LMFDB - Embedded newform 420.2.n.b.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(71,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))

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

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

chi := DirichletCharacter("420.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.n (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	420.71
Dual form			420.2.n.b.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41258 + 0.0678578i) q^{2} +(1.66901 + 0.463024i) q^{3} +(1.99079 - 0.191710i) q^{4} -1.00000i q^{5} +(-2.38904 - 0.540805i) q^{6} -1.00000i q^{7} +(-2.79915 + 0.405897i) q^{8} +(2.57122 + 1.54559i) q^{9} +O(q^{10})$	\(q+(-1.41258 + 0.0678578i) q^{2} +(1.66901 + 0.463024i) q^{3} +(1.99079 - 0.191710i) q^{4} -1.00000i q^{5} +(-2.38904 - 0.540805i) q^{6} -1.00000i q^{7} +(-2.79915 + 0.405897i) q^{8} +(2.57122 + 1.54559i) q^{9} +(0.0678578 + 1.41258i) q^{10} -0.648120 q^{11} +(3.41142 + 0.601817i) q^{12} +4.96381 q^{13} +(0.0678578 + 1.41258i) q^{14} +(0.463024 - 1.66901i) q^{15} +(3.92649 - 0.763309i) q^{16} -6.88118i q^{17} +(-3.73694 - 2.00880i) q^{18} +4.22288i q^{19} +(-0.191710 - 1.99079i) q^{20} +(0.463024 - 1.66901i) q^{21} +(0.915524 - 0.0439800i) q^{22} +1.33148 q^{23} +(-4.85976 - 0.618626i) q^{24} -1.00000 q^{25} +(-7.01180 + 0.336833i) q^{26} +(3.57575 + 3.77014i) q^{27} +(-0.191710 - 1.99079i) q^{28} +4.10451i q^{29} +(-0.540805 + 2.38904i) q^{30} -7.63684i q^{31} +(-5.49471 + 1.34468i) q^{32} +(-1.08172 - 0.300095i) q^{33} +(0.466942 + 9.72025i) q^{34} -1.00000 q^{35} +(5.41506 + 2.58401i) q^{36} -2.29722 q^{37} +(-0.286556 - 5.96518i) q^{38} +(8.28466 + 2.29836i) q^{39} +(0.405897 + 2.79915i) q^{40} +10.9561i q^{41} +(-0.540805 + 2.38904i) q^{42} -5.13687i q^{43} +(-1.29027 + 0.124251i) q^{44} +(1.54559 - 2.57122i) q^{45} +(-1.88082 + 0.0903511i) q^{46} +9.62134 q^{47} +(6.90681 + 0.544089i) q^{48} -1.00000 q^{49} +(1.41258 - 0.0678578i) q^{50} +(3.18615 - 11.4848i) q^{51} +(9.88190 - 0.951611i) q^{52} -5.56316i q^{53} +(-5.30689 - 5.08300i) q^{54} +0.648120i q^{55} +(0.405897 + 2.79915i) q^{56} +(-1.95530 + 7.04805i) q^{57} +(-0.278524 - 5.79797i) q^{58} +0.421507 q^{59} +(0.601817 - 3.41142i) q^{60} +0.179252 q^{61} +(0.518219 + 10.7877i) q^{62} +(1.54559 - 2.57122i) q^{63} +(7.67049 - 2.27234i) q^{64} -4.96381i q^{65} +(1.54839 + 0.350506i) q^{66} +10.4894i q^{67} +(-1.31919 - 13.6990i) q^{68} +(2.22225 + 0.616506i) q^{69} +(1.41258 - 0.0678578i) q^{70} -2.09646 q^{71} +(-7.82458 - 3.28268i) q^{72} -16.6256 q^{73} +(3.24501 - 0.155884i) q^{74} +(-1.66901 - 0.463024i) q^{75} +(0.809569 + 8.40688i) q^{76} +0.648120i q^{77} +(-11.8588 - 2.68445i) q^{78} +7.10256i q^{79} +(-0.763309 - 3.92649i) q^{80} +(4.22232 + 7.94808i) q^{81} +(-0.743459 - 15.4764i) q^{82} -0.766970 q^{83} +(0.601817 - 3.41142i) q^{84} -6.88118 q^{85} +(0.348577 + 7.25626i) q^{86} +(-1.90049 + 6.85049i) q^{87} +(1.81419 - 0.263070i) q^{88} +11.5147i q^{89} +(-2.00880 + 3.73694i) q^{90} -4.96381i q^{91} +(2.65069 - 0.255257i) q^{92} +(3.53604 - 12.7460i) q^{93} +(-13.5910 + 0.652884i) q^{94} +4.22288 q^{95} +(-9.79337 - 0.299890i) q^{96} -14.8262 q^{97} +(1.41258 - 0.0678578i) q^{98} +(-1.66646 - 1.00173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41258	+	0.0678578i	−0.998848	+	0.0479827i
$2$	−1.41258	+	0.0678578i	−0.998848	+	0.0479827i
$3$	1.66901	+	0.463024i	0.963606	+	0.267327i
$3$	1.66901	+	0.463024i	0.963606	+	0.267327i
$4$	1.99079	−	0.191710i	0.995395	−	0.0958550i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.38904	−	0.540805i	−0.975323	−	0.220783i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.79915	+	0.405897i	−0.989649	+	0.143506i
$9$	2.57122	+	1.54559i	0.857072	+	0.515196i
$10$	0.0678578	+	1.41258i	0.0214585	+	0.446698i
$11$	−0.648120			−0.195415			−0.0977077	−	0.995215i	$-0.531151\pi$
$11$	−0.648120			−0.195415			−0.0977077	+	0.995215i	$0.531151\pi$
$12$	3.41142	+	0.601817i	0.984793	+	0.173730i
$13$	4.96381			1.37671			0.688356	−	0.725373i	$-0.258333\pi$
$13$	4.96381			1.37671			0.688356	+	0.725373i	$0.258333\pi$
$14$	0.0678578	+	1.41258i	0.0181358	+	0.377529i
$15$	0.463024	−	1.66901i	0.119552	−	0.430938i
$16$	3.92649	−	0.763309i	0.981624	−	0.190827i
$17$		−	6.88118i		−	1.66893i	−0.551060	−	0.834466i	$-0.685776\pi$
$17$		−	6.88118i		−	1.66893i	0.551060	−	0.834466i	$-0.314224\pi$
$18$	−3.73694	−	2.00880i	−0.880806	−	0.473478i
$19$			4.22288i			0.968796i	0.874848	+	0.484398i	$0.160961\pi$
$19$			4.22288i			0.968796i	−0.874848	+	0.484398i	$0.839039\pi$
$20$	−0.191710	−	1.99079i	−0.0428676	−	0.445154i
$21$	0.463024	−	1.66901i	0.101040	−	0.364209i
$22$	0.915524	−	0.0439800i	0.195190	−	0.00937657i
$23$	1.33148			0.277632			0.138816	−	0.990318i	$-0.455670\pi$
$23$	1.33148			0.277632			0.138816	+	0.990318i	$0.455670\pi$
$24$	−4.85976	−	0.618626i	−0.991995	−	0.126277i
$25$	−1.00000			−0.200000
$26$	−7.01180	+	0.336833i	−1.37513	+	0.0660584i
$27$	3.57575	+	3.77014i	0.688154	+	0.725564i
$28$	−0.191710	−	1.99079i	−0.0362298	−	0.376224i
$29$			4.10451i			0.762189i	0.924536	+	0.381095i	$0.124453\pi$
$29$			4.10451i			0.762189i	−0.924536	+	0.381095i	$0.875547\pi$
$30$	−0.540805	+	2.38904i	−0.0987370	+	0.436178i
$31$		−	7.63684i		−	1.37162i	−0.727782	−	0.685808i	$-0.759449\pi$
$31$		−	7.63684i		−	1.37162i	0.727782	−	0.685808i	$-0.240551\pi$
$32$	−5.49471	+	1.34468i	−0.971337	+	0.237708i
$33$	−1.08172	−	0.300095i	−0.188304	−	0.0522398i
$34$	0.466942	+	9.72025i	0.0800799	+	1.66701i
$35$	−1.00000			−0.169031
$36$	5.41506	+	2.58401i	0.902510	+	0.430669i
$37$	−2.29722			−0.377660			−0.188830	−	0.982010i	$-0.560469\pi$
$37$	−2.29722			−0.377660			−0.188830	+	0.982010i	$0.560469\pi$
$38$	−0.286556	−	5.96518i	−0.0464855	−	0.967680i
$39$	8.28466	+	2.29836i	1.32661	+	0.368032i
$40$	0.405897	+	2.79915i	0.0641780	+	0.442585i
$41$			10.9561i			1.71106i	0.517754	+	0.855529i	$0.326768\pi$
$41$			10.9561i			1.71106i	−0.517754	+	0.855529i	$0.673232\pi$
$42$	−0.540805	+	2.38904i	−0.0834480	+	0.368637i
$43$		−	5.13687i		−	0.783365i	−0.920100	−	0.391682i	$-0.871893\pi$
$43$		−	5.13687i		−	0.783365i	0.920100	−	0.391682i	$-0.128107\pi$
$44$	−1.29027	+	0.124251i	−0.194516	+	0.0187315i
$45$	1.54559	−	2.57122i	0.230403	−	0.383294i
$46$	−1.88082	+	0.0903511i	−0.277312	+	0.0133215i
$47$	9.62134			1.40342			0.701708	−	0.712464i	$-0.252421\pi$
$47$	9.62134			1.40342			0.701708	+	0.712464i	$0.252421\pi$
$48$	6.90681	+	0.544089i	0.996912	+	0.0785324i
$49$	−1.00000			−0.142857
$50$	1.41258	−	0.0678578i	0.199770	−	0.00959655i
$51$	3.18615	−	11.4848i	0.446151	−	1.60819i
$52$	9.88190	−	0.951611i	1.37037	−	0.131965i
$53$		−	5.56316i		−	0.764158i	−0.924130	−	0.382079i	$-0.875208\pi$
$53$		−	5.56316i		−	0.764158i	0.924130	−	0.382079i	$-0.124792\pi$
$54$	−5.30689	−	5.08300i	−0.722176	−	0.691709i
$55$			0.648120i			0.0873925i
$56$	0.405897	+	2.79915i	0.0542403	+	0.374052i
$57$	−1.95530	+	7.04805i	−0.258985	+	0.933537i
$58$	−0.278524	−	5.79797i	−0.0365719	−	0.761311i
$59$	0.421507			0.0548755			0.0274378	−	0.999624i	$-0.491265\pi$
$59$	0.421507			0.0548755			0.0274378	+	0.999624i	$0.491265\pi$
$60$	0.601817	−	3.41142i	0.0776943	−	0.440413i
$61$	0.179252			0.0229509			0.0114754	−	0.999934i	$-0.496347\pi$
$61$	0.179252			0.0229509			0.0114754	+	0.999934i	$0.496347\pi$
$62$	0.518219	+	10.7877i	0.0658139	+	1.37004i
$63$	1.54559	−	2.57122i	0.194726	−	0.323943i
$64$	7.67049	−	2.27234i	0.958812	−	0.284042i
$65$		−	4.96381i		−	0.615684i
$66$	1.54839	+	0.350506i	0.190593	+	0.0431444i
$67$			10.4894i			1.28149i	0.767754	+	0.640745i	$0.221374\pi$
$67$			10.4894i			1.28149i	−0.767754	+	0.640745i	$0.778626\pi$
$68$	−1.31919	−	13.6990i	−0.159975	−	1.66125i
$69$	2.22225	+	0.616506i	0.267528	+	0.0742186i
$70$	1.41258	−	0.0678578i	0.168836	−	0.00811056i
$71$	−2.09646			−0.248804			−0.124402	−	0.992232i	$-0.539701\pi$
$71$	−2.09646			−0.248804			−0.124402	+	0.992232i	$0.539701\pi$
$72$	−7.82458	−	3.28268i	−0.922135	−	0.386868i
$73$	−16.6256			−1.94588			−0.972941	−	0.231055i	$-0.925782\pi$
$73$	−16.6256			−1.94588			−0.972941	+	0.231055i	$0.925782\pi$
$74$	3.24501	−	0.155884i	0.377225	−	0.0181212i
$75$	−1.66901	−	0.463024i	−0.192721	−	0.0534654i
$76$	0.809569	+	8.40688i	0.0928639	+	0.964335i
$77$			0.648120i			0.0738601i
$78$	−11.8588	−	2.68445i	−1.34274	−	0.303954i
$79$			7.10256i			0.799100i	0.916711	+	0.399550i	$0.130834\pi$
$79$			7.10256i			0.799100i	−0.916711	+	0.399550i	$0.869166\pi$
$80$	−0.763309	−	3.92649i	−0.0853405	−	0.438995i
$81$	4.22232	+	7.94808i	0.469146	+	0.883120i
$82$	−0.743459	−	15.4764i	−0.0821013	−	1.70909i
$83$	−0.766970			−0.0841859			−0.0420930	−	0.999114i	$-0.513403\pi$
$83$	−0.766970			−0.0841859			−0.0420930	+	0.999114i	$0.513403\pi$
$84$	0.601817	−	3.41142i	0.0656637	−	0.372217i
$85$	−6.88118			−0.746369
$86$	0.348577	+	7.25626i	0.0375880	+	0.782463i
$87$	−1.90049	+	6.85049i	−0.203754	+	0.734450i
$88$	1.81419	−	0.263070i	0.193393	−	0.0280434i
$89$			11.5147i			1.22056i	0.792186	+	0.610280i	$0.208943\pi$
$89$			11.5147i			1.22056i	−0.792186	+	0.610280i	$0.791057\pi$
$90$	−2.00880	+	3.73694i	−0.211746	+	0.393908i
$91$		−	4.96381i		−	0.520348i
$92$	2.65069	−	0.255257i	0.276354	−	0.0266124i
$93$	3.53604	−	12.7460i	0.366670	−	1.32170i
$94$	−13.5910	+	0.652884i	−1.40180	+	0.0673398i
$95$	4.22288			0.433259
$96$	−9.79337	−	0.299890i	−0.999531	−	0.0306074i
$97$	−14.8262			−1.50537			−0.752685	−	0.658380i	$-0.771242\pi$
$97$	−14.8262			−1.50537			−0.752685	+	0.658380i	$0.771242\pi$
$98$	1.41258	−	0.0678578i	0.142693	−	0.00685468i
$99$	−1.66646	−	1.00173i	−0.167485	−	0.100677i
$100$	−1.99079	+	0.191710i	−0.199079	+	0.0191710i
$101$		−	3.56719i		−	0.354948i	−0.984125	−	0.177474i	$-0.943207\pi$
$101$		−	3.56719i		−	0.354948i	0.984125	−	0.177474i	$-0.0567926\pi$
$102$	−3.72138	+	16.4394i	−0.368471	+	1.62775i
$103$		−	9.56713i		−	0.942678i	−0.881952	−	0.471339i	$-0.843771\pi$
$103$		−	9.56713i		−	0.942678i	0.881952	−	0.471339i	$-0.156229\pi$
$104$	−13.8944	+	2.01480i	−1.36246	+	0.197567i
$105$	−1.66901	−	0.463024i	−0.162879	−	0.0451865i
$106$	0.377504	+	7.85843i	0.0366664	+	0.763278i
$107$	−11.2400			−1.08661			−0.543305	−	0.839535i	$-0.682827\pi$
$107$	−11.2400			−1.08661			−0.543305	+	0.839535i	$0.682827\pi$
$108$	7.84135	+	6.82006i	0.754534	+	0.656260i
$109$	−9.16851			−0.878184			−0.439092	−	0.898442i	$-0.644700\pi$
$109$	−9.16851			−0.878184			−0.439092	+	0.898442i	$0.644700\pi$
$110$	−0.0439800	−	0.915524i	−0.00419333	−	0.0872918i
$111$	−3.83409	−	1.06367i	−0.363915	−	0.100959i
$112$	−0.763309	−	3.92649i	−0.0721259	−	0.371019i
$113$			3.10716i			0.292297i	0.989263	+	0.146149i	$0.0466877\pi$
$113$			3.10716i			0.292297i	−0.989263	+	0.146149i	$0.953312\pi$
$114$	2.28376	−	10.0887i	0.213893	−	0.944889i
$115$		−	1.33148i		−	0.124161i
$116$	0.786876	+	8.17123i	0.0730596	+	0.758680i
$117$	12.7630	+	7.67200i	1.17994	+	0.709276i
$118$	−0.595414	+	0.0286025i	−0.0548123	+	0.00263308i
$119$	−6.88118			−0.630797
$120$	−0.618626	+	4.85976i	−0.0564726	+	0.443634i
$121$	−10.5799			−0.961813
$122$	−0.253209	+	0.0121637i	−0.0229245	+	0.00110125i
$123$	−5.07295	+	18.2859i	−0.457412	+	1.64879i
$124$	−1.46406	−	15.2033i	−0.131476	−	1.36530i
$125$			1.00000i			0.0894427i
$126$	−2.00880	+	3.73694i	−0.178958	+	0.332913i
$127$		−	5.01119i		−	0.444671i	−0.974970	−	0.222335i	$-0.928632\pi$
$127$		−	5.01119i		−	0.444671i	0.974970	−	0.222335i	$-0.0713680\pi$
$128$	−10.6810	+	3.73037i	−0.944078	+	0.329721i
$129$	2.37849	−	8.57350i	0.209415	−	0.754855i
$130$	0.336833	+	7.01180i	0.0295422	+	0.614975i
$131$	−18.0995			−1.58136			−0.790681	−	0.612228i	$-0.790274\pi$
$131$	−18.0995			−1.58136			−0.790681	+	0.612228i	$0.790274\pi$
$132$	−2.21101	−	0.390050i	−0.192444	−	0.0339495i
$133$	4.22288			0.366170
$134$	−0.711791	−	14.8172i	−0.0614894	−	1.28001i
$135$	3.77014	−	3.57575i	0.324482	−	0.307752i
$136$	2.79305	+	19.2615i	0.239502	+	1.65166i
$137$		−	12.2502i		−	1.04661i	−0.852146	−	0.523304i	$-0.824699\pi$
$137$		−	12.2502i		−	1.04661i	0.852146	−	0.523304i	$-0.175301\pi$
$138$	−3.18096	−	0.720069i	−0.270781	−	0.0612964i
$139$			12.5062i			1.06076i	0.847760	+	0.530380i	$0.177951\pi$
$139$			12.5062i			1.06076i	−0.847760	+	0.530380i	$0.822049\pi$
$140$	−1.99079	+	0.191710i	−0.168253	+	0.0162024i
$141$	16.0582	+	4.45491i	1.35234	+	0.375171i
$142$	2.96143	−	0.142261i	0.248517	−	0.0119383i
$143$	−3.21714			−0.269031
$144$	11.2756	+	4.10611i	0.939636	+	0.342176i
$145$	4.10451			0.340861
$146$	23.4851	−	1.12818i	1.94364	−	0.0933687i
$147$	−1.66901	−	0.463024i	−0.137658	−	0.0381896i
$148$	−4.57327	+	0.440399i	−0.375921	+	0.0362006i
$149$		−	7.75155i		−	0.635031i	−0.948253	−	0.317516i	$-0.897151\pi$
$149$		−	7.75155i		−	0.635031i	0.948253	−	0.317516i	$-0.102849\pi$
$150$	2.38904	+	0.540805i	0.195065	+	0.0441565i
$151$			1.99824i			0.162614i	0.996689	+	0.0813072i	$0.0259095\pi$
$151$			1.99824i			0.162614i	−0.996689	+	0.0813072i	$0.974090\pi$
$152$	−1.71406	−	11.8205i	−0.139028	−	0.958768i
$153$	10.6355	−	17.6930i	0.859827	−	1.43040i
$154$	−0.0439800	−	0.915524i	−0.00354401	−	0.0737750i
$155$	−7.63684			−0.613406
$156$	16.9337	+	2.98731i	1.35578	+	0.239176i
$157$	12.8513			1.02565			0.512824	−	0.858494i	$-0.328599\pi$
$157$	12.8513			1.02565			0.512824	+	0.858494i	$0.328599\pi$
$158$	−0.481964	−	10.0330i	−0.0383430	−	0.798180i
$159$	2.57588	−	9.28499i	0.204280	−	0.736347i
$160$	1.34468	+	5.49471i	0.106306	+	0.434395i
$161$		−	1.33148i		−	0.104935i
$162$	−6.50372	−	10.9408i	−0.510981	−	0.859592i
$163$		−	3.76566i		−	0.294949i	−0.989066	−	0.147474i	$-0.952886\pi$
$163$		−	3.76566i		−	0.294949i	0.989066	−	0.147474i	$-0.0471144\pi$
$164$	2.10040	+	21.8113i	0.164013	+	1.70318i
$165$	−0.300095	+	1.08172i	−0.0233624	+	0.0842119i
$166$	1.08341	−	0.0520449i	0.0840889	−	0.00403947i
$167$	−12.3052			−0.952203			−0.476101	−	0.879390i	$-0.657950\pi$
$167$	−12.3052			−0.952203			−0.476101	+	0.879390i	$0.657950\pi$
$168$	−0.618626	+	4.85976i	−0.0477280	+	0.374939i
$169$	11.6394			0.895337
$170$	9.72025	−	0.466942i	0.745509	−	0.0358128i
$171$	−6.52684	+	10.8580i	−0.499120	+	0.830328i
$172$	−0.984788	−	10.2264i	−0.0750894	−	0.779758i
$173$			18.5642i			1.41141i	0.708506	+	0.705705i	$0.249370\pi$
$173$			18.5642i			1.41141i	−0.708506	+	0.705705i	$0.750630\pi$
$174$	2.21974	−	9.80586i	0.168278	−	0.743381i
$175$			1.00000i			0.0755929i
$176$	−2.54484	+	0.494715i	−0.191824	+	0.0372906i
$177$	0.703501	+	0.195168i	0.0528784	+	0.0146697i
$178$	−0.781366	−	16.2655i	−0.0585658	−	1.21915i
$179$	12.1268			0.906401			0.453201	−	0.891408i	$-0.350282\pi$
$179$	12.1268			0.906401			0.453201	+	0.891408i	$0.350282\pi$
$180$	2.58401	−	5.41506i	0.192601	−	0.403615i
$181$	−0.0867806			−0.00645035			−0.00322517	−	0.999995i	$-0.501027\pi$
$181$	−0.0867806			−0.00645035			−0.00322517	+	0.999995i	$0.501027\pi$
$182$	0.336833	+	7.01180i	0.0249677	+	0.519749i
$183$	0.299175	+	0.0829981i	0.0221156	+	0.00613540i
$184$	−3.72700	+	0.540443i	−0.274758	+	0.0398420i
$185$			2.29722i			0.168895i
$186$	−4.13004	+	18.2447i	−0.302829	+	1.33777i
$187$			4.45983i			0.326135i
$188$	19.1541	−	1.84451i	1.39695	−	0.134524i
$189$	3.77014	−	3.57575i	0.274238	−	0.260098i
$190$	−5.96518	+	0.286556i	−0.432760	+	0.0207889i
$191$	17.7041			1.28102			0.640512	−	0.767948i	$-0.278722\pi$
$191$	17.7041			1.28102			0.640512	+	0.767948i	$0.278722\pi$
$192$	13.8543	−	0.240937i	0.999849	−	0.0173881i
$193$	−14.0241			−1.00947			−0.504737	−	0.863273i	$-0.668410\pi$
$193$	−14.0241			−1.00947			−0.504737	+	0.863273i	$0.668410\pi$
$194$	20.9432	−	1.00607i	1.50364	−	0.0722318i
$195$	2.29836	−	8.28466i	0.164589	−	0.593277i
$196$	−1.99079	+	0.191710i	−0.142199	+	0.0136936i
$197$			6.66618i			0.474946i	0.971394	+	0.237473i	$0.0763191\pi$
$197$			6.66618i			0.474946i	−0.971394	+	0.237473i	$0.923681\pi$
$198$	2.42199	+	1.30194i	0.172123	+	0.0925249i
$199$			0.390542i			0.0276848i	0.999904	+	0.0138424i	$0.00440631\pi$
$199$			0.390542i			0.0276848i	−0.999904	+	0.0138424i	$0.995594\pi$
$200$	2.79915	−	0.405897i	0.197930	−	0.0287013i
$201$	−4.85687	+	17.5070i	−0.342577	+	1.23485i
$202$	0.242062	+	5.03895i	0.0170314	+	0.354539i
$203$	4.10451			0.288080
$204$	4.14121	−	23.4746i	0.289943	−	1.64355i
$205$	10.9561			0.765209
$206$	0.649205	+	13.5144i	0.0452323	+	0.941592i
$207$	3.42352	+	2.05791i	0.237951	+	0.143035i
$208$	19.4904	−	3.78892i	1.35141	−	0.262714i
$209$		−	2.73693i		−	0.189318i
$210$	2.38904	+	0.540805i	0.164860	+	0.0373191i
$211$		−	28.5906i		−	1.96826i	−0.177461	−	0.984128i	$-0.556788\pi$
$211$		−	28.5906i		−	1.96826i	0.177461	−	0.984128i	$-0.443212\pi$
$212$	−1.06651	−	11.0751i	−0.0732484	−	0.760640i
$213$	−3.49902	−	0.970711i	−0.239749	−	0.0665120i
$214$	15.8774	−	0.762721i	1.08536	−	0.0521385i
$215$	−5.13687			−0.350331
$216$	−11.5394	−	9.10181i	−0.785155	−	0.619300i
$217$	−7.63684			−0.518422
$218$	12.9513	−	0.622155i	0.877172	−	0.0421377i
$219$	−27.7484	−	7.69806i	−1.87506	−	0.520187i
$220$	0.124251	+	1.29027i	0.00837700	+	0.0869900i
$221$		−	34.1569i		−	2.29764i
$222$	5.48815	+	1.24235i	0.368340	+	0.0833808i
$223$			29.4239i			1.97037i	0.171489	+	0.985186i	$0.445142\pi$
$223$			29.4239i			1.97037i	−0.171489	+	0.985186i	$0.554858\pi$
$224$	1.34468	+	5.49471i	0.0898453	+	0.367131i
$225$	−2.57122	−	1.54559i	−0.171414	−	0.103039i
$226$	−0.210845	−	4.38913i	−0.0140252	−	0.291960i
$227$	20.6406			1.36997			0.684983	−	0.728559i	$-0.259809\pi$
$227$	20.6406			1.36997			0.684983	+	0.728559i	$0.259809\pi$
$228$	−2.54140	+	14.4060i	−0.168309	+	0.954064i
$229$	−1.01566			−0.0671167			−0.0335583	−	0.999437i	$-0.510684\pi$
$229$	−1.01566			−0.0671167			−0.0335583	+	0.999437i	$0.510684\pi$
$230$	0.0903511	+	1.88082i	0.00595758	+	0.124018i
$231$	−0.300095	+	1.08172i	−0.0197448	+	0.0711720i
$232$	−1.66601	−	11.4892i	−0.109379	−	0.754300i
$233$		−	5.71810i		−	0.374605i	−0.982302	−	0.187302i	$-0.940026\pi$
$233$		−	5.71810i		−	0.374605i	0.982302	−	0.187302i	$-0.0599744\pi$
$234$	−18.5495	−	9.97127i	−1.21262	−	0.651843i
$235$		−	9.62134i		−	0.627627i
$236$	0.839132	−	0.0808070i	0.0546228	−	0.00526009i
$237$	−3.28866	+	11.8543i	−0.213621	+	0.770018i
$238$	9.72025	−	0.466942i	0.630070	−	0.0302674i
$239$	−18.4859			−1.19575			−0.597876	−	0.801589i	$-0.703988\pi$
$239$	−18.4859			−1.19575			−0.597876	+	0.801589i	$0.703988\pi$
$240$	0.544089	−	6.90681i	0.0351208	−	0.445832i
$241$	11.7580			0.757400			0.378700	−	0.925519i	$-0.376371\pi$
$241$	11.7580			0.757400			0.378700	+	0.925519i	$0.376371\pi$
$242$	14.9451	−	0.717932i	0.960705	−	0.0461504i
$243$	3.36696	+	15.2205i	0.215990	+	0.976396i
$244$	0.356854	−	0.0343644i	0.0228452	−	0.00219996i
$245$			1.00000i			0.0638877i
$246$	5.92512	−	26.1747i	0.377772	−	1.66883i
$247$			20.9616i			1.33375i
$248$	3.09977	+	21.3767i	0.196836	+	1.35742i
$249$	−1.28008	−	0.355126i	−0.0811220	−	0.0225052i
$250$	−0.0678578	−	1.41258i	−0.00429171	−	0.0893397i
$251$	11.5446			0.728691			0.364345	−	0.931264i	$-0.381293\pi$
$251$	11.5446			0.728691			0.364345	+	0.931264i	$0.381293\pi$
$252$	2.58401	−	5.41506i	0.162778	−	0.341117i
$253$	−0.862956			−0.0542536
$254$	0.340048	+	7.07872i	0.0213365	+	0.444159i
$255$	−11.4848	−	3.18615i	−0.719205	−	0.199525i
$256$	14.8347	−	5.99425i	0.927170	−	0.374641i
$257$			8.63514i			0.538645i	0.963050	+	0.269323i	$0.0867998\pi$
$257$			8.63514i			0.538645i	−0.963050	+	0.269323i	$0.913200\pi$
$258$	−2.77804	+	12.2722i	−0.172953	+	0.764034i
$259$			2.29722i			0.142742i
$260$	−0.951611	−	9.88190i	−0.0590164	−	0.612849i
$261$	−6.34389	+	10.5536i	−0.392677	+	0.653251i
$262$	25.5671	−	1.22819i	1.57954	−	0.0758781i
$263$	−16.2106			−0.999591			−0.499795	−	0.866144i	$-0.666591\pi$
$263$	−16.2106			−0.999591			−0.499795	+	0.866144i	$0.666591\pi$
$264$	3.14971	+	0.400944i	0.193851	+	0.0246764i
$265$	−5.56316			−0.341742
$266$	−5.96518	+	0.286556i	−0.365749	+	0.0175699i
$267$	−5.33160	+	19.2183i	−0.326289	+	1.17614i
$268$	2.01093	+	20.8823i	0.122837	+	1.27559i
$269$			12.9285i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$269$			12.9285i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$270$	−5.08300	+	5.30689i	−0.309342	+	0.322967i
$271$		−	7.98971i		−	0.485340i	−0.970109	−	0.242670i	$-0.921977\pi$
$271$		−	7.98971i		−	0.485340i	0.970109	−	0.242670i	$-0.0780233\pi$
$272$	−5.25246	−	27.0189i	−0.318477	−	1.63826i
$273$	2.29836	−	8.28466i	0.139103	−	0.501411i
$274$	0.831275	+	17.3045i	0.0502192	+	1.04540i
$275$	0.648120			0.0390831
$276$	4.54223	+	0.801306i	0.273410	+	0.0482329i
$277$	23.8395			1.43238			0.716188	−	0.697908i	$-0.245885\pi$
$277$	23.8395			1.43238			0.716188	+	0.697908i	$0.245885\pi$
$278$	−0.848641	−	17.6660i	−0.0508981	−	1.05954i
$279$	11.8034	−	19.6360i	0.706651	−	1.17557i
$280$	2.79915	−	0.405897i	0.167281	−	0.0242570i
$281$		−	1.52045i		−	0.0907025i	−0.998971	−	0.0453513i	$-0.985559\pi$
$281$		−	1.52045i		−	0.0907025i	0.998971	−	0.0453513i	$-0.0144407\pi$
$282$	−22.9858	−	5.20327i	−1.36878	−	0.309850i
$283$		−	6.56172i		−	0.390054i	−0.980798	−	0.195027i	$-0.937521\pi$
$283$		−	6.56172i		−	0.390054i	0.980798	−	0.195027i	$-0.0624794\pi$
$284$	−4.17361	+	0.401912i	−0.247658	+	0.0238491i
$285$	7.04805	+	1.95530i	0.417491	+	0.115822i
$286$	4.54448	−	0.218308i	0.268721	−	0.0129088i
$287$	10.9561			0.646719
$288$	−16.2064	−	5.03509i	−0.954972	−	0.296695i
$289$	−30.3507			−1.78533
$290$	−5.79797	+	0.278524i	−0.340469	+	0.0163555i
$291$	−24.7451	−	6.86488i	−1.45058	−	0.402426i
$292$	−33.0981	+	3.18730i	−1.93692	+	0.186522i
$293$			21.0744i			1.23118i	0.788066	+	0.615591i	$0.211083\pi$
$293$			21.0744i			1.23118i	−0.788066	+	0.615591i	$0.788917\pi$
$294$	2.38904	+	0.540805i	0.139332	+	0.0315404i
$295$		−	0.421507i		−	0.0245411i
$296$	6.43025	−	0.932433i	0.373751	−	0.0541966i
$297$	−2.31752	−	2.44350i	−0.134476	−	0.141787i
$298$	0.526003	+	10.9497i	0.0304705	+	0.634300i
$299$	6.60919			0.382219
$300$	−3.41142	−	0.601817i	−0.196959	−	0.0347459i
$301$	−5.13687			−0.296084
$302$	−0.135596	−	2.82268i	−0.00780269	−	0.162427i
$303$	1.65169	−	5.95368i	0.0948873	−	0.342030i
$304$	3.22336	+	16.5811i	0.184873	+	0.950993i
$305$		−	0.179252i		−	0.0102640i
$306$	−13.8229	+	25.7146i	−0.790202	+	1.47000i
$307$			25.3127i			1.44467i	0.691542	+	0.722336i	$0.256932\pi$
$307$			25.3127i			1.44467i	−0.691542	+	0.722336i	$0.743068\pi$
$308$	0.124251	+	1.29027i	0.00707986	+	0.0735200i
$309$	4.42981	−	15.9677i	0.252003	−	0.908370i
$310$	10.7877	−	0.518219i	0.612699	−	0.0294329i
$311$	−18.2961			−1.03748			−0.518739	−	0.854933i	$-0.673598\pi$
$311$	−18.2961			−1.03748			−0.518739	+	0.854933i	$0.673598\pi$
$312$	−24.1229	−	3.07074i	−1.36569	−	0.173846i
$313$	20.8802			1.18022			0.590110	−	0.807323i	$-0.299084\pi$
$313$	20.8802			1.18022			0.590110	+	0.807323i	$0.299084\pi$
$314$	−18.1536	+	0.872064i	−1.02447	+	0.0492134i
$315$	−2.57122	−	1.54559i	−0.144872	−	0.0870840i
$316$	1.36163	+	14.1397i	0.0765977	+	0.795421i
$317$		−	25.7694i		−	1.44735i	−0.690140	−	0.723676i	$-0.742451\pi$
$317$		−	25.7694i		−	1.44735i	0.690140	−	0.723676i	$-0.257549\pi$
$318$	−3.00858	+	13.2906i	−0.168713	+	0.745301i
$319$		−	2.66022i		−	0.148944i
$320$	−2.27234	−	7.67049i	−0.127027	−	0.428794i
$321$	−18.7597	−	5.20438i	−1.04706	−	0.290480i
$322$	0.0903511	+	1.88082i	0.00503507	+	0.104814i
$323$	29.0584			1.61685
$324$	9.92948	+	15.0135i	0.551638	+	0.834084i
$325$	−4.96381			−0.275342
$326$	0.255529	+	5.31931i	0.0141525	+	0.294609i
$327$	−15.3024	−	4.24524i	−0.846223	−	0.234762i
$328$	−4.44706	−	30.6678i	−0.245548	−	1.69335i
$329$		−	9.62134i		−	0.530442i
$330$	0.350506	−	1.54839i	0.0192947	−	0.0852359i
$331$		−	21.4801i		−	1.18065i	−0.807164	−	0.590327i	$-0.798999\pi$
$331$		−	21.4801i		−	1.18065i	0.807164	−	0.590327i	$-0.201001\pi$
$332$	−1.52688	+	0.147036i	−0.0837983	+	0.00806964i
$333$	−5.90664	−	3.55055i	−0.323682	−	0.194569i
$334$	17.3821	−	0.835002i	0.951106	−	0.0456893i
$335$	10.4894			0.573100
$336$	0.544089	−	6.90681i	0.0296825	−	0.376797i
$337$	−10.7117			−0.583504			−0.291752	−	0.956494i	$-0.594238\pi$
$337$	−10.7117			−0.583504			−0.291752	+	0.956494i	$0.594238\pi$
$338$	−16.4416	+	0.789823i	−0.894305	+	0.0429607i
$339$	−1.43869	+	5.18590i	−0.0781389	+	0.281659i
$340$	−13.6990	+	1.31919i	−0.742932	+	0.0715432i
$341$			4.94959i			0.268035i
$342$	8.48291	−	15.7807i	0.458703	−	0.853321i
$343$			1.00000i			0.0539949i
$344$	2.08504	+	14.3789i	0.112418	+	0.775257i
$345$	0.616506	−	2.22225i	0.0331915	−	0.119642i
$346$	−1.25973	−	26.2235i	−0.0677233	−	1.40978i
$347$	10.5606			0.566923			0.283462	−	0.958984i	$-0.408517\pi$
$347$	10.5606			0.566923			0.283462	+	0.958984i	$0.408517\pi$
$348$	−2.47017	+	14.0022i	−0.132415	+	0.750599i
$349$	21.7269			1.16301			0.581507	−	0.813541i	$-0.302463\pi$
$349$	21.7269			1.16301			0.581507	+	0.813541i	$0.302463\pi$
$350$	−0.0678578	−	1.41258i	−0.00362715	−	0.0755058i
$351$	17.7494	+	18.7143i	0.947390	+	0.998893i
$352$	3.56123	−	0.871515i	0.189814	−	0.0464519i
$353$			21.0359i			1.11963i	0.828618	+	0.559814i	$0.189128\pi$
$353$			21.0359i			1.11963i	−0.828618	+	0.559814i	$0.810872\pi$
$354$	−1.00700	−	0.227953i	−0.0535214	−	0.0121156i
$355$			2.09646i			0.111269i
$356$	2.20749	+	22.9234i	0.116997	+	1.21494i
$357$	−11.4848	−	3.18615i	−0.607840	−	0.168629i
$358$	−17.1302	+	0.822900i	−0.905357	+	0.0434916i
$359$	1.14792			0.0605850			0.0302925	−	0.999541i	$-0.490356\pi$
$359$	1.14792			0.0605850			0.0302925	+	0.999541i	$0.490356\pi$
$360$	−3.28268	+	7.82458i	−0.173013	+	0.412391i
$361$	1.16725			0.0614344
$362$	0.122585	−	0.00588874i	0.00644292	−	0.000309505i
$363$	−17.6581	−	4.89877i	−0.926808	−	0.257119i
$364$	−0.951611	−	9.88190i	−0.0498780	−	0.517952i
$365$			16.6256i			0.870225i
$366$	−0.428241	−	0.0969405i	−0.0223845	−	0.00506716i
$367$		−	4.83851i		−	0.252568i	−0.991994	−	0.126284i	$-0.959695\pi$
$367$		−	4.83851i		−	0.252568i	0.991994	−	0.126284i	$-0.0403051\pi$
$368$	5.22804	−	1.01633i	0.272530	−	0.0529797i
$369$	−16.9336	+	28.1706i	−0.881530	+	1.46650i
$370$	−0.155884	−	3.24501i	−0.00810403	−	0.168700i
$371$	−5.56316			−0.288825
$372$	4.59598	−	26.0525i	0.238291	−	1.35076i
$373$	12.1232			0.627716			0.313858	−	0.949470i	$-0.398378\pi$
$373$	12.1232			0.627716			0.313858	+	0.949470i	$0.398378\pi$
$374$	−0.302634	−	6.29989i	−0.0156489	−	0.325759i
$375$	−0.463024	+	1.66901i	−0.0239105	+	0.0861875i
$376$	−26.9316	+	3.90528i	−1.38889	+	0.201399i
$377$			20.3740i			1.04932i
$378$	−5.08300	+	5.30689i	−0.261441	+	0.272957i
$379$			23.0839i			1.18574i	0.805299	+	0.592869i	$0.202005\pi$
$379$			23.0839i			1.18574i	−0.805299	+	0.592869i	$0.797995\pi$
$380$	8.40688	−	0.809569i	0.431264	−	0.0415300i
$381$	2.32030	−	8.36374i	0.118873	−	0.428487i
$382$	−25.0086	+	1.20136i	−1.27955	+	0.0614671i
$383$	1.63222			0.0834028			0.0417014	−	0.999130i	$-0.486722\pi$
$383$	1.63222			0.0834028			0.0417014	+	0.999130i	$0.486722\pi$
$384$	−19.5540	+	1.28047i	−0.997863	+	0.0653436i
$385$	0.648120			0.0330312
$386$	19.8102	−	0.951642i	1.00831	−	0.0484373i
$387$	7.93948	−	13.2080i	0.403586	−	0.671400i
$388$	−29.5158	+	2.84233i	−1.49844	+	0.144297i
$389$		−	26.6447i		−	1.35094i	−0.737388	−	0.675470i	$-0.763941\pi$
$389$		−	26.6447i		−	1.35094i	0.737388	−	0.675470i	$-0.236059\pi$
$390$	−2.68445	+	11.8588i	−0.135932	+	0.600491i
$391$		−	9.16213i		−	0.463349i
$392$	2.79915	−	0.405897i	0.141378	−	0.0205009i
$393$	−30.2084	−	8.38052i	−1.52381	−	0.422741i
$394$	−0.452353	−	9.41654i	−0.0227892	−	0.474399i
$395$	7.10256			0.357369
$396$	−3.50961	−	1.67475i	−0.176364	−	0.0841594i
$397$	−7.86336			−0.394651			−0.197325	−	0.980338i	$-0.563226\pi$
$397$	−7.86336			−0.394651			−0.197325	+	0.980338i	$0.563226\pi$
$398$	−0.0265013	−	0.551674i	−0.00132839	−	0.0276529i
$399$	7.04805	+	1.95530i	0.352844	+	0.0978873i
$400$	−3.92649	+	0.763309i	−0.196325	+	0.0381654i
$401$		−	11.3925i		−	0.568913i	−0.958689	−	0.284457i	$-0.908187\pi$
$401$		−	11.3925i		−	0.568913i	0.958689	−	0.284457i	$-0.0918132\pi$
$402$	5.67274	−	25.0597i	0.282931	−	1.24987i
$403$		−	37.9078i		−	1.88832i
$404$	−0.683865	−	7.10152i	−0.0340236	−	0.353314i
$405$	7.94808	−	4.22232i	0.394943	−	0.209809i
$406$	−5.79797	+	0.278524i	−0.287749	+	0.0138229i
$407$	1.48887			0.0738006
$408$	−4.25688	+	33.4409i	−0.210747	+	1.65557i
$409$	−8.80374			−0.435317			−0.217658	−	0.976025i	$-0.569842\pi$
$409$	−8.80374			−0.435317			−0.217658	+	0.976025i	$0.569842\pi$
$410$	−15.4764	+	0.743459i	−0.764327	+	0.0367168i
$411$	5.67216	−	20.4458i	0.279787	−	1.00852i
$412$	−1.83411	−	19.0462i	−0.0903603	−	0.938337i
$413$		−	0.421507i		−	0.0207410i
$414$	−4.97565	−	2.67466i	−0.244540	−	0.131453i
$415$			0.766970i			0.0376491i
$416$	−27.2747	+	6.67474i	−1.33725	+	0.327256i
$417$	−5.79066	+	20.8730i	−0.283570	+	1.02215i
$418$	0.185723	+	3.86615i	0.00908398	+	0.189100i
$419$	26.0781			1.27400			0.637000	−	0.770864i	$-0.280175\pi$
$419$	26.0781			1.27400			0.637000	+	0.770864i	$0.280175\pi$
$420$	−3.41142	−	0.601817i	−0.166460	−	0.0293657i
$421$	16.4876			0.803556			0.401778	−	0.915737i	$-0.368392\pi$
$421$	16.4876			0.803556			0.401778	+	0.915737i	$0.368392\pi$
$422$	1.94009	+	40.3866i	0.0944423	+	1.96599i
$423$	24.7386	+	14.8706i	1.20283	+	0.723035i
$424$	2.25807	+	15.5721i	0.109662	+	0.756249i
$425$			6.88118i			0.333786i
$426$	5.00853	+	1.13378i	0.242664	+	0.0549316i
$427$		−	0.179252i		−	0.00867462i
$428$	−22.3764	+	2.15482i	−1.08161	+	0.104157i
$429$	−5.36946	−	1.48961i	−0.259240	−	0.0719192i
$430$	7.25626	−	0.348577i	0.349928	−	0.0168099i
$431$	−5.09236			−0.245290			−0.122645	−	0.992451i	$-0.539138\pi$
$431$	−5.09236			−0.245290			−0.122645	+	0.992451i	$0.539138\pi$
$432$	16.9180	+	12.0740i	0.813966	+	0.580913i
$433$	1.38310			0.0664673			0.0332337	−	0.999448i	$-0.489419\pi$
$433$	1.38310			0.0664673			0.0332337	+	0.999448i	$0.489419\pi$
$434$	10.7877	−	0.518219i	0.517825	−	0.0248753i
$435$	6.85049	+	1.90049i	0.328456	+	0.0911215i
$436$	−18.2526	+	1.75769i	−0.874140	+	0.0841783i
$437$			5.62267i			0.268969i
$438$	39.7193	+	8.99122i	1.89786	+	0.429617i
$439$			18.7957i			0.897069i	0.893765	+	0.448535i	$0.148054\pi$
$439$			18.7957i			0.897069i	−0.893765	+	0.448535i	$0.851946\pi$
$440$	−0.263070	−	1.81419i	−0.0125414	−	0.0864879i
$441$	−2.57122	−	1.54559i	−0.122439	−	0.0735994i
$442$	2.31781	+	48.2494i	0.110247	+	2.29499i
$443$	8.85852			0.420881			0.210441	−	0.977607i	$-0.432510\pi$
$443$	8.85852			0.420881			0.210441	+	0.977607i	$0.432510\pi$
$444$	−7.83678	−	1.38250i	−0.371917	−	0.0656107i
$445$	11.5147			0.545851
$446$	−1.99664	−	41.5638i	−0.0945439	−	1.96810i
$447$	3.58915	−	12.9374i	0.169761	−	0.611920i
$448$	−2.27234	−	7.67049i	−0.107358	−	0.362397i
$449$		−	1.38236i		−	0.0652376i	−0.999468	−	0.0326188i	$-0.989615\pi$
$449$		−	1.38236i		−	0.0652376i	0.999468	−	0.0326188i	$-0.0103847\pi$
$450$	3.73694	+	2.00880i	0.176161	+	0.0946955i
$451$		−	7.10088i		−	0.334367i
$452$	0.595673	+	6.18571i	0.0280181	+	0.290951i
$453$	−0.925233	+	3.33509i	−0.0434713	+	0.156696i
$454$	−29.1566	+	1.40063i	−1.36839	+	0.0657348i
$455$	−4.96381			−0.232707
$456$	2.61239	−	20.5222i	0.122336	−	0.961041i
$457$	31.0264			1.45135			0.725676	−	0.688036i	$-0.241527\pi$
$457$	31.0264			1.45135			0.725676	+	0.688036i	$0.241527\pi$
$458$	1.43470	−	0.0689205i	0.0670394	−	0.00322044i
$459$	25.9430	−	24.6054i	1.21092	−	1.14848i
$460$	−0.255257	−	2.65069i	−0.0119014	−	0.123589i
$461$		−	28.1673i		−	1.31188i	−0.754812	−	0.655941i	$-0.772272\pi$
$461$		−	28.1673i		−	1.31188i	0.754812	−	0.655941i	$-0.227728\pi$
$462$	0.350506	−	1.54839i	0.0163070	−	0.0720375i
$463$		−	26.2326i		−	1.21913i	−0.792735	−	0.609566i	$-0.791344\pi$
$463$		−	26.2326i		−	1.21913i	0.792735	−	0.609566i	$-0.208656\pi$
$464$	3.13301	+	16.1164i	0.145446	+	0.748183i
$465$	−12.7460	−	3.53604i	−0.591081	−	0.163980i
$466$	0.388018	+	8.07729i	0.0179746	+	0.374173i
$467$	35.8633			1.65956			0.829778	−	0.558094i	$-0.188467\pi$
$467$	35.8633			1.65956			0.829778	+	0.558094i	$0.188467\pi$
$468$	26.8793	+	12.8265i	1.24250	+	0.592907i
$469$	10.4894			0.484358
$470$	0.652884	+	13.5910i	0.0301153	+	0.626904i
$471$	21.4491	+	5.95047i	0.988320	+	0.274183i
$472$	−1.17986	+	0.171088i	−0.0543075	+	0.00787498i
$473$			3.32931i			0.153082i
$474$	3.84110	−	16.9683i	0.176428	−	0.779381i
$475$		−	4.22288i		−	0.193759i
$476$	−13.6990	+	1.31919i	−0.627892	+	0.0604650i
$477$	8.59835	−	14.3041i	0.393691	−	0.654939i
$478$	26.1128	−	1.25441i	1.19437	−	0.0573754i
$479$	33.1353			1.51399			0.756995	−	0.653421i	$-0.226667\pi$
$479$	33.1353			1.51399			0.756995	+	0.653421i	$0.226667\pi$
$480$	−0.299890	+	9.79337i	−0.0136880	+	0.447004i
$481$	−11.4029			−0.519929
$482$	−16.6092	+	0.797873i	−0.756528	+	0.0363421i
$483$	0.616506	−	2.22225i	0.0280520	−	0.101116i
$484$	−21.0624	+	2.02828i	−0.957384	+	0.0921945i
$485$			14.8262i			0.673222i
$486$	−5.78894	−	21.2718i	−0.262592	−	0.964907i
$487$		−	25.5792i		−	1.15910i	−0.814935	−	0.579552i	$-0.803228\pi$
$487$		−	25.5792i		−	1.15910i	0.814935	−	0.579552i	$-0.196772\pi$
$488$	−0.501754	+	0.0727580i	−0.0227133	+	0.00329360i
$489$	1.74359	−	6.28493i	0.0788478	−	0.284215i
$490$	−0.0678578	−	1.41258i	−0.00306551	−	0.0638141i
$491$	22.5226			1.01643			0.508216	−	0.861229i	$-0.330305\pi$
$491$	22.5226			1.01643			0.508216	+	0.861229i	$0.330305\pi$
$492$	−6.59358	+	37.3760i	−0.297262	+	1.68504i
$493$	28.2439			1.27204
$494$	−1.42241	−	29.6100i	−0.0639971	−	1.33222i
$495$	−1.00173	+	1.66646i	−0.0450242	+	0.0749017i
$496$	−5.82926	−	29.9860i	−0.261742	−	1.34641i
$497$			2.09646i			0.0940391i
$498$	1.83233	+	0.414781i	0.0821085	+	0.0185868i
$499$			37.4978i			1.67863i	0.543643	+	0.839316i	$0.317044\pi$
$499$			37.4978i			1.67863i	−0.543643	+	0.839316i	$0.682956\pi$
$500$	0.191710	+	1.99079i	0.00857353	+	0.0890309i
$501$	−20.5375	−	5.69759i	−0.917548	−	0.254550i
$502$	−16.3078	+	0.783394i	−0.727851	+	0.0349646i
$503$	−24.6073			−1.09718			−0.548592	−	0.836090i	$-0.684836\pi$
$503$	−24.6073			−1.09718			−0.548592	+	0.836090i	$0.684836\pi$
$504$	−3.28268	+	7.82458i	−0.146222	+	0.348534i
$505$	−3.56719			−0.158738
$506$	1.21900	−	0.0585584i	0.0541911	−	0.00260324i
$507$	19.4263	+	5.38931i	0.862752	+	0.239348i
$508$	−0.960694	−	9.97622i	−0.0426239	−	0.442623i
$509$		−	20.0506i		−	0.888728i	−0.895846	−	0.444364i	$-0.853430\pi$
$509$		−	20.0506i		−	0.888728i	0.895846	−	0.444364i	$-0.146570\pi$
$510$	16.4394	+	3.72138i	0.727951	+	0.164785i
$511$			16.6256i			0.735474i
$512$	−20.5485	+	9.47404i	−0.908126	+	0.418698i
$513$	−15.9209	+	15.1000i	−0.702924	+	0.666681i
$514$	−0.585962	−	12.1979i	−0.0258457	−	0.538025i
$515$	−9.56713			−0.421578
$516$	3.09146	−	17.5240i	0.136094	−	0.771453i
$517$	−6.23578			−0.274249
$518$	−0.155884	−	3.24501i	−0.00684915	−	0.142578i
$519$	−8.59567	+	30.9839i	−0.377308	+	1.36004i
$520$	2.01480	+	13.8944i	0.0883546	+	0.609312i
$521$		−	23.9103i		−	1.04753i	−0.851863	−	0.523765i	$-0.824527\pi$
$521$		−	23.9103i		−	1.04753i	0.851863	−	0.523765i	$-0.175473\pi$
$522$	8.24513	−	15.3383i	0.360880	−	0.671341i
$523$			19.7289i			0.862683i	0.902189	+	0.431342i	$0.141960\pi$
$523$			19.7289i			0.862683i	−0.902189	+	0.431342i	$0.858040\pi$
$524$	−36.0324	+	3.46986i	−1.57408	+	0.151581i
$525$	−0.463024	+	1.66901i	−0.0202080	+	0.0728418i
$526$	22.8989	−	1.10002i	0.998439	−	0.0479631i
$527$	−52.5505			−2.28913
$528$	−4.47644	−	0.352635i	−0.194812	−	0.0153464i
$529$	−21.2272			−0.922920
$530$	7.85843	−	0.377504i	0.341348	−	0.0163977i
$531$	1.08379	+	0.651476i	0.0470323	+	0.0282716i
$532$	8.40688	−	0.809569i	0.364484	−	0.0350993i
$533$			54.3841i			2.35564i
$534$	6.22723	−	27.5092i	0.269479	−	1.19044i
$535$			11.2400i			0.485947i
$536$	−4.25764	−	29.3615i	−0.183902	−	1.26823i
$537$	20.2398	+	5.61501i	0.873414	+	0.242306i
$538$	−0.877299	−	18.2626i	−0.0378230	−	0.787356i
$539$	0.648120			0.0279165
$540$	6.82006	−	7.84135i	0.293489	−	0.337438i
$541$	0.669466			0.0287826			0.0143913	−	0.999896i	$-0.495419\pi$
$541$	0.669466			0.0287826			0.0143913	+	0.999896i	$0.495419\pi$
$542$	0.542165	+	11.2861i	0.0232880	+	0.484781i
$543$	−0.144838	−	0.0401815i	−0.00621559	−	0.00172435i
$544$	9.25300	+	37.8101i	0.396719	+	1.62109i
$545$			9.16851i			0.392736i
$546$	−2.68445	+	11.8588i	−0.114884	+	0.507508i
$547$		−	9.39985i		−	0.401909i	−0.979601	−	0.200954i	$-0.935596\pi$
$547$		−	9.39985i		−	0.401909i	0.979601	−	0.200954i	$-0.0644043\pi$
$548$	−2.34849	−	24.3877i	−0.100323	−	1.04179i
$549$	0.460897	+	0.277050i	0.0196706	+	0.0118242i
$550$	−0.915524	+	0.0439800i	−0.0390381	+	0.00187531i
$551$	−17.3329			−0.738406
$552$	−6.47066	−	0.823686i	−0.275410	−	0.0350584i
$553$	7.10256			0.302032
$554$	−33.6753	+	1.61770i	−1.43073	+	0.0687293i
$555$	−1.06367	+	3.83409i	−0.0451501	+	0.162748i
$556$	2.39756	+	24.8972i	0.101679	+	1.05587i
$557$		−	39.5568i		−	1.67608i	−0.545612	−	0.838038i	$-0.683703\pi$
$557$		−	39.5568i		−	1.67608i	0.545612	−	0.838038i	$-0.316297\pi$
$558$	−15.3408	+	28.5384i	−0.649430	+	1.20813i
$559$		−	25.4984i		−	1.07847i
$560$	−3.92649	+	0.763309i	−0.165925	+	0.0322557i
$561$	−2.06501	+	7.44352i	−0.0871847	+	0.314266i
$562$	0.103175	+	2.14777i	0.00435216	+	0.0905980i
$563$	−38.2888			−1.61368			−0.806840	−	0.590770i	$-0.798824\pi$
$563$	−38.2888			−1.61368			−0.806840	+	0.590770i	$0.798824\pi$
$564$	32.8225	+	5.79029i	1.38208	+	0.243815i
$565$	3.10716			0.130719
$566$	0.445264	+	9.26899i	0.0187159	+	0.389605i
$567$	7.94808	−	4.22232i	0.333788	−	0.177321i
$568$	5.86831	−	0.850947i	0.246229	−	0.0357050i
$569$			8.99657i			0.377156i	0.982058	+	0.188578i	$0.0603878\pi$
$569$			8.99657i			0.377156i	−0.982058	+	0.188578i	$0.939612\pi$
$570$	−10.0887	−	2.28376i	−0.422567	−	0.0956560i
$571$			4.98330i			0.208545i	0.994549	+	0.104272i	$0.0332514\pi$
$571$			4.98330i			0.208545i	−0.994549	+	0.104272i	$0.966749\pi$
$572$	−6.40466	+	0.616758i	−0.267792	+	0.0257879i
$573$	29.5484	+	8.19743i	1.23440	+	0.342453i
$574$	−15.4764	+	0.743459i	−0.645974	+	0.0310314i
$575$	−1.33148			−0.0555264
$576$	23.2346	+	6.01275i	0.968108	+	0.250531i
$577$	−35.7825			−1.48964			−0.744822	−	0.667264i	$-0.767465\pi$
$577$	−35.7825			−1.48964			−0.744822	+	0.667264i	$0.767465\pi$
$578$	42.8729	−	2.05953i	1.78328	−	0.0856652i
$579$	−23.4063	−	6.49348i	−0.972735	−	0.269860i
$580$	8.17123	−	0.786876i	0.339292	−	0.0326732i
$581$			0.766970i			0.0318193i
$582$	35.4204	+	8.01807i	1.46822	+	0.332360i
$583$			3.60559i			0.149328i
$584$	46.5376	−	6.74829i	1.92574	−	0.279246i
$585$	7.67200	−	12.7630i	0.317198	−	0.527686i
$586$	−1.43007	−	29.7694i	−0.0590755	−	1.22976i
$587$	−28.7200			−1.18540			−0.592700	−	0.805423i	$-0.701938\pi$
$587$	−28.7200			−1.18540			−0.592700	+	0.805423i	$0.701938\pi$
$588$	−3.41142	−	0.601817i	−0.140685	−	0.0248185i
$589$	32.2495			1.32882
$590$	0.0286025	+	0.595414i	0.00117755	+	0.0245128i
$591$	−3.08660	+	11.1259i	−0.126966	+	0.457660i
$592$	−9.02000	+	1.75348i	−0.370720	+	0.0720678i
$593$		−	1.56786i		−	0.0643843i	−0.999482	−	0.0321921i	$-0.989751\pi$
$593$		−	1.56786i		−	0.0643843i	0.999482	−	0.0321921i	$-0.0102488\pi$
$594$	3.43950	+	3.29440i	0.141124	+	0.135171i
$595$			6.88118i			0.282101i
$596$	−1.48605	−	15.4317i	−0.0608709	−	0.632107i
$597$	−0.180830	+	0.651820i	−0.00740089	+	0.0266772i
$598$	−9.33604	+	0.448486i	−0.381779	+	0.0183399i
$599$	−31.8120			−1.29980			−0.649902	−	0.760018i	$-0.725190\pi$
$599$	−31.8120			−1.29980			−0.649902	+	0.760018i	$0.725190\pi$
$600$	4.85976	+	0.618626i	0.198399	+	0.0252553i
$601$	15.8470			0.646413			0.323206	−	0.946329i	$-0.395239\pi$
$601$	15.8470			0.646413			0.323206	+	0.946329i	$0.395239\pi$
$602$	7.25626	−	0.348577i	0.295743	−	0.0142069i
$603$	−16.2124	+	26.9706i	−0.660218	+	1.09833i
$604$	0.383082	+	3.97808i	0.0155874	+	0.161866i
$605$			10.5799i			0.430136i
$606$	−1.92915	+	8.52216i	−0.0783664	+	0.346189i
$607$		−	9.71499i		−	0.394319i	−0.980371	−	0.197160i	$-0.936828\pi$
$607$		−	9.71499i		−	0.394319i	0.980371	−	0.197160i	$-0.0631717\pi$
$608$	−5.67843	−	23.2035i	−0.230291	−	0.941027i
$609$	6.85049	+	1.90049i	0.277596	+	0.0770117i
$610$	0.0121637	+	0.253209i	0.000492493	+	0.0102521i
$611$	47.7585			1.93210
$612$	17.7811	−	37.2620i	0.718757	−	1.50623i
$613$	−33.8272			−1.36627			−0.683134	−	0.730293i	$-0.739384\pi$
$613$	−33.8272			−1.36627			−0.683134	+	0.730293i	$0.739384\pi$
$614$	−1.71767	−	35.7563i	−0.0693194	−	1.44301i
$615$	18.2859	+	5.07295i	0.737360	+	0.204561i
$616$	−0.263070	−	1.81419i	−0.0105994	−	0.0730956i
$617$			6.52428i			0.262658i	0.991339	+	0.131329i	$0.0419243\pi$
$617$			6.52428i			0.262658i	−0.991339	+	0.131329i	$0.958076\pi$
$618$	−5.17395	+	22.8563i	−0.208127	+	0.919415i
$619$		−	22.4852i		−	0.903757i	−0.892080	−	0.451878i	$-0.850754\pi$
$619$		−	22.4852i		−	0.903757i	0.892080	−	0.451878i	$-0.149246\pi$
$620$	−15.2033	+	1.46406i	−0.610581	+	0.0587980i
$621$	4.76103	+	5.01986i	0.191054	+	0.201440i
$622$	25.8448	−	1.24154i	1.03628	−	0.0497810i
$623$	11.5147			0.461328
$624$	34.2840	+	2.70075i	1.37246	+	0.108117i
$625$	1.00000			0.0400000
$626$	−29.4951	+	1.41689i	−1.17886	+	0.0566302i
$627$	1.26727	−	4.56798i	0.0506098	−	0.182428i
$628$	25.5843	−	2.46373i	1.02092	−	0.0983134i
$629$			15.8076i			0.630288i
$630$	3.73694	+	2.00880i	0.148883	+	0.0800323i
$631$			9.46183i			0.376669i	0.982105	+	0.188335i	$0.0603090\pi$
$631$			9.46183i			0.376669i	−0.982105	+	0.188335i	$0.939691\pi$
$632$	−2.88291	−	19.8811i	−0.114676	−	0.790829i
$633$	13.2381	−	47.7181i	0.526168	−	1.89662i
$634$	1.74865	+	36.4014i	0.0694479	+	1.44568i
$635$	−5.01119			−0.198863
$636$	3.34800	−	18.9783i	0.132757	−	0.752538i
$637$	−4.96381			−0.196673
$638$	0.180517	+	3.75778i	0.00714672	+	0.148772i
$639$	−5.39045	−	3.24026i	−0.213243	−	0.128183i
$640$	3.73037	+	10.6810i	0.147456	+	0.422205i
$641$			20.1292i			0.795056i	0.917590	+	0.397528i	$0.130132\pi$
$641$			20.1292i			0.795056i	−0.917590	+	0.397528i	$0.869868\pi$
$642$	26.8528	+	6.07864i	1.05980	+	0.239905i
$643$		−	23.2477i		−	0.916799i	−0.888746	−	0.458399i	$-0.848423\pi$
$643$		−	23.2477i		−	0.916799i	0.888746	−	0.458399i	$-0.151577\pi$
$644$	−0.255257	−	2.65069i	−0.0100585	−	0.104452i
$645$	−8.57350	−	2.37849i	−0.337581	−	0.0936531i
$646$	−41.0475	+	1.97184i	−1.61499	+	0.0775811i
$647$	−11.4212			−0.449013			−0.224507	−	0.974473i	$-0.572077\pi$
$647$	−11.4212			−0.449013			−0.224507	+	0.974473i	$0.572077\pi$
$648$	−15.0450	−	20.5341i	−0.591024	−	0.806654i
$649$	−0.273187			−0.0107235
$650$	7.01180	−	0.336833i	0.275025	−	0.0132117i
$651$	−12.7460	−	3.53604i	−0.499555	−	0.138588i
$652$	−0.721914	−	7.49663i	−0.0282723	−	0.293591i
$653$			26.0879i			1.02090i	0.859907	+	0.510450i	$0.170521\pi$
$653$			26.0879i			1.02090i	−0.859907	+	0.510450i	$0.829479\pi$
$654$	21.9040	+	4.95838i	0.856513	+	0.193888i
$655$			18.0995i			0.707207i
$656$	8.36290	+	43.0192i	0.326516	+	1.67962i
$657$	−42.7481	−	25.6963i	−1.66776	−	1.00251i
$658$	0.652884	+	13.5910i	0.0254521	+	0.529831i
$659$	−11.6383			−0.453363			−0.226682	−	0.973969i	$-0.572788\pi$
$659$	−11.6383			−0.453363			−0.226682	+	0.973969i	$0.572788\pi$
$660$	−0.390050	+	2.21101i	−0.0151827	+	0.0860635i
$661$	3.03792			0.118161			0.0590807	−	0.998253i	$-0.481183\pi$
$661$	3.03792			0.118161			0.0590807	+	0.998253i	$0.481183\pi$
$662$	1.45759	+	30.3425i	0.0566510	+	1.17929i
$663$	15.8154	−	57.0083i	0.614221	−	2.21402i
$664$	2.14687	−	0.311311i	0.0833145	−	0.0120812i
$665$		−	4.22288i		−	0.163756i
$666$	8.58456	+	4.61464i	0.332645	+	0.178814i
$667$			5.46506i			0.211608i
$668$	−24.4970	+	2.35902i	−0.947818	+	0.0912733i
$669$	−13.6240	+	49.1090i	−0.526734	+	1.89866i
$670$	−14.8172	+	0.711791i	−0.572440	+	0.0274989i
$671$	−0.116177			−0.00448496
$672$	−0.299890	+	9.79337i	−0.0115685	+	0.377787i
$673$	−4.54733			−0.175287			−0.0876433	−	0.996152i	$-0.527934\pi$
$673$	−4.54733			−0.175287			−0.0876433	+	0.996152i	$0.527934\pi$
$674$	15.1312	−	0.726874i	0.582832	−	0.0279981i
$675$	−3.57575	−	3.77014i	−0.137631	−	0.145113i
$676$	23.1716	−	2.23138i	0.891214	−	0.0858225i
$677$		−	27.6263i		−	1.06177i	−0.847445	−	0.530883i	$-0.821860\pi$
$677$		−	27.6263i		−	1.06177i	0.847445	−	0.530883i	$-0.178140\pi$
$678$	1.68037	−	7.42314i	0.0645341	−	0.285084i
$679$			14.8262i			0.568977i
$680$	19.2615	−	2.79305i	0.738643	−	0.107109i
$681$	34.4495	+	9.55711i	1.32011	+	0.366229i
$682$	−0.335868	−	6.99171i	−0.0128611	−	0.267726i
$683$	25.8932			0.990776			0.495388	−	0.868672i	$-0.335026\pi$
$683$	25.8932			0.990776			0.495388	+	0.868672i	$0.335026\pi$
$684$	−10.9120	+	22.8672i	−0.417230	+	0.874348i
$685$	−12.2502			−0.468058
$686$	−0.0678578	−	1.41258i	−0.00259082	−	0.0539327i
$687$	−1.69515	−	0.470275i	−0.0646740	−	0.0179421i
$688$	−3.92101	−	20.1699i	−0.149487	−	0.768969i
$689$		−	27.6144i		−	1.05203i
$690$	−0.720069	+	3.18096i	−0.0274126	+	0.121097i
$691$			51.4334i			1.95662i	0.207149	+	0.978309i	$0.433582\pi$
$691$			51.4334i			1.95662i	−0.207149	+	0.978309i	$0.566418\pi$
$692$	3.55894	+	36.9574i	0.135291	+	1.40491i
$693$	−1.00173	+	1.66646i	−0.0380524	+	0.0633035i
$694$	−14.9178	+	0.716621i	−0.566270	+	0.0272025i
$695$	12.5062			0.474386
$696$	2.53916	−	19.9470i	0.0962466	−	0.756088i
$697$	75.3911			2.85564
$698$	−30.6911	+	1.47434i	−1.16167	+	0.0558046i
$699$	2.64762	−	9.54358i	0.100142	−	0.360972i
$700$	0.191710	+	1.99079i	0.00724595	+	0.0752448i
$701$		−	17.1426i		−	0.647465i	−0.946149	−	0.323733i	$-0.895062\pi$
$701$		−	17.1426i		−	0.647465i	0.946149	−	0.323733i	$-0.104938\pi$
$702$	−26.3424	−	25.2310i	−0.994229	−	0.952284i
$703$		−	9.70087i		−	0.365875i
$704$	−4.97140	+	1.47275i	−0.187367	+	0.0555062i
$705$	4.45491	−	16.0582i	0.167782	−	0.604785i
$706$	−1.42745	−	29.7150i	−0.0537229	−	1.11834i
$707$	−3.56719			−0.134158
$708$	1.43794	+	0.253670i	0.0540410	+	0.00953351i
$709$	7.68687			0.288686			0.144343	−	0.989528i	$-0.453893\pi$
$709$	7.68687			0.288686			0.144343	+	0.989528i	$0.453893\pi$
$710$	−0.142261	−	2.96143i	−0.00533897	−	0.111140i
$711$	−10.9776	+	18.2622i	−0.411693	+	0.684887i
$712$	−4.67380	−	32.2315i	−0.175158	−	1.20793i
$713$		−	10.1683i		−	0.380805i
$714$	16.4394	+	3.72138i	0.615231	+	0.139269i
$715$			3.21714i			0.120314i
$716$	24.1420	−	2.32483i	0.902228	−	0.0868831i
$717$	−30.8532	−	8.55940i	−1.15223	−	0.319657i
$718$	−1.62154	+	0.0778955i	−0.0605152	+	0.00290703i
$719$	−18.4627			−0.688541			−0.344271	−	0.938870i	$-0.611874\pi$
$719$	−18.4627			−0.688541			−0.344271	+	0.938870i	$0.611874\pi$
$720$	4.10611	−	11.2756i	0.153026	−	0.420218i
$721$	−9.56713			−0.356299
$722$	−1.64884	+	0.0792073i	−0.0613636	+	0.00294779i
$723$	19.6243	+	5.44424i	0.729835	+	0.202474i
$724$	−0.172762	+	0.0166367i	−0.00642065	+	0.000618298i
$725$		−	4.10451i		−	0.152438i
$726$	25.2759	+	5.72168i	0.938078	+	0.212352i
$727$		−	37.2227i		−	1.38052i	−0.723564	−	0.690258i	$-0.757497\pi$
$727$		−	37.2227i		−	1.38052i	0.723564	−	0.690258i	$-0.242503\pi$
$728$	2.01480	+	13.8944i	0.0746733	+	0.514962i
$729$	−1.42796	+	26.9622i	−0.0528874	+	0.998600i
$730$	−1.12818	−	23.4851i	−0.0417558	−	0.869222i
$731$	−35.3477			−1.30738
$732$	0.611505	+	0.107877i	0.0226019	+	0.00398725i
$733$	24.9461			0.921404			0.460702	−	0.887555i	$-0.347598\pi$
$733$	24.9461			0.921404			0.460702	+	0.887555i	$0.347598\pi$
$734$	0.328331	+	6.83480i	0.0121189	+	0.252277i
$735$	−0.463024	+	1.66901i	−0.0170789	+	0.0615625i
$736$	−7.31608	+	1.79041i	−0.269674	+	0.0659955i
$737$		−	6.79842i		−	0.250423i
$738$	22.0086	−	40.9424i	0.810148	−	1.50711i
$739$		−	25.3947i		−	0.934159i	−0.884215	−	0.467079i	$-0.845306\pi$
$739$		−	25.3947i		−	0.934159i	0.884215	−	0.467079i	$-0.154694\pi$
$740$	0.440399	+	4.57327i	0.0161894	+	0.168117i
$741$	−9.70572	+	34.9852i	−0.356548	+	1.28521i
$742$	7.85843	−	0.377504i	0.288492	−	0.0138586i
$743$	−23.2422			−0.852674			−0.426337	−	0.904564i	$-0.640196\pi$
$743$	−23.2422			−0.852674			−0.426337	+	0.904564i	$0.640196\pi$
$744$	−4.72435	+	37.1132i	−0.173203	+	1.36064i
$745$	−7.75155			−0.283995
$746$	−17.1251	+	0.822655i	−0.626993	+	0.0301195i
$747$	−1.97205	−	1.18542i	−0.0721534	−	0.0433722i
$748$	0.854994	+	8.87859i	0.0312617	+	0.324633i
$749$			11.2400i			0.410700i
$750$	0.540805	−	2.38904i	0.0197474	−	0.0872355i
$751$			33.3902i			1.21842i	0.793007	+	0.609212i	$0.208514\pi$
$751$			33.3902i			1.21842i	−0.793007	+	0.609212i	$0.791486\pi$
$752$	37.7781	−	7.34405i	1.37763	−	0.267810i
$753$	19.2682	+	5.34544i	0.702171	+	0.194799i
$754$	−1.38254	−	28.7800i	−0.0503490	−	1.04811i
$755$	1.99824			0.0727234
$756$	6.82006	−	7.84135i	0.248043	−	0.285187i
$757$	−36.3015			−1.31940			−0.659700	−	0.751529i	$-0.729317\pi$
$757$	−36.3015			−1.31940			−0.659700	+	0.751529i	$0.729317\pi$
$758$	−1.56642	−	32.6079i	−0.0568950	−	1.18437i
$759$	−1.44029	−	0.399570i	−0.0522791	−	0.0145035i
$760$	−11.8205	+	1.71406i	−0.428774	+	0.0621754i
$761$		−	18.6295i		−	0.675320i	−0.941268	−	0.337660i	$-0.890365\pi$
$761$		−	18.6295i		−	0.675320i	0.941268	−	0.337660i	$-0.109635\pi$
$762$	−2.71007	+	11.9719i	−0.0981756	+	0.433698i
$763$			9.16851i			0.331922i
$764$	35.2452	−	3.39405i	1.27513	−	0.122793i
$765$	−17.6930	−	10.6355i	−0.639692	−	0.384526i
$766$	−2.30566	+	0.110759i	−0.0833067	+	0.00400189i
$767$	2.09228			0.0755478
$768$	27.5348	−	3.13566i	0.993578	−	0.113149i
$769$	45.9947			1.65861			0.829305	−	0.558796i	$-0.188736\pi$
$769$	45.9947			1.65861			0.829305	+	0.558796i	$0.188736\pi$
$770$	−0.915524	+	0.0439800i	−0.0329932	+	0.00158493i
$771$	−3.99828	+	14.4122i	−0.143994	+	0.519042i
$772$	−27.9190	+	2.68855i	−1.00483	+	0.0967630i
$773$		−	8.85871i		−	0.318626i	−0.987228	−	0.159313i	$-0.949072\pi$
$773$		−	8.85871i		−	0.318626i	0.987228	−	0.159313i	$-0.0509278\pi$
$774$	−10.3189	+	19.1962i	−0.370906	+	0.689992i
$775$			7.63684i			0.274323i
$776$	41.5007	−	6.01791i	1.48979	−	0.216030i
$777$	−1.06367	+	3.83409i	−0.0381588	+	0.137547i
$778$	1.80805	+	37.6379i	0.0648218	+	1.34938i
$779$	−46.2664			−1.65767
$780$	2.98731	−	16.9337i	0.106963	−	0.606322i
$781$	1.35876			0.0486202
$782$	0.621723	+	12.9423i	0.0222328	+	0.462815i
$783$	−15.4746	+	14.6767i	−0.553017	+	0.524504i
$784$	−3.92649	+	0.763309i	−0.140232	+	0.0272610i
$785$		−	12.8513i		−	0.458684i
$786$	43.2406	+	9.78831i	1.54234	+	0.349138i
$787$		−	40.2027i		−	1.43307i	−0.697550	−	0.716536i	$-0.745727\pi$
$787$		−	40.2027i		−	1.43307i	0.697550	−	0.716536i	$-0.254273\pi$
$788$	1.27797	+	13.2710i	0.0455259	+	0.472759i
$789$	−27.0558	−	7.50591i	−0.963211	−	0.267218i
$790$	−10.0330	+	0.481964i	−0.356957	+	0.0171475i
$791$	3.10716			0.110478
$792$	5.07126	+	2.12757i	0.180199	+	0.0756000i
$793$	0.889774			0.0315968
$794$	11.1077	−	0.533591i	0.394196	−	0.0189364i
$795$	−9.28499	−	2.57588i	−0.329305	−	0.0913569i
$796$	0.0748708	+	0.777487i	0.00265372	+	0.0275573i
$797$		−	15.6352i		−	0.553828i	−0.960895	−	0.276914i	$-0.910688\pi$
$797$		−	15.6352i		−	0.553828i	0.960895	−	0.276914i	$-0.0893116\pi$
$798$	−10.0887	−	2.28376i	−0.357134	−	0.0808441i
$799$		−	66.2062i		−	2.34221i
$800$	5.49471	−	1.34468i	0.194267	−	0.0475417i
$801$	−17.7970	+	29.6069i	−0.628828	+	1.04611i
$802$	0.773069	+	16.0928i	0.0272980	+	0.568258i
$803$	10.7754			0.380255
$804$	−6.31273	+	35.7840i	−0.222633	+	1.26200i
$805$	−1.33148			−0.0469284
$806$	2.57234	+	53.5480i	0.0906068	+	1.88615i
$807$	−5.98620	+	21.5778i	−0.210724	+	0.759575i
$808$	1.44791	+	9.98509i	0.0509373	+	0.351274i
$809$			25.0407i			0.880383i	0.897904	+	0.440191i	$0.145089\pi$
$809$			25.0407i			0.880383i	−0.897904	+	0.440191i	$0.854911\pi$
$810$	−10.9408	+	6.50372i	−0.384421	+	0.228517i
$811$			27.3047i			0.958798i	0.877597	+	0.479399i	$0.159145\pi$
$811$			27.3047i			0.958798i	−0.877597	+	0.479399i	$0.840855\pi$
$812$	8.17123	−	0.786876i	0.286754	−	0.0276139i
$813$	3.69943	−	13.3349i	0.129745	−	0.467677i
$814$	−2.10316	+	0.101032i	−0.0737156	+	0.00354115i
$815$	−3.76566			−0.131905
$816$	3.74397	−	47.5270i	0.131065	−	1.66378i
$817$	21.6924			0.758921
$818$	12.4360	−	0.597403i	0.434816	−	0.0208877i
$819$	7.67200	−	12.7630i	0.268081	−	0.445976i
$820$	21.8113	−	2.10040i	0.761685	−	0.0733490i
$821$		−	47.2633i		−	1.64950i	−0.565497	−	0.824751i	$-0.691315\pi$
$821$		−	47.2633i		−	1.64950i	0.565497	−	0.824751i	$-0.308685\pi$
$822$	−6.62499	+	29.2664i	−0.231073	+	1.02078i
$823$			54.9448i			1.91526i	0.288008	+	0.957628i	$0.407007\pi$
$823$			54.9448i			1.91526i	−0.288008	+	0.957628i	$0.592993\pi$
$824$	3.88327	+	26.7799i	0.135280	+	0.932920i
$825$	1.08172	+	0.300095i	0.0376607	+	0.0104480i
$826$	0.0286025	+	0.595414i	0.000995210	+	0.0207171i
$827$	−5.81055			−0.202053			−0.101026	−	0.994884i	$-0.532213\pi$
$827$	−5.81055			−0.202053			−0.101026	+	0.994884i	$0.532213\pi$
$828$	7.21003	+	3.44055i	0.250566	+	0.119567i
$829$	47.1522			1.63766			0.818832	−	0.574033i	$-0.194622\pi$
$829$	47.1522			1.63766			0.818832	+	0.574033i	$0.194622\pi$
$830$	−0.0520449	−	1.08341i	−0.00180651	−	0.0376057i
$831$	39.7884	+	11.0383i	1.38025	+	0.382913i
$832$	38.0749	−	11.2794i	1.32001	−	0.391044i
$833$			6.88118i			0.238419i
$834$	6.76340	−	29.8778i	0.234197	−	1.03458i
$835$			12.3052i			0.425838i
$836$	−0.524698	−	5.44866i	−0.0181470	−	0.188446i
$837$	28.7920	−	27.3075i	0.995196	−	0.943884i
$838$	−36.8375	+	1.76960i	−1.27253	+	0.0611300i
$839$	−8.94935			−0.308966			−0.154483	−	0.987995i	$-0.549371\pi$
$839$	−8.94935			−0.308966			−0.154483	+	0.987995i	$0.549371\pi$
$840$	4.85976	+	0.618626i	0.167678	+	0.0213446i
$841$	12.1530			0.419068
$842$	−23.2901	+	1.11881i	−0.802631	+	0.0385568i
$843$	0.704005	−	2.53765i	0.0242472	−	0.0874015i
$844$	−5.48109	−	56.9178i	−0.188667	−	1.95919i
$845$		−	11.6394i		−	0.400407i
$846$	−35.9544	−	19.3273i	−1.23614	−	0.664487i
$847$			10.5799i			0.363531i
$848$	−4.24641	−	21.8437i	−0.145822	−	0.750116i
$849$	3.03823	−	10.9516i	0.104272	−	0.375858i
$850$	−0.466942	−	9.72025i	−0.0160160	−	0.333402i
$851$	−3.05869			−0.104850
$852$	−7.15191	−	1.26169i	−0.245021	−	0.0432246i
$853$	−24.8720			−0.851600			−0.425800	−	0.904817i	$-0.640007\pi$
$853$	−24.8720			−0.851600			−0.425800	+	0.904817i	$0.640007\pi$
$854$	0.0121637	+	0.253209i	0.000416232	+	0.00866463i
$855$	10.8580	+	6.52684i	0.371334	+	0.223213i
$856$	31.4624	−	4.56228i	1.07536	−	0.155935i
$857$			31.9912i			1.09280i	0.837524	+	0.546400i	$0.184002\pi$
$857$			31.9912i			1.09280i	−0.837524	+	0.546400i	$0.815998\pi$
$858$	7.68589	+	1.73985i	0.262392	+	0.0593974i
$859$			19.8605i			0.677631i	0.940853	+	0.338815i	$0.110026\pi$
$859$			19.8605i			0.677631i	−0.940853	+	0.338815i	$0.889974\pi$
$860$	−10.2264	+	0.984788i	−0.348718	+	0.0335810i
$861$	18.2859	+	5.07295i	0.623183	+	0.172886i
$862$	7.19339	−	0.345557i	0.245008	−	0.0117697i
$863$	−11.6750			−0.397422			−0.198711	−	0.980058i	$-0.563676\pi$
$863$	−11.6750			−0.397422			−0.198711	+	0.980058i	$0.563676\pi$
$864$	−24.7174	−	15.9076i	−0.840902	−	0.541187i
$865$	18.5642			0.631202
$866$	−1.95374	+	0.0938539i	−0.0663908	+	0.00318928i
$867$	−50.6557	−	14.0531i	−1.72036	−	0.477268i
$868$	−15.2033	+	1.46406i	−0.516035	+	0.0496933i
$869$		−	4.60331i		−	0.156157i
$870$	−9.80586	−	2.21974i	−0.332450	−	0.0752563i
$871$			52.0676i			1.76424i
$872$	25.6640	−	3.72147i	0.869094	−	0.126025i
$873$	−38.1213	−	22.9152i	−1.29021	−	0.775561i
$874$	−0.381542	−	7.94250i	−0.0129059	−	0.268659i
$875$	1.00000			0.0338062
$876$	−56.7170	−	10.0056i	−1.91629	−	0.338057i
$877$	−30.3924			−1.02628			−0.513139	−	0.858306i	$-0.671517\pi$
$877$	−30.3924			−1.02628			−0.513139	+	0.858306i	$0.671517\pi$
$878$	−1.27543	−	26.5505i	−0.0430438	−	0.896036i
$879$	−9.75798	+	35.1736i	−0.329128	+	1.18637i
$880$	0.494715	+	2.54484i	0.0166769	+	0.0857865i
$881$			25.6017i			0.862543i	0.902222	+	0.431272i	$0.141935\pi$
$881$			25.6017i			0.862543i	−0.902222	+	0.431272i	$0.858065\pi$
$882$	3.73694	+	2.00880i	0.125829	+	0.0676397i
$883$			4.94104i			0.166279i	0.996538	+	0.0831397i	$0.0264948\pi$
$883$			4.94104i			0.166279i	−0.996538	+	0.0831397i	$0.973505\pi$
$884$	−6.54821	−	67.9991i	−0.220240	−	2.28706i
$885$	0.195168	−	0.703501i	0.00656049	−	0.0236479i
$886$	−12.5134	+	0.601120i	−0.420396	+	0.0201950i
$887$	−7.24181			−0.243156			−0.121578	−	0.992582i	$-0.538796\pi$
$887$	−7.24181			−0.243156			−0.121578	+	0.992582i	$0.538796\pi$
$888$	11.1639	+	1.42112i	0.374637	+	0.0476896i
$889$	−5.01119			−0.168070
$890$	−16.2655	+	0.781366i	−0.545222	+	0.0261914i
$891$	−2.73657	−	5.15131i	−0.0916785	−	0.172575i
$892$	5.64086	+	58.5769i	0.188870	+	1.96130i
$893$			40.6298i			1.35962i
$894$	−4.19207	+	18.5188i	−0.140204	+	0.619361i
$895$		−	12.1268i		−	0.405355i
$896$	3.73037	+	10.6810i	0.124623	+	0.356828i
$897$	11.0308	+	3.06022i	0.368309	+	0.102178i
$898$	0.0938039	+	1.95270i	0.00313028	+	0.0651624i
$899$	31.3455			1.04543
$900$	−5.41506	−	2.58401i	−0.180502	−	0.0861338i
$901$	−38.2811			−1.27533
$902$	0.481850	+	10.0306i	0.0160439	+	0.333982i
$903$	−8.57350	−	2.37849i	−0.285308	−	0.0791513i
$904$	−1.26119	−	8.69741i	−0.0419465	−	0.289272i
$905$			0.0867806i			0.00288468i
$906$	1.08066	−	4.77388i	0.0359025	−	0.158602i
$907$		−	16.4936i		−	0.547662i	−0.961778	−	0.273831i	$-0.911709\pi$
$907$		−	16.4936i		−	0.547662i	0.961778	−	0.273831i	$-0.0882909\pi$
$908$	41.0912	−	3.95701i	1.36366	−	0.131318i
$909$	5.51340	−	9.17201i	0.182868	−	0.304216i
$910$	7.01180	−	0.336833i	0.232439	−	0.0111659i
$911$	−4.20368			−0.139274			−0.0696371	−	0.997572i	$-0.522184\pi$
$911$	−4.20368			−0.139274			−0.0696371	+	0.997572i	$0.522184\pi$
$912$	−2.29762	+	29.1666i	−0.0760819	+	0.965804i
$913$	0.497089			0.0164512
$914$	−43.8274	+	2.10538i	−1.44968	+	0.0696399i
$915$	0.0829981	−	0.299175i	0.00274383	−	0.00989041i
$916$	−2.02197	+	0.194712i	−0.0668076	+	0.00643347i
$917$			18.0995i			0.597699i
$918$	−34.9771	+	36.5177i	−1.15442	+	1.20526i
$919$		−	24.4559i		−	0.806727i	−0.915040	−	0.403363i	$-0.867841\pi$
$919$		−	24.4559i		−	0.806727i	0.915040	−	0.403363i	$-0.132159\pi$
$920$	0.540443	+	3.72700i	0.0178179	+	0.122876i
$921$	−11.7204	+	42.2473i	−0.386200	+	1.39210i
$922$	1.91137	+	39.7887i	0.0629477	+	1.31037i
$923$	−10.4064			−0.342532
$924$	−0.390050	+	2.21101i	−0.0128317	+	0.0727369i
$925$	2.29722			0.0755320
$926$	1.78009	+	37.0558i	0.0584973	+	1.21773i
$927$	14.7868	−	24.5992i	0.485664	−	0.807943i
$928$	−5.51926	−	22.5531i	−0.181179	−	0.740342i
$929$			19.5942i			0.642864i	0.946933	+	0.321432i	$0.104164\pi$
$929$			19.5942i			0.642864i	−0.946933	+	0.321432i	$0.895836\pi$
$930$	18.2447	+	4.13004i	0.598269	+	0.135429i
$931$		−	4.22288i		−	0.138399i
$932$	−1.09622	−	11.3835i	−0.0359077	−	0.372880i
$933$	−30.5365	−	8.47154i	−0.999720	−	0.277346i
$934$	−50.6600	+	2.43361i	−1.65764	+	0.0796300i
$935$	4.45983			0.145852
$936$	−38.8397	−	16.2946i	−1.26951	−	0.532606i
$937$	−18.7661			−0.613061			−0.306531	−	0.951861i	$-0.599168\pi$
$937$	−18.7661			−0.613061			−0.306531	+	0.951861i	$0.599168\pi$
$938$	−14.8172	+	0.711791i	−0.483800	+	0.0232408i
$939$	34.8494	+	9.66805i	1.13727	+	0.315505i
$940$	−1.84451	−	19.1541i	−0.0601612	−	0.624737i
$941$			18.7595i			0.611543i	0.952105	+	0.305772i	$0.0989144\pi$
$941$			18.7595i			0.611543i	−0.952105	+	0.305772i	$0.901086\pi$
$942$	−30.7024	−	6.95006i	−1.00034	−	0.226445i
$943$			14.5878i			0.475045i
$944$	1.65504	−	0.321740i	0.0538671	−	0.0104717i
$945$	−3.57575	−	3.77014i	−0.116319	−	0.122643i
$946$	−0.225919	−	4.70293i	−0.00734528	−	0.152905i
$947$	−4.70695			−0.152955			−0.0764776	−	0.997071i	$-0.524367\pi$
$947$	−4.70695			−0.152955			−0.0764776	+	0.997071i	$0.524367\pi$
$948$	−4.27444	+	24.2298i	−0.138827	+	0.786949i
$949$	−82.5263			−2.67892
$950$	0.286556	+	5.96518i	0.00929710	+	0.193536i
$951$	11.9318	−	43.0094i	0.386916	−	1.39468i
$952$	19.2615	−	2.79305i	0.624268	−	0.0905233i
$953$		−	51.9232i		−	1.68196i	−0.541068	−	0.840979i	$-0.681980\pi$
$953$		−	51.9232i		−	1.68196i	0.541068	−	0.840979i	$-0.318020\pi$
$954$	−11.1752	+	20.7892i	−0.361812	+	0.673075i
$955$		−	17.7041i		−	0.572892i
$956$	−36.8015	+	3.54392i	−1.19025	+	0.114619i
$957$	1.23174	−	4.43994i	0.0398166	−	0.143523i
$958$	−46.8064	+	2.24849i	−1.51225	+	0.0726454i
$959$	−12.2502			−0.395581
$960$	−0.240937	−	13.8543i	−0.00777620	−	0.447146i
$961$	−27.3213			−0.881332
$962$	16.1076	−	0.773779i	0.519330	−	0.0249476i
$963$	−28.9004	−	17.3724i	−0.931303	−	0.559817i
$964$	23.4077	−	2.25413i	0.753913	−	0.0726006i
$965$			14.0241i			0.451450i
$966$	−0.720069	+	3.18096i	−0.0231678	+	0.102346i
$967$		−	20.9108i		−	0.672445i	−0.941783	−	0.336222i	$-0.890851\pi$
$967$		−	20.9108i		−	0.672445i	0.941783	−	0.336222i	$-0.109149\pi$
$968$	29.6149	−	4.29437i	0.951857	−	0.138026i
$969$	48.4989	+	13.4548i	1.55801	+	0.432229i
$970$	−1.00607	−	20.9432i	−0.0323031	−	0.672447i
$971$	−28.9974			−0.930572			−0.465286	−	0.885160i	$-0.654049\pi$
$971$	−28.9974			−0.930572			−0.465286	+	0.885160i	$0.654049\pi$
$972$	9.62083	+	29.6553i	0.308588	+	0.951196i
$973$	12.5062			0.400929
$974$	1.73575	+	36.1328i	0.0556170	+	1.15777i
$975$	−8.28466	−	2.29836i	−0.265322	−	0.0736065i
$976$	0.703833	−	0.136825i	0.0225291	−	0.00437965i
$977$			22.2874i			0.713038i	0.934288	+	0.356519i	$0.116036\pi$
$977$			22.2874i			0.713038i	−0.934288	+	0.356519i	$0.883964\pi$
$978$	−2.03649	+	8.99632i	−0.0651196	+	0.287671i
$979$		−	7.46293i		−	0.238516i
$980$	0.191710	+	1.99079i	0.00612395	+	0.0635935i
$981$	−23.5742	−	14.1707i	−0.752667	−	0.452437i
$982$	−31.8151	+	1.52834i	−1.01526	+	0.0487712i
$983$	−12.6173			−0.402430			−0.201215	−	0.979547i	$-0.564489\pi$
$983$	−12.6173			−0.402430			−0.201215	+	0.979547i	$0.564489\pi$
$984$	6.77774	−	53.2442i	0.216067	−	1.69736i
$985$	6.66618			0.212402
$986$	−39.8969	+	1.91657i	−1.27058	+	0.0610360i
$987$	4.45491	−	16.0582i	0.141801	−	0.511137i
$988$	4.01854	+	41.7301i	0.127847	+	1.32761i
$989$		−	6.83962i		−	0.217487i
$990$	1.30194	−	2.42199i	0.0413784	−	0.0769758i
$991$		−	6.83164i		−	0.217014i	−0.994096	−	0.108507i	$-0.965393\pi$
$991$		−	6.83164i		−	0.217014i	0.994096	−	0.108507i	$-0.0346070\pi$
$992$	10.2691	+	41.9622i	0.326045	+	1.33230i
$993$	9.94581	−	35.8506i	0.315621	−	1.13769i
$994$	−0.142261	−	2.96143i	−0.00451225	−	0.0939308i
$995$	0.390542			0.0123810
$996$	−2.61646	−	0.461576i	−0.0829057	−	0.0146256i
$997$	−33.6015			−1.06417			−0.532084	−	0.846691i	$-0.678591\pi$
$997$	−33.6015			−1.06417			−0.532084	+	0.846691i	$0.678591\pi$
$998$	−2.54452	−	52.9688i	−0.0805454	−	1.67670i
$999$	−8.21428	−	8.66083i	−0.259888	−	0.274017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.n.b.71.2	yes	24
3.2	odd	2		420.2.n.a.71.23	✓	24
4.3	odd	2		420.2.n.a.71.24	yes	24
12.11	even	2	inner	420.2.n.b.71.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.n.a.71.23	✓	24	3.2	odd	2
420.2.n.a.71.24	yes	24	4.3	odd	2
420.2.n.b.71.1	yes	24	12.11	even	2	inner
420.2.n.b.71.2	yes	24	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41258 + 0.0678578i) q^{2} +(1.66901 + 0.463024i) q^{3} +(1.99079 - 0.191710i) q^{4} -1.00000i q^{5} +(-2.38904 - 0.540805i) q^{6} -1.00000i q^{7} +(-2.79915 + 0.405897i) q^{8} +(2.57122 + 1.54559i) q^{9} +O(q^{10})\)	\(q+(-1.41258 + 0.0678578i) q^{2} +(1.66901 + 0.463024i) q^{3} +(1.99079 - 0.191710i) q^{4} -1.00000i q^{5} +(-2.38904 - 0.540805i) q^{6} -1.00000i q^{7} +(-2.79915 + 0.405897i) q^{8} +(2.57122 + 1.54559i) q^{9} +(0.0678578 + 1.41258i) q^{10} -0.648120 q^{11} +(3.41142 + 0.601817i) q^{12} +4.96381 q^{13} +(0.0678578 + 1.41258i) q^{14} +(0.463024 - 1.66901i) q^{15} +(3.92649 - 0.763309i) q^{16} -6.88118i q^{17} +(-3.73694 - 2.00880i) q^{18} +4.22288i q^{19} +(-0.191710 - 1.99079i) q^{20} +(0.463024 - 1.66901i) q^{21} +(0.915524 - 0.0439800i) q^{22} +1.33148 q^{23} +(-4.85976 - 0.618626i) q^{24} -1.00000 q^{25} +(-7.01180 + 0.336833i) q^{26} +(3.57575 + 3.77014i) q^{27} +(-0.191710 - 1.99079i) q^{28} +4.10451i q^{29} +(-0.540805 + 2.38904i) q^{30} -7.63684i q^{31} +(-5.49471 + 1.34468i) q^{32} +(-1.08172 - 0.300095i) q^{33} +(0.466942 + 9.72025i) q^{34} -1.00000 q^{35} +(5.41506 + 2.58401i) q^{36} -2.29722 q^{37} +(-0.286556 - 5.96518i) q^{38} +(8.28466 + 2.29836i) q^{39} +(0.405897 + 2.79915i) q^{40} +10.9561i q^{41} +(-0.540805 + 2.38904i) q^{42} -5.13687i q^{43} +(-1.29027 + 0.124251i) q^{44} +(1.54559 - 2.57122i) q^{45} +(-1.88082 + 0.0903511i) q^{46} +9.62134 q^{47} +(6.90681 + 0.544089i) q^{48} -1.00000 q^{49} +(1.41258 - 0.0678578i) q^{50} +(3.18615 - 11.4848i) q^{51} +(9.88190 - 0.951611i) q^{52} -5.56316i q^{53} +(-5.30689 - 5.08300i) q^{54} +0.648120i q^{55} +(0.405897 + 2.79915i) q^{56} +(-1.95530 + 7.04805i) q^{57} +(-0.278524 - 5.79797i) q^{58} +0.421507 q^{59} +(0.601817 - 3.41142i) q^{60} +0.179252 q^{61} +(0.518219 + 10.7877i) q^{62} +(1.54559 - 2.57122i) q^{63} +(7.67049 - 2.27234i) q^{64} -4.96381i q^{65} +(1.54839 + 0.350506i) q^{66} +10.4894i q^{67} +(-1.31919 - 13.6990i) q^{68} +(2.22225 + 0.616506i) q^{69} +(1.41258 - 0.0678578i) q^{70} -2.09646 q^{71} +(-7.82458 - 3.28268i) q^{72} -16.6256 q^{73} +(3.24501 - 0.155884i) q^{74} +(-1.66901 - 0.463024i) q^{75} +(0.809569 + 8.40688i) q^{76} +0.648120i q^{77} +(-11.8588 - 2.68445i) q^{78} +7.10256i q^{79} +(-0.763309 - 3.92649i) q^{80} +(4.22232 + 7.94808i) q^{81} +(-0.743459 - 15.4764i) q^{82} -0.766970 q^{83} +(0.601817 - 3.41142i) q^{84} -6.88118 q^{85} +(0.348577 + 7.25626i) q^{86} +(-1.90049 + 6.85049i) q^{87} +(1.81419 - 0.263070i) q^{88} +11.5147i q^{89} +(-2.00880 + 3.73694i) q^{90} -4.96381i q^{91} +(2.65069 - 0.255257i) q^{92} +(3.53604 - 12.7460i) q^{93} +(-13.5910 + 0.652884i) q^{94} +4.22288 q^{95} +(-9.79337 - 0.299890i) q^{96} -14.8262 q^{97} +(1.41258 - 0.0678578i) q^{98} +(-1.66646 - 1.00173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more