i	0.539994	+	0.619978i
$67$	10.5377	+	2.09608i	1.28739	+	0.256078i	0.790889	−	0.611960i	$-0.209618\pi$
$67$	10.5377	+	2.09608i	1.28739	+	0.256078i	0.496499	+	0.868037i	$0.334618\pi$
$68$	0.0480885	−	1.79568i	0.00583158	−	0.217759i
$69$	−3.10779	−	0.799534i	−0.374134	−	0.0962526i
$70$	2.90497	−	0.537512i	0.347210	−	0.0642450i
$71$	−8.81850	+	3.65274i	−1.04656	+	0.433501i	−0.838664	−	0.544649i	$-0.816663\pi$
$71$	−8.81850	+	3.65274i	−1.04656	+	0.433501i	−0.207900	+	0.978150i	$0.566663\pi$
$72$	1.27705	−	8.38863i	0.150502	−	0.988610i
$73$	10.5330	+	4.36291i	1.23279	+	0.510640i	0.901456	−	0.432871i	$-0.142500\pi$
$73$	10.5330	+	4.36291i	1.23279	+	0.510640i	0.331339	+	0.943512i	$0.392500\pi$
$74$	−0.961327	+	4.51610i	−0.111752	+	0.524986i
$75$	1.49127	−	0.880970i	0.172197	−	0.101726i
$76$	3.61773	−	15.9441i	0.414983	−	1.82891i
$77$	3.16471	+	4.73632i	0.360652	+	0.539754i
$78$	11.1687	+	5.55503i	1.26461	+	0.628983i
$79$	−9.58802	−	9.58802i	−1.07874	−	1.07874i	−0.996623	−	0.0821130i	$-0.973833\pi$
$79$	−9.58802	−	9.58802i	−1.07874	−	1.07874i	−0.0821130	−	0.996623i	$-0.526167\pi$
$80$	−3.20217	−	2.39710i	−0.358014	−	0.268004i
$81$	7.60820	−	4.80784i	0.845355	−	0.534205i
$82$	1.98846	+	0.0266208i	0.219589	+	0.00293978i
$83$	−3.05217	−	4.56789i	−0.335019	−	0.501391i	0.625266	−	0.780411i	$-0.284990\pi$
$83$	−3.05217	−	4.56789i	−0.335019	−	0.501391i	−0.960285	+	0.279020i	$0.909990\pi$
$84$	1.98997	−	6.95748i	0.217123	−	0.759123i
$85$	−0.175223	−	0.880906i	−0.0190056	−	0.0955476i
$86$	13.5602	−	8.80036i	1.46223	−	0.948968i
$87$	7.49349	+	0.415999i	0.803386	+	0.0445998i
$88$	1.80716	−	7.49795i	0.192644	−	0.799284i
$89$	1.06646	−	0.441740i	0.113044	−	0.0468244i	−0.325445	−	0.945561i	$-0.605514\pi$
$89$	1.06646	−	0.441740i	0.113044	−	0.0468244i	0.438489	+	0.898737i	$0.355514\pi$
$90$	−0.305406	−	4.23163i	−0.0321926	−	0.446053i
$91$	8.84525	+	5.91021i	0.927235	+	0.619558i
$92$	1.32585	+	3.46009i	0.138229	+	0.360740i
$93$	−0.727577	−	5.12987i	−0.0754463	−	0.531943i
$94$	13.7730	+	5.92220i	1.42058	+	0.610828i
$95$		−	8.17469i		−	0.838706i
$96$	−8.75034	+	4.40813i	−0.893077	+	0.449903i
$97$			10.3774i			1.05366i	0.849970	+	0.526832i	$0.176620\pi$
$97$			10.3774i			1.05366i	−0.849970	+	0.526832i	$0.823380\pi$
$98$	−1.47264	+	3.42486i	−0.148759	+	0.345963i
$99$	7.26311	−	3.76403i	0.729970	−	0.378300i
$100$	−1.82661	−	0.814558i	−0.182661	−	0.0814558i
$101$	4.15733	+	2.77784i	0.413670	+	0.276405i	0.744941	−	0.667130i	$-0.232478\pi$
$101$	4.15733	+	2.77784i	0.413670	+	0.276405i	−0.331271	+	0.943536i	$0.607478\pi$
$102$	−2.12313	−	0.576624i	−0.210221	−	0.0570943i
$103$	−7.77176	+	3.21917i	−0.765774	+	0.317194i	−0.731159	−	0.682207i	$-0.761020\pi$
$103$	−7.77176	+	3.21917i	−0.765774	+	0.317194i	−0.0346147	+	0.999401i	$0.511020\pi$
$104$	−2.24056	−	14.2283i	−0.219705	−	1.39520i
$105$	0.200557	−	3.61267i	0.0195723	−	0.352561i
$106$	9.90820	+	15.2672i	0.962369	+	1.48288i
$107$	−0.477141	−	2.39875i	−0.0461270	−	0.231896i	0.950844	−	0.309670i	$-0.100219\pi$
$107$	−0.477141	−	2.39875i	−0.0461270	−	0.231896i	−0.996971	+	0.0777743i	$0.975219\pi$
$108$	−9.61392	−	3.94619i	−0.925100	−	0.379723i
$109$	1.58535	+	2.37265i	0.151849	+	0.227259i	0.899593	−	0.436728i	$-0.143863\pi$
$109$	1.58535	+	2.37265i	0.151849	+	0.227259i	−0.747744	+	0.663987i	$0.768863\pi$
$110$	0.0516224	−	3.85598i	0.00492200	−	0.367653i
$111$	5.09655	+	2.45034i	0.483743	+	0.232576i
$112$	−7.87998	+	2.77992i	−0.744588	+	0.262678i
$113$	6.28131	+	6.28131i	0.590896	+	0.590896i	0.937874	−	0.346977i	$-0.112792\pi$
$113$	6.28131	+	6.28131i	0.590896	+	0.590896i	−0.346977	+	0.937874i	$0.612792\pi$
$114$	−17.9287	−	8.91723i	−1.67917	−	0.835175i
$115$	1.02931	+	1.54047i	0.0959837	+	0.143650i
$116$	−4.61998	−	7.33187i	−0.428954	−	0.680747i
$117$	9.84154	−	11.6851i	0.909851	−	1.08029i
$118$	12.7163	+	2.70688i	1.17063	+	0.249188i
$119$	−1.73343	−	0.718011i	−0.158903	−	0.0658200i
$120$	−3.77900	+	3.11755i	−0.344974	+	0.284592i
$121$	−3.29305	+	1.36403i	−0.299368	+	0.124002i
$122$	2.46722	+	13.3340i	0.223372	+	1.20721i
$123$	0.606836	−	2.35877i	0.0547166	−	0.212683i
$124$	−4.34218	+	4.11568i	−0.389939	+	0.369599i
$125$	−0.980785	−	0.195090i	−0.0877241	−	0.0174494i
$126$	−7.70450	−	4.38068i	−0.686372	−	0.390262i
$127$			12.8815i			1.14305i	0.820585	+	0.571525i	$0.193648\pi$
$127$			12.8815i			1.14305i	−0.820585	+	0.571525i	$0.806352\pi$
$128$	10.0015	+	5.28862i	0.884018	+	0.467452i
$129$	−6.55108	−	18.6834i	−0.576791	−	1.64498i
$130$	−2.66671	−	6.68992i	−0.233886	−	0.586745i
$131$	0.0460168	−	0.231342i	0.00402050	−	0.0202124i	−0.978723	−	0.205186i	$-0.934220\pi$
$131$	0.0460168	−	0.231342i	0.00402050	−	0.0202124i	0.982743	+	0.184974i	$0.0592200\pi$
$132$	−8.40059	−	4.31945i	−0.731177	−	0.375960i
$133$	−14.1989	−	9.48739i	−1.23120	−	0.822661i
$134$	−14.9409	+	2.76455i	−1.29070	+	0.238821i
$135$	−5.12440	−	0.860519i	−0.441038	−	0.0740617i
$136$	0.877150	+	2.38415i	0.0752149	+	0.204440i
$137$	−4.17660	+	10.0832i	−0.356831	+	0.861466i	0.638911	+	0.769281i	$0.279385\pi$
$137$	−4.17660	+	10.0832i	−0.356831	+	0.861466i	−0.995742	+	0.0921851i	$0.970615\pi$
$138$	4.50135	−	0.577075i	0.383181	−	0.0491239i
$139$	−1.81672	−	9.13329i	−0.154093	−	0.774676i	−0.978106	−	0.208106i	$-0.933270\pi$
$139$	−1.81672	−	9.13329i	−0.154093	−	0.774676i	0.824014	−	0.566570i	$-0.191730\pi$
$140$	−3.53476	+	2.22733i	−0.298741	+	0.188244i
$141$	11.0318	−	14.6783i	0.929044	−	1.23613i
$142$	9.67200	−	9.41645i	0.811656	−	0.790211i
$143$	9.81910	−	9.81910i	0.821114	−	0.821114i
$144$	2.71512	+	11.6888i	0.226260	+	0.974067i
$145$	−3.06391	−	3.06391i	−0.254444	−	0.254444i
$146$	−16.1218	−	0.215832i	−1.33425	−	0.0178624i
$147$	3.64997	+	2.74321i	0.301044	+	0.226256i
$148$	−1.10200	−	6.43616i	−0.0905839	−	0.529049i
$149$	2.43692	−	0.484733i	0.199640	−	0.0397108i	−0.0942573	−	0.995548i	$-0.530048\pi$
$149$	2.43692	−	0.484733i	0.199640	−	0.0397108i	0.293897	+	0.955837i	$0.405048\pi$
$150$	−1.49774	+	1.93824i	−0.122290	+	0.158256i
$151$	−9.52608	−	3.94583i	−0.775221	−	0.321107i	−0.0402359	−	0.999190i	$-0.512811\pi$
$151$	−9.52608	−	3.94583i	−0.775221	−	0.321107i	−0.734985	+	0.678083i	$0.762811\pi$
$152$	3.59666	+	22.8401i	0.291728	+	1.85257i
$153$	−1.30035	+	2.35995i	−0.105127	+	0.190791i
$154$	−6.63766	−	4.56484i	−0.534878	−	0.367845i
$155$	−1.66192	+	2.48724i	−0.133489	+	0.199780i
$156$	−17.5812	−	1.44899i	−1.40762	−	0.116012i
$157$	19.2327	+	3.82562i	1.53494	+	0.305318i	0.888941	−	0.458022i	$-0.151442\pi$
$157$	19.2327	+	3.82562i	1.53494	+	0.305318i	0.645996	+	0.763340i	$0.276442\pi$
$158$	17.6165	+	7.57485i	1.40150	+	0.602623i
$159$	21.0354	−	7.37577i	1.66822	−	0.584936i
$160$	5.46192	+	1.47221i	0.431803	+	0.116388i
$161$	3.87029			0.305022
$162$	−7.47715	+	10.3001i	−0.587460	+	0.809253i
$163$	−1.56808	+	7.88326i	−0.122821	+	0.617464i	0.869516	+	0.493905i	$0.164431\pi$
$163$	−1.56808	+	7.88326i	−0.122821	+	0.617464i	−0.992337	+	0.123559i	$0.960569\pi$
$164$	−2.62617	+	1.00630i	−0.205069	+	0.0785790i
$165$	−4.57407	−	1.17676i	−0.356091	−	0.0916108i
$166$	6.40161	+	4.40250i	0.496861	+	0.341701i
$167$	−8.09727	−	19.5485i	−0.626586	−	1.51271i	−0.843839	−	0.536597i	$-0.819710\pi$
$167$	−8.09727	−	19.5485i	−0.626586	−	1.51271i	0.217253	−	0.976115i	$-0.430290\pi$
$168$	1.02913	+	10.1820i	0.0793993	+	0.785561i
$169$	4.94931	−	11.9487i	0.380716	−	0.919130i
$170$	0.691482	+	1.06548i	0.0530342	+	0.0817186i
$171$	−15.7982	+	18.7576i	−1.20812	+	1.43443i
$172$	−13.2055	+	18.6618i	−1.00691	+	1.42295i
$173$	−3.34483	+	2.23495i	−0.254303	+	0.169920i	−0.676187	−	0.736730i	$-0.736369\pi$
$173$	−3.34483	+	2.23495i	−0.254303	+	0.169920i	0.421884	+	0.906650i	$0.361369\pi$
$174$	−10.0620	+	3.37753i	−0.762795	+	0.256050i
$175$	−1.47714	+	1.47714i	−0.111661	+	0.111661i
$176$	1.55230	+	10.7963i	0.117009	+	0.813803i
$177$	6.89958	−	14.3507i	0.518604	−	1.07866i
$178$	−1.16967	+	1.13877i	−0.0876706	+	0.0853542i
$179$	−14.2471	+	9.51960i	−1.06488	+	0.711529i	−0.959159	−	0.282867i	$-0.908714\pi$
$179$	−14.2471	+	9.51960i	−1.06488	+	0.711529i	−0.105719	+	0.994396i	$0.533714\pi$
$180$	2.61714	+	5.39913i	0.195070	+	0.402427i
$181$	−1.85435	+	0.368852i	−0.137832	+	0.0274166i	−0.263524	−	0.964653i	$-0.584885\pi$
$181$	−1.85435	+	0.368852i	−0.137832	+	0.0274166i	0.125692	+	0.992069i	$0.459885\pi$
$182$	−14.7149	−	3.13230i	−1.09074	−	0.232182i
$183$	16.5824	+	0.920570i	1.22581	+	0.0680505i
$184$	−3.55366	−	3.85120i	−0.261979	−	0.283914i
$185$	−1.24943	−	3.01638i	−0.0918597	−	0.221769i
$186$	3.64211	+	6.35807i	0.267052	+	0.466196i
$187$	−1.36067	+	2.03639i	−0.0995021	+	0.148915i
$188$	−21.1947	−	0.567594i	−1.54578	−	0.0413961i
$189$	−7.44194	+	7.90203i	−0.541322	+	0.574788i
$190$	4.28074	+	10.7390i	0.310557	+	0.779090i
$191$	13.4823			0.975541			0.487771	−	0.872972i	$-0.337810\pi$
$191$	13.4823			0.975541			0.487771	+	0.872972i	$0.337810\pi$
$192$	9.18688	−	10.3731i	0.663006	−	0.748614i
$193$	−0.829017			−0.0596740			−0.0298370	−	0.999555i	$-0.509499\pi$
$193$	−0.829017			−0.0596740			−0.0298370	+	0.999555i	$0.509499\pi$
$194$	−5.43419	−	13.6327i	−0.390152	−	0.978768i
$195$	−8.73300	+	1.23861i	−0.625383	+	0.0886990i
$196$	0.141140	−	5.27036i	0.0100815	−	0.376454i
$197$	−7.54838	+	11.2970i	−0.537800	+	0.804875i	−0.996489	−	0.0837222i	$-0.973319\pi$
$197$	−7.54838	+	11.2970i	−0.537800	+	0.804875i	0.458689	+	0.888597i	$0.348319\pi$
$198$	−7.57041	+	8.74815i	−0.538006	+	0.621704i
$199$	7.47512	+	18.0465i	0.529898	+	1.27929i	0.931590	+	0.363511i	$0.118422\pi$
$199$	7.47512	+	18.0465i	0.529898	+	1.27929i	−0.401692	+	0.915775i	$0.631578\pi$
$200$	2.82615	+	0.113560i	0.199839	+	0.00802993i
$201$	−1.03151	+	18.5808i	−0.0727572	+	1.31059i
$202$	−6.91608	−	1.47221i	−0.486614	−	0.103584i
$203$	−8.87772	+	1.76589i	−0.623094	+	0.123941i
$204$	3.09109	−	0.354289i	0.216420	−	0.0248052i
$205$	−1.16920	+	0.781233i	−0.0816603	+	0.0545637i
$206$	8.52394	−	8.29873i	0.593891	−	0.578200i
$207$	0.615220	−	5.52398i	0.0427607	−	0.383943i
$208$	10.3942	+	17.5183i	0.720706	+	1.21468i
$209$	−15.7621	+	15.7621i	−1.09029	+	1.09029i
$210$	1.62833	+	4.85096i	0.112366	+	0.334748i
$211$	3.04768	−	2.03640i	0.209811	−	0.140191i	−0.446225	−	0.894921i	$-0.647232\pi$
$211$	3.04768	−	2.03640i	0.209811	−	0.140191i	0.656036	+	0.754729i	$0.272232\pi$
$212$	−21.0111	−	14.8679i	−1.44305	−	1.02113i
$213$	−8.40893	−	14.2343i	−0.576170	−	0.975319i
$214$	1.88294	+	2.90136i	0.128715	+	0.198333i
$215$	−4.37437	+	10.5607i	−0.298329	+	0.720230i
$216$	14.6962	+	0.149676i	0.999948	+	0.0101841i
$217$	2.39137	+	5.77328i	0.162337	+	0.391916i
$218$	−3.32512	−	2.28675i	−0.225206	−	0.154878i
$219$	−4.92002	+	19.1241i	−0.332464	+	1.29229i
$220$	1.95140	+	5.09260i	0.131563	+	0.343343i
$221$	−0.892317	+	4.48598i	−0.0600237	+	0.301760i
$222$	−7.97842	−	0.550141i	−0.535477	−	0.0369230i
$223$	−7.13448			−0.477760			−0.238880	−	0.971049i	$-0.576780\pi$
$223$	−7.13448			−0.477760			−0.238880	+	0.971049i	$0.576780\pi$
$224$	8.89613	−	7.77836i	0.594397	−	0.519714i
$225$	1.87348	+	2.34309i	0.124899	+	0.156206i
$226$	−11.5410	−	4.96245i	−0.767693	−	0.330097i
$227$	−23.5196	−	4.67835i	−1.56105	−	0.310513i	−0.662393	−	0.749157i	$-0.730459\pi$
$227$	−23.5196	−	4.67835i	−1.56105	−	0.310513i	−0.898661	+	0.438644i	$0.855459\pi$
$228$	28.2223	+	2.32600i	1.86907	+	0.154043i
$229$	6.58601	−	9.85666i	0.435216	−	0.651346i	−0.547427	−	0.836853i	$-0.684393\pi$
$229$	6.58601	−	9.85666i	0.435216	−	0.651346i	0.982643	+	0.185507i	$0.0593927\pi$
$230$	−2.15887	−	1.48470i	−0.142352	−	0.0978980i
$231$	−7.35253	+	6.57912i	−0.483761	+	0.432874i
$232$	9.90861	+	7.21252i	0.650532	+	0.473525i
$233$	17.3125	+	7.17109i	1.13418	+	0.469794i	0.869200	−	0.494460i	$-0.164634\pi$
$233$	17.3125	+	7.17109i	1.13418	+	0.469794i	0.264982	+	0.964253i	$0.414634\pi$
$234$	−6.80973	+	20.5043i	−0.445166	+	1.34041i
$235$	−10.3974	+	2.06818i	−0.678254	+	0.134913i
$236$	−18.1227	+	3.10298i	−1.17969	+	0.201987i
$237$	14.1103	−	18.7744i	0.916564	−	1.21953i
$238$	2.65319	+	0.0355198i	0.171980	+	0.00230241i
$239$	2.75476	+	2.75476i	0.178191	+	0.178191i	0.790567	−	0.612376i	$-0.209786\pi$
$239$	2.75476	+	2.75476i	0.178191	+	0.178191i	−0.612376	+	0.790567i	$0.709786\pi$
$240$	3.33191	−	6.07440i	0.215074	−	0.392101i
$241$	−12.3370	+	12.3370i	−0.794695	+	0.794695i	−0.982253	−	0.187558i	$-0.939943\pi$
$241$	−12.3370	+	12.3370i	−0.794695	+	0.794695i	0.187558	+	0.982253i	$0.439943\pi$
$242$	3.61177	−	3.51634i	0.232173	−	0.226039i
$243$	10.0954	+	11.8778i	0.647621	+	0.761962i
$244$	−10.2236	−	16.2248i	−0.654500	−	1.03869i
$245$	−0.514282	−	2.58547i	−0.0328563	−	0.165180i
$246$	0.437993	+	3.41647i	0.0279254	+	0.217826i
$247$	−15.9308	+	38.4605i	−1.01366	+	2.44718i
$248$	3.54907	−	7.68054i	0.225366	−	0.487715i
$249$	7.09106	−	6.34515i	0.449377	−	0.402108i
$250$	1.39061	−	0.257307i	0.0879498	−	0.0162735i
$251$	19.0817	+	12.7500i	1.20443	+	0.804772i	0.985285	−	0.170921i	$-0.0546744\pi$
$251$	19.0817	+	12.7500i	1.20443	+	0.804772i	0.219141	+	0.975693i	$0.429674\pi$
$252$	12.4153	+	1.72034i	0.782091	+	0.108371i
$253$	0.985603	−	4.95496i	0.0619643	−	0.311516i
$254$	−6.74550	−	16.9223i	−0.423250	−	1.06180i
$255$	1.46804	−	0.514746i	0.0919320	−	0.0322347i
$256$	−15.9083	−	1.71024i	−0.994271	−	0.106890i
$257$		−	8.71605i		−	0.543692i	−0.962341	−	0.271846i	$-0.912366\pi$
$257$		−	8.71605i		−	0.543692i	0.962341	−	0.271846i	$-0.0876342\pi$
$258$	18.3898	+	21.1137i	1.14490	+	1.31448i
$259$	−6.68931	−	1.33059i	−0.415654	−	0.0826786i
$260$	7.00645	+	7.39204i	0.434522	+	0.458435i
$261$	1.10921	+	12.9517i	0.0686585	+	0.801688i
$262$	0.0606921	+	0.328009i	0.00374957	+	0.0202644i
$263$	15.2623	−	6.32183i	0.941111	−	0.389821i	0.141228	−	0.989977i	$-0.454895\pi$
$263$	15.2623	−	6.32183i	0.941111	−	0.389821i	0.799883	+	0.600156i	$0.204895\pi$
$264$	13.2977	+	1.27539i	0.818416	+	0.0784949i
$265$	−11.8901	−	4.92503i	−0.730402	−	0.302542i
$266$	23.6211	+	5.02814i	1.44830	+	0.308295i
$267$	1.01692	+	1.72141i	0.0622347	+	0.105349i
$268$	18.1801	−	11.4557i	1.11053	−	0.699769i
$269$	−4.26505	−	6.38310i	−0.260045	−	0.389184i	0.678356	−	0.734733i	$-0.262693\pi$
$269$	−4.26505	−	6.38310i	−0.260045	−	0.389184i	−0.938401	+	0.345549i	$0.887693\pi$
$270$	7.18250	−	1.55298i	0.437113	−	0.0945111i
$271$	21.0126	+	21.0126i	1.27642	+	1.27642i	0.942656	+	0.333766i	$0.108320\pi$
$271$	21.0126	+	21.0126i	1.27642	+	1.27642i	0.333766	+	0.942656i	$0.391680\pi$
$272$	−2.40078	−	2.67271i	−0.145569	−	0.162057i
$273$	−7.98396	+	16.6061i	−0.483211	+	1.00505i
$274$	0.206615	−	15.4333i	0.0124821	−	0.932360i
$275$	1.51495	+	2.26728i	0.0913548	+	0.136722i
$276$	−5.61120	+	3.11527i	−0.337754	+	0.187517i
$277$	−5.83262	−	29.3225i	−0.350448	−	1.76182i	−0.606427	−	0.795139i	$-0.707398\pi$
$277$	−5.83262	−	29.3225i	−0.350448	−	1.76182i	0.255979	−	0.966682i	$-0.417602\pi$
$278$	7.16933	+	11.0470i	0.429988	+	0.662554i
$279$	8.62019	−	2.49543i	0.516078	−	0.149397i
$280$	3.47722	−	4.77703i	0.207803	−	0.285482i
$281$	8.97455	−	3.71738i	0.535377	−	0.221760i	−0.0985794	−	0.995129i	$-0.531430\pi$
$281$	8.97455	−	3.71738i	0.535377	−	0.221760i	0.633956	+	0.773369i	$0.281430\pi$
$282$	−6.80596	+	25.0596i	−0.405289	+	1.49228i
$283$	−5.03743	−	3.36590i	−0.299444	−	0.200082i	0.396767	−	0.917919i	$-0.370132\pi$
$283$	−5.03743	−	3.36590i	−0.299444	−	0.200082i	−0.696211	+	0.717837i	$0.745132\pi$
$284$	−7.77502	+	17.4351i	−0.461362	+	1.03458i
$285$	14.0187	−	1.98829i	0.830395	−	0.117776i
$286$	−7.75741	+	18.0411i	−0.458705	+	1.06679i
$287$			2.93750i			0.173395i
$288$	−9.68775	−	13.9337i	−0.570856	−	0.821050i
$289$			16.1933i			0.952547i
$290$	5.62947	+	2.42059i	0.330574	+	0.142142i
$291$	−17.7960	+	2.52404i	−1.04322	+	0.147962i
$292$	21.2920	−	8.15875i	1.24602	−	0.477455i
$293$	−14.8510	−	9.92313i	−0.867605	−	0.579715i	0.0401601	−	0.999193i	$-0.487213\pi$
$293$	−14.8510	−	9.92313i	−0.867605	−	0.579715i	−0.907766	+	0.419478i	$0.862213\pi$
$294$	−6.23143	−	1.69240i	−0.363424	−	0.0987028i
$295$	−8.49344	+	3.51810i	−0.494507	+	0.204832i
$296$	4.81803	+	7.87805i	0.280042	+	0.457902i
$297$	8.22146	+	11.5399i	0.477058	+	0.669613i
$298$	−2.94752	+	1.91290i	−0.170745	+	0.110811i
$299$	−1.84065	−	9.25357i	−0.106447	−	0.535148i
$300$	0.952599	−	3.33055i	0.0549983	−	0.192289i
$301$	13.2663	+	19.8545i	0.764658	+	1.14439i
$302$	14.5806	+	0.195199i	0.839018	+	0.0112325i
$303$	−3.75252	+	7.80500i	−0.215577	+	0.448386i
$304$	−16.6853	−	28.1214i	−0.956966	−	1.61287i
$305$	−6.78018	−	6.78018i	−0.388232	−	0.388232i
$306$	0.472446	−	3.78118i	0.0270079	−	0.216156i
$307$	−17.5629	−	26.2848i	−1.00237	−	1.50015i	−0.859972	−	0.510341i	$-0.829519\pi$
$307$	−17.5629	−	26.2848i	−1.00237	−	1.50015i	−0.142397	−	0.989810i	$-0.545481\pi$
$308$	11.1102	+	2.52093i	0.633065	+	0.143643i
$309$	−7.41080	−	12.5447i	−0.421586	−	0.713644i
$310$	0.880787	−	4.13774i	0.0500253	−	0.235008i
$311$	26.0889	+	10.8064i	1.47937	+	0.612774i	0.968973	−	0.247167i	$-0.0794995\pi$
$311$	26.0889	+	10.8064i	1.47937	+	0.612774i	0.510394	+	0.859941i	$0.329499\pi$
$312$	23.8550	−	7.30299i	1.35053	−	0.413451i
$313$	−24.3573	+	10.0891i	−1.37676	+	0.570272i	−0.943612	−	0.331053i	$-0.892596\pi$
$313$	−24.3573	+	10.0891i	−1.37676	+	0.570272i	−0.433145	+	0.901324i	$0.642596\pi$
$314$	−27.2691	+	5.04566i	−1.53889	+	0.284743i
$315$	6.24411	−	0.534761i	0.351816	−	0.0301303i
$316$	−27.1093	−	0.725988i	−1.52502	−	0.0408400i
$317$	4.17974	+	0.831403i	0.234758	+	0.0466962i	0.311067	−	0.950388i	$-0.399314\pi$
$317$	4.17974	+	0.831403i	0.234758	+	0.0466962i	−0.0763093	+	0.997084i	$0.524314\pi$
$318$	−23.7716	+	20.7048i	−1.33305	+	1.16107i
$319$			11.8154i			0.661538i
$320$	−7.94621	+	0.926148i	−0.444207	+	0.0517732i
$321$	3.99754	−	1.40168i	0.223121	−	0.0782341i
$322$	−5.08436	+	2.02671i	−0.283341	+	0.112944i
$323$	1.43239	−	7.20113i	0.0797006	−	0.400682i
$324$	4.42893	−	17.4466i	0.246052	−	0.969257i
$325$	4.23423	+	2.82922i	0.234873	+	0.156937i
$326$	−2.06816	−	11.1773i	−0.114545	−	0.619053i
$327$	−3.68323	+	3.29579i	−0.203683	+	0.182258i
$328$	2.92301	−	2.69718i	0.161396	−	0.148927i
$329$	−8.47478	+	20.4599i	−0.467230	+	1.12799i
$330$	6.62513	−	0.849345i	0.364702	−	0.0467549i
$331$	0.599720	+	3.01500i	0.0329636	+	0.165719i	0.993761	−	0.111533i	$-0.0355762\pi$
$331$	0.599720	+	3.01500i	0.0329636	+	0.165719i	−0.960797	+	0.277252i	$0.910576\pi$
$332$	−10.7151	−	2.43128i	−0.588070	−	0.133434i
$333$	−2.96245	+	9.33599i	−0.162341	+	0.511609i
$334$	20.8741	+	21.4405i	1.14218	+	1.17317i
$335$	7.59728	−	7.59728i	0.415084	−	0.415084i
$336$	−6.68386	−	12.8371i	−0.364635	−	0.700323i
$337$	−4.95980	−	4.95980i	−0.270178	−	0.270178i	0.558994	−	0.829172i	$-0.311187\pi$
$337$	−4.95980	−	4.95980i	−0.270178	−	0.270178i	−0.829172	+	0.558994i	$0.811187\pi$
$338$	−0.244841	+	18.2886i	−0.0133176	+	0.994770i
$339$	−9.24398	+	12.2995i	−0.502064	+	0.668018i
$340$	−1.46634	−	1.03761i	−0.0795234	−	0.0562724i
$341$	8.00025	−	1.59135i	0.433238	−	0.0861764i
$342$	10.9313	−	32.9145i	0.591100	−	1.77981i
$343$	−18.5975	−	7.70333i	−1.00417	−	0.415940i
$344$	7.57554	−	31.4310i	0.408446	−	1.69465i
$345$	−2.39138	+	2.13983i	−0.128748	+	0.115205i
$346$	3.22373	−	4.68757i	0.173309	−	0.252006i
$347$	3.50572	−	5.24668i	0.188197	−	0.281657i	−0.725358	−	0.688372i	$-0.758326\pi$
$347$	3.50572	−	5.24668i	0.188197	−	0.281657i	0.913555	+	0.406715i	$0.133326\pi$
$348$	11.4496	−	9.70604i	0.613765	−	0.520299i
$349$	−19.8401	−	3.94644i	−1.06202	−	0.211248i	−0.366984	−	0.930227i	$-0.619610\pi$
$349$	−19.8401	−	3.94644i	−1.06202	−	0.211248i	−0.695032	+	0.718979i	$0.744610\pi$
$350$	1.16699	−	2.71402i	0.0623781	−	0.145070i
$351$	22.4324	+	14.0350i	1.19735	+	0.749134i
$352$	−7.69282	−	13.3701i	−0.410029	−	0.712631i
$353$	33.0730			1.76030			0.880150	−	0.474696i	$-0.157442\pi$
$353$	33.0730			1.76030			0.880150	+	0.474696i	$0.157442\pi$
$354$	−1.54907	+	22.4654i	−0.0823321	+	1.19402i
$355$	−1.86215	+	9.36167i	−0.0988328	+	0.496866i
$356$	0.940263	−	2.10850i	0.0498338	−	0.111750i
$357$	0.809695	−	3.14728i	0.0428536	−	0.166572i
$358$	13.7313	−	19.9664i	0.725720	−	1.05526i
$359$	−3.54244	−	8.55221i	−0.186963	−	0.451368i	0.802409	−	0.596774i	$-0.203551\pi$
$359$	−3.54244	−	8.55221i	−0.186963	−	0.451368i	−0.989372	+	0.145406i	$0.953551\pi$
$360$	−6.26540	−	5.72230i	−0.330216	−	0.301592i
$361$	18.3021	−	44.1851i	0.963267	−	2.32553i
$362$	2.24288	−	1.45560i	0.117883	−	0.0765046i
$363$	−3.14011	−	5.31545i	−0.164813	−	0.278989i
$364$	20.9710	−	3.59066i	1.09918	−	0.188202i
$365$	9.47945	−	6.33397i	0.496177	−	0.331535i
$366$	−22.2663	+	7.47417i	−1.16388	+	0.390681i
$367$	5.95354	−	5.95354i	0.310772	−	0.310772i	−0.534437	−	0.845209i	$-0.679476\pi$
$367$	5.95354	−	5.95354i	0.310772	−	0.310772i	0.845209	+	0.534437i	$0.179476\pi$
$368$	6.68512	+	3.19839i	0.348486	+	0.166728i
$369$	4.19262	+	0.466944i	0.218259	+	0.0243081i
$370$	3.22091	+	3.30832i	0.167447	+	0.171992i
$371$	−22.3538	+	14.9364i	−1.16055	+	0.775457i
$372$	−8.11405	−	6.44531i	−0.420694	−	0.334174i
$373$	−10.3387	+	2.05649i	−0.535317	+	0.106481i	−0.455343	−	0.890316i	$-0.650483\pi$
$373$	−10.3387	+	2.05649i	−0.535317	+	0.106481i	−0.0799733	+	0.996797i	$0.525483\pi$
$374$	0.721131	−	3.38771i	0.0372888	−	0.175174i
$375$	0.0960065	−	1.72939i	0.00495775	−	0.0893052i
$376$	28.1405	−	10.3531i	1.45123	−	0.533921i
$377$	8.44421	+	20.3861i	0.434899	+	1.04994i
$378$	5.63845	−	14.2779i	0.290011	−	0.734374i
$379$	−10.0374	+	15.0220i	−0.515584	+	0.771627i	−0.994331	−	0.106326i	$-0.966091\pi$
$379$	−10.0374	+	15.0220i	−0.515584	+	0.771627i	0.478747	+	0.877953i	$0.341091\pi$
$380$	−11.2471	−	11.8661i	−0.576966	−	0.608718i
$381$	−22.0904	+	3.13311i	−1.13172	+	0.160514i
$382$	−17.7115	+	7.06008i	−0.906199	+	0.361225i
$383$	−10.0009			−0.511021			−0.255510	−	0.966806i	$-0.582243\pi$
$383$	−10.0009			−0.511021			−0.255510	+	0.966806i	$0.582243\pi$
$384$	−6.63677	+	18.4378i	−0.338681	+	0.940901i
$385$	5.69633			0.290312
$386$	1.08907	−	0.434121i	0.0554323	−	0.0220962i
$387$	30.4466	−	15.7787i	1.54769	−	0.802074i
$388$	14.2777	+	15.0634i	0.724840	+	0.764731i
$389$	−2.18079	+	3.26378i	−0.110570	+	0.165480i	−0.882628	−	0.470073i	$-0.844228\pi$
$389$	−2.18079	+	3.26378i	−0.110570	+	0.165480i	0.772057	+	0.635553i	$0.219228\pi$
$390$	10.8239	−	6.20026i	0.548087	−	0.313962i
$391$	0.636799	+	1.53737i	0.0322043	+	0.0777481i
$392$	2.57445	+	6.99753i	0.130029	+	0.353429i
$393$	0.407918	+	0.0226455i	0.0205767	+	0.00114231i
$394$	4.00051	−	18.7935i	0.201543	−	0.946801i
$395$	−13.2990	+	2.64533i	−0.669143	+	0.133101i
$396$	5.36414	−	15.4567i	0.269558	−	0.776727i
$397$	−12.8879	+	8.61143i	−0.646826	+	0.432195i	−0.835233	−	0.549896i	$-0.814667\pi$
$397$	−12.8879	+	8.61143i	−0.646826	+	0.432195i	0.188407	+	0.982091i	$0.439667\pi$
$398$	−19.2702	−	19.7932i	−0.965928	−	0.992142i
$399$	12.8163	−	26.6571i	0.641617	−	1.33452i
$400$	−3.77215	+	1.33075i	−0.188607	+	0.0665375i
$401$	−0.0922059	+	0.0922059i	−0.00460454	+	0.00460454i	−0.709405	−	0.704801i	$-0.751036\pi$
$401$	−0.0922059	+	0.0922059i	−0.00460454	+	0.00460454i	0.704801	+	0.709405i	$0.251036\pi$
$402$	−8.37491	−	24.9496i	−0.417703	−	1.24438i
$403$	12.6662	−	8.46326i	0.630946	−	0.421585i
$404$	9.85653	−	1.68764i	0.490381	−	0.0839631i
$405$	0.229310	−	8.99708i	0.0113945	−	0.447068i
$406$	10.7379	−	6.96872i	0.532911	−	0.345852i
$407$	−3.40698	+	8.22518i	−0.168878	+	0.407707i
$408$	−3.87521	+	2.08410i	−0.191852	+	0.103178i
$409$	−6.71196	−	16.2041i	−0.331885	−	0.801242i	−0.998443	−	0.0557880i	$-0.982233\pi$
$409$	−6.71196	−	16.2041i	−0.331885	−	0.801242i	0.666558	−	0.745454i	$-0.267767\pi$
$410$	1.12687	−	1.63856i	0.0556519	−	0.0809226i
$411$	−18.3074	−	4.70991i	−0.903038	−	0.232323i
$412$	−6.85213	+	15.3656i	−0.337580	+	0.757008i
$413$	−3.74663	+	18.8356i	−0.184359	+	0.926837i
$414$	2.08446	+	7.57896i	0.102446	+	0.372485i
$415$	−5.49375			−0.269678
$416$	−22.8283	−	17.5707i	−1.11925	−	0.861474i
$417$	15.2207	−	5.33693i	0.745361	−	0.261350i
$418$	12.4526	−	28.9605i	0.609077	−	1.41651i
$419$	0.729294	+	0.145066i	0.0356283	+	0.00708692i	0.212872	−	0.977080i	$-0.431718\pi$
$419$	0.729294	+	0.145066i	0.0356283	+	0.00708692i	−0.177244	+	0.984167i	$0.556718\pi$
$420$	−4.67937	−	5.51997i	−0.228330	−	0.269347i
$421$	−2.93811	+	4.39719i	−0.143195	+	0.214306i	−0.896133	−	0.443785i	$-0.853636\pi$
$421$	−2.93811	+	4.39719i	−0.143195	+	0.214306i	0.752939	+	0.658090i	$0.228636\pi$
$422$	−2.93734	+	4.27114i	−0.142987	+	0.207916i
$423$	27.8548	+	15.3482i	1.35435	+	0.746253i
$424$	35.3878	+	8.52919i	1.71858	+	0.414214i
$425$	−0.829795	−	0.343712i	−0.0402510	−	0.0166725i
$426$	18.5006	+	14.2961i	0.896358	+	0.692647i
$427$	−19.6456	+	3.90776i	−0.950719	+	0.189110i
$428$	−3.99292	−	2.82547i	−0.193005	−	0.136574i
$429$	19.2269	+	14.4504i	0.928284	+	0.697672i
$430$	0.216399	−	16.1641i	0.0104357	−	0.779502i
$431$	9.90028	+	9.90028i	0.476880	+	0.476880i	0.904132	−	0.427253i	$-0.140519\pi$
$431$	9.90028	+	9.90028i	0.476880	+	0.476880i	−0.427253	+	0.904132i	$0.640519\pi$
$432$	−19.3846	+	7.49913i	−0.932642	+	0.360802i
$433$	−1.07022	+	1.07022i	−0.0514313	+	0.0514313i	−0.732355	−	0.680923i	$-0.761579\pi$
$433$	−1.07022	+	1.07022i	−0.0514313	+	0.0514313i	0.680923	+	0.732355i	$0.261579\pi$
$434$	−6.16474	−	6.33204i	−0.295917	−	0.303948i
$435$	4.50905	−	5.99949i	0.216192	−	0.287653i
$436$	5.56565	+	1.26285i	0.266546	+	0.0604797i
$437$	2.95471	+	14.8543i	0.141343	+	0.710578i
$438$	−3.55109	−	27.6995i	−0.169678	−	1.32354i
$439$	6.89989	−	16.6578i	0.329314	−	0.795034i	−0.669330	−	0.742966i	$-0.733419\pi$
$439$	6.89989	−	16.6578i	0.329314	−	0.795034i	0.998644	−	0.0520686i	$-0.0165814\pi$
$440$	−5.23031	−	5.66823i	−0.249345	−	0.270222i
$441$	−3.81654	+	6.92650i	−0.181740	+	0.329833i
$442$	−1.17689	−	6.36046i	−0.0559788	−	0.302536i
$443$	11.6553	+	7.78785i	0.553762	+	0.370012i	0.800743	−	0.599009i	$-0.204439\pi$
$443$	11.6553	+	7.78785i	0.553762	+	0.370012i	−0.246981	+	0.969020i	$0.579439\pi$
$444$	10.7693	−	3.45524i	0.511087	−	0.163979i
$445$	0.225197	−	1.13214i	0.0106754	−	0.0536687i
$446$	9.37250	−	3.73602i	0.443801	−	0.176906i
$447$	1.42398	+	4.06114i	0.0673520	+	0.192085i
$448$	−7.61356	+	14.8769i	−0.359707	+	0.702867i
$449$			17.0148i			0.802977i	0.915864	+	0.401488i	$0.131507\pi$
$449$			17.0148i			0.802977i	−0.915864	+	0.401488i	$0.868493\pi$
$450$	−3.68815	−	2.09703i	−0.173861	−	0.0988552i
$451$	3.76075	+	0.748060i	0.177087	+	0.0352247i
$452$	17.7599	+	0.475610i	0.835354	+	0.0223708i
$453$	4.44968	−	17.2959i	0.209064	−	0.812631i
$454$	33.3474	−	6.17034i	1.56507	−	0.289588i
$455$	9.82832	−	4.07102i	0.460759	−	0.190853i
$456$	−38.2934	+	11.7232i	−1.79325	+	0.548987i
$457$	−0.267222	−	0.110687i	−0.0125001	−	0.00517772i	0.376425	−	0.926447i	$-0.377153\pi$
$457$	−0.267222	−	0.110687i	−0.0125001	−	0.00517772i	−0.388925	+	0.921270i	$0.627153\pi$
$458$	−3.49047	+	16.3974i	−0.163099	+	0.766201i
$459$	−4.36333	−	1.65595i	−0.203663	−	0.0772931i
$460$	3.61357	+	0.819922i	0.168483	+	0.0382291i
$461$	−22.9630	−	34.3666i	−1.06949	−	1.60061i	−0.760252	−	0.649628i	$-0.774925\pi$
$461$	−22.9630	−	34.3666i	−1.06949	−	1.60061i	−0.309242	−	0.950983i	$-0.600075\pi$
$462$	6.21374	−	12.4931i	0.289090	−	0.581233i
$463$	−29.4497	−	29.4497i	−1.36865	−	1.36865i	−0.862374	−	0.506272i	$-0.831023\pi$
$463$	−29.4497	−	29.4497i	−1.36865	−	1.36865i	−0.506272	−	0.862374i	$-0.668977\pi$
$464$	−16.7937	−	4.28630i	−0.779630	−	0.198986i
$465$	−4.66955	−	2.24505i	−0.216545	−	0.104112i
$466$	−26.4985	−	0.354752i	−1.22752	−	0.0164336i
$467$	−3.52891	−	5.28139i	−0.163299	−	0.244394i	0.740792	−	0.671735i	$-0.234450\pi$
$467$	−3.52891	−	5.28139i	−0.163299	−	0.244394i	−0.904091	+	0.427341i	$0.859450\pi$
$468$	−1.79132	−	30.5022i	−0.0828040	−	1.40997i
$469$	−4.37870	−	22.0132i	−0.202189	−	1.01648i
$470$	12.5760	−	8.16165i	0.580088	−	0.376469i
$471$	−1.88264	+	33.9124i	−0.0867474	+	1.56260i
$472$	22.1828	−	13.5665i	1.02105	−	0.624447i
$473$	28.7972	−	11.9282i	1.32409	−	0.548458i
$474$	−8.70524	+	32.0528i	−0.399845	+	1.47223i
$475$	−6.79701	−	4.54162i	−0.311868	−	0.208384i
$476$	−3.50407	+	1.34270i	−0.160609	+	0.0615425i
$477$	17.7650	+	34.2794i	0.813401	+	1.56955i
$478$	−5.06146	−	2.17635i	−0.231506	−	0.0995441i
$479$			4.86884i			0.222463i	0.993795	+	0.111231i	$0.0354795\pi$
$479$			4.86884i			0.222463i	−0.993795	+	0.111231i	$0.964521\pi$
$480$	−1.19620	+	9.72466i	−0.0545988	+	0.443868i
$481$			16.6264i			0.758100i
$482$	9.74663	−	22.6673i	0.443947	−	1.03247i
$483$	0.941352	+	6.63711i	0.0428330	+	0.301999i
$484$	−2.90339	+	6.51071i	−0.131972	+	0.295941i
$485$	8.62848	+	5.76536i	0.391799	+	0.261792i
$486$	−19.4822	−	10.3172i	−0.883729	−	0.467999i
$487$	−6.40137	+	2.65153i	−0.290074	+	0.120152i	−0.522975	−	0.852348i	$-0.675178\pi$
$487$	−6.40137	+	2.65153i	−0.290074	+	0.120152i	0.232902	+	0.972500i	$0.425178\pi$
$488$	21.9269	+	15.9607i	0.992584	+	0.722506i
$489$	−13.9003	−	0.771671i	−0.628593	−	0.0348962i
$490$	2.02951	+	3.12720i	0.0916839	+	0.141273i
$491$	−7.39567	−	37.1805i	−0.333762	−	1.67793i	−0.674891	−	0.737917i	$-0.735809\pi$
$491$	−7.39567	−	37.1805i	−0.333762	−	1.67793i	0.341130	−	0.940016i	$-0.389191\pi$
$492$	−2.36445	−	4.25882i	−0.106597	−	0.192003i
$493$	−2.16215	−	3.23589i	−0.0973783	−	0.145737i
$494$	0.788095	−	58.8675i	0.0354581	−	2.64857i
$495$	0.905486	−	8.13024i	0.0406986	−	0.365427i
$496$	−0.640414	+	11.9483i	−0.0287554	+	0.536497i
$497$	14.0994	+	14.0994i	0.632444	+	0.632444i
$498$	−5.99277	+	12.0488i	−0.268542	+	0.539922i
$499$	14.8706	+	22.2555i	0.665701	+	0.996292i	0.998577	+	0.0533214i	$0.0169808\pi$
$499$	14.8706	+	22.2555i	0.665701	+	0.996292i	−0.332876	+	0.942970i	$0.608019\pi$
$500$	−1.69209	+	1.06622i	−0.0756725	+	0.0476830i
$501$	31.5541	−	18.6406i	1.40973	−	0.832801i
$502$	−31.7441	−	6.75726i	−1.41681	−	0.301591i
$503$	−3.68425	−	1.52607i	−0.164273	−	0.0680440i	0.299032	−	0.954243i	$-0.403336\pi$
$503$	−3.68425	−	1.52607i	−0.164273	−	0.0680440i	−0.463304	+	0.886199i	$0.653336\pi$
$504$	−17.2107	+	4.24137i	−0.766628	+	0.188926i
$505$	4.61938	−	1.91341i	0.205560	−	0.0851456i
$506$	1.29992	+	7.02540i	0.0577887	+	0.312317i
$507$	21.6945	+	5.58129i	0.963485	+	0.247874i
$508$	17.7230	+	18.6984i	0.786331	+	0.829606i
$509$	4.64662	+	0.924271i	0.205958	+	0.0409676i	0.296991	−	0.954880i	$-0.404017\pi$
$509$	4.64662	+	0.924271i	0.205958	+	0.0409676i	−0.0910330	+	0.995848i	$0.529017\pi$
$510$	−1.65899	+	1.44497i	−0.0734615	+	0.0639841i
$511$		−	23.8162i		−	1.05357i
$512$	21.7942	−	6.08379i	0.963177	−	0.268868i
$513$	−36.0097	−	22.5298i	−1.58987	−	0.994714i
$514$	4.56422	+	11.4502i	0.201319	+	0.505046i
$515$	−1.64112	+	8.25045i	−0.0723163	+	0.363558i
$516$	−35.2149	−	18.1069i	−1.55025	−	0.797114i
$517$	24.0358	+	16.0602i	1.05709	+	0.706326i
$518$	9.48446	−	1.75493i	0.416723	−	0.0771071i
$519$	−4.64623	−	5.19242i	−0.203947	−	0.227922i
$520$	−13.0752	−	6.04188i	−0.573386	−	0.264954i
$521$	9.55028	−	23.0564i	0.418405	−	1.01012i	−0.564404	−	0.825498i	$-0.690894\pi$
$521$	9.55028	−	23.0564i	0.418405	−	1.01012i	0.982810	−	0.184621i	$-0.0591059\pi$
$522$	−8.23940	−	16.4336i	−0.360629	−	0.719281i
$523$	−3.97200	−	19.9686i	−0.173684	−	0.873167i	−0.965099	−	0.261887i	$-0.915655\pi$
$523$	−3.97200	−	19.9686i	−0.173684	−	0.873167i	0.791415	−	0.611279i	$-0.209345\pi$
$524$	−0.251495	−	0.399120i	−0.0109866	−	0.0174356i
$525$	−2.89240	−	2.17385i	−0.126235	−	0.0948746i
$526$	−16.7394	+	16.2971i	−0.729873	+	0.710588i
$527$	−1.89981	+	1.89981i	−0.0827572	+	0.0827572i
$528$	−18.1369	+	5.28796i	−0.789308	+	0.230129i
$529$	13.8363	+	13.8363i	0.601578	+	0.601578i
$530$	18.1989	+	0.243640i	0.790511	+	0.0105831i
$531$	26.2880	+	8.34157i	1.14080	+	0.361993i
$532$	−33.6638	+	5.76393i	−1.45951	+	0.249898i
$533$	7.02334	−	1.39703i	0.304214	−	0.0605120i
$534$	−2.23735	−	1.72888i	−0.0968197	−	0.0748159i
$535$	−2.25957	−	0.935946i	−0.0976899	−	0.0404645i
$536$	−17.8842	+	24.5694i	−0.772478	+	1.06124i
$537$	−19.7903	−	22.1168i	−0.854015	−	0.954409i
$538$	8.94551	+	6.15199i	0.385668	+	0.265231i
$539$	−3.99359	+	5.97683i	−0.172016	+	0.257440i
$540$	−8.62235	+	5.80130i	−0.371047	+	0.249648i
$541$	−8.60447	−	1.71154i	−0.369935	−	0.0735847i	0.00662203	−	0.999978i	$-0.497892\pi$
$541$	−8.60447	−	1.71154i	−0.369935	−	0.0735847i	−0.376557	+	0.926393i	$0.622892\pi$
$542$	−38.6074	−	16.6006i	−1.65833	−	0.713058i
$543$	−1.08356	−	3.09028i	−0.0465002	−	0.132617i
$544$	4.55347	+	2.25393i	0.195229	+	0.0966366i
$545$	2.85356			0.122233
$546$	1.79253	−	25.9962i	0.0767132	−	1.11253i
$547$	3.58171	−	18.0065i	0.153143	−	0.769901i	−0.825511	−	0.564386i	$-0.809113\pi$
$547$	3.58171	−	18.0065i	0.153143	−	0.769901i	0.978654	−	0.205515i	$-0.0658870\pi$
$548$	7.81034	+	20.3828i	0.333641	+	0.870709i
$549$	2.45459	+	28.6609i	0.104759	+	1.22322i
$550$	−3.17745	−	2.18519i	−0.135487	−	0.0931768i
$551$	−13.5551	−	32.7249i	−0.577466	−	1.39413i
$552$	5.74004	−	7.03084i	0.244312	−	0.299252i
$553$	−10.8398	+	26.1695i	−0.460953	+	1.11284i
$554$	23.0172	+	35.4665i	0.977908	+	1.50683i
$555$	4.86887	−	2.87629i	0.206672	−	0.122092i
$556$	−15.2031	−	10.7580i	−0.644756	−	0.456242i
$557$	−2.22968	+	1.48982i	−0.0944745	+	0.0631258i	−0.601910	−	0.798564i	$-0.705593\pi$
$557$	−2.22968	+	1.48982i	−0.0944745	+	0.0631258i	0.507436	+	0.861690i	$0.330593\pi$
$558$	−10.0175	+	7.79225i	−0.424075	+	0.329872i
$559$	41.1612	−	41.1612i	1.74093	−	1.74093i
$560$	−2.06646	+	8.09640i	−0.0873239	+	0.342135i
$561$	−3.82313	−	1.83810i	−0.161413	−	0.0776046i
$562$	−9.84315	+	9.58308i	−0.415208	+	0.404238i
$563$	−23.1971	+	15.4998i	−0.977642	+	0.653239i	−0.938240	−	0.345984i	$-0.887545\pi$
$563$	−23.1971	+	15.4998i	−0.977642	+	0.653239i	−0.0394015	+	0.999223i	$0.512545\pi$
$564$	−4.18172	−	36.4846i	−0.176082	−	1.53628i
$565$	8.71243	−	1.73301i	0.366535	−	0.0729083i
$566$	8.38021	+	1.78387i	0.352246	+	0.0749816i
$567$	−15.3612	−	10.8401i	−0.645109	−	0.455242i
$568$	1.08394	−	26.9758i	0.0454812	−	1.13188i
$569$	1.73932	+	4.19908i	0.0729160	+	0.176035i	0.956135	−	0.292925i	$-0.0946288\pi$
$569$	1.73932	+	4.19908i	0.0729160	+	0.176035i	−0.883219	+	0.468960i	$0.844629\pi$
$570$	−17.3750	+	9.95299i	−0.727760	+	0.416885i
$571$	3.53998	−	5.29795i	0.148143	−	0.221712i	−0.749975	−	0.661466i	$-0.769934\pi$
$571$	3.53998	−	5.29795i	0.148143	−	0.221712i	0.898118	+	0.439754i	$0.144934\pi$
$572$	0.743485	−	27.7626i	0.0310867	−	1.16081i
$573$	3.27922	+	23.1206i	0.136991	+	0.965875i
$574$	−1.53824	−	3.85897i	−0.0642050	−	0.161070i
$575$	1.85271			0.0772633
$576$	20.0232	+	13.2315i	0.834299	+	0.551312i
$577$	−29.9344			−1.24618			−0.623092	−	0.782149i	$-0.714124\pi$
$577$	−29.9344			−1.24618			−0.623092	+	0.782149i	$0.714124\pi$
$578$	−8.47974	−	21.2730i	−0.352711	−	0.884840i
$579$	−0.201638	−	1.42167i	−0.00837978	−	0.0590827i
$580$	−8.66295	−	0.231994i	−0.359709	−	0.00963303i
$581$	−6.37594	+	9.54227i	−0.264519	+	0.395880i
$582$	22.0568	−	12.6348i	0.914282	−	0.523731i
$583$	13.4298	+	32.4223i	0.556203	+	1.34279i
$584$	−23.6988	+	21.8678i	−0.980662	+	0.904897i
$585$	−4.24817	−	14.6749i	−0.175640	−	0.606731i
$586$	24.7060	+	5.25908i	1.02059	+	0.217251i
$587$	6.88054	−	1.36862i	0.283990	−	0.0564892i	−0.0510398	−	0.998697i	$-0.516254\pi$
$587$	6.88054	−	1.36862i	0.283990	−	0.0564892i	0.335030	+	0.942207i	$0.391254\pi$
$588$	9.07241	−	1.03984i	0.374140	−	0.0428824i
$589$	−20.3324	+	13.5857i	−0.837782	+	0.559788i
$590$	9.31548	−	9.06935i	0.383512	−	0.373379i
$591$	−21.2090	−	10.1969i	−0.872420	−	0.419446i
$592$	−10.4548	−	7.82632i	−0.429690	−	0.321660i
$593$	−21.0009	+	21.0009i	−0.862403	+	0.862403i	−0.991617	−	0.129214i	$-0.958755\pi$
$593$	−21.0009	+	21.0009i	−0.862403	+	0.862403i	0.129214	+	0.991617i	$0.458755\pi$
$594$	−16.8434	−	10.8546i	−0.691094	−	0.445371i
$595$	−1.56005	+	1.04239i	−0.0639557	+	0.0427339i
$596$	2.87043	−	4.05645i	0.117577	−	0.166158i
$597$	−29.1297	+	17.2084i	−1.19220	+	0.704292i
$598$	7.26374	+	11.1925i	0.297036	+	0.457693i
$599$	4.97865	−	12.0195i	0.203422	−	0.491105i	−0.788939	−	0.614472i	$-0.789369\pi$
$599$	4.97865	−	12.0195i	0.203422	−	0.491105i	0.992361	+	0.123367i	$0.0393692\pi$
$600$	0.492646	+	4.87415i	0.0201122	+	0.198986i
$601$	16.4232	+	39.6491i	0.669916	+	1.61732i	0.781750	+	0.623593i	$0.214328\pi$
$601$	16.4232	+	39.6491i	0.669916	+	1.61732i	−0.111834	+	0.993727i	$0.535672\pi$
$602$	−27.8248	−	19.1356i	−1.13405	−	0.779909i
$603$	−32.1150	+	2.75040i	−1.30782	+	0.112005i
$604$	−19.2566	+	7.37880i	−0.783539	+	0.300239i
$605$	−0.695375	+	3.49588i	−0.0282710	+	0.142128i
$606$	0.842502	−	12.2184i	0.0342243	−	0.496338i
$607$	−0.134552			−0.00546129			−0.00273065	−	0.999996i	$-0.500869\pi$
$607$	−0.134552			−0.00546129			−0.00273065	+	0.999996i	$0.500869\pi$
$608$	36.6453	+	28.2054i	1.48616	+	1.14388i
$609$	−5.18759	−	14.7948i	−0.210212	−	0.599515i
$610$	12.4575	+	5.35656i	0.504391	+	0.216881i
$611$	52.9486	+	10.5321i	2.14207	+	0.426084i
$612$	1.35940	+	5.21471i	0.0549504	+	0.210792i
$613$	4.52156	−	6.76700i	0.182624	−	0.273317i	−0.728850	−	0.684673i	$-0.759945\pi$
$613$	4.52156	−	6.76700i	0.182624	−	0.273317i	0.911474	+	0.411357i	$0.134945\pi$
$614$	36.8365	+	25.3331i	1.48660	+	1.02236i
$615$	−1.62411	−	1.81503i	−0.0654903	−	0.0731890i
$616$	−15.9155	+	2.50624i	−0.641255	+	0.100979i
$617$	28.2027	+	11.6819i	1.13540	+	0.470297i	0.869612	−	0.493736i	$-0.164369\pi$
$617$	28.2027	+	11.6819i	1.13540	+	0.470297i	0.265785	+	0.964032i	$0.414369\pi$
$618$	16.3046	+	12.5992i	0.655868	+	0.506812i
$619$	−3.05782	+	0.608239i	−0.122904	+	0.0244472i	−0.256159	−	0.966635i	$-0.582457\pi$
$619$	−3.05782	+	0.608239i	−0.122904	+	0.0244472i	0.133255	+	0.991082i	$0.457457\pi$
$620$	1.00967	+	5.89694i	0.0405495	+	0.236827i
$621$	9.62264	−	0.288536i	0.386143	−	0.0115785i
$622$	−39.9316	−	0.534589i	−1.60111	−	0.0214351i
$623$	−1.70509	−	1.70509i	−0.0683132	−	0.0683132i
$624$	−27.5139	+	22.0857i	−1.10144	+	0.884137i
$625$	−0.707107	+	0.707107i	−0.0282843	+	0.0282843i
$626$	26.7147	−	26.0089i	1.06774	−	1.03952i
$627$	−30.8641	−	23.1966i	−1.23259	−	0.926382i
$628$	33.1810	−	20.9081i	1.32407	−	0.834325i
$629$	−0.572087	−	2.87608i	−0.0228106	−	0.114677i
$630$	−7.92280	+	3.97228i	−0.315652	+	0.158260i
$631$	6.54309	−	15.7964i	0.260476	−	0.628845i	−0.738492	−	0.674262i	$-0.764462\pi$
$631$	6.54309	−	15.7964i	0.260476	−	0.628845i	0.998968	+	0.0454172i	$0.0144617\pi$
$632$	35.9934	−	13.2423i	1.43174	−	0.526749i
$633$	4.23347	+	4.73113i	0.168265	+	0.188046i
$634$	−5.92626	+	1.09655i	−0.235362	+	0.0435495i
$635$	10.7106	+	7.15659i	0.425037	+	0.284001i
$636$	20.3863	−	39.6479i	0.808371	−	1.57214i
$637$	−2.61896	+	13.1664i	−0.103767	+	0.521673i
$638$	−6.18725	−	15.5218i	−0.244955	−	0.614516i
$639$	22.3650	−	17.8825i	0.884745	−	0.707421i
$640$	9.95388	−	5.37776i	0.393462	−	0.212575i
$641$		−	26.1350i		−	1.03227i	−0.856508	−	0.516134i	$-0.827371\pi$
$641$		−	26.1350i		−	1.03227i	0.856508	−	0.516134i	$-0.172629\pi$
$642$	−4.51752	+	3.93471i	−0.178292	+	0.155291i
$643$	23.7350	+	4.72119i	0.936017	+	0.186185i	0.639455	−	0.768828i	$-0.279160\pi$
$643$	23.7350	+	4.72119i	0.936017	+	0.186185i	0.296562	+	0.955014i	$0.404160\pi$
$644$	5.61798	−	5.32493i	0.221379	−	0.209832i
$645$	−19.1743	−	4.93293i	−0.754987	−	0.194234i
$646$	1.88920	+	10.2101i	0.0743297	+	0.401713i
$647$	15.1614	−	6.28005i	0.596056	−	0.246894i	−0.0641977	−	0.997937i	$-0.520449\pi$
$647$	15.1614	−	6.28005i	0.596056	−	0.246894i	0.660254	+	0.751043i	$0.270449\pi$
$648$	3.31780	+	25.2387i	0.130336	+	0.991470i
$649$	23.1602	+	9.59327i	0.909118	+	0.376569i
$650$	−7.04401	−	1.49944i	−0.276289	−	0.0588127i
$651$	−9.31888	+	5.50514i	−0.365236	+	0.215763i
$652$	8.56999	+	13.6005i	0.335627	+	0.532637i
$653$	4.02082	+	6.01758i	0.157347	+	0.235486i	0.901764	−	0.432229i	$-0.142273\pi$
$653$	4.02082	+	6.01758i	0.157347	+	0.235486i	−0.744417	+	0.667715i	$0.767273\pi$
$654$	3.11276	−	6.25841i	0.121719	−	0.244723i
$655$	−0.166788	−	0.166788i	−0.00651696	−	0.00651696i
$656$	−2.42753	+	5.07392i	−0.0947793	+	0.198103i
$657$	−33.9924	−	3.78582i	−1.32617	−	0.147699i
$658$	0.419245	−	31.3159i	0.0163439	−	1.22082i
$659$	19.9606	+	29.8731i	0.777554	+	1.16369i	0.982744	+	0.184969i	$0.0592186\pi$
$659$	19.9606	+	29.8731i	0.777554	+	1.16369i	−0.205190	+	0.978722i	$0.565781\pi$
$660$	−8.25861	+	4.58508i	−0.321466	+	0.178474i
$661$	−6.04309	−	30.3807i	−0.235049	−	1.18167i	−0.900374	−	0.435117i	$-0.856707\pi$
$661$	−6.04309	−	30.3807i	−0.235049	−	1.18167i	0.665325	−	0.746554i	$-0.268293\pi$
$662$	−2.36667	−	3.64672i	−0.0919833	−	0.141734i
$663$	−7.90998	−	0.439121i	−0.307198	−	0.0170540i
$664$	15.3495	−	2.41712i	0.595678	−	0.0938023i
$665$	−15.7769	+	6.53503i	−0.611804	+	0.253417i
$666$	−0.997122	−	13.8159i	−0.0386377	−	0.535356i
$667$	6.67491	+	4.46003i	0.258453	+	0.172693i
$668$	−38.6496	−	17.2354i	−1.49540	−	0.666857i
$669$	−1.73528	−	12.2348i	−0.0670900	−	0.473026i
$670$	−6.00210	+	13.9588i	−0.231881	+	0.539277i
$671$			26.1466i			1.00938i
$672$	15.5028	+	13.3640i	0.598033	+	0.515526i
$673$		−	33.0559i		−	1.27421i	−0.770777	−	0.637105i	$-0.780132\pi$
$673$		−	33.0559i		−	1.27421i	0.770777	−	0.637105i	$-0.219868\pi$
$674$	9.11288	+	3.91841i	0.351015	+	0.150931i
$675$	−3.56246	+	3.78271i	−0.137119	+	0.145596i
$676$	−9.25533	−	24.1538i	−0.355974	−	0.928993i
$677$	34.4445	+	23.0151i	1.32381	+	0.884542i	0.998141	−	0.0609412i	$-0.0194102\pi$
$677$	34.4445	+	23.0151i	1.32381	+	0.884542i	0.325670	+	0.945484i	$0.394410\pi$
$678$	5.70299	−	20.9984i	0.219022	−	0.806440i
$679$	20.0281	−	8.29590i	0.768607	−	0.318367i
$680$	2.46967	+	0.595242i	0.0947075	+	0.0228265i
$681$	2.30228	−	41.4715i	0.0882234	−	1.58919i
$682$	−9.67653	+	6.27993i	−0.370534	+	0.240471i
$683$	−8.55527	−	43.0103i	−0.327358	−	1.64574i	−0.697368	−	0.716714i	$-0.745645\pi$
$683$	−8.55527	−	43.0103i	−0.327358	−	1.64574i	0.370009	−	0.929028i	$-0.379355\pi$
$684$	2.87553	+	48.9638i	0.109949	+	1.87218i
$685$	6.06348	+	9.07464i	0.231674	+	0.346724i
$686$	28.4652	+	0.381082i	1.08681	+	0.0145498i
$687$	18.5050	+	8.89688i	0.706008	+	0.339437i
$688$	6.50719	+	45.2577i	0.248084	+	1.72543i
$689$	46.3428	+	46.3428i	1.76552	+	1.76552i
$690$	2.02100	−	4.06334i	0.0769381	−	0.154689i
$691$	6.11514	+	9.15196i	0.232631	+	0.348157i	0.929358	−	0.369179i	$-0.120361\pi$
$691$	6.11514	+	9.15196i	0.232631	+	0.348157i	−0.696727	+	0.717336i	$0.745361\pi$
$692$	−1.78030	+	7.84615i	−0.0676769	+	0.298266i
$693$	−13.0708	−	11.0086i	−0.496517	−	0.418180i
$694$	−1.85797	+	8.72831i	−0.0705275	+	0.331322i
$695$	−8.60337	−	3.56363i	−0.326345	−	0.135176i
$696$	−9.95864	+	18.7464i	−0.377481	+	0.710581i
$697$	−1.16684	+	0.483322i	−0.0441973	+	0.0183071i
$698$	28.1303	−	5.20501i	1.06475	−	0.197013i
$699$	−8.08677	+	31.4333i	−0.305870	+	1.18891i
$700$	−0.111846	+	4.17648i	−0.00422739	+	0.157856i
$701$	8.59255	+	1.70916i	0.324536	+	0.0645542i	0.354670	−	0.934992i	$-0.384593\pi$
$701$	8.59255	+	1.70916i	0.324536	+	0.0645542i	−0.0301337	+	0.999546i	$0.509593\pi$
$702$	−36.8188	−	6.69078i	−1.38964	−	0.252527i
$703$		−	26.6896i		−	1.00662i
$704$	17.1074	+	13.5358i	0.644758	+	0.510151i
$705$	−6.07562	−	17.3274i	−0.228821	−	0.652588i
$706$	−43.4477	+	17.3189i	−1.63518	+	0.651807i
$707$	2.03770	−	10.2442i	0.0766356	−	0.385273i
$708$	−9.72917	−	30.3238i	−0.365645	−	1.13964i
$709$	6.31030	+	4.21641i	0.236988	+	0.158350i	0.668394	−	0.743808i	$-0.266982\pi$
$709$	6.31030	+	4.21641i	0.236988	+	0.158350i	−0.431405	+	0.902158i	$0.641982\pi$
$710$	−2.45602	−	13.2735i	−0.0921727	−	0.498144i
$711$	35.6280	+	19.6312i	1.33616	+	0.736228i
$712$	−0.131085	+	3.26229i	−0.00491263	+	0.122259i
$713$	2.12089	−	5.12028i	0.0794279	−	0.191756i
$714$	0.584409	+	4.55856i	0.0218710	+	0.170600i
$715$	−2.70908	−	13.6195i	−0.101314	−	0.509340i
$716$	−7.58307	+	33.4202i	−0.283393	+	1.24897i
$717$	−4.05408	+	5.39414i	−0.151402	+	0.201448i
$718$	9.13210	+	9.37993i	0.340807	+	0.350056i
$719$	−10.5048	+	10.5048i	−0.391763	+	0.391763i	−0.875315	−	0.483552i	$-0.839346\pi$
$719$	−10.5048	+	10.5048i	−0.391763	+	0.391763i	0.483552	+	0.875315i	$0.339346\pi$
$720$	11.2273	+	4.23641i	0.418418	+	0.157882i
$721$	12.4258	+	12.4258i	0.462762	+	0.462762i
$722$	−0.905399	+	67.6296i	−0.0336955	+	2.51691i
$723$	−24.1572	−	18.1559i	−0.898416	−	0.675225i
$724$	−2.18422	+	3.08671i	−0.0811759	+	0.114717i
$725$	−4.24977	+	0.845332i	−0.157832	+	0.0313948i
$726$	6.90860	+	5.33852i	0.256402	+	0.198131i
$727$	21.1233	+	8.74954i	0.783418	+	0.324503i	0.738294	−	0.674479i	$-0.235632\pi$
$727$	21.1233	+	8.74954i	0.783418	+	0.324503i	0.0451243	+	0.998981i	$0.485632\pi$
$728$	−25.6692	+	15.6986i	−0.951362	+	0.581831i
$729$	−17.9137	+	20.2015i	−0.663469	+	0.748204i
$730$	−9.13624	+	13.2849i	−0.338147	+	0.491695i
$731$	−5.70387	+	8.53645i	−0.210965	+	0.315732i
$732$	25.3371	−	21.4786i	0.936485	−	0.793873i
$733$	39.2566	+	7.80861i	1.44997	+	0.288418i	0.856380	−	0.516347i	$-0.172708\pi$
$733$	39.2566	+	7.80861i	1.44997	+	0.288418i	0.593594	+	0.804764i	$0.297708\pi$
$734$	−4.70349	+	10.9387i	−0.173609	+	0.403755i
$735$	4.30871	−	1.51079i	0.158929	−	0.0557263i
$736$	−10.4570	−	0.700980i	−0.385452	−	0.0258385i
$737$	−29.2976			−1.07919
$738$	−5.75233	+	1.58208i	−0.211746	+	0.0582371i
$739$	−4.06894	+	20.4560i	−0.149678	+	0.752484i	0.830910	+	0.556407i	$0.187820\pi$
$739$	−4.06894	+	20.4560i	−0.149678	+	0.752484i	−0.980588	+	0.196077i	$0.937180\pi$
$740$	−5.96371	−	2.65946i	−0.219230	−	0.0977636i
$741$	−69.8302	−	17.9651i	−2.56528	−	0.659963i
$742$	21.5445	−	31.3275i	0.790923	−	1.15007i
$743$	−12.6313	−	30.4946i	−0.463397	−	1.11874i	−0.966994	−	0.254801i	$-0.917990\pi$
$743$	−12.6313	−	30.4946i	−0.463397	−	1.11874i	0.503596	−	0.863939i	$-0.332010\pi$
$744$	14.0345	+	4.21816i	0.514529	+	0.154645i
$745$	0.950837	−	2.29552i	0.0348360	−	0.0841015i
$746$	12.5049	−	8.11552i	0.457838	−	0.297130i
$747$	12.6059	+	10.6171i	0.461227	+	0.388458i
$748$	0.826656	+	4.82803i	0.0302255	+	0.176530i
$749$	−4.24809	+	2.83848i	−0.155222	+	0.103716i
$750$	0.779484	+	2.32216i	0.0284627	+	0.0847931i
$751$	2.17827	−	2.17827i	0.0794861	−	0.0794861i	−0.666246	−	0.745732i	$-0.732100\pi$
$751$	2.17827	−	2.17827i	0.0794861	−	0.0794861i	0.745732	+	0.666246i	$0.232100\pi$
$752$	−31.5464	+	28.3368i	−1.15038	+	1.03334i
$753$	−17.2236	+	35.8241i	−0.627665	+	1.30550i
$754$	−21.7684	−	22.3592i	−0.792759	−	0.814273i
$755$	−8.57324	+	5.72846i	−0.312012	+	0.208480i
$756$	0.0695244	+	21.7093i	0.00252858	+	0.789560i
$757$	−18.8048	+	3.74051i	−0.683473	+	0.135951i	−0.524601	−	0.851348i	$-0.675786\pi$
$757$	−18.8048	+	3.74051i	−0.683473	+	0.135951i	−0.158872	+	0.987299i	$0.550786\pi$
$758$	5.31962	−	24.9904i	0.193217	−	0.907690i
$759$	8.73692	+	0.485028i	0.317130	+	0.0176054i
$760$	20.9890	+	9.69875i	0.761352	+	0.351811i
$761$	14.7075	+	35.5069i	0.533145	+	1.28713i	0.929430	+	0.368998i	$0.120299\pi$
$761$	14.7075	+	35.5069i	0.533145	+	1.28713i	−0.396286	+	0.918127i	$0.629701\pi$
$762$	27.3792	−	15.6837i	0.991845	−	0.568161i
$763$	3.31179	−	4.95644i	0.119895	−	0.179435i
$764$	19.5704	−	18.5495i	0.708031	−	0.671098i
$765$	1.23980	+	2.39232i	0.0448249	+	0.0864945i
$766$	13.1380	−	5.23703i	0.474697	−	0.189222i
$767$	46.8162			1.69044
$768$	−0.936437	−	27.6970i	−0.0337908	−	0.999429i
$769$	−28.7207			−1.03569			−0.517847	−	0.855473i	$-0.673266\pi$
$769$	−28.7207			−1.03569			−0.517847	+	0.855473i	$0.673266\pi$
$770$	−7.48321	+	2.98292i	−0.269676	+	0.107497i
$771$	14.9470	−	2.11996i	0.538305	−	0.0763485i
$772$	−1.20337	+	1.14060i	−0.0433103	+	0.0410511i
$773$	21.7687	−	32.5791i	0.782964	−	1.17179i	−0.198492	−	0.980102i	$-0.563604\pi$
$773$	21.7687	−	32.5791i	0.782964	−	1.17179i	0.981456	−	0.191686i	$-0.0613956\pi$
$774$	−31.7348	+	36.6719i	−1.14068	+	1.31814i
$775$	1.14475	+	2.76367i	0.0411206	+	0.0992740i
$776$	−26.6446	−	12.3121i	−0.956484	−	0.441978i
$777$	0.654799	−	11.7951i	0.0234908	−	0.423145i
$778$	1.15578	−	5.42958i	0.0414367	−	0.194660i
$779$	−11.2742	+	2.24258i	−0.403941	+	0.0803489i
$780$	−10.9724	+	13.8132i	−0.392874	+	0.494592i
$781$	21.6414	−	14.4603i	0.774389	−	0.517430i
$782$	−1.64161	−	1.68616i	−0.0587039	−	0.0602971i
$783$	−21.9409	+	5.05235i	−0.784103	+	0.180556i
$784$	−7.04634	−	7.84446i	−0.251655	−	0.280159i
$785$	13.8660	−	13.8660i	0.494899	−	0.494899i
$786$	−0.547736	+	0.183860i	−0.0195371	+	0.00655807i
$787$	29.1627	−	19.4859i	1.03954	−	0.694598i	0.0861318	−	0.996284i	$-0.472549\pi$
$787$	29.1627	−	19.4859i	1.03954	−	0.694598i	0.953407	+	0.301686i	$0.0975494\pi$
$788$	4.58591	+	26.7837i	0.163366	+	0.954130i
$789$	14.5534	+	24.6354i	0.518115	+	0.877044i
$790$	16.0855	−	10.4392i	0.572295	−	0.371412i
$791$	7.10135	−	17.1442i	0.252495	−	0.609577i
$792$	1.04718	+	23.1142i	0.0372099	+	0.821329i
$793$	18.6863	+	45.1127i	0.663570	+	1.60200i
$794$	12.4213	−	18.0616i	0.440815	−	0.640982i
$795$	5.55392	−	21.5881i	0.196977	−	0.765649i
$796$	35.6799	+	15.9111i	1.26464	+	0.563955i
$797$	−8.06317	+	40.5363i	−0.285612	+	1.43587i	0.525408	+	0.850850i	$0.323913\pi$
$797$	−8.06317	+	40.5363i	−0.285612	+	1.43587i	−0.811020	+	0.585018i	$0.801087\pi$
$798$	−2.87747	+	41.7305i	−0.101861	+	1.47724i
$799$	−9.52156			−0.336849
$800$	4.25858	−	3.72351i	0.150564	−	0.131646i
$801$	−2.70468	+	2.16260i	−0.0955653	+	0.0764118i
$802$	0.0728457	−	0.169414i	0.00257227	−	0.00598223i
$803$	−30.4909	−	6.06501i	−1.07600	−	0.214029i
$804$	24.0671	+	28.3905i	0.848782	+	1.00126i
$805$	2.15022	−	3.21803i	0.0757852	−	0.113421i
$806$	−12.2076	+	17.7508i	−0.429993	+	0.625246i
$807$	9.90893	−	8.86661i	0.348811	−	0.312120i
$808$	−12.0647	+	7.37848i	−0.424434	+	0.259574i
$809$	−25.8782	−	10.7191i	−0.909829	−	0.376864i	−0.121838	−	0.992550i	$-0.538879\pi$
$809$	−25.8782	−	10.7191i	−0.909829	−	0.376864i	−0.787991	+	0.615686i	$0.788879\pi$
$810$	4.41014	+	11.9395i	0.154957	+	0.419510i
$811$	54.0898	−	10.7591i	1.89935	−	0.377804i	0.900927	−	0.433971i	$-0.142888\pi$
$811$	54.0898	−	10.7591i	1.89935	−	0.377804i	0.998421	+	0.0561671i	$0.0178879\pi$
$812$	−10.4570	+	14.7777i	−0.366969	+	0.518595i
$813$	−30.9234	+	41.1450i	−1.08453	+	1.44302i
$814$	0.168543	−	12.5894i	0.00590741	−	0.441259i
$815$	5.68351	+	5.68351i	0.199085	+	0.199085i
$816$	3.99948	−	4.76715i	0.140010	−	0.166883i
$817$	−66.0742	+	66.0742i	−2.31164	+	2.31164i
$818$	17.3028	+	17.7724i	0.604980	+	0.621398i
$819$	−30.4196	−	9.65257i	−1.06295	−	0.337288i
$820$	−0.622310	+	2.74265i	−0.0217320	+	0.0957775i
$821$	−5.94193	−	29.8721i	−0.207375	−	1.04254i	−0.934479	−	0.356017i	$-0.884135\pi$
$821$	−5.94193	−	29.8721i	−0.207375	−	1.04254i	0.727105	−	0.686527i	$-0.240865\pi$
$822$	26.5167	−	3.39945i	0.924874	−	0.118569i
$823$	−12.2058	+	29.4674i	−0.425467	+	1.02717i	0.555241	+	0.831690i	$0.312626\pi$
$823$	−12.2058	+	29.4674i	−0.425467	+	1.02717i	−0.980708	+	0.195479i	$0.937374\pi$
$824$	0.955280	−	23.7738i	0.0332788	−	0.828199i
$825$	−3.51966	+	3.14943i	−0.122539	+	0.109649i
$826$	−4.94147	−	26.7060i	−0.171936	−	0.929222i
$827$	−36.4439	−	24.3510i	−1.26728	−	0.846768i	−0.273911	−	0.961755i	$-0.588318\pi$
$827$	−36.4439	−	24.3510i	−1.26728	−	0.846768i	−0.993367	+	0.114987i	$0.963318\pi$
$828$	−6.70712	−	8.86486i	−0.233088	−	0.308075i
$829$	2.20627	−	11.0917i	0.0766270	−	0.385230i	−0.923372	−	0.383906i	$-0.874579\pi$
$829$	2.20627	−	11.0917i	0.0766270	−	0.385230i	0.999999	−	0.00132389i	$-0.000421408\pi$
$830$	7.21709	−	2.87685i	0.250509	−	0.0998568i
$831$	48.8663	−	17.1343i	1.69515	−	0.594381i
$832$	39.1904	+	11.1282i	1.35868	+	0.385802i
$833$		−	2.36767i		−	0.0820349i
$834$	−17.2006	+	14.9815i	−0.595607	+	0.518767i
$835$	−20.7526	−	4.12795i	−0.718174	−	0.142854i
$836$	−1.19348	+	44.5661i	−0.0412774	+	1.54135i
$837$	6.37603	+	14.1757i	0.220388	+	0.489985i
$838$	−1.03403	+	0.191329i	−0.0357200	+	0.00660935i
$839$	−27.8657	+	11.5424i	−0.962031	+	0.398486i	−0.807740	−	0.589539i	$-0.799309\pi$
$839$	−27.8657	+	11.5424i	−0.962031	+	0.398486i	−0.154291	+	0.988025i	$0.549309\pi$
$840$	9.03781	+	4.80114i	0.311834	+	0.165655i
$841$	9.44655	+	3.91289i	0.325743	+	0.134927i
$842$	1.55714	−	7.31510i	0.0536627	−	0.252095i
$843$	8.55773	+	14.4862i	0.294744	+	0.498931i
$844$	1.62214	−	7.14911i	0.0558364	−	0.246083i
$845$	−7.18528	−	10.7535i	−0.247181	−	0.369933i
$846$	−44.6298	−	5.57634i	−1.53440	−	0.191719i
$847$	5.26507	+	5.26507i	0.180910	+	0.180910i
$848$	−50.9549	+	7.32635i	−1.74980	+	0.251588i
$849$	4.54692	−	9.45730i	0.156050	−	0.324574i
$850$	1.27008	+	0.0170034i	0.0435634	+	0.000583210i
$851$	3.36061	+	5.02950i	0.115200	+	0.172409i
$852$	−31.7903	−	9.09263i	−1.08912	−	0.311508i
$853$	−5.60612	−	28.1838i	−0.191950	−	0.964997i	−0.949869	−	0.312648i	$-0.898784\pi$
$853$	−5.60612	−	28.1838i	−0.191950	−	0.964997i	0.757919	−	0.652348i	$-0.226216\pi$
$854$	23.7620	−	15.4212i	0.813118	−	0.527702i
$855$	6.81939	+	23.5569i	0.233218	+	0.805628i
$856$	6.72503	+	1.62087i	0.229857	+	0.0554003i
$857$	28.9772	−	12.0027i	0.989842	−	0.410006i	0.171780	−	0.985135i	$-0.445048\pi$
$857$	28.9772	−	12.0027i	0.989842	−	0.410006i	0.818063	+	0.575129i	$0.195048\pi$
$858$	−32.8253	−	8.91505i	−1.12064	−	0.304355i
$859$	13.4695	+	9.00005i	0.459574	+	0.307078i	0.763720	−	0.645548i	$-0.223371\pi$
$859$	13.4695	+	9.00005i	0.459574	+	0.307078i	−0.304145	+	0.952626i	$0.598371\pi$
$860$	8.18017	+	21.3479i	0.278941	+	0.727959i
$861$	−5.03748	+	0.714474i	−0.171677	+	0.0243492i
$862$	−18.1903	−	7.82155i	−0.619562	−	0.266403i
$863$		−	9.47044i		−	0.322377i	−0.986924	−	0.161189i	$-0.948467\pi$
$863$		−	9.47044i		−	0.322377i	0.986924	−	0.161189i	$-0.0515328\pi$
$864$	21.5384	−	20.0024i	0.732751	−	0.680497i
$865$			4.02280i			0.136779i
$866$	0.845507	−	1.96636i	0.0287315	−	0.0668196i
$867$	−27.7697	+	3.93862i	−0.943109	+	0.133762i
$868$	11.4144	+	5.09013i	0.387429	+	0.172770i
$869$	30.7432	+	20.5419i	1.04289	+	0.696838i
$870$	−2.78182	+	10.2427i	−0.0943124	+	0.347259i
$871$	−50.5494	+	20.9383i	−1.71280	+	0.709466i
$872$	−7.97285	+	1.25550i	−0.269995	+	0.0425165i
$873$	−8.65689	−	29.9043i	−0.292991	−	1.01211i
$874$	−11.6601	−	17.9667i	−0.394410	−	0.607734i
$875$	0.407542	+	2.04885i	0.0137774	+	0.0692638i
$876$	19.1701	+	34.5291i	0.647698	+	1.16663i
$877$	−9.81243	−	14.6853i	−0.331342	−	0.495889i	0.627969	−	0.778238i	$-0.283886\pi$
$877$	−9.81243	−	14.6853i	−0.331342	−	0.495889i	−0.959312	+	0.282349i	$0.908886\pi$
$878$	−0.341336	+	25.4964i	−0.0115195	+	0.860462i
$879$	13.4049	−	27.8814i	0.452137	−	0.940416i
$880$	9.83922	+	4.70742i	0.331680	+	0.158687i
$881$	−35.0718	−	35.0718i	−1.18160	−	1.18160i	−0.979330	−	0.202268i	$-0.935169\pi$
$881$	−35.0718	−	35.0718i	−1.18160	−	1.18160i	−0.202268	−	0.979330i	$-0.564831\pi$
$882$	1.38664	−	11.0978i	0.0466905	−	0.373684i
$883$	11.5448	+	17.2781i	0.388514	+	0.581453i	0.973244	−	0.229776i	$-0.0737992\pi$
$883$	11.5448	+	17.2781i	0.388514	+	0.581453i	−0.584729	+	0.811229i	$0.698799\pi$
$884$	4.87677	+	7.73938i	0.164023	+	0.260304i
$885$	−8.09896	−	13.7096i	−0.272244	−	0.460844i
$886$	−19.3897	−	4.12742i	−0.651409	−	0.138663i
$887$	−0.742205	−	0.307431i	−0.0249208	−	0.0103225i	0.370188	−	0.928957i	$-0.379293\pi$
$887$	−0.742205	−	0.307431i	−0.0249208	−	0.0103225i	−0.395109	+	0.918634i	$0.629293\pi$
$888$	−12.3381	+	10.1785i	−0.414040	+	0.341569i
$889$	24.8610	−	10.2978i	0.833811	−	0.345376i
$890$	0.297016	+	1.60521i	0.00995599	+	0.0538068i
$891$	−17.7900	+	16.9057i	−0.595987	+	0.566362i
$892$	−10.3562	+	9.81595i	−0.346750	+	0.328662i
$893$	−84.9959	−	16.9067i	−2.84428	−	0.565762i
$894$	−3.99732	−	4.58940i	−0.133690	−	0.153493i
$895$			17.1348i			0.572754i
$896$	2.21147	−	23.5305i	0.0738800	−	0.786100i
$897$	15.4211	−	5.40721i	0.514897	−	0.180541i
$898$	−8.90991	−	22.3522i	−0.297328	−	0.745901i
$899$	−2.52870	+	12.7127i	−0.0843370	+	0.423991i
$900$	5.94321	+	0.823528i	0.198107	+	0.0274509i
$901$	−9.61106	−	6.42191i	−0.320191	−	0.213945i
$902$	−5.33219	+	0.986625i	−0.177542	+	0.0328510i
$903$	−30.8215	+	27.5794i	−1.02567	+	0.917784i
$904$	−23.5800	+	8.67528i	−0.784260	+	0.288536i
$905$	−0.723530	+	1.74676i	−0.0240509	+	0.0580641i
$906$	3.21162	+	25.0515i	0.106699	+	0.832282i
$907$	−5.34123	−	26.8522i	−0.177353	−	0.891611i	−0.962288	−	0.272034i	$-0.912304\pi$
$907$	−5.34123	−	26.8522i	−0.177353	−	0.891611i	0.784935	−	0.619578i	$-0.212696\pi$
$908$	−40.5770	+	25.5685i	−1.34660	+	0.848521i
$909$	−14.2974	−	4.53678i	−0.474215	−	0.150475i
$910$	−10.7796	+	10.4947i	−0.357339	+	0.347897i
$911$	−32.1941	+	32.1941i	−1.06664	+	1.06664i	−0.0690213	+	0.997615i	$0.521988\pi$
$911$	−32.1941	+	32.1941i	−1.06664	+	1.06664i	−0.997615	+	0.0690213i	$0.978012\pi$
$912$	44.1667	−	35.4532i	1.46251	−	1.17397i
$913$	10.5929	+	10.5929i	0.350572	+	0.350572i
$914$	0.409009	+	0.00547566i	0.0135288	+	0.000181119i
$915$	9.97814	−	13.2764i	0.329867	−	0.438903i
$916$	−4.00123	−	23.3689i	−0.132205	−	0.772131i
$917$	−0.483271	+	0.0961285i	−0.0159590	+	0.00317444i
$918$	6.59922	−	0.109487i	0.217807	−	0.00361360i
$919$	12.5882	+	5.21421i	0.415247	+	0.172001i	0.580518	−	0.814247i	$-0.302850\pi$
$919$	12.5882	+	5.21421i	0.415247	+	0.172001i	−0.165271	+	0.986248i	$0.552850\pi$
$920$	−5.17647	+	0.815147i	−0.170663	+	0.0268746i
$921$	40.8037	−	36.5116i	1.34453	−	1.20310i
$922$	48.1626	+	33.1223i	1.58615	+	1.09082i
$923$	27.0051	−	40.4160i	0.888885	−	1.33031i
$924$	−1.62082	+	19.6660i	−0.0533210	+	0.646963i
$925$	−3.20218	−	0.636952i	−0.105287	−	0.0209429i
$926$	54.1094	+	23.2663i	1.77815	+	0.764577i
$927$	19.7103	−	15.7599i	0.647371	−	0.517622i
$928$	24.3063	−	3.16329i	0.797894	−	0.103840i
$929$	8.28275			0.271748			0.135874	−	0.990726i	$-0.456616\pi$
$929$	8.28275			0.271748			0.135874	+	0.990726i	$0.456616\pi$
$930$	7.30998	+	0.504050i	0.239704	+	0.0165284i
$931$	4.20410	−	21.1354i	0.137784	−	0.692686i
$932$	34.9966	−	13.4101i	1.14635	−	0.439263i
$933$	−12.1863	+	47.3680i	−0.398960	+	1.55076i
$934$	7.40154	+	5.09017i	0.242186	+	0.166556i
$935$	0.937247	+	2.26271i	0.0306512	+	0.0739986i
$936$	18.3260	+	39.1324i	0.599003	+	1.27908i
$937$	−0.113711	+	0.274523i	−0.00371478	+	0.00896827i	−0.925726	−	0.378195i	$-0.876545\pi$
$937$	−0.113711	+	0.274523i	−0.00371478	+	0.00896827i	0.922011	+	0.387163i	$0.126545\pi$
$938$	17.2796	+	26.6256i	0.564200	+	0.869357i
$939$	−23.2260	−	39.3162i	−0.757953	−	1.28303i
$940$	−12.2471	+	17.3074i	−0.399455	+	0.564505i
$941$	35.5981	−	23.7859i	1.16046	−	0.775397i	0.182302	−	0.983243i	$-0.441645\pi$
$941$	35.5981	−	23.7859i	1.16046	−	0.775397i	0.978162	+	0.207846i	$0.0666451\pi$
$942$	−15.2853	−	45.5363i	−0.498022	−	1.48365i
$943$	1.84219	−	1.84219i	0.0599899	−	0.0599899i
$944$	−22.0371	+	29.4383i	−0.717247	+	0.958136i
$945$	2.43578	+	10.5779i	0.0792359	+	0.344099i
$946$	−31.5843	+	30.7498i	−1.02689	+	0.999761i
$947$	13.4820	−	9.00836i	0.438105	−	0.292732i	−0.316891	−	0.948462i	$-0.602639\pi$
$947$	13.4820	−	9.00836i	0.438105	−	0.292732i	0.754996	+	0.655730i	$0.227639\pi$
$948$	−5.34867	−	46.6660i	−0.173717	−	1.51564i
$949$	−56.9428	+	11.3266i	−1.84844	+	0.367678i
$950$	11.3074	+	2.40697i	0.366861	+	0.0780926i
$951$	−0.409144	+	7.37001i	−0.0132674	+	0.238989i
$952$	3.90014	−	3.59882i	0.126404	−	0.116638i
$953$	−10.7458	−	25.9426i	−0.348089	−	0.840362i	−0.996846	−	0.0793658i	$-0.974710\pi$
$953$	−10.7458	−	25.9426i	−0.348089	−	0.840362i	0.648756	−	0.760996i	$-0.275290\pi$
$954$	−41.2883	−	35.7298i	−1.33676	−	1.15679i
$955$	7.49034	−	11.2101i	0.242382	−	0.362750i
$956$	7.78885	+	0.208586i	0.251909	+	0.00674614i
$957$	−20.2622	+	2.87381i	−0.654983	+	0.0928972i
$958$	−2.54960	−	6.39614i	−0.0823739	−	0.206650i
$959$	22.7992			0.736224
$960$	−3.52096	−	13.4016i	−0.113638	−	0.432535i
$961$	−22.0517			−0.711344
$962$	−8.70656	−	21.8420i	−0.280711	−	0.704214i
$963$	3.37602	+	6.51440i	0.108791	+	0.209924i
$964$	−0.934135	+	34.8818i	−0.0300865	+	1.12347i
$965$	−0.460577	+	0.689303i	−0.0148265	+	0.0221894i
$966$	−4.71222	−	8.22617i	−0.151613	−	0.264673i
$967$	1.16030	+	2.80122i	0.0373128	+	0.0900810i	0.941437	−	0.337188i	$-0.109476\pi$
$967$	1.16030	+	2.80122i	0.0373128	+	0.0900810i	−0.904125	+	0.427269i	$0.859476\pi$
$968$	0.404772	−	10.0734i	0.0130099	−	0.323773i
$969$	12.6975	+	0.704900i	0.407903	+	0.0226447i
$970$	−14.3542	−	3.05554i	−0.460886	−	0.0981074i
$971$	−59.7063	+	11.8763i	−1.91607	+	0.381130i	−0.999811	−	0.0194613i	$-0.993805\pi$
$971$	−59.7063	+	11.8763i	−1.91607	+	0.381130i	−0.916257	+	0.400591i	$0.868805\pi$
$972$	30.9962	+	3.35167i	0.994205	+	0.107505i
$973$	−16.1747	+	10.8076i	−0.518537	+	0.346475i
$974$	7.02092	−	6.83542i	0.224965	−	0.219021i
$975$	−3.82193	+	7.94936i	−0.122400	+	0.254583i
$976$	−37.1631	−	9.48521i	−1.18956	−	0.303614i
$977$	−10.4312	+	10.4312i	−0.333723	+	0.333723i	−0.853999	−	0.520275i	$-0.825829\pi$
$977$	−10.4312	+	10.4312i	−0.333723	+	0.333723i	0.520275	+	0.853999i	$0.325829\pi$
$978$	18.6648	−	6.26526i	0.596834	−	0.200341i
$979$	−2.61717	+	1.74874i	−0.0836452	+	0.0558900i
$980$	−4.30373	−	3.04541i	−0.137478	−	0.0972820i
$981$	−6.54777	−	5.51471i	−0.209054	−	0.176071i
$982$	29.1855	+	44.9709i	0.931346	+	1.43508i
$983$	−4.09916	+	9.89626i	−0.130743	+	0.315642i	−0.975671	−	0.219238i	$-0.929643\pi$
$983$	−4.09916	+	9.89626i	−0.130743	+	0.315642i	0.844928	+	0.534879i	$0.179643\pi$
$984$	5.33632	+	4.35662i	0.170116	+	0.138884i
$985$	5.19942	+	12.5525i	0.165667	+	0.399956i
$986$	4.53489	+	3.11873i	0.144420	+	0.0993205i
$987$	−37.1478	−	9.55693i	−1.18243	−	0.304200i
$988$	29.7911	+	77.7463i	0.947780	+	2.47344i
$989$	4.13160	−	20.7710i	0.131377	−	0.660478i
$990$	3.06793	+	11.1548i	0.0975052	+	0.354522i
$991$	10.9953			0.349279			0.174639	−	0.984632i	$-0.444124\pi$
$991$	10.9953			0.349279			0.174639	+	0.984632i	$0.444124\pi$
$992$	−5.41554	−	16.0318i	−0.171943	−	0.509010i
$993$	−5.02452	+	1.76178i	−0.159448	+	0.0559083i
$994$	−25.9055	−	11.1390i	−0.821673	−	0.353307i
$995$	19.1581	+	3.81079i	0.607353	+	0.120810i
$996$	1.56318	−	18.9666i	0.0495312	−	0.600980i
$997$	12.6777	−	18.9735i	0.401507	−	0.600898i	−0.574535	−	0.818480i	$-0.694817\pi$
$997$	12.6777	−	18.9735i	0.401507	−	0.600898i	0.976042	+	0.217582i	$0.0698170\pi$
$998$	−31.1897	−	21.4497i	−0.987291	−	0.678978i
$999$	−16.7307	−	2.80952i	−0.529336	−	0.0888892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.131.17	✓	1024
3.2	odd	2	inner	960.2.cn.a.131.112	yes	1024
64.43	odd	16	inner	960.2.cn.a.491.112	yes	1024
192.107	even	16	inner	960.2.cn.a.491.17	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.131.17	✓	1024	1.1	even	1	trivial
960.2.cn.a.131.112	yes	1024	3.2	odd	2	inner
960.2.cn.a.491.17	yes	1024	192.107	even	16	inner
960.2.cn.a.491.112	yes	1024	64.43	odd	16	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31369 + 0.523657i) q^{2} +(0.243225 + 1.71489i) q^{3} +(1.45157 - 1.37585i) q^{4} +(0.555570 - 0.831470i) q^{5} +(-1.21754 - 2.12547i) q^{6} +(-0.799421 - 1.92997i) q^{7} +(-1.18644 + 2.56756i) q^{8} +(-2.88168 + 0.834208i) q^{9} +O(q^{10})\)	\(q+(-1.31369 + 0.523657i) q^{2} +(0.243225 + 1.71489i) q^{3} +(1.45157 - 1.37585i) q^{4} +(0.555570 - 0.831470i) q^{5} +(-1.21754 - 2.12547i) q^{6} +(-0.799421 - 1.92997i) q^{7} +(-1.18644 + 2.56756i) q^{8} +(-2.88168 + 0.834208i) q^{9} +(-0.294442 + 1.38322i) q^{10} +(-2.67444 + 0.531979i) q^{11} +(2.71248 + 2.15463i) q^{12} +(-4.23423 + 2.82922i) q^{13} +(2.06084 + 2.11677i) q^{14} +(1.56101 + 0.750507i) q^{15} +(0.214087 - 3.99427i) q^{16} +(0.635098 - 0.635098i) q^{17} +(3.34880 - 2.60491i) q^{18} +(6.79701 - 4.54162i) q^{19} +(-0.337529 - 1.97131i) q^{20} +(3.11525 - 1.84034i) q^{21} +(3.23481 - 2.09935i) q^{22} +(-0.709001 + 1.71168i) q^{23} +(-4.69165 - 1.41011i) q^{24} +(-0.382683 - 0.923880i) q^{25} +(4.08092 - 5.93400i) q^{26} +(-2.13147 - 4.73886i) q^{27} +(-3.81576 - 1.70160i) q^{28} +(0.845332 - 4.24977i) q^{29} +(-2.44369 - 0.168501i) q^{30} -2.99137 q^{31} +(1.81038 + 5.35934i) q^{32} +(-1.56278 - 4.45697i) q^{33} +(-0.501748 + 1.16690i) q^{34} +(-2.04885 - 0.407542i) q^{35} +(-3.03521 + 5.17566i) q^{36} +(1.81389 - 2.71467i) q^{37} +(-6.55092 + 9.52558i) q^{38} +(-5.88167 - 6.57309i) q^{39} +(1.47570 + 2.41295i) q^{40} +(-1.29914 - 0.538123i) q^{41} +(-3.12877 + 4.04896i) q^{42} +(-11.2111 + 2.23003i) q^{43} +(-3.15020 + 4.45182i) q^{44} +(-0.907359 + 2.85949i) q^{45} +(0.0350741 - 2.61989i) q^{46} +(-7.49614 - 7.49614i) q^{47} +(6.90179 - 0.604371i) q^{48} +(1.86402 - 1.86402i) q^{49} +(0.986524 + 1.01330i) q^{50} +(1.24359 + 0.934650i) q^{51} +(-2.25368 + 9.93245i) q^{52} +(-2.51076 - 12.6224i) q^{53} +(5.28163 + 5.10924i) q^{54} +(-1.04351 + 2.51927i) q^{55} +(5.90379 + 0.237226i) q^{56} +(9.44157 + 10.5515i) q^{57} +(1.11492 + 6.02555i) q^{58} +(-7.64390 - 5.10749i) q^{59} +(3.29849 - 1.05830i) q^{60} +(1.87065 - 9.40437i) q^{61} +(3.92974 - 1.56646i) q^{62} +(3.91368 + 4.89469i) q^{63} +(-5.18474 - 6.09249i) q^{64} +5.09246i q^{65} +(4.38693 + 5.03673i) q^{66} +(10.5377 + 2.09608i) q^{67} +(0.0480885 - 1.79568i) q^{68} +(-3.10779 - 0.799534i) q^{69} +(2.90497 - 0.537512i) q^{70} +(-8.81850 + 3.65274i) q^{71} +(1.27705 - 8.38863i) q^{72} +(10.5330 + 4.36291i) q^{73} +(-0.961327 + 4.51610i) q^{74} +(1.49127 - 0.880970i) q^{75} +(3.61773 - 15.9441i) q^{76} +(3.16471 + 4.73632i) q^{77} +(11.1687 + 5.55503i) q^{78} +(-9.58802 - 9.58802i) q^{79} +(-3.20217 - 2.39710i) q^{80} +(7.60820 - 4.80784i) q^{81} +(1.98846 + 0.0266208i) q^{82} +(-3.05217 - 4.56789i) q^{83} +(1.98997 - 6.95748i) q^{84} +(-0.175223 - 0.880906i) q^{85} +(13.5602 - 8.80036i) q^{86} +(7.49349 + 0.415999i) q^{87} +(1.80716 - 7.49795i) q^{88} +(1.06646 - 0.441740i) q^{89} +(-0.305406 - 4.23163i) q^{90} +(8.84525 + 5.91021i) q^{91} +(1.32585 + 3.46009i) q^{92} +(-0.727577 - 5.12987i) q^{93} +(13.7730 + 5.92220i) q^{94} -8.17469i q^{95} +(-8.75034 + 4.40813i) q^{96} +10.3774i q^{97} +(-1.47264 + 3.42486i) q^{98} +(7.26311 - 3.76403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more