LMFDB - Embedded newform 162.2.g.b.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			151.3
Character	$\chi$	$=$	162.151
Dual form			162.2.g.b.103.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686242 + 0.727374i) q^{2} +(0.851057 + 1.50854i) q^{3} +(-0.0581448 - 0.998308i) q^{4} +(-3.77668 - 0.441430i) q^{5} +(-1.68131 - 0.416189i) q^{6} +(-3.13446 + 1.57418i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-1.55140 + 2.56771i) q^{9} +O(q^{10})$	\(q+(-0.686242 + 0.727374i) q^{2} +(0.851057 + 1.50854i) q^{3} +(-0.0581448 - 0.998308i) q^{4} +(-3.77668 - 0.441430i) q^{5} +(-1.68131 - 0.416189i) q^{6} +(-3.13446 + 1.57418i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-1.55140 + 2.56771i) q^{9} +(2.91280 - 2.44413i) q^{10} +(-1.41437 + 3.27887i) q^{11} +(1.45651 - 0.937331i) q^{12} +(6.00411 - 1.42300i) q^{13} +(1.00598 - 3.36019i) q^{14} +(-2.54825 - 6.07296i) q^{15} +(-0.993238 + 0.116093i) q^{16} +(-0.0237611 - 0.134756i) q^{17} +(-0.803048 - 2.89052i) q^{18} +(-0.591493 + 3.35452i) q^{19} +(-0.221089 + 3.79596i) q^{20} +(-5.04232 - 3.38874i) q^{21} +(-1.41437 - 3.27887i) q^{22} +(1.62119 + 0.814194i) q^{23} +(-0.317725 + 1.70266i) q^{24} +(9.20321 + 2.18120i) q^{25} +(-3.08522 + 5.34375i) q^{26} +(-5.19384 - 0.155090i) q^{27} +(1.75377 + 3.03762i) q^{28} +(-0.375745 - 1.25508i) q^{29} +(6.16603 + 2.31399i) q^{30} +(0.265030 - 0.174313i) q^{31} +(0.597159 - 0.802123i) q^{32} +(-6.15002 + 0.656872i) q^{33} +(0.114324 + 0.0751919i) q^{34} +(12.5327 - 4.56154i) q^{35} +(2.65357 + 1.39948i) q^{36} +(-7.16975 - 2.60958i) q^{37} +(-2.03408 - 2.73225i) q^{38} +(7.25649 + 7.84640i) q^{39} +(-2.60936 - 2.76576i) q^{40} +(4.36125 + 4.62265i) q^{41} +(5.92513 - 1.34216i) q^{42} +(1.92691 + 2.58828i) q^{43} +(3.35556 + 1.22132i) q^{44} +(6.99262 - 9.01259i) q^{45} +(-1.70475 + 0.620480i) q^{46} +(3.99017 + 2.62437i) q^{47} +(-1.02043 - 1.39954i) q^{48} +(3.16665 - 4.25355i) q^{49} +(-7.90218 + 5.19734i) q^{50} +(0.183063 - 0.150530i) q^{51} +(-1.76970 - 5.91121i) q^{52} +(-2.78294 - 4.82020i) q^{53} +(3.67704 - 3.67143i) q^{54} +(6.78900 - 11.7589i) q^{55} +(-3.41300 - 0.808895i) q^{56} +(-5.56384 + 1.96260i) q^{57} +(1.17076 + 0.587978i) q^{58} +(1.85601 + 4.30271i) q^{59} +(-5.91452 + 2.89705i) q^{60} +(-0.784513 + 13.4696i) q^{61} +(-0.0550839 + 0.312396i) q^{62} +(0.820759 - 10.4906i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-23.3037 + 2.72382i) q^{65} +(3.74261 - 4.92414i) q^{66} +(-2.79770 + 9.34496i) q^{67} +(-0.133146 + 0.0315562i) q^{68} +(0.151481 + 3.13857i) q^{69} +(-5.28253 + 12.2463i) q^{70} +(3.05189 - 2.56084i) q^{71} +(-2.83894 + 0.969758i) q^{72} +(-10.7055 - 8.98301i) q^{73} +(6.81832 - 3.42429i) q^{74} +(4.54202 + 15.7398i) q^{75} +(3.38324 + 0.395444i) q^{76} +(-0.728272 - 12.5039i) q^{77} +(-10.6870 - 0.106345i) q^{78} +(2.36891 - 2.51090i) q^{79} +3.80239 q^{80} +(-4.18629 - 7.96712i) q^{81} -6.35527 q^{82} +(0.597161 - 0.632954i) q^{83} +(-3.08982 + 5.23083i) q^{84} +(0.0302527 + 0.519418i) q^{85} +(-3.20497 - 0.374608i) q^{86} +(1.57355 - 1.63497i) q^{87} +(-3.19108 + 1.60262i) q^{88} +(6.42404 + 5.39041i) q^{89} +(1.75689 + 11.2711i) q^{90} +(-16.5795 + 13.9119i) q^{91} +(0.718553 - 1.66579i) q^{92} +(0.488514 + 0.251459i) q^{93} +(-4.64712 + 1.10139i) q^{94} +(3.71467 - 12.4078i) q^{95} +(1.71825 + 0.218187i) q^{96} +(-6.91065 + 0.807739i) q^{97} +(0.920833 + 5.22230i) q^{98} +(-6.22494 - 8.71853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

Coefficient data

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

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

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

$2$	−0.686242	+	0.727374i	−0.485246	+	0.514331i
$2$	−0.686242	+	0.727374i	−0.485246	+	0.514331i
$3$	0.851057	+	1.50854i	0.491358	+	0.870958i
$3$	0.851057	+	1.50854i	0.491358	+	0.870958i
$4$	−0.0581448	−	0.998308i	−0.0290724	−	0.499154i
$5$	−3.77668	−	0.441430i	−1.68898	−	0.197414i	−0.783380	−	0.621543i	$-0.786506\pi$
$5$	−3.77668	−	0.441430i	−1.68898	−	0.197414i	−0.905602	+	0.424129i	$0.860580\pi$
$6$	−1.68131	−	0.416189i	−0.686390	−	0.169908i
$7$	−3.13446	+	1.57418i	−1.18471	+	0.594985i	−0.928391	−	0.371606i	$-0.878807\pi$
$7$	−3.13446	+	1.57418i	−1.18471	+	0.594985i	−0.256323	+	0.966591i	$0.582511\pi$
$8$	0.766044	+	0.642788i	0.270838	+	0.227260i
$9$	−1.55140	+	2.56771i	−0.517135	+	0.855904i
$10$	2.91280	−	2.44413i	0.921108	−	0.772901i
$11$	−1.41437	+	3.27887i	−0.426447	+	0.988616i	0.560585	+	0.828097i	$0.310576\pi$
$11$	−1.41437	+	3.27887i	−0.426447	+	0.988616i	−0.987033	+	0.160519i	$0.948683\pi$
$12$	1.45651	−	0.937331i	0.420457	−	0.270584i
$13$	6.00411	−	1.42300i	1.66524	−	0.394669i	0.713277	−	0.700883i	$-0.247210\pi$
$13$	6.00411	−	1.42300i	1.66524	−	0.394669i	0.951963	+	0.306214i	$0.0990621\pi$
$14$	1.00598	−	3.36019i	0.268858	−	0.898049i
$15$	−2.54825	−	6.07296i	−0.657956	−	1.56803i
$16$	−0.993238	+	0.116093i	−0.248310	+	0.0290232i
$17$	−0.0237611	−	0.134756i	−0.00576291	−	0.0326831i	0.981791	−	0.189966i	$-0.0608377\pi$
$17$	−0.0237611	−	0.134756i	−0.00576291	−	0.0326831i	−0.987554	+	0.157283i	$0.949727\pi$
$18$	−0.803048	−	2.89052i	−0.189280	−	0.681302i
$19$	−0.591493	+	3.35452i	−0.135698	+	0.769580i	0.838674	+	0.544634i	$0.183332\pi$
$19$	−0.591493	+	3.35452i	−0.135698	+	0.769580i	−0.974371	+	0.224946i	$0.927780\pi$
$20$	−0.221089	+	3.79596i	−0.0494371	+	0.848802i
$21$	−5.04232	−	3.38874i	−1.10033	−	0.739484i
$22$	−1.41437	−	3.27887i	−0.301544	−	0.699057i
$23$	1.62119	+	0.814194i	0.338042	+	0.169771i	0.609720	−	0.792617i	$-0.291282\pi$
$23$	1.62119	+	0.814194i	0.338042	+	0.169771i	−0.271677	+	0.962388i	$0.587578\pi$
$24$	−0.317725	+	1.70266i	−0.0648554	+	0.347554i
$25$	9.20321	+	2.18120i	1.84064	+	0.436240i
$26$	−3.08522	+	5.34375i	−0.605061	+	1.04800i
$27$	−5.19384	−	0.155090i	−0.999554	−	0.0298472i
$28$	1.75377	+	3.03762i	0.331432	+	0.574057i
$29$	−0.375745	−	1.25508i	−0.0697741	−	0.233062i	0.915989	−	0.401204i	$-0.131408\pi$
$29$	−0.375745	−	1.25508i	−0.0697741	−	0.233062i	−0.985763	+	0.168143i	$0.946223\pi$
$30$	6.16603	+	2.31399i	1.12576	+	0.422475i
$31$	0.265030	−	0.174313i	0.0476007	−	0.0313075i	−0.525486	−	0.850802i	$-0.676116\pi$
$31$	0.265030	−	0.174313i	0.0476007	−	0.0313075i	0.573086	+	0.819495i	$0.305746\pi$
$32$	0.597159	−	0.802123i	0.105564	−	0.141797i
$33$	−6.15002	+	0.656872i	−1.07058	+	0.114347i
$34$	0.114324	+	0.0751919i	0.0196064	+	0.0128953i
$35$	12.5327	−	4.56154i	2.11842	−	0.771041i
$36$	2.65357	+	1.39948i	0.442262	+	0.233247i
$37$	−7.16975	−	2.60958i	−1.17870	−	0.429012i	−0.322958	−	0.946413i	$-0.604677\pi$
$37$	−7.16975	−	2.60958i	−1.17870	−	0.429012i	−0.855743	+	0.517402i	$0.826899\pi$
$38$	−2.03408	−	2.73225i	−0.329972	−	0.443229i
$39$	7.25649	+	7.84640i	1.16197	+	1.25643i
$40$	−2.60936	−	2.76576i	−0.412576	−	0.437305i
$41$	4.36125	+	4.62265i	0.681112	+	0.721937i	0.972042	−	0.234807i	$-0.0754460\pi$
$41$	4.36125	+	4.62265i	0.681112	+	0.721937i	−0.290929	+	0.956745i	$0.593964\pi$
$42$	5.92513	−	1.34216i	0.914268	−	0.207099i
$43$	1.92691	+	2.58828i	0.293850	+	0.394710i	0.924391	−	0.381447i	$-0.124574\pi$
$43$	1.92691	+	2.58828i	0.293850	+	0.394710i	−0.630540	+	0.776157i	$0.717167\pi$
$44$	3.35556	+	1.22132i	0.505870	+	0.184121i
$45$	6.99262	−	9.01259i	1.04240	−	1.34352i
$46$	−1.70475	+	0.620480i	−0.251352	+	0.0914848i
$47$	3.99017	+	2.62437i	0.582026	+	0.382804i	0.806110	−	0.591765i	$-0.201569\pi$
$47$	3.99017	+	2.62437i	0.582026	+	0.382804i	−0.224085	+	0.974570i	$0.571939\pi$
$48$	−1.02043	−	1.39954i	−0.147287	−	0.202006i
$49$	3.16665	−	4.25355i	0.452379	−	0.607650i
$50$	−7.90218	+	5.19734i	−1.11754	+	0.735015i
$51$	0.183063	−	0.150530i	0.0256339	−	0.0210783i
$52$	−1.76970	−	5.91121i	−0.245413	−	0.819737i
$53$	−2.78294	−	4.82020i	−0.382266	−	0.662105i	0.609119	−	0.793078i	$-0.291523\pi$
$53$	−2.78294	−	4.82020i	−0.382266	−	0.662105i	−0.991386	+	0.130974i	$0.958190\pi$
$54$	3.67704	−	3.67143i	0.500381	−	0.499618i
$55$	6.78900	−	11.7589i	0.915428	−	1.58557i
$56$	−3.41300	−	0.808895i	−0.456081	−	0.108093i
$57$	−5.56384	+	1.96260i	−0.736948	+	0.259952i
$58$	1.17076	+	0.587978i	0.153728	+	0.0772053i
$59$	1.85601	+	4.30271i	0.241631	+	0.560165i	0.995273	−	0.0971215i	$-0.0309635\pi$
$59$	1.85601	+	4.30271i	0.241631	+	0.560165i	−0.753641	+	0.657286i	$0.771704\pi$
$60$	−5.91452	+	2.89705i	−0.763562	+	0.374008i
$61$	−0.784513	+	13.4696i	−0.100447	+	1.72460i	0.452824	+	0.891600i	$0.350417\pi$
$61$	−0.784513	+	13.4696i	−0.100447	+	1.72460i	−0.553270	+	0.833002i	$0.686620\pi$
$62$	−0.0550839	+	0.312396i	−0.00699566	+	0.0396744i
$63$	0.820759	−	10.4906i	0.103406	−	1.32169i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−23.3037	+	2.72382i	−2.89047	+	0.337848i
$66$	3.74261	−	4.92414i	0.460683	−	0.606119i
$67$	−2.79770	+	9.34496i	−0.341793	+	1.14167i	0.598449	+	0.801161i	$0.295784\pi$
$67$	−2.79770	+	9.34496i	−0.341793	+	1.14167i	−0.940242	+	0.340507i	$0.889401\pi$
$68$	−0.133146	+	0.0315562i	−0.0161464	+	0.00382676i
$69$	0.151481	+	3.13857i	0.0182362	+	0.377839i
$70$	−5.28253	+	12.2463i	−0.631384	+	1.46371i
$71$	3.05189	−	2.56084i	0.362193	−	0.303916i	−0.443471	−	0.896289i	$-0.646253\pi$
$71$	3.05189	−	2.56084i	0.362193	−	0.303916i	0.805664	+	0.592373i	$0.201809\pi$
$72$	−2.83894	+	0.969758i	−0.334572	+	0.114287i
$73$	−10.7055	−	8.98301i	−1.25299	−	1.05138i	−0.996393	−	0.0848624i	$-0.972955\pi$
$73$	−10.7055	−	8.98301i	−1.25299	−	1.05138i	−0.256595	−	0.966519i	$-0.582601\pi$
$74$	6.81832	−	3.42429i	0.792614	−	0.398066i
$75$	4.54202	+	15.7398i	0.524468	+	1.81747i
$76$	3.38324	+	0.395444i	0.388084	+	0.0453605i
$77$	−0.728272	−	12.5039i	−0.0829942	−	1.42496i
$78$	−10.6870	−	0.106345i	−1.21006	−	0.0120412i
$79$	2.36891	−	2.51090i	0.266523	−	0.282498i	−0.580266	−	0.814427i	$-0.697051\pi$
$79$	2.36891	−	2.51090i	0.266523	−	0.282498i	0.846789	+	0.531929i	$0.178533\pi$
$80$	3.80239			0.425120
$81$	−4.18629	−	7.96712i	−0.465143	−	0.885235i
$82$	−6.35527			−0.701822
$83$	0.597161	−	0.632954i	0.0655470	−	0.0694757i	−0.693770	−	0.720196i	$-0.744052\pi$
$83$	0.597161	−	0.632954i	0.0655470	−	0.0694757i	0.759317	+	0.650721i	$0.225533\pi$
$84$	−3.08982	+	5.23083i	−0.337127	+	0.570730i
$85$	0.0302527	+	0.519418i	0.00328136	+	0.0563388i
$86$	−3.20497	−	0.374608i	−0.345601	−	0.0403950i
$87$	1.57355	−	1.63497i	0.168703	−	0.175287i
$88$	−3.19108	+	1.60262i	−0.340171	+	0.170840i
$89$	6.42404	+	5.39041i	0.680947	+	0.571382i	0.916283	−	0.400532i	$-0.131175\pi$
$89$	6.42404	+	5.39041i	0.680947	+	0.571382i	−0.235336	+	0.971914i	$0.575619\pi$
$90$	1.75689	+	11.2711i	0.185192	+	1.18807i
$91$	−16.5795	+	13.9119i	−1.73801	+	1.45836i
$92$	0.718553	−	1.66579i	0.0749143	−	0.173671i
$93$	0.488514	+	0.251459i	0.0506565	+	0.0260750i
$94$	−4.64712	+	1.10139i	−0.479314	+	0.113599i
$95$	3.71467	−	12.4078i	0.381117	−	1.27302i
$96$	1.71825	+	0.218187i	0.175368	+	0.0222686i
$97$	−6.91065	+	0.807739i	−0.701670	+	0.0820134i	−0.459444	−	0.888207i	$-0.651951\pi$
$97$	−6.91065	+	0.807739i	−0.701670	+	0.0820134i	−0.242225	+	0.970220i	$0.577877\pi$
$98$	0.920833	+	5.22230i	0.0930182	+	0.527532i
$99$	−6.22494	−	8.71853i	−0.625630	−	0.876246i
$100$	1.64239	−	9.31447i	0.164239	−	0.931447i
$101$	0.234720	−	4.03000i	0.0233556	−	0.400999i	−0.966289	−	0.257460i	$-0.917114\pi$
$101$	0.234720	−	4.03000i	0.0233556	−	0.400999i	0.989645	−	0.143540i	$-0.0458485\pi$
$102$	−0.0161342	+	0.236455i	−0.00159752	+	0.0234125i
$103$	0.547289	+	1.26876i	0.0539260	+	0.125015i	0.943049	−	0.332654i	$-0.107944\pi$
$103$	0.547289	+	1.26876i	0.0539260	+	0.125015i	−0.889123	+	0.457668i	$0.848685\pi$
$104$	5.51410	+	2.76928i	0.540702	+	0.271551i
$105$	17.5473	+	15.0240i	1.71245	+	1.46619i
$106$	5.41585	+	1.28358i	0.526034	+	0.124672i
$107$	7.35361	−	12.7368i	0.710900	−	1.23132i	−0.253619	−	0.967304i	$-0.581621\pi$
$107$	7.35361	−	12.7368i	0.710900	−	1.23132i	0.964520	−	0.264011i	$-0.0850456\pi$
$108$	0.147167	+	5.19407i	0.0141611	+	0.499799i
$109$	1.46896	+	2.54431i	0.140700	+	0.243700i	0.927761	−	0.373176i	$-0.121731\pi$
$109$	1.46896	+	2.54431i	0.140700	+	0.243700i	−0.787060	+	0.616876i	$0.788398\pi$
$110$	3.89421	+	13.0076i	0.371299	+	1.24022i
$111$	−2.16521	−	13.0368i	−0.205513	−	1.23740i
$112$	2.93051	−	1.92743i	0.276907	−	0.182125i
$113$	10.8899	−	14.6277i	1.02444	−	1.37606i	0.0998862	−	0.994999i	$-0.468152\pi$
$113$	10.8899	−	14.6277i	1.02444	−	1.37606i	0.924551	−	0.381059i	$-0.124440\pi$
$114$	2.39059	−	5.39380i	0.223900	−	0.505176i
$115$	−5.76332	−	3.79059i	−0.537432	−	0.353475i
$116$	−1.23110	+	0.448085i	−0.114305	+	0.0416037i
$117$	−5.66094	+	17.6245i	−0.523354	+	1.62938i
$118$	−4.40334	−	1.60269i	−0.405361	−	0.147539i
$119$	0.286608	+	0.384982i	0.0262734	+	0.0352912i
$120$	1.95155	−	6.29015i	0.178152	−	0.574209i
$121$	−1.20189	−	1.27393i	−0.109263	−	0.115812i
$122$	−9.25904	−	9.81401i	−0.838274	−	0.888519i
$123$	−3.26180	+	10.5133i	−0.294107	+	0.947950i
$124$	−0.189428	−	0.254446i	−0.0170111	−	0.0228499i
$125$	−15.9293	−	5.79781i	−1.42476	−	0.518572i
$126$	7.06733	+	7.79607i	0.629608	+	0.694529i
$127$	9.76218	−	3.55314i	0.866254	−	0.315291i	0.129605	−	0.991566i	$-0.458629\pi$
$127$	9.76218	−	3.55314i	0.866254	−	0.315291i	0.736649	+	0.676275i	$0.236407\pi$
$128$	−0.835488	−	0.549509i	−0.0738474	−	0.0485702i
$129$	−2.26463	+	5.10960i	−0.199390	+	0.449875i
$130$	14.0108	−	18.8197i	1.22883	−	1.65060i
$131$	−14.5872	+	9.59417i	−1.27449	+	0.838246i	−0.992627	−	0.121208i	$-0.961323\pi$
$131$	−14.5872	+	9.59417i	−1.27449	+	0.838246i	−0.281864	+	0.959454i	$0.590953\pi$
$132$	1.01335	+	6.10142i	0.0882010	+	0.531061i
$133$	−3.42662	−	11.4457i	−0.297126	−	0.992470i
$134$	−4.87738	−	8.44787i	−0.421341	−	0.729785i
$135$	19.5470	+	2.87844i	1.68234	+	0.247737i
$136$	0.0684173	−	0.118502i	0.00586674	−	0.0101615i
$137$	15.7191	+	3.72549i	1.34297	+	0.318290i	0.838388	−	0.545073i	$-0.183498\pi$
$137$	15.7191	+	3.72549i	1.34297	+	0.318290i	0.504583	+	0.863363i	$0.331646\pi$
$138$	−2.38686	−	2.04363i	−0.203183	−	0.173965i
$139$	14.7919	+	7.42880i	1.25464	+	0.630102i	0.946949	−	0.321385i	$-0.104148\pi$
$139$	14.7919	+	7.42880i	1.25464	+	0.630102i	0.307688	+	0.951487i	$0.400445\pi$
$140$	−5.28253	−	12.2463i	−0.446456	−	1.03500i
$141$	−0.563122	+	8.25283i	−0.0474234	+	0.695014i
$142$	−0.231647	+	3.97722i	−0.0194394	+	0.333761i
$143$	−3.82618	+	21.6993i	−0.319961	+	1.81459i
$144$	1.24282	−	2.73046i	0.103568	−	0.227538i
$145$	0.865039	+	4.90588i	0.0718376	+	0.407411i
$146$	13.8806	−	1.62241i	1.14877	−	0.134271i
$147$	9.11167	+	1.15702i	0.751518	+	0.0954291i
$148$	−2.18828	+	7.30936i	−0.179875	+	0.600825i
$149$	−5.44321	+	1.29006i	−0.445925	+	0.105686i	−0.447443	−	0.894313i	$-0.647665\pi$
$149$	−5.44321	+	1.29006i	−0.445925	+	0.105686i	0.00151744	+	0.999999i	$0.499517\pi$
$150$	−14.5656	−	7.49754i	−1.18928	−	0.612172i
$151$	4.67318	−	10.8336i	0.380298	−	0.881630i	−0.615334	−	0.788266i	$-0.710979\pi$
$151$	4.67318	−	10.8336i	0.380298	−	0.881630i	0.995632	−	0.0933632i	$-0.0297618\pi$
$152$	−2.60936	+	2.18951i	−0.211647	+	0.177593i
$153$	0.382877	+	0.148049i	0.0309538	+	0.0119691i
$154$	9.59481	+	8.05100i	0.773172	+	0.648768i
$155$	−1.07788	+	0.541331i	−0.0865773	+	0.0434808i
$156$	7.41120	−	7.70044i	0.593371	−	0.616529i
$157$	−4.03153	−	0.471218i	−0.321751	−	0.0376073i	−0.0463156	−	0.998927i	$-0.514748\pi$
$157$	−4.03153	−	0.471218i	−0.321751	−	0.0376073i	−0.275436	+	0.961320i	$0.588822\pi$
$158$	0.200716	+	3.44617i	0.0159681	+	0.274162i
$159$	4.90303	−	8.30045i	0.388836	−	0.658268i
$160$	−2.60936	+	2.76576i	−0.206288	+	0.218652i
$161$	−6.36325			−0.501494
$162$	8.66788	+	2.42237i	0.681013	+	0.190319i
$163$	−3.63802			−0.284951			−0.142476	−	0.989798i	$-0.545506\pi$
$163$	−3.63802			−0.284951			−0.142476	+	0.989798i	$0.545506\pi$
$164$	4.36125	−	4.62265i	0.340556	−	0.360969i
$165$	23.5166	+	0.234011i	1.83077	+	0.0182177i
$166$	0.0505971	+	0.868719i	0.00392710	+	0.0674257i
$167$	−9.37145	−	1.09537i	−0.725185	−	0.0847619i	−0.254512	−	0.967070i	$-0.581915\pi$
$167$	−9.37145	−	1.09537i	−0.725185	−	0.0847619i	−0.470673	+	0.882308i	$0.655989\pi$
$168$	−1.68440	−	5.83707i	−0.129954	−	0.450340i
$169$	22.4071	−	11.2533i	1.72363	−	0.865638i
$170$	−0.398572	−	0.334441i	−0.0305691	−	0.0256505i
$171$	−7.69580	−	6.72300i	−0.588513	−	0.514121i
$172$	2.47187	−	2.07414i	0.188478	−	0.158152i
$173$	−5.23397	+	12.1337i	−0.397931	+	0.922508i	0.594990	+	0.803733i	$0.297156\pi$
$173$	−5.23397	+	12.1337i	−0.397931	+	0.922508i	−0.992921	+	0.118775i	$0.962103\pi$
$174$	0.109394	+	2.26655i	0.00829312	+	0.171826i
$175$	−32.2807	+	7.65066i	−2.44019	+	0.578336i
$176$	1.02415	−	3.42090i	0.0771981	−	0.257860i
$177$	−4.91125	+	6.46172i	−0.369152	+	0.485692i
$178$	−8.32928	+	0.973553i	−0.624306	+	0.0729709i
$179$	2.39591	+	13.5879i	0.179079	+	1.01561i	0.933330	+	0.359020i	$0.116889\pi$
$179$	2.39591	+	13.5879i	0.179079	+	1.01561i	−0.754251	+	0.656586i	$0.772000\pi$
$180$	−9.40392	−	6.45675i	−0.700927	−	0.481258i
$181$	−1.34675	+	7.63781i	−0.100103	+	0.567714i	0.892960	+	0.450135i	$0.148624\pi$
$181$	−1.34675	+	7.63781i	−0.100103	+	0.567714i	−0.993064	+	0.117578i	$0.962487\pi$
$182$	1.25843	−	21.6064i	0.0932812	−	1.60158i
$183$	−20.9871	+	10.2799i	−1.55141	+	0.759912i
$184$	0.718553	+	1.66579i	0.0529724	+	0.122804i
$185$	25.9259	+	13.0205i	1.90611	+	0.957285i
$186$	−0.518143	+	0.182771i	−0.0379921	+	0.0134014i
$187$	0.475454	+	0.112685i	0.0347686	+	0.00824031i
$188$	2.38793	−	4.13601i	0.174157	−	0.301650i
$189$	16.5240	−	7.68993i	1.20194	−	0.559360i
$190$	6.47598	+	11.2167i	0.469817	+	0.813747i
$191$	−0.167520	−	0.559557i	−0.0121213	−	0.0404881i	0.951715	−	0.306983i	$-0.0993196\pi$
$191$	−0.167520	−	0.559557i	−0.0121213	−	0.0404881i	−0.963836	+	0.266495i	$0.914134\pi$
$192$	−1.33784	+	1.10008i	−0.0965503	+	0.0793917i
$193$	17.7592	−	11.6804i	1.27834	−	0.840775i	0.285283	−	0.958443i	$-0.407912\pi$
$193$	17.7592	−	11.6804i	1.27834	−	0.840775i	0.993053	+	0.117668i	$0.0375420\pi$
$194$	4.15485	−	5.58093i	0.298300	−	0.400687i
$195$	−23.9418	−	32.8366i	−1.71451	−	2.35148i
$196$	−4.43048	−	2.91397i	−0.316463	−	0.208141i
$197$	0.511789	−	0.186276i	0.0364634	−	0.0132716i	−0.323724	−	0.946152i	$-0.604935\pi$
$197$	0.511789	−	0.186276i	0.0364634	−	0.0132716i	0.360187	+	0.932880i	$0.382713\pi$
$198$	10.6134	+	1.45517i	0.754265	+	0.103414i
$199$	2.08507	+	0.758905i	0.147807	+	0.0537973i	0.414864	−	0.909883i	$-0.363829\pi$
$199$	2.08507	+	0.758905i	0.147807	+	0.0537973i	−0.267057	+	0.963681i	$0.586051\pi$
$200$	5.64802	+	7.58661i	0.399375	+	0.536454i
$201$	−16.4783	+	3.73265i	−1.16229	+	0.263281i
$202$	2.77024	+	2.93628i	0.194913	+	0.206596i
$203$	3.15347	+	3.34249i	0.221331	+	0.234597i
$204$	−0.160919	−	0.174001i	−0.0112666	−	0.0121825i
$205$	−14.4305	−	19.3835i	−1.00787	−	1.35380i
$206$	−1.29843	−	0.472592i	−0.0904662	−	0.0329270i
$207$	−4.60574	+	2.89962i	−0.320121	+	0.201537i
$208$	−5.79831	+	2.11041i	−0.402040	+	0.146331i
$209$	−10.1624	−	6.68395i	−0.702951	−	0.462338i
$210$	−22.9698	+	2.45336i	−1.58507	+	0.169298i
$211$	−2.25553	+	3.02970i	−0.155277	+	0.208573i	−0.872953	−	0.487804i	$-0.837798\pi$
$211$	−2.25553	+	3.02970i	−0.155277	+	0.208573i	0.717677	+	0.696377i	$0.245206\pi$
$212$	−4.65023	+	3.05850i	−0.319379	+	0.210059i
$213$	6.46047	+	2.42449i	0.442664	+	0.166123i
$214$	4.21808	+	14.0894i	0.288342	+	0.963129i
$215$	−6.13476	−	10.6257i	−0.418387	−	0.724668i
$216$	−3.87902	−	3.45734i	−0.263934	−	0.235242i
$217$	−0.556324	+	0.963581i	−0.0377657	+	0.0654122i
$218$	−2.85872	−	0.677529i	−0.193617	−	0.0458880i
$219$	4.44024	−	23.7948i	0.300043	−	1.60790i
$220$	−12.1337	−	6.09379i	−0.818056	−	0.410843i
$221$	−0.334422	−	0.775276i	−0.0224956	−	0.0521507i
$222$	10.9685	+	7.37146i	0.736155	+	0.494740i
$223$	−1.16390	+	19.9834i	−0.0779407	+	1.33819i	0.701928	+	0.712248i	$0.252323\pi$
$223$	−1.16390	+	19.9834i	−0.0779407	+	1.33819i	−0.779869	+	0.625943i	$0.784714\pi$
$224$	−0.609079	+	3.45426i	−0.0406958	+	0.230797i
$225$	−19.8786	+	20.2473i	−1.32524	+	1.34982i
$226$	3.16669	+	17.9592i	0.210645	+	1.19463i
$227$	7.26607	−	0.849281i	0.482266	−	0.0563688i	0.128513	−	0.991708i	$-0.458980\pi$
$227$	7.26607	−	0.849281i	0.482266	−	0.0563688i	0.353753	+	0.935339i	$0.384905\pi$
$228$	2.28279	+	5.44031i	0.151181	+	0.360293i
$229$	2.65299	−	8.86162i	0.175315	−	0.585592i	−0.824491	−	0.565875i	$-0.808538\pi$
$229$	2.65299	−	8.86162i	0.175315	−	0.585592i	0.999806	−	0.0197168i	$-0.00627644\pi$
$230$	6.71221	−	1.59082i	0.442590	−	0.104896i
$231$	18.2429	−	11.7402i	1.20030	−	0.772448i
$232$	0.518910	−	1.20297i	0.0340681	−	0.0789787i
$233$	6.59355	−	5.53265i	0.431958	−	0.362456i	−0.400732	−	0.916195i	$-0.631244\pi$
$233$	6.59355	−	5.53265i	0.431958	−	0.362456i	0.832690	+	0.553740i	$0.186800\pi$
$234$	−8.93480	−	16.2123i	−0.584086	−	1.05983i
$235$	−13.9111	−	11.6728i	−0.907460	−	0.761449i
$236$	4.18751	−	2.10305i	0.272584	−	0.136897i
$237$	5.80387	+	1.43669i	0.377002	+	0.0933227i
$238$	−0.476708	−	0.0557192i	−0.0309004	−	0.00361174i
$239$	1.65960	+	28.4943i	0.107351	+	1.84314i	0.437506	+	0.899216i	$0.355862\pi$
$239$	1.65960	+	28.4943i	0.107351	+	1.84314i	−0.330155	+	0.943927i	$0.607101\pi$
$240$	3.23605	+	5.73607i	0.208886	+	0.370262i
$241$	4.35262	−	4.61351i	0.280377	−	0.297182i	−0.571846	−	0.820361i	$-0.693773\pi$
$241$	4.35262	−	4.61351i	0.280377	−	0.297182i	0.852223	+	0.523179i	$0.175254\pi$
$242$	1.75141			0.112585
$243$	8.45597	−	13.0957i	0.542451	−	0.840088i
$244$	13.4924			0.863762
$245$	−13.8371	+	14.6664i	−0.884018	+	0.937005i
$246$	−5.40869	−	9.58719i	−0.344846	−	0.611257i
$247$	1.22210	+	20.9826i	0.0777602	+	1.33509i
$248$	0.315071	+	0.0368265i	0.0200070	+	0.00233848i
$249$	1.46306	+	0.362164i	0.0927174	+	0.0229512i
$250$	15.1486	−	7.60789i	0.958079	−	0.481165i
$251$	6.55985	+	5.50437i	0.414054	+	0.347433i	0.825896	−	0.563823i	$-0.190670\pi$
$251$	6.55985	+	5.50437i	0.414054	+	0.347433i	−0.411842	+	0.911255i	$0.635114\pi$
$252$	−10.5205	−	0.209398i	−0.662732	−	0.0131908i
$253$	−4.96260	+	4.16411i	−0.311996	+	0.261796i
$254$	−4.11475	+	9.53907i	−0.258183	+	0.598535i
$255$	−0.757818	+	0.487692i	−0.0474564	+	0.0305405i
$256$	0.973045	−	0.230616i	0.0608153	−	0.0144135i
$257$	−0.974583	+	3.25533i	−0.0607928	+	0.203062i	−0.982990	−	0.183657i	$-0.941206\pi$
$257$	−0.974583	+	3.25533i	−0.0607928	+	0.203062i	0.922198	+	0.386719i	$0.126392\pi$
$258$	−2.16250	−	5.15365i	−0.134632	−	0.320852i
$259$	26.5812	−	3.10690i	1.65168	−	0.193053i
$260$	4.07420	+	23.1059i	0.252671	+	1.43297i
$261$	3.80560	+	0.982324i	0.235561	+	0.0608043i
$262$	3.03182	−	17.1943i	0.187306	−	1.06227i
$263$	−0.0936222	+	1.60743i	−0.00577299	+	0.0991185i	−0.999964	−	0.00851389i	$-0.997290\pi$
$263$	−0.0936222	+	1.60743i	−0.00577299	+	0.0991185i	0.994191	+	0.107632i	$0.0343269\pi$
$264$	−5.13342	−	3.44996i	−0.315940	−	0.212331i
$265$	8.38249	+	19.4328i	0.514932	+	1.19375i
$266$	10.6768	+	5.36209i	0.654637	+	0.328771i
$267$	−2.66444	+	14.2785i	−0.163061	+	0.873829i
$268$	9.49182	+	2.24960i	0.579805	+	0.137416i
$269$	−13.8706	+	24.0246i	−0.845706	+	1.46481i	0.0393011	+	0.999227i	$0.487487\pi$
$269$	−13.8706	+	24.0246i	−0.845706	+	1.46481i	−0.885007	+	0.465578i	$0.845846\pi$
$270$	−15.5077	+	12.2427i	−0.943766	+	0.745064i
$271$	−15.3007	−	26.5016i	−0.929450	−	1.60985i	−0.784243	−	0.620454i	$-0.786948\pi$
$271$	−15.3007	−	26.5016i	−0.929450	−	1.60985i	−0.145207	−	0.989401i	$-0.546385\pi$
$272$	0.0392446	+	0.131086i	0.00237955	+	0.00794827i
$273$	−35.0968	−	13.1711i	−2.12416	−	0.797154i
$274$	−13.4969	+	8.87706i	−0.815378	+	0.536283i
$275$	−20.1686	+	27.0911i	−1.21621	+	1.63366i
$276$	3.12445	−	0.333717i	0.188070	−	0.0200874i
$277$	−1.61396	−	1.06152i	−0.0969732	−	0.0637803i	0.500096	−	0.865970i	$-0.333298\pi$
$277$	−1.61396	−	1.06152i	−0.0969732	−	0.0637803i	−0.597069	+	0.802190i	$0.703668\pi$
$278$	−15.5544	+	5.66133i	−0.932889	+	0.339544i
$279$	0.0364169	+	0.950950i	0.00218022	+	0.0569319i
$280$	12.5327	+	4.56154i	0.748974	+	0.272604i
$281$	−9.34931	−	12.5583i	−0.557733	−	0.749166i	0.430421	−	0.902628i	$-0.358365\pi$
$281$	−9.34931	−	12.5583i	−0.557733	−	0.749166i	−0.988155	+	0.153462i	$0.950958\pi$
$282$	−5.61645	−	6.07304i	−0.334455	−	0.361644i
$283$	−9.87257	−	10.4643i	−0.586863	−	0.622039i	0.364094	−	0.931362i	$-0.381379\pi$
$283$	−9.87257	−	10.4643i	−0.586863	−	0.622039i	−0.950957	+	0.309324i	$0.899897\pi$
$284$	−2.73396	−	2.89783i	−0.162231	−	0.171955i
$285$	21.8792	−	4.95605i	1.29601	−	0.293571i
$286$	−13.1578	−	17.6740i	−0.778039	−	1.04509i
$287$	−20.9470	−	7.62410i	−1.23646	−	0.450036i
$288$	1.13319	+	2.77775i	0.0667737	+	0.163680i
$289$	15.9572	−	5.80794i	0.938658	−	0.341643i
$290$	−4.16203	−	2.73741i	−0.244403	−	0.160746i
$291$	−7.09986	−	9.73757i	−0.416201	−	0.570827i
$292$	−8.34534	+	11.2097i	−0.488374	+	0.656000i
$293$	−9.37716	+	6.16746i	−0.547820	+	0.360307i	−0.793048	−	0.609159i	$-0.791507\pi$
$293$	−9.37716	+	6.16746i	−0.547820	+	0.360307i	0.245229	+	0.969465i	$0.421137\pi$
$294$	−7.09439	+	5.83359i	−0.413753	+	0.340222i
$295$	−5.11019	−	17.0692i	−0.297527	−	0.993810i
$296$	−3.81495	−	6.60768i	−0.221739	−	0.384064i
$297$	7.85451	−	16.8106i	0.455765	−	0.975447i
$298$	2.79700	−	4.84454i	0.162026	−	0.280637i
$299$	10.8924	+	2.58155i	0.629925	+	0.149295i
$300$	15.4490	−	5.44953i	0.891951	−	0.314628i
$301$	−10.1142	−	5.07956i	−0.582975	−	0.292781i
$302$	4.67318	+	10.8336i	0.268911	+	0.623406i
$303$	6.27918	−	3.07567i	0.360730	−	0.176693i
$304$	0.198057	−	3.40051i	0.0113594	−	0.195033i
$305$	8.90873	−	50.5239i	0.510112	−	2.89299i
$306$	−0.370433	+	0.176897i	−0.0211763	+	0.0101125i
$307$	1.10143	+	6.24651i	0.0628618	+	0.356507i	0.999972	+	0.00747364i	$0.00237896\pi$
$307$	1.10143	+	6.24651i	0.0628618	+	0.356507i	−0.937110	+	0.349034i	$0.886510\pi$
$308$	−12.4404	+	1.45408i	−0.708860	+	0.0828538i
$309$	−1.44820	+	1.90540i	−0.0823854	+	0.108394i
$310$	0.345935	−	1.15550i	0.0196478	−	0.0656283i
$311$	31.9847	−	7.58051i	1.81369	−	0.429851i	0.823233	−	0.567704i	$-0.192168\pi$
$311$	31.9847	−	7.58051i	1.81369	−	0.429851i	0.990453	+	0.137853i	$0.0440201\pi$
$312$	0.515227	+	10.6751i	0.0291690	+	0.604357i
$313$	−5.58611	+	12.9501i	−0.315746	+	0.731981i	0.684251	+	0.729247i	$0.260129\pi$
$313$	−5.58611	+	12.9501i	−0.315746	+	0.731981i	−0.999996	+	0.00273378i	$0.999130\pi$
$314$	3.10935	−	2.60906i	0.175471	−	0.147238i
$315$	−7.73060	+	39.2572i	−0.435570	+	2.21189i
$316$	−2.64439	−	2.21891i	−0.148759	−	0.124823i
$317$	15.2914	−	7.67964i	0.858852	−	0.431332i	0.0358411	−	0.999358i	$-0.488589\pi$
$317$	15.2914	−	7.67964i	0.858852	−	0.431332i	0.823011	+	0.568026i	$0.192293\pi$
$318$	2.67286	+	9.26245i	0.149887	+	0.519412i
$319$	4.64667	+	0.543118i	0.260163	+	0.0304087i
$320$	−0.221089	−	3.79596i	−0.0123593	−	0.212200i
$321$	25.4724	+	0.253472i	1.42173	+	0.0141474i
$322$	4.36673	−	4.62846i	0.243348	−	0.257934i
$323$	0.466096			0.0259343
$324$	−7.71023	+	4.64246i	−0.428346	+	0.257914i
$325$	58.3609			3.23728
$326$	2.49656	−	2.64620i	0.138272	−	0.146559i
$327$	−2.58803	+	4.38133i	−0.143118	+	0.242288i
$328$	0.369526	+	6.34451i	0.0204036	+	0.350317i
$329$	−16.6382	−	1.94473i	−0.917296	−	0.107217i
$330$	−16.3083	+	16.9448i	−0.897742	+	0.932779i
$331$	5.61386	−	2.81938i	0.308565	−	0.154967i	−0.287777	−	0.957697i	$-0.592916\pi$
$331$	5.61386	−	2.81938i	0.308565	−	0.154967i	0.596343	+	0.802730i	$0.296620\pi$
$332$	−0.666605	−	0.559348i	−0.0365847	−	0.0306982i
$333$	17.8238	−	14.3614i	0.976740	−	0.786997i
$334$	7.22782	−	6.06486i	0.395489	−	0.331854i
$335$	14.6911	−	34.0579i	0.802663	−	1.86078i
$336$	5.40164	+	2.78045i	0.294684	+	0.151686i
$337$	2.27688	−	0.539631i	0.124030	−	0.0293956i	−0.168132	−	0.985764i	$-0.553774\pi$
$337$	2.27688	−	0.539631i	0.124030	−	0.0293956i	0.292162	+	0.956369i	$0.405625\pi$
$338$	−7.19137	+	24.0208i	−0.391159	+	1.30656i
$339$	31.3344	+	3.97890i	1.70185	+	0.216104i
$340$	0.516781	−	0.0604030i	0.0280264	−	0.00327581i
$341$	0.196700	+	1.11554i	0.0106519	+	0.0604099i
$342$	10.1713	−	0.984120i	0.550002	−	0.0532151i
$343$	1.03369	−	5.86233i	0.0558139	−	0.316536i
$344$	−0.187621	+	3.22133i	−0.0101159	+	0.173683i
$345$	0.813362	−	11.9202i	0.0437899	−	0.641763i
$346$	−5.23397	−	12.1337i	−0.281380	−	0.652312i
$347$	−30.3340	−	15.2343i	−1.62841	−	0.817819i	−0.999175	−	0.0406056i	$-0.987071\pi$
$347$	−30.3340	−	15.2343i	−1.62841	−	0.817819i	−0.629237	−	0.777214i	$-0.716632\pi$
$348$	−1.72370	−	1.47583i	−0.0923998	−	0.0791127i
$349$	−18.0733	−	4.28345i	−0.967441	−	0.229288i	−0.283619	−	0.958937i	$-0.591535\pi$
$349$	−18.0733	−	4.28345i	−0.967441	−	0.229288i	−0.683821	+	0.729649i	$0.739683\pi$
$350$	16.5875	−	28.7303i	0.886637	−	1.53570i
$351$	−31.4050	+	6.45965i	−1.67628	+	0.344791i
$352$	1.78546	+	3.09250i	0.0951651	+	0.164831i
$353$	0.522544	+	1.74542i	0.0278122	+	0.0928992i	0.970769	−	0.240016i	$-0.0771528\pi$
$353$	0.522544	+	1.74542i	0.0278122	+	0.0928992i	−0.942957	+	0.332915i	$0.891968\pi$
$354$	−1.32978	−	8.00661i	−0.0706768	−	0.425547i
$355$	−12.6565	+	8.32428i	−0.671735	+	0.441807i
$356$	5.00776	−	6.72659i	0.265411	−	0.356509i
$357$	−0.336842	+	0.760003i	−0.0178276	+	0.0402236i
$358$	−11.5276	−	7.58185i	−0.609255	−	0.400713i
$359$	10.6366	−	3.87139i	0.561376	−	0.204324i	−0.0457175	−	0.998954i	$-0.514557\pi$
$359$	10.6366	−	3.87139i	0.561376	−	0.204324i	0.607094	+	0.794630i	$0.292335\pi$
$360$	11.1498	−	2.40927i	0.587648	−	0.126980i
$361$	6.95120	+	2.53003i	0.365853	+	0.133160i
$362$	−4.63134	−	6.22097i	−0.243418	−	0.326967i
$363$	0.898899	−	2.89729i	0.0471800	−	0.152068i
$364$	14.8524	+	15.7426i	0.778476	+	0.825136i
$365$	36.4660	+	38.6517i	1.90872	+	2.02312i
$366$	6.92489	−	22.3200i	0.361970	−	1.16668i
$367$	−2.86793	−	3.85230i	−0.149705	−	0.201088i	0.720944	−	0.692993i	$-0.243708\pi$
$367$	−2.86793	−	3.85230i	−0.149705	−	0.201088i	−0.870649	+	0.491905i	$0.836301\pi$
$368$	−1.70475	−	0.620480i	−0.0888665	−	0.0323447i
$369$	−18.6357	+	4.02683i	−0.970136	+	0.209628i
$370$	−27.2622	+	9.92263i	−1.41729	+	0.515853i
$371$	16.3109	+	10.7278i	0.846819	+	0.556961i
$372$	0.222629	−	0.502308i	0.0115428	−	0.0260435i
$373$	12.6149	−	16.9448i	0.653176	−	0.877368i	−0.344946	−	0.938623i	$-0.612103\pi$
$373$	12.6149	−	16.9448i	0.653176	−	0.877368i	0.998122	+	0.0612544i	$0.0195101\pi$
$374$	−0.408240	+	0.268504i	−0.0211096	+	0.0138840i
$375$	−4.81054	−	28.9644i	−0.248415	−	1.49571i
$376$	1.36973	+	4.57522i	0.0706384	+	0.235949i
$377$	−4.04198	−	7.00092i	−0.208173	−	0.360566i
$378$	−5.74600	+	17.2963i	−0.295543	+	0.889624i
$379$	−8.13502	+	14.0903i	−0.417868	+	0.723768i	−0.995725	−	0.0923698i	$-0.970556\pi$
$379$	−8.13502	+	14.0903i	−0.417868	+	0.723768i	0.577857	+	0.816138i	$0.303889\pi$
$380$	−12.6028	−	2.98693i	−0.646512	−	0.153226i
$381$	13.6682	+	11.7027i	0.700246	+	0.599550i
$382$	0.521966	+	0.262141i	0.0267061	+	0.0134123i
$383$	−4.74133	−	10.9916i	−0.242270	−	0.561646i	0.753084	−	0.657924i	$-0.228565\pi$
$383$	−4.74133	−	10.9916i	−0.242270	−	0.561646i	−0.995354	+	0.0962784i	$0.969306\pi$
$384$	0.117910	−	1.72803i	0.00601708	−	0.0881833i
$385$	−2.76917	+	47.5448i	−0.141130	+	2.42311i
$386$	−3.69108	+	20.9332i	−0.187871	+	1.06547i
$387$	−9.63538	+	0.932266i	−0.489794	+	0.0473897i
$388$	1.20819	+	6.85199i	0.0613366	+	0.347857i
$389$	−8.21291	+	0.959952i	−0.416411	+	0.0486715i	−0.321719	−	0.946835i	$-0.604261\pi$
$389$	−8.21291	+	0.959952i	−0.416411	+	0.0486715i	−0.0946920	+	0.995507i	$0.530187\pi$
$390$	40.3143	+	5.11918i	2.04139	+	0.259220i
$391$	0.0711961	−	0.237811i	0.00360054	−	0.0120266i
$392$	5.15993	−	1.22293i	0.260616	−	0.0617671i
$393$	−26.8878	−	13.8403i	−1.35631	−	0.698149i
$394$	−0.215719	+	0.500092i	−0.0108677	+	0.0251943i
$395$	−10.0550	+	8.43714i	−0.505922	+	0.424519i
$396$	−8.34184	+	6.72134i	−0.419193	+	0.337760i
$397$	25.2439	+	21.1822i	1.26696	+	1.06310i	0.994905	+	0.100820i	$0.0321465\pi$
$397$	25.2439	+	21.1822i	1.26696	+	1.06310i	0.272051	+	0.962283i	$0.412298\pi$
$398$	−1.98287	+	0.995835i	−0.0993923	+	0.0499167i
$399$	14.3501	−	14.9102i	0.718404	−	0.746442i
$400$	−9.39421	−	1.09803i	−0.469710	−	0.0549013i
$401$	0.849467	+	14.5848i	0.0424204	+	0.728330i	0.950728	+	0.310027i	$0.100338\pi$
$401$	0.849467	+	14.5848i	0.0424204	+	0.728330i	−0.908307	+	0.418303i	$0.862625\pi$
$402$	8.59305	−	14.5474i	0.428582	−	0.725556i
$403$	1.34322	−	1.42373i	0.0669105	−	0.0709210i
$404$	−4.03682			−0.200840
$405$	12.2933	+	31.9372i	0.610861	+	1.58697i
$406$	−4.59528			−0.228060
$407$	18.6971	−	19.8178i	0.926781	−	0.982331i
$408$	0.236993	+	0.00235828i	0.0117329	+	0.000116752i
$409$	0.296826	+	5.09630i	0.0146771	+	0.251996i	0.997664	+	0.0683181i	$0.0217633\pi$
$409$	0.296826	+	5.09630i	0.0146771	+	0.251996i	−0.982986	+	0.183678i	$0.941200\pi$
$410$	24.0018	+	2.80541i	1.18536	+	0.138549i
$411$	7.75777	+	26.8835i	0.382663	+	1.32607i
$412$	1.23479	−	0.620135i	0.0608338	−	0.0305519i
$413$	−12.5908	−	10.5650i	−0.619554	−	0.519867i
$414$	1.05155	−	5.33993i	0.0516808	−	0.262443i
$415$	−2.53469	+	2.12686i	−0.124423	+	0.104403i
$416$	2.44398	−	5.66579i	0.119826	−	0.277788i
$417$	1.38213	+	28.6366i	0.0676834	+	1.40234i
$418$	11.8356	−	2.80509i	0.578899	−	0.137202i
$419$	7.80974	−	26.0864i	0.381531	−	1.27440i	−0.524580	−	0.851361i	$-0.675777\pi$
$419$	7.80974	−	26.0864i	0.381531	−	1.27440i	0.906111	−	0.423041i	$-0.139037\pi$
$420$	13.9783	−	18.3912i	0.682072	−	0.897400i
$421$	−3.94940	+	0.461619i	−0.192482	+	0.0224979i	−0.211788	−	0.977316i	$-0.567929\pi$
$421$	−3.94940	+	0.461619i	−0.192482	+	0.0224979i	0.0193056	+	0.999814i	$0.493854\pi$
$422$	−0.655887	−	3.71972i	−0.0319281	−	0.181073i
$423$	−12.9290	+	6.17414i	−0.628629	+	0.300197i
$424$	0.966505	−	5.48132i	0.0469376	−	0.266197i
$425$	0.0752513	−	1.29201i	0.00365022	−	0.0626719i
$426$	−6.19696	+	3.03539i	−0.300244	+	0.147065i
$427$	−18.7445	−	43.4547i	−0.907112	−	2.10292i
$428$	−13.1429	−	6.60059i	−0.635284	−	0.319051i
$429$	−35.9906	+	12.6954i	−1.73764	+	0.612940i
$430$	11.9388	+	2.82955i	0.575740	+	0.136453i
$431$	−20.1905	+	34.9710i	−0.972542	+	1.68449i	−0.284724	+	0.958610i	$0.591902\pi$
$431$	−20.1905	+	34.9710i	−0.972542	+	1.68449i	−0.687818	+	0.725883i	$0.741431\pi$
$432$	5.17672	−	0.448926i	0.249065	−	0.0215990i
$433$	16.5183	+	28.6105i	0.793818	+	1.37493i	0.923587	+	0.383388i	$0.125243\pi$
$433$	16.5183	+	28.6105i	0.793818	+	1.37493i	−0.129770	+	0.991544i	$0.541424\pi$
$434$	−0.319111	−	1.06590i	−0.0153178	−	0.0511651i
$435$	−6.66454	+	5.48013i	−0.319540	+	0.262752i
$436$	2.45459	−	1.61441i	0.117553	−	0.0773161i
$437$	−3.69016	+	4.95674i	−0.176524	+	0.237113i
$438$	14.2606	+	19.5587i	0.681400	+	0.934551i
$439$	−31.1967	−	20.5184i	−1.48894	−	0.979291i	−0.993884	−	0.110429i	$-0.964778\pi$
$439$	−31.1967	−	20.5184i	−1.48894	−	0.979291i	−0.495055	−	0.868862i	$-0.664852\pi$
$440$	12.7591	−	4.64395i	0.608268	−	0.221392i
$441$	6.00914	+	14.7300i	0.286150	+	0.701430i
$442$	0.793410	+	0.288778i	0.0377386	+	0.0137357i
$443$	−12.0343	−	16.1649i	−0.571767	−	0.768017i	0.418346	−	0.908288i	$-0.362610\pi$
$443$	−12.0343	−	16.1649i	−0.571767	−	0.768017i	−0.990113	+	0.140271i	$0.955203\pi$
$444$	−12.8888	+	2.91957i	−0.611677	+	0.138557i
$445$	−21.8820	−	23.1936i	−1.03731	−	1.09948i
$446$	−13.7367	−	14.5601i	−0.650452	−	0.689439i
$447$	−6.57860	−	7.11340i	−0.311157	−	0.336452i
$448$	−2.09456	−	2.81348i	−0.0989587	−	0.132925i
$449$	−16.4473	−	5.98634i	−0.776198	−	0.282513i	−0.0766114	−	0.997061i	$-0.524410\pi$
$449$	−16.4473	−	5.98634i	−0.776198	−	0.282513i	−0.699586	+	0.714548i	$0.746632\pi$
$450$	−1.08581	−	28.3537i	−0.0511857	−	1.33661i
$451$	−21.3255	+	7.76184i	−1.00418	+	0.365491i
$452$	−15.2361	−	10.0210i	−0.716648	−	0.471347i
$453$	20.3202	−	2.17036i	0.954724	−	0.101972i
$454$	−4.36853	+	5.86796i	−0.205025	+	0.275397i
$455$	68.7567	−	45.2220i	3.22337	−	2.12004i
$456$	−5.52368	−	2.07293i	−0.258670	−	0.0970737i
$457$	−7.98243	−	26.6632i	−0.373402	−	1.24725i	−0.913912	−	0.405913i	$-0.866954\pi$
$457$	−7.98243	−	26.6632i	−0.373402	−	1.24725i	0.540509	−	0.841338i	$-0.318232\pi$
$458$	4.62511	+	8.01093i	0.216117	+	0.374326i
$459$	0.102512	+	0.703585i	0.00478485	+	0.0328405i
$460$	−3.44907	+	5.97397i	−0.160814	+	0.278538i
$461$	−0.638507	−	0.151329i	−0.0297382	−	0.00704809i	0.215720	−	0.976455i	$-0.430790\pi$
$461$	−0.638507	−	0.151329i	−0.0297382	−	0.00704809i	−0.245458	+	0.969407i	$0.578938\pi$
$462$	−3.97955	+	21.3260i	−0.185145	+	0.992177i
$463$	35.7204	+	17.9395i	1.66007	+	0.833718i	0.996315	+	0.0857667i	$0.0273340\pi$
$463$	35.7204	+	17.9395i	1.66007	+	0.833718i	0.663754	+	0.747951i	$0.268962\pi$
$464$	0.518910	+	1.20297i	0.0240898	+	0.0558464i
$465$	−1.73396	−	1.16532i	−0.0804104	−	0.0540406i
$466$	−0.500468	+	8.59271i	−0.0231837	+	0.398050i
$467$	−3.49400	+	19.8154i	−0.161683	+	0.916949i	0.790736	+	0.612157i	$0.209698\pi$
$467$	−3.49400	+	19.8154i	−0.161683	+	0.916949i	−0.952419	+	0.304792i	$0.901413\pi$
$468$	17.9238	+	4.62659i	0.828528	+	0.213864i
$469$	−5.94142	−	33.6954i	−0.274349	−	1.55591i
$470$	18.0369	−	2.10821i	0.831978	−	0.0972443i
$471$	−2.72021	−	6.48277i	−0.125341	−	0.298710i
$472$	−1.34394	+	4.48908i	−0.0618600	+	0.206627i
$473$	−11.2120	+	2.65729i	−0.515528	+	0.122182i
$474$	−5.02787	+	3.23567i	−0.230938	+	0.148619i
$475$	−12.7605	+	29.5822i	−0.585493	+	1.35733i
$476$	0.367666	−	0.308508i	0.0168519	−	0.0141405i
$477$	16.6943	+	0.332279i	0.764381	+	0.0152140i
$478$	−21.8649	−	18.3468i	−1.00008	−	0.839164i
$479$	−14.7708	+	7.41817i	−0.674894	+	0.338945i	−0.753019	−	0.657999i	$-0.771403\pi$
$479$	−14.7708	+	7.41817i	−0.674894	+	0.338945i	0.0781245	+	0.996944i	$0.475107\pi$
$480$	−6.39298	−	1.58251i	−0.291798	−	0.0722314i
$481$	−46.7614	−	5.46562i	−2.13214	−	0.249211i
$482$	0.368795	+	6.33196i	0.0167981	+	0.288413i
$483$	−5.41549	−	9.59924i	−0.246413	−	0.436780i
$484$	−1.20189	+	1.27393i	−0.0546313	+	0.0579058i
$485$	26.4558			1.20130
$486$	3.72261	+	15.1374i	0.168861	+	0.686648i
$487$	−22.8688			−1.03628			−0.518142	−	0.855295i	$-0.673376\pi$
$487$	−22.8688			−1.03628			−0.518142	+	0.855295i	$0.673376\pi$
$488$	−9.25904	+	9.81401i	−0.419137	+	0.444260i
$489$	−3.09616	−	5.48810i	−0.140013	−	0.248181i
$490$	−1.17241	−	20.1294i	−0.0529639	−	0.909356i
$491$	−20.7899	−	2.42999i	−0.938236	−	0.109664i	−0.366790	−	0.930304i	$-0.619543\pi$
$491$	−20.7899	−	2.42999i	−0.938236	−	0.109664i	−0.571446	+	0.820640i	$0.693617\pi$
$492$	10.6851	+	2.64499i	0.481723	+	0.119245i
$493$	−0.160201	+	0.0804558i	−0.00721507	+	0.00362355i
$494$	−16.1008	−	13.5102i	−0.724411	−	0.607853i
$495$	19.6610	+	35.6750i	0.883694	+	1.60347i
$496$	−0.243001	+	0.203902i	−0.0109111	+	0.00915548i
$497$	−5.53479	+	12.8311i	−0.248269	+	0.575553i
$498$	−1.26744	+	0.815657i	−0.0567953	+	0.0365505i
$499$	17.5900	−	4.16891i	0.787436	−	0.186626i	0.182824	−	0.983146i	$-0.441476\pi$
$499$	17.5900	−	4.16891i	0.787436	−	0.186626i	0.604612	+	0.796520i	$0.293328\pi$
$500$	−4.86179	+	16.2395i	−0.217426	+	0.726253i
$501$	−6.32323	−	15.0695i	−0.282501	−	0.673254i
$502$	−8.50538	+	0.994136i	−0.379614	+	0.0443705i
$503$	−2.56772	−	14.5622i	−0.114489	−	0.649298i	−0.987002	−	0.160708i	$-0.948622\pi$
$503$	−2.56772	−	14.5622i	−0.114489	−	0.649298i	0.872513	−	0.488590i	$-0.162489\pi$
$504$	7.37195	−	7.50867i	0.328373	−	0.334463i
$505$	−2.66543	+	15.1164i	−0.118610	+	0.672670i
$506$	0.376674	−	6.46725i	0.0167452	−	0.287504i
$507$	36.0458	+	24.2249i	1.60085	+	1.07587i
$508$	−4.11475	−	9.53907i	−0.182563	−	0.423228i
$509$	−32.6449	−	16.3949i	−1.44696	−	0.726690i	−0.460038	−	0.887899i	$-0.652164\pi$
$509$	−32.6449	−	16.3949i	−1.44696	−	0.726690i	−0.986920	+	0.161210i	$0.948460\pi$
$510$	0.165312	−	0.885892i	0.00732014	−	0.0392279i
$511$	47.6969	+	11.3044i	2.10999	+	0.500076i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	3.59237	−	17.3311i	0.158607	−	0.765187i
$514$	−1.69904	−	2.94283i	−0.0749417	−	0.129803i
$515$	−1.50687	−	5.03329i	−0.0664005	−	0.221793i
$516$	5.23263	+	1.96370i	0.230354	+	0.0864472i
$517$	−14.2485	+	9.37141i	−0.626650	+	0.412154i
$518$	−15.9813	+	21.4666i	−0.702177	+	0.943187i
$519$	−22.7586	+	2.43080i	−0.998992	+	0.106700i
$520$	−19.6025	−	12.8928i	−0.859628	−	0.565386i
$521$	10.0480	−	3.65717i	0.440210	−	0.160223i	−0.112400	−	0.993663i	$-0.535854\pi$
$521$	10.0480	−	3.65717i	0.440210	−	0.160223i	0.552611	+	0.833440i	$0.313632\pi$
$522$	−3.32608	+	2.09398i	−0.145579	+	0.0916512i
$523$	27.4132	+	9.97760i	1.19870	+	0.436290i	0.862769	−	0.505598i	$-0.168728\pi$
$523$	27.4132	+	9.97760i	1.19870	+	0.436290i	0.335927	+	0.941888i	$0.390950\pi$
$524$	10.4261	+	14.0047i	0.455467	+	0.611798i
$525$	−39.0141	−	42.1856i	−1.70271	−	1.84113i
$526$	−1.10496	−	1.17118i	−0.0481784	−	0.0510661i
$527$	−0.0297871	−	0.0315724i	−0.00129754	−	0.00137532i
$528$	6.03218	−	1.36640i	0.262517	−	0.0594651i
$529$	−11.7693	−	15.8089i	−0.511708	−	0.687343i
$530$	−19.8873	−	7.23839i	−0.863850	−	0.314416i
$531$	−13.9275	−	1.90955i	−0.604403	−	0.0828673i
$532$	−11.2271	+	4.08634i	−0.486757	+	0.177165i
$533$	32.7634	+	21.5488i	1.41914	+	0.933384i
$534$	−8.55734	−	11.7365i	−0.370312	−	0.507889i
$535$	−33.3946	+	44.8568i	−1.44378	+	1.93933i
$536$	−8.14998	+	5.36033i	−0.352026	+	0.231531i
$537$	−18.4589	+	15.1784i	−0.796558	+	0.654996i
$538$	−7.95627	−	26.5758i	−0.343019	−	1.14576i
$539$	9.46803	+	16.3991i	0.407817	+	0.706360i
$540$	1.73702	−	19.6813i	0.0747493	−	0.846948i
$541$	−12.5176	+	21.6812i	−0.538175	+	0.932147i	0.460827	+	0.887490i	$0.347553\pi$
$541$	−12.5176	+	21.6812i	−0.538175	+	0.932147i	−0.999002	+	0.0446570i	$0.985781\pi$
$542$	29.7765	+	7.05716i	1.27901	+	0.303131i
$543$	−12.6681	+	4.46858i	−0.543641	+	0.191765i
$544$	−0.122280	−	0.0614113i	−0.00524271	−	0.00263299i
$545$	−4.42464	−	10.2575i	−0.189531	−	0.439382i
$546$	33.6652	−	16.4899i	1.44074	−	0.705703i
$547$	−0.200489	+	3.44227i	−0.00857231	+	0.147181i	0.991306	+	0.131577i	$0.0420041\pi$
$547$	−0.200489	+	3.44227i	−0.00857231	+	0.147181i	−0.999878	+	0.0156038i	$0.995033\pi$
$548$	2.80520	−	15.9091i	0.119832	−	0.679603i
$549$	−33.3689	−	22.9111i	−1.42415	−	0.977824i
$550$	−5.86484	−	33.2611i	−0.250078	−	1.41826i
$551$	4.43243	−	0.518077i	0.188828	−	0.0220708i
$552$	−1.90139	+	2.50165i	−0.0809285	+	0.106477i
$553$	−3.47263	+	11.5994i	−0.147671	+	0.493257i
$554$	1.87968	−	0.445493i	0.0798600	−	0.0189272i
$555$	2.42247	+	50.1915i	0.102828	+	2.13051i
$556$	6.55615	−	15.1989i	0.278043	−	0.644576i
$557$	6.01226	−	5.04489i	0.254748	−	0.213759i	−0.506466	−	0.862260i	$-0.669048\pi$
$557$	6.01226	−	5.04489i	0.254748	−	0.213759i	0.761213	+	0.648501i	$0.224604\pi$
$558$	−0.716687	−	0.626093i	−0.0303398	−	0.0265046i
$559$	15.2525	+	12.7984i	0.645111	+	0.541313i
$560$	−11.9184	+	5.98566i	−0.503645	+	0.252940i
$561$	0.234649	+	0.813143i	0.00990687	+	0.0343309i
$562$	15.5505	+	1.81759i	0.655957	+	0.0766704i
$563$	−1.20456	−	20.6815i	−0.0507660	−	0.871619i	−0.923542	−	0.383498i	$-0.874719\pi$
$563$	−1.20456	−	20.6815i	−0.0507660	−	0.871619i	0.872776	−	0.488121i	$-0.162318\pi$
$564$	8.27161	+	0.0823096i	0.348298	+	0.00346586i
$565$	−47.5848	+	50.4370i	−2.00191	+	2.12190i
$566$	14.3864			0.604707
$567$	25.6634	+	18.3826i	1.07776	+	0.771996i
$568$	3.98396			0.167163
$569$	17.7236	−	18.7859i	0.743010	−	0.787545i	−0.240063	−	0.970757i	$-0.577168\pi$
$569$	17.7236	−	18.7859i	0.743010	−	0.787545i	0.983073	+	0.183213i	$0.0586497\pi$
$570$	−11.4095	+	19.3154i	−0.477891	+	0.809032i
$571$	0.326901	+	5.61267i	0.0136804	+	0.234883i	0.998216	+	0.0597005i	$0.0190146\pi$
$571$	0.326901	+	5.61267i	0.0136804	+	0.234883i	−0.984536	+	0.175183i	$0.943948\pi$
$572$	21.8851	+	2.55800i	0.915061	+	0.106955i
$573$	0.701546	−	0.728926i	0.0293075	−	0.0304513i
$574$	19.9203	−	10.0044i	0.831457	−	0.417574i
$575$	13.1443	+	11.0294i	0.548154	+	0.459956i
$576$	−2.79810	−	1.08196i	−0.116588	−	0.0450815i
$577$	4.53375	−	3.80427i	0.188743	−	0.158374i	−0.543520	−	0.839396i	$-0.682909\pi$
$577$	4.53375	−	3.80427i	0.188743	−	0.158374i	0.732263	+	0.681022i	$0.238464\pi$
$578$	−6.72594	+	15.5925i	−0.279762	+	0.648562i
$579$	32.7345	+	16.8498i	1.36040	+	0.700255i
$580$	4.84728	−	1.14883i	0.201273	−	0.0477025i
$581$	−0.875390	+	2.92401i	−0.0363173	+	0.121308i
$582$	11.9551	+	1.51808i	0.495554	+	0.0629263i
$583$	19.7409	−	2.30738i	0.817584	−	0.0955619i
$584$	−2.42675	−	13.7628i	−0.100419	−	0.569507i
$585$	29.1595	−	64.0630i	1.20560	−	2.64868i
$586$	1.94895	−	11.0531i	0.0805105	−	0.456598i
$587$	0.583214	−	10.0134i	0.0240718	−	0.413297i	−0.964650	−	0.263534i	$-0.915112\pi$
$587$	0.583214	−	10.0134i	0.0240718	−	0.413297i	0.988722	−	0.149763i	$-0.0478511\pi$
$588$	0.625262	−	9.16353i	0.0257854	−	0.377897i
$589$	0.427973	+	0.992153i	0.0176343	+	0.0408810i
$590$	15.9225	+	7.99660i	0.655521	+	0.329215i
$591$	0.716567	+	0.613524i	0.0294756	+	0.0252370i
$592$	7.42423	+	1.75957i	0.305134	+	0.0723181i
$593$	14.9501	−	25.8943i	0.613927	−	1.06335i	−0.376644	−	0.926358i	$-0.622922\pi$
$593$	14.9501	−	25.8943i	0.613927	−	1.06335i	0.990572	−	0.136995i	$-0.0437445\pi$
$594$	6.83746	+	17.2493i	0.280545	+	0.707746i
$595$	−0.912485	−	1.58047i	−0.0374082	−	0.0647930i
$596$	1.60438	+	5.35899i	0.0657178	+	0.219513i
$597$	0.629676	+	3.79129i	0.0257709	+	0.155167i
$598$	−9.35258	+	6.15129i	−0.382456	+	0.251545i
$599$	−9.81231	+	13.1802i	−0.400920	+	0.538529i	−0.956038	−	0.293242i	$-0.905266\pi$
$599$	−9.81231	+	13.1802i	−0.400920	+	0.538529i	0.555118	+	0.831772i	$0.312673\pi$
$600$	−6.63794	+	14.9769i	−0.270993	+	0.611430i
$601$	18.6165	+	12.2443i	0.759384	+	0.499455i	0.869178	−	0.494499i	$-0.164649\pi$
$601$	18.6165	+	12.2443i	0.759384	+	0.499455i	−0.109794	+	0.993954i	$0.535019\pi$
$602$	10.6355	−	3.87102i	0.433473	−	0.157771i
$603$	−19.6548	−	21.6815i	−0.800405	−	0.882938i
$604$	−11.0870	−	4.03535i	−0.451125	−	0.164196i
$605$	3.97680	+	5.34177i	0.161680	+	0.217174i
$606$	−2.07187	+	6.67796i	−0.0841642	+	0.271274i
$607$	11.7322	+	12.4354i	0.476193	+	0.504735i	0.920286	−	0.391245i	$-0.127956\pi$
$607$	11.7322	+	12.4354i	0.476193	+	0.504735i	−0.444093	+	0.895981i	$0.646474\pi$
$608$	2.33753	+	2.47763i	0.0947992	+	0.100481i
$609$	−2.35850	+	7.60180i	−0.0955712	+	0.308040i
$610$	30.6362	+	41.1516i	1.24042	+	1.66618i
$611$	27.6919	+	10.0790i	1.12029	+	0.407753i
$612$	0.125536	−	0.390838i	0.00507450	−	0.0157987i
$613$	18.3744	−	6.68772i	0.742133	−	0.270114i	0.0568418	−	0.998383i	$-0.481897\pi$
$613$	18.3744	−	6.68772i	0.742133	−	0.270114i	0.685292	+	0.728269i	$0.259675\pi$
$614$	−5.29939	−	3.48547i	−0.213866	−	0.140662i
$615$	16.9596	−	38.2654i	0.683879	−	1.54301i
$616$	7.47949	−	10.0467i	0.301357	−	0.404793i
$617$	28.7378	−	18.9012i	1.15694	−	0.760932i	0.181979	−	0.983302i	$-0.441750\pi$
$617$	28.7378	−	18.9012i	1.15694	−	0.760932i	0.974962	+	0.222370i	$0.0713793\pi$
$618$	−0.392117	−	2.36095i	−0.0157733	−	0.0949712i
$619$	−0.631086	−	2.10797i	−0.0253655	−	0.0847266i	0.944370	−	0.328886i	$-0.106673\pi$
$619$	−0.631086	−	2.10797i	−0.0253655	−	0.0847266i	−0.969735	+	0.244159i	$0.921488\pi$
$620$	0.603088	+	1.04458i	0.0242206	+	0.0419513i
$621$	−8.29394	−	4.48022i	−0.332825	−	0.179785i
$622$	−16.4354	+	28.4669i	−0.658998	+	1.14142i
$623$	−28.6213	−	6.78338i	−1.14669	−	0.271771i
$624$	−8.11834	−	6.95092i	−0.324994	−	0.278259i
$625$	15.3401	+	7.70409i	0.613604	+	0.308163i
$626$	−5.58611	−	12.9501i	−0.223266	−	0.517589i
$627$	1.43420	−	21.0189i	0.0572764	−	0.839415i
$628$	−0.236008	+	4.05211i	−0.00941776	+	0.161697i
$629$	−0.181295	+	1.02817i	−0.00722869	+	0.0409959i
$630$	−23.2496	−	32.5630i	−0.926286	−	1.29734i
$631$	−4.88620	−	27.7110i	−0.194517	−	1.10316i	−0.913106	−	0.407723i	$-0.866323\pi$
$631$	−4.88620	−	27.7110i	−0.194517	−	1.10316i	0.718589	−	0.695435i	$-0.244788\pi$
$632$	3.42866	−	0.400753i	0.136385	−	0.0159411i
$633$	−6.49001	−	0.824114i	−0.257955	−	0.0327556i
$634$	−4.90764	+	16.3927i	−0.194907	+	0.651036i
$635$	−38.4371	+	9.10976i	−1.52533	+	0.361510i
$636$	−8.57149	−	4.41211i	−0.339882	−	0.174951i
$637$	12.9601	−	30.0449i	0.513498	−	1.19042i
$638$	−3.58379	+	3.00715i	−0.141883	+	0.119054i
$639$	1.84079	+	11.8093i	0.0728204	+	0.467168i
$640$	2.91280	+	2.44413i	0.115138	+	0.0966127i
$641$	−11.9322	+	5.99260i	−0.471295	+	0.236693i	−0.668562	−	0.743656i	$-0.733090\pi$
$641$	−11.9322	+	5.99260i	−0.471295	+	0.236693i	0.197267	+	0.980350i	$0.436794\pi$
$642$	−17.6646	+	18.3540i	−0.697166	+	0.724375i
$643$	45.0701	+	5.26794i	1.77739	+	0.207747i	0.940540	−	0.339682i	$-0.110319\pi$
$643$	45.0701	+	5.26794i	1.77739	+	0.207747i	0.836852	+	0.547429i	$0.184393\pi$
$644$	0.369990	+	6.35249i	0.0145797	+	0.250323i
$645$	10.8083	−	18.2976i	0.425577	−	0.720469i
$646$	−0.319854	+	0.339026i	−0.0125845	+	0.0133388i
$647$	10.1080			0.397388			0.198694	−	0.980062i	$-0.436330\pi$
$647$	10.1080			0.397388			0.198694	+	0.980062i	$0.436330\pi$
$648$	1.91428	−	8.79406i	0.0752000	−	0.345463i
$649$	−16.7331			−0.656831
$650$	−40.0497	+	42.4502i	−1.57088	+	1.66503i
$651$	−1.92707	−	0.0191760i	−0.0755277	−	0.000751566i
$652$	0.211532	+	3.63186i	0.00828423	+	0.142235i
$653$	25.9543	+	3.03362i	1.01567	+	0.118715i	0.607606	−	0.794238i	$-0.292130\pi$
$653$	25.9543	+	3.03362i	1.01567	+	0.118715i	0.408064	+	0.912953i	$0.366204\pi$
$654$	−1.41085	−	4.88912i	−0.0551687	−	0.191180i
$655$	59.3264	−	29.7948i	2.31807	−	1.16418i
$656$	−4.86842	−	4.08509i	−0.190080	−	0.159496i
$657$	39.6744	−	13.5524i	1.54784	−	0.528731i
$658$	12.8324	−	10.7677i	0.500259	−	0.419767i
$659$	−8.94916	+	20.7465i	−0.348610	+	0.808168i	0.650217	+	0.759748i	$0.274678\pi$
$659$	−8.94916	+	20.7465i	−0.348610	+	0.808168i	−0.998827	+	0.0484199i	$0.984581\pi$
$660$	−1.13375	−	23.4904i	−0.0441313	−	0.914364i
$661$	36.7996	−	8.72168i	1.43134	−	0.339234i	0.559421	−	0.828884i	$-0.311023\pi$
$661$	36.7996	−	8.72168i	1.43134	−	0.339234i	0.871919	+	0.489650i	$0.162875\pi$
$662$	−1.80172	+	6.01815i	−0.0700257	+	0.233902i
$663$	0.884926	−	1.16429i	0.0343677	−	0.0452174i
$664$	0.864307	−	0.101023i	0.0335416	−	0.00392045i
$665$	7.88877	+	44.7394i	0.305913	+	1.73492i
$666$	−1.78538	+	22.8199i	−0.0691821	+	0.884255i
$667$	0.412720	−	2.34065i	0.0159806	−	0.0906303i
$668$	−0.548611	+	9.41929i	−0.0212264	+	0.364443i
$669$	−31.1364	+	15.2513i	−1.20380	+	0.589648i
$670$	14.6911	+	34.0579i	0.567569	+	1.31577i
$671$	−43.0554	−	21.6232i	−1.66213	−	0.834755i
$672$	−5.72926	+	2.02095i	−0.221011	+	0.0779598i
$673$	−43.4096	−	10.2883i	−1.67332	−	0.396584i	−0.718914	−	0.695099i	$-0.755360\pi$
$673$	−43.4096	−	10.2883i	−1.67332	−	0.396584i	−0.954405	+	0.298516i	$0.903509\pi$
$674$	−1.16998	+	2.02646i	−0.0450658	+	0.0780563i
$675$	−47.4617	−	12.7561i	−1.82680	−	0.490984i
$676$	−12.5371	−	21.7149i	−0.482197	−	0.835189i
$677$	2.60218	+	8.69190i	0.100010	+	0.334057i	0.993321	−	0.115382i	$-0.0368092\pi$
$677$	2.60218	+	8.69190i	0.100010	+	0.334057i	−0.893311	+	0.449439i	$0.851624\pi$
$678$	−24.3971	+	20.0614i	−0.936967	+	0.770452i
$679$	20.3896	−	13.4104i	0.782481	−	0.514646i
$680$	−0.310701	+	0.417344i	−0.0119148	+	0.0160044i
$681$	7.46501	+	10.2384i	0.286060	+	0.392336i
$682$	−0.946398	−	0.622456i	−0.0362394	−	0.0238351i
$683$	20.2951	−	7.38680i	0.776569	−	0.282648i	0.0768276	−	0.997044i	$-0.475521\pi$
$683$	20.2951	−	7.38680i	0.776569	−	0.282648i	0.699741	+	0.714396i	$0.253299\pi$
$684$	−6.26416	+	8.07369i	−0.239516	+	0.308705i
$685$	−57.7214	−	21.0089i	−2.20542	−	0.802707i
$686$	3.55475	+	4.77486i	0.135721	+	0.182305i
$687$	15.6260	−	3.53958i	0.596168	−	0.135044i
$688$	−2.21436	−	2.34708i	−0.0844216	−	0.0894817i
$689$	−23.5682	−	24.9808i	−0.897877	−	0.951694i
$690$	8.11229	+	8.77177i	0.308830	+	0.333936i
$691$	12.6379	+	16.9757i	0.480769	+	0.645784i	0.974647	−	0.223746i	$-0.0718288\pi$
$691$	12.6379	+	16.9757i	0.480769	+	0.645784i	−0.493879	+	0.869531i	$0.664421\pi$
$692$	12.4175	+	4.51960i	0.472042	+	0.171809i
$693$	33.2364	+	17.5287i	1.26254	+	0.665859i
$694$	31.8974	−	11.6097i	1.21081	−	0.440699i
$695$	−52.5851	−	34.5858i	−1.99467	−	1.31191i
$696$	2.25635	−	0.240997i	0.0855267	−	0.00913495i
$697$	0.519301	−	0.697543i	0.0196699	−	0.0264213i
$698$	15.5183	−	10.2065i	0.587376	−	0.386324i
$699$	13.9577	+	5.23806i	0.527930	+	0.198122i
$700$	9.51467	+	31.7812i	0.359621	+	1.20122i
$701$	9.63781	+	16.6932i	0.364015	+	0.630493i	0.988618	−	0.150450i	$-0.0480723\pi$
$701$	9.63781	+	16.6932i	0.364015	+	0.630493i	−0.624602	+	0.780943i	$0.714739\pi$
$702$	16.8529	−	27.2761i	0.636071	−	1.02947i
$703$	12.9947	−	22.5076i	0.490106	−	0.848888i
$704$	−3.47466	−	0.823509i	−0.130956	−	0.0310372i
$705$	5.76978	−	30.9197i	0.217302	−	1.16450i
$706$	−1.62816	−	0.817693i	−0.0612767	−	0.0307743i
$707$	5.60823	+	13.0013i	0.210919	+	0.488966i
$708$	6.73635	+	4.52723i	0.253167	+	0.170144i
$709$	0.694133	−	11.9178i	0.0260687	−	0.447582i	−0.959867	−	0.280456i	$-0.909514\pi$
$709$	0.694133	−	11.9178i	0.0260687	−	0.447582i	0.985936	−	0.167126i	$-0.0534487\pi$
$710$	2.63052	−	14.9184i	0.0987218	−	0.559879i
$711$	2.77213	+	9.97810i	0.103963	+	0.374208i
$712$	1.45621	+	8.25858i	0.0545738	+	0.309503i
$713$	0.571589	−	0.0668092i	0.0214062	−	0.00250202i
$714$	−0.321651	−	0.766555i	−0.0120375	−	0.0286876i
$715$	24.0290	−	80.2624i	0.898633	−	3.00164i
$716$	13.4256	−	3.18192i	0.501738	−	0.118914i
$717$	−41.5724	+	26.7538i	−1.55255	+	0.999141i
$718$	−4.48330	+	10.3935i	−0.167315	+	0.387881i
$719$	−0.280815	+	0.235632i	−0.0104726	+	0.00878758i	−0.648009	−	0.761633i	$-0.724398\pi$
$719$	−0.280815	+	0.235632i	−0.0104726	+	0.00878758i	0.637536	+	0.770420i	$0.279954\pi$
$720$	−5.89904	+	9.76344i	−0.219844	+	0.363862i
$721$	−3.71271	−	3.11534i	−0.138269	−	0.116021i
$722$	−6.61048	+	3.31991i	−0.246017	+	0.123554i
$723$	10.6640	+	2.63976i	0.396599	+	0.0981736i
$724$	7.70319	+	0.900374i	0.286287	+	0.0334621i
$725$	−0.720488	−	12.3703i	−0.0267583	−	0.459422i
$726$	1.49055	+	2.64208i	0.0553194	+	0.0980566i
$727$	−28.8159	+	30.5430i	−1.06872	+	1.13278i	−0.0779889	+	0.996954i	$0.524850\pi$
$727$	−28.8159	+	30.5430i	−1.06872	+	1.13278i	−0.990733	+	0.135825i	$0.956632\pi$
$728$	−21.6431			−0.802145
$729$	26.9519	+	1.61103i	0.998218	+	0.0596677i
$730$	−53.1387			−1.96675
$731$	0.303001	−	0.321162i	0.0112069	−	0.0118786i
$732$	11.4828	+	20.3539i	0.424416	+	0.752300i
$733$	−3.12616	−	53.6741i	−0.115467	−	1.98250i	−0.176237	−	0.984348i	$-0.556392\pi$
$733$	−3.12616	−	53.6741i	−0.115467	−	1.98250i	0.0607694	−	0.998152i	$-0.480645\pi$
$734$	4.77015	+	0.557551i	0.176070	+	0.0205796i
$735$	−33.9011	−	8.39184i	−1.25046	−	0.309538i
$736$	1.62119	−	0.814194i	0.0597580	−	0.0300116i
$737$	−26.6839	−	22.3905i	−0.982915	−	0.824763i
$738$	9.85958	−	16.3185i	0.362936	−	0.600692i
$739$	19.6431	−	16.4825i	0.722581	−	0.606318i	−0.205517	−	0.978654i	$-0.565887\pi$
$739$	19.6431	−	16.4825i	0.722581	−	0.606318i	0.928098	+	0.372336i	$0.121443\pi$
$740$	11.4910	−	26.6391i	0.422417	−	0.979273i
$741$	−30.6131	+	19.7010i	−1.12460	+	0.723733i
$742$	−18.9963	+	4.50222i	−0.697378	+	0.165282i
$743$	−10.9043	+	36.4229i	−0.400040	+	1.33623i	0.486542	+	0.873657i	$0.338258\pi$
$743$	−10.9043	+	36.4229i	−0.400040	+	1.33623i	−0.886583	+	0.462570i	$0.846927\pi$
$744$	0.212589	+	0.506639i	0.00779388	+	0.0185743i
$745$	21.1267	−	2.46936i	0.774023	−	0.0904704i
$746$	3.66831	+	20.8040i	0.134306	+	0.761688i
$747$	0.698805	+	2.51531i	0.0255679	+	0.0920302i
$748$	0.0848488	−	0.481201i	0.00310238	−	0.0175945i
$749$	−2.99947	+	51.4989i	−0.109598	+	1.88173i
$750$	24.3691	+	16.3775i	0.889834	+	0.598022i
$751$	7.83039	+	18.1529i	0.285735	+	0.662408i	0.999270	−	0.0382118i	$-0.0121661\pi$
$751$	7.83039	+	18.1529i	0.285735	+	0.662408i	−0.713535	+	0.700620i	$0.752907\pi$
$752$	−4.26786	−	2.14340i	−0.155633	−	0.0781617i
$753$	−2.72077	+	14.5804i	−0.0991504	+	0.531338i
$754$	7.86606	+	1.86429i	0.286465	+	0.0678935i
$755$	−22.4314	+	38.8523i	−0.816362	+	1.41398i
$756$	−8.63770	−	16.0489i	−0.314150	−	0.583693i
$757$	−22.2454	−	38.5302i	−0.808524	−	1.40040i	−0.913886	−	0.405971i	$-0.866933\pi$
$757$	−22.2454	−	38.5302i	−0.808524	−	1.40040i	0.105362	−	0.994434i	$-0.466400\pi$
$758$	−4.66630	−	15.5865i	−0.169488	−	0.566128i
$759$	−10.5052	−	3.94239i	−0.381314	−	0.143100i
$760$	10.8212	−	7.11722i	0.392527	−	0.258169i
$761$	19.9164	−	26.7523i	0.721968	−	0.969772i	−0.277989	−	0.960584i	$-0.589668\pi$
$761$	19.9164	−	26.7523i	0.721968	−	0.969772i	0.999958	−	0.00918761i	$-0.00292455\pi$
$762$	−17.8920	+	1.91101i	−0.648158	+	0.0692286i
$763$	−8.60958	−	5.66261i	−0.311688	−	0.205000i
$764$	−0.548869	+	0.199772i	−0.0198574	+	0.00722750i
$765$	−1.38065	−	0.728148i	−0.0499175	−	0.0263262i
$766$	11.2487	+	4.09420i	0.406433	+	0.147929i
$767$	17.2664	+	23.1928i	0.623454	+	0.837444i
$768$	1.17601	+	1.27161i	0.0424356	+	0.0458854i
$769$	25.0218	+	26.5216i	0.902310	+	0.956393i	0.999243	−	0.0388983i	$-0.0123848\pi$
$769$	25.0218	+	26.5216i	0.902310	+	0.956393i	−0.0969333	+	0.995291i	$0.530903\pi$
$770$	−32.6825	−	34.6415i	−1.17780	−	1.24839i
$771$	−5.74024	+	1.30027i	−0.206730	+	0.0468282i
$772$	−12.6933	−	17.0500i	−0.456840	−	0.613643i
$773$	30.0204	+	10.9265i	1.07976	+	0.393001i	0.819818	−	0.572624i	$-0.194074\pi$
$773$	30.0204	+	10.9265i	1.07976	+	0.393001i	0.259942	+	0.965624i	$0.416297\pi$
$774$	5.93409	−	7.64828i	0.213297	−	0.274912i
$775$	2.81934	−	1.02615i	0.101274	−	0.0368606i
$776$	−5.81307	−	3.82331i	−0.208677	−	0.137249i
$777$	27.3090	+	37.4548i	0.979706	+	1.34368i
$778$	4.93780	−	6.63261i	0.177029	−	0.237791i
$779$	−18.0864	+	11.8956i	−0.648014	+	0.426205i
$780$	−31.3889	+	25.8106i	−1.12390	+	0.924167i
$781$	4.08017	+	13.6287i	0.146000	+	0.487674i
$782$	0.124120	+	0.214982i	0.00443853	+	0.00768775i
$783$	1.75691	+	6.57693i	0.0627868	+	0.235040i
$784$	−2.65143	+	4.59242i	−0.0946940	+	0.164015i
$785$	15.0178	+	3.55928i	0.536008	+	0.127036i
$786$	28.5186	−	10.0597i	1.01722	−	0.358817i
$787$	−35.2810	−	17.7188i	−1.25763	−	0.631606i	−0.309928	−	0.950760i	$-0.600305\pi$
$787$	−35.2810	−	17.7188i	−1.25763	−	0.631606i	−0.947703	+	0.319154i	$0.896601\pi$
$788$	−0.215719	−	0.500092i	−0.00768466	−	0.0178150i
$789$	−2.50456	+	1.22678i	−0.0891646	+	0.0436746i
$790$	0.763201	−	13.1037i	0.0271535	−	0.466207i
$791$	−11.1073	+	62.9926i	−0.394930	+	2.23976i
$792$	0.835587	−	10.6801i	0.0296913	−	0.379501i
$793$	14.4569	+	81.9891i	0.513379	+	2.91152i
$794$	−32.7308	+	3.82568i	−1.16157	+	0.135768i
$795$	−22.1812	+	29.1838i	−0.786688	+	1.03504i
$796$	0.636384	−	2.12567i	0.0225560	−	0.0753424i
$797$	−15.4179	+	3.65410i	−0.546129	+	0.129435i	−0.494413	−	0.869227i	$-0.664617\pi$
$797$	−15.4179	+	3.65410i	−0.546129	+	0.129435i	−0.0517155	+	0.998662i	$0.516469\pi$
$798$	0.997622	+	20.6699i	0.0353154	+	0.731705i
$799$	0.258839	−	0.600056i	0.00915707	−	0.0212285i
$800$	7.24537	−	6.07959i	0.256163	−	0.214946i
$801$	−23.8073	+	8.13238i	−0.841189	+	0.287343i
$802$	−11.1915	−	9.39081i	−0.395187	−	0.331601i
$803$	44.5956	−	22.3968i	1.57375	−	0.790365i
$804$	4.68446	+	16.2334i	0.165208	+	0.572506i
$805$	24.0320	+	2.80893i	0.847015	+	0.0990019i
$806$	0.113810	+	1.95405i	0.00400879	+	0.0688283i
$807$	−48.0468	−	0.478107i	−1.69133	−	0.0168302i
$808$	2.77024	−	2.93628i	0.0974566	−	0.103298i
$809$	−33.7382			−1.18617			−0.593085	−	0.805140i	$-0.702090\pi$
$809$	−33.7382			−1.18617			−0.593085	+	0.805140i	$0.702090\pi$
$810$	−31.6665	−	12.9748i	−1.11265	−	0.455887i
$811$	−15.4404			−0.542186			−0.271093	−	0.962553i	$-0.587385\pi$
$811$	−15.4404			−0.542186			−0.271093	+	0.962553i	$0.587385\pi$
$812$	3.15347	−	3.34249i	0.110665	−	0.117298i
$813$	26.9570	−	45.6361i	0.945423	−	1.60053i
$814$	1.58419	+	27.1996i	0.0555260	+	0.953345i
$815$	13.7396	+	1.60593i	0.481278	+	0.0562533i
$816$	−0.164350	+	0.170764i	−0.00575339	+	0.00597794i
$817$	−9.82221	+	4.93290i	−0.343636	+	0.172580i
$818$	−3.91061	−	3.28139i	−0.136731	−	0.114731i
$819$	−10.0002	−	64.1545i	−0.349434	−	2.24174i
$820$	−18.5116	+	15.5331i	−0.646453	+	0.542439i
$821$	9.28297	−	21.5203i	0.323978	−	0.751065i	−0.675923	−	0.736972i	$-0.736255\pi$
$821$	9.28297	−	21.5203i	0.323978	−	0.751065i	0.999901	−	0.0140925i	$-0.00448594\pi$
$822$	−24.8781	−	12.8058i	−0.867722	−	0.446653i
$823$	−19.6089	+	4.64740i	−0.683524	+	0.161998i	−0.557685	−	0.830053i	$-0.688310\pi$
$823$	−19.6089	+	4.64740i	−0.683524	+	0.161998i	−0.125839	+	0.992051i	$0.540162\pi$
$824$	−0.396295	+	1.32372i	−0.0138056	+	0.0461139i
$825$	−58.0327	−	7.36910i	−2.02044	−	0.256559i
$826$	16.3250	−	1.90812i	0.568020	−	0.0663920i
$827$	−9.56425	−	54.2416i	−0.332582	−	1.88616i	−0.449914	−	0.893072i	$-0.648545\pi$
$827$	−9.56425	−	54.2416i	−0.332582	−	1.88616i	0.117332	−	0.993093i	$-0.462566\pi$
$828$	3.16251	+	4.42935i	0.109905	+	0.153931i
$829$	−3.41774	+	19.3830i	−0.118703	+	0.673198i	0.866147	+	0.499789i	$0.166589\pi$
$829$	−3.41774	+	19.3830i	−0.118703	+	0.673198i	−0.984850	+	0.173408i	$0.944522\pi$
$830$	0.192390	−	3.30321i	0.00667795	−	0.114656i
$831$	0.227773	−	3.33813i	0.00790137	−	0.115799i
$832$	2.44398	+	5.66579i	0.0847299	+	0.196426i
$833$	−0.648434	−	0.325656i	−0.0224669	−	0.0112833i
$834$	−21.7780	−	18.6463i	−0.754111	−	0.645669i
$835$	34.9094	+	8.27369i	1.20809	+	0.286323i
$836$	−6.08175	+	10.5339i	−0.210342	+	0.364322i
$837$	−1.40356	+	0.864249i	−0.0485140	+	0.0298728i
$838$	13.6152	+	23.5822i	0.470328	+	0.814632i
$839$	10.2053	+	34.0881i	0.352327	+	1.17685i	0.932138	+	0.362102i	$0.117941\pi$
$839$	10.2053	+	34.0881i	0.352327	+	1.17685i	−0.579812	+	0.814750i	$0.696874\pi$
$840$	3.78479	+	22.7883i	0.130588	+	0.786270i
$841$	22.7951	−	14.9926i	0.786038	−	0.516986i
$842$	2.37447	−	3.18947i	0.0818298	−	0.109916i
$843$	10.9879	−	24.7917i	0.378445	−	0.853871i
$844$	3.15572	+	2.07555i	0.108624	+	0.0714434i
$845$	−89.5921	+	32.6089i	−3.08206	+	1.12178i
$846$	4.38151	−	13.6412i	0.150640	−	0.468993i
$847$	5.77267	+	2.10108i	0.198351	+	0.0721939i
$848$	3.32371	+	4.46452i	0.114137	+	0.153312i
$849$	7.38374	−	23.7989i	0.253409	−	0.816777i
$850$	0.888137	+	0.941370i	0.0304628	+	0.0322887i
$851$	−9.49886	−	10.0682i	−0.325617	−	0.345134i
$852$	2.04474	−	6.59052i	0.0700518	−	0.225787i
$853$	4.76281	+	6.39757i	0.163076	+	0.219049i	0.876148	−	0.482041i	$-0.160105\pi$
$853$	4.76281	+	6.39757i	0.163076	+	0.219049i	−0.713073	+	0.701090i	$0.752697\pi$
$854$	44.4711	+	16.1862i	1.52177	+	0.553879i
$855$	26.0968	+	28.7878i	0.892493	+	0.984521i
$856$	13.8203	−	5.03017i	0.472367	−	0.171928i
$857$	26.2584	+	17.2704i	0.896970	+	0.589947i	0.912113	−	0.409939i	$-0.134450\pi$
$857$	26.2584	+	17.2704i	0.896970	+	0.589947i	−0.0151428	+	0.999885i	$0.504820\pi$
$858$	15.4640	−	34.8908i	0.527931	−	1.19115i
$859$	−9.73790	+	13.0803i	−0.332253	+	0.446293i	−0.936585	−	0.350439i	$-0.886032\pi$
$859$	−9.73790	+	13.0803i	−0.332253	+	0.446293i	0.604333	+	0.796732i	$0.293440\pi$
$860$	−10.2510	+	6.74221i	−0.349557	+	0.229907i
$861$	−6.32584	−	38.0881i	−0.215584	−	1.29804i
$862$	−11.5814	−	38.6846i	−0.394464	−	1.31760i
$863$	−5.98842	−	10.3722i	−0.203848	−	0.353075i	0.745917	−	0.666039i	$-0.232012\pi$
$863$	−5.98842	−	10.3722i	−0.203848	−	0.353075i	−0.949765	+	0.312964i	$0.898678\pi$
$864$	−3.22595	+	4.07348i	−0.109749	+	0.138583i
$865$	25.1232	−	43.5146i	0.854214	−	1.47954i
$866$	−32.1460	−	7.61875i	−1.09237	−	0.258896i
$867$	22.3420	+	19.1292i	0.758774	+	0.649662i
$868$	0.994298	+	0.499355i	0.0337487	+	0.0169492i
$869$	4.88240	+	11.3187i	0.165624	+	0.383960i
$870$	0.587377	−	8.60830i	0.0199139	−	0.291849i
$871$	−3.49980	+	60.0892i	−0.118586	+	2.03605i
$872$	−0.510163	+	2.89328i	−0.0172763	+	0.0979787i
$873$	8.64716	−	18.9977i	0.292662	−	0.642974i
$874$	−1.07306	−	6.08565i	−0.0362969	−	0.205850i
$875$	59.0567	−	6.90273i	1.99648	−	0.233355i
$876$	−24.0127	−	3.04918i	−0.811315	−	0.103022i
$877$	−5.29657	+	17.6918i	−0.178852	+	0.597409i	0.820804	+	0.571210i	$0.193526\pi$
$877$	−5.29657	+	17.6918i	−0.178852	+	0.597409i	−0.999657	+	0.0261993i	$0.991660\pi$
$878$	36.3331	−	8.61109i	1.22618	−	0.290610i
$879$	−17.2844	−	8.89700i	−0.582987	−	0.300088i
$880$	−5.37797	+	12.4675i	−0.181291	+	0.420280i
$881$	16.0785	−	13.4914i	0.541697	−	0.454538i	−0.330421	−	0.943834i	$-0.607191\pi$
$881$	16.0785	−	13.4914i	0.541697	−	0.454538i	0.872118	+	0.489296i	$0.162746\pi$
$882$	−14.8380	−	5.73747i	−0.499620	−	0.193191i
$883$	−3.17319	−	2.66262i	−0.106786	−	0.0896043i	0.587831	−	0.808984i	$-0.299982\pi$
$883$	−3.17319	−	2.66262i	−0.106786	−	0.0896043i	−0.694618	+	0.719379i	$0.744426\pi$
$884$	−0.754520	+	0.378934i	−0.0253773	+	0.0127449i
$885$	21.4006	−	22.2358i	0.719374	−	0.747450i
$886$	20.0164	+	2.33958i	0.672462	+	0.0785996i
$887$	0.0930967	+	1.59841i	0.00312588	+	0.0536693i	0.999510	−	0.0312892i	$-0.00996127\pi$
$887$	0.0930967	+	1.59841i	0.00312588	+	0.0536693i	−0.996384	+	0.0849585i	$0.972924\pi$
$888$	6.72123	−	11.3785i	0.225550	−	0.381838i
$889$	−25.0058	+	26.5046i	−0.838669	+	0.888937i
$890$	31.8868			1.06885
$891$	32.0441	−	2.45788i	1.07352	−	0.0823420i
$892$	20.0173			0.670229
$893$	−11.1637	+	11.8328i	−0.373578	+	0.395970i
$894$	9.68861	+	0.0964100i	0.324036	+	0.00322443i
$895$	−3.05048	−	52.3747i	−0.101966	−	1.75069i
$896$	3.48383	+	0.407201i	0.116387	+	0.0136036i
$897$	5.37569	+	18.6287i	0.179489	+	0.621995i
$898$	15.6411	−	7.85528i	0.521952	−	0.262134i
$899$	−0.318359	−	0.267135i	−0.0106179	−	0.00890946i
$900$	21.3689	+	18.6677i	0.712295	+	0.622257i
$901$	−0.583424	+	0.489551i	−0.0194367	+	0.0163093i
$902$	8.98867	−	20.8381i	0.299290	−	0.693832i
$903$	−0.945056	−	19.5808i	−0.0314495	−	0.651607i
$904$	17.7447	−	4.20556i	0.590179	−	0.139875i
$905$	8.45781	−	28.2511i	0.281147	−	0.939097i
$906$	−12.3659	+	16.2697i	−0.410829	+	0.540526i
$907$	−26.6880	+	3.11939i	−0.886162	+	0.103577i	−0.546982	−	0.837144i	$-0.684224\pi$
$907$	−26.6880	+	3.11939i	−0.886162	+	0.103577i	−0.339180	+	0.940722i	$0.610149\pi$
$908$	−1.27033	−	7.20439i	−0.0421573	−	0.239086i
$909$	9.98372	+	6.85485i	0.331139	+	0.227361i
$910$	−14.2904	+	81.0451i	−0.473723	+	2.68662i
$911$	−1.86958	+	32.0995i	−0.0619421	+	1.06350i	0.813931	+	0.580962i	$0.197324\pi$
$911$	−1.86958	+	32.0995i	−0.0619421	+	1.06350i	−0.875873	+	0.482542i	$0.839714\pi$
$912$	5.29837	−	2.59525i	0.175447	−	0.0859373i
$913$	1.23077	+	2.85324i	0.0407325	+	0.0944285i
$914$	24.8720	+	12.4912i	0.822692	+	0.413171i
$915$	83.7994	−	29.5595i	2.77032	−	0.977208i
$916$	−9.00088	−	2.13325i	−0.297397	−	0.0704845i
$917$	30.6200	−	53.0355i	1.01116	−	1.75139i
$918$	−0.582117	−	0.408265i	−0.0192127	−	0.0134747i
$919$	2.42523	+	4.20062i	0.0800009	+	0.138566i	0.903250	−	0.429115i	$-0.141174\pi$
$919$	2.42523	+	4.20062i	0.0800009	+	0.138566i	−0.823249	+	0.567680i	$0.807841\pi$
$920$	−1.97841	−	6.60835i	−0.0652263	−	0.217871i
$921$	−8.48575	+	6.97769i	−0.279615	+	0.229923i
$922$	0.548243	−	0.360585i	0.0180554	−	0.0118752i
$923$	14.6798	−	19.7184i	0.483192	−	0.649039i
$924$	−12.7811	−	17.5294i	−0.420466	−	0.576676i
$925$	−60.2928	−	39.6552i	−1.98241	−	1.30385i
$926$	−37.5615	+	13.6713i	−1.23435	+	0.449266i
$927$	−4.10687	−	0.563077i	−0.134887	−	0.0184939i
$928$	−1.23110	−	0.448085i	−0.0404130	−	0.0147091i
$929$	22.0831	+	29.6627i	0.724522	+	0.973202i	0.999929	+	0.0118742i	$0.00377978\pi$
$929$	22.0831	+	29.6627i	0.724522	+	0.973202i	−0.275408	+	0.961328i	$0.588813\pi$
$930$	2.03754	−	0.461542i	0.0668136	−	0.0151346i
$931$	12.3956	+	13.1386i	0.406249	+	0.430599i
$932$	−5.90667	−	6.26070i	−0.193479	−	0.205076i
$933$	38.6563	+	41.7988i	1.26555	+	1.36843i
$934$	−12.0155	−	16.1396i	−0.393159	−	0.528105i
$935$	−1.74589	−	0.635453i	−0.0570968	−	0.0207815i
$936$	−15.6653	+	9.86234i	−0.512037	+	0.322361i
$937$	−38.4478	+	13.9939i	−1.25604	+	0.457160i	−0.882437	−	0.470431i	$-0.844099\pi$
$937$	−38.4478	+	13.9939i	−1.25604	+	0.457160i	−0.373599	+	0.927590i	$0.621876\pi$
$938$	28.5864	+	18.8016i	0.933380	+	0.613894i
$939$	−24.2898	+	2.59435i	−0.792668	+	0.0846634i
$940$	−10.8442	+	14.5663i	−0.353699	+	0.475100i
$941$	24.5476	−	16.1452i	0.800229	−	0.526319i	−0.0822826	−	0.996609i	$-0.526221\pi$
$941$	24.5476	−	16.1452i	0.800229	−	0.526319i	0.882512	+	0.470290i	$0.155851\pi$
$942$	6.58212	+	2.47014i	0.214457	+	0.0804814i
$943$	3.30669	+	11.0451i	0.107681	+	0.359679i
$944$	−2.34297	−	4.05814i	−0.0762572	−	0.132081i
$945$	−65.8004	+	21.7482i	−2.14049	+	0.707469i
$946$	5.76129	−	9.97885i	0.187316	−	0.324441i
$947$	−51.9003	−	12.3006i	−1.68653	−	0.399715i	−0.728198	−	0.685367i	$-0.759642\pi$
$947$	−51.9003	−	12.3006i	−1.68653	−	0.399715i	−0.958334	+	0.285651i	$0.907790\pi$
$948$	1.09679	−	5.87759i	0.0356221	−	0.190895i
$949$	−77.0600	−	38.7010i	−2.50147	−	1.25629i
$950$	−12.7605	−	29.5822i	−0.414006	−	0.959774i
$951$	24.5989	+	16.5320i	0.797675	+	0.536085i
$952$	−0.0279068	+	0.479142i	−0.000904465	+	0.0155291i
$953$	3.46243	−	19.6364i	0.112159	−	0.636085i	−0.875959	−	0.482386i	$-0.839770\pi$
$953$	3.46243	−	19.6364i	0.112159	−	0.636085i	0.988118	−	0.153699i	$-0.0491187\pi$
$954$	−11.6980	+	11.9150i	−0.378738	+	0.385762i
$955$	0.385665	+	2.18721i	0.0124798	+	0.0707766i
$956$	28.3496	−	3.31359i	0.916891	−	0.107169i
$957$	3.13526	+	7.47192i	0.101349	+	0.241533i
$958$	4.74055	−	15.8345i	0.153160	−	0.511591i
$959$	−55.1354	+	13.0673i	−1.78041	+	0.421966i
$960$	5.53820	−	3.56410i	0.178745	−	0.115031i
$961$	−12.2386	+	28.3723i	−0.394794	+	0.915236i
$962$	36.0652	−	30.2623i	1.16279	−	0.975695i
$963$	21.2961	+	38.6419i	0.686257	+	1.24522i
$964$	−4.85879	−	4.07701i	−0.156491	−	0.131312i
$965$	−72.2269	+	36.2737i	−2.32507	+	1.16769i
$966$	10.6986	+	2.64831i	0.344221	+	0.0852081i
$967$	−9.32149	−	1.08953i	−0.299759	−	0.0350368i	−0.0351160	−	0.999383i	$-0.511180\pi$
$967$	−9.32149	−	1.08953i	−0.299759	−	0.0350368i	−0.264643	+	0.964346i	$0.585254\pi$
$968$	−0.101835	−	1.74845i	−0.00327311	−	0.0561972i
$969$	0.396674	+	0.703126i	0.0127430	+	0.0225877i
$970$	−18.1551	+	19.2433i	−0.582925	+	0.617865i
$971$	24.4749			0.785436			0.392718	−	0.919659i	$-0.371535\pi$
$971$	24.4749			0.785436			0.392718	+	0.919659i	$0.371535\pi$
$972$	−13.5652	−	7.68022i	−0.435104	−	0.246343i
$973$	−58.0590			−1.86129
$974$	15.6935	−	16.6342i	0.502853	−	0.532993i
$975$	49.6685	+	88.0400i	1.59066	+	2.81954i
$976$	−0.784513	−	13.4696i	−0.0251117	−	0.431150i
$977$	−0.364697	−	0.0426270i	−0.0116677	−	0.00136376i	0.110257	−	0.993903i	$-0.464833\pi$
$977$	−0.364697	−	0.0426270i	−0.0116677	−	0.00136376i	−0.121925	+	0.992539i	$0.538907\pi$
$978$	6.11662	+	1.51410i	0.195588	+	0.0484156i
$979$	−26.7604	+	13.4396i	−0.855265	+	0.429530i
$980$	15.4462	+	12.9609i	0.493410	+	0.414020i
$981$	−8.81199	−	0.175391i	−0.281345	−	0.00559981i
$982$	16.0344	−	13.4545i	0.511679	−	0.429350i
$983$	−0.429299	+	0.995227i	−0.0136925	+	0.0317428i	−0.924925	−	0.380149i	$-0.875873\pi$
$983$	−0.429299	+	0.995227i	−0.0136925	+	0.0317428i	0.911233	+	0.411892i	$0.135132\pi$
$984$	−9.25648	+	5.95699i	−0.295086	+	0.189902i
$985$	−2.01509	+	0.477585i	−0.0642061	+	0.0152171i
$986$	0.0514149	−	0.171738i	0.00163738	−	0.00546925i
$987$	−11.2264	−	26.7546i	−0.357340	−	0.851608i
$988$	20.8760	−	2.44006i	0.664155	−	0.0776286i
$989$	1.01652	+	5.76499i	0.0323235	+	0.183316i
$990$	−39.4412	−	10.1808i	−1.25352	−	0.323567i
$991$	7.72758	−	43.8253i	0.245475	−	1.39216i	−0.573913	−	0.818917i	$-0.694575\pi$
$991$	7.72758	−	43.8253i	0.245475	−	1.39216i	0.819387	−	0.573240i	$-0.194314\pi$
$992$	0.0184444	−	0.316679i	0.000585612	−	0.0100546i
$993$	9.03087	+	6.06929i	0.286586	+	0.192603i
$994$	−5.53479	−	12.8311i	−0.175553	−	0.406977i
$995$	−7.53965	−	3.78655i	−0.239023	−	0.120042i
$996$	0.276482	−	1.48164i	0.00876066	−	0.0469475i
$997$	30.0328	+	7.11791i	0.951149	+	0.225426i	0.676769	−	0.736195i	$-0.263379\pi$
$997$	30.0328	+	7.11791i	0.951149	+	0.225426i	0.274379	+	0.961622i	$0.411528\pi$
$998$	−9.03864	+	15.6554i	−0.286113	+	0.495562i
$999$	36.8338	+	14.6657i	1.16537	+	0.464001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.151.3	yes	90
3.2	odd	2		486.2.g.b.127.5		90
81.22	even	27	inner	162.2.g.b.103.3	✓	90
81.59	odd	54		486.2.g.b.199.5		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.103.3	✓	90	81.22	even	27	inner
162.2.g.b.151.3	yes	90	1.1	even	1	trivial
486.2.g.b.127.5		90	3.2	odd	2
486.2.g.b.199.5		90	81.59	odd	54

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686242 + 0.727374i) q^{2} +(0.851057 + 1.50854i) q^{3} +(-0.0581448 - 0.998308i) q^{4} +(-3.77668 - 0.441430i) q^{5} +(-1.68131 - 0.416189i) q^{6} +(-3.13446 + 1.57418i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-1.55140 + 2.56771i) q^{9} +O(q^{10})\)	\(q+(-0.686242 + 0.727374i) q^{2} +(0.851057 + 1.50854i) q^{3} +(-0.0581448 - 0.998308i) q^{4} +(-3.77668 - 0.441430i) q^{5} +(-1.68131 - 0.416189i) q^{6} +(-3.13446 + 1.57418i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-1.55140 + 2.56771i) q^{9} +(2.91280 - 2.44413i) q^{10} +(-1.41437 + 3.27887i) q^{11} +(1.45651 - 0.937331i) q^{12} +(6.00411 - 1.42300i) q^{13} +(1.00598 - 3.36019i) q^{14} +(-2.54825 - 6.07296i) q^{15} +(-0.993238 + 0.116093i) q^{16} +(-0.0237611 - 0.134756i) q^{17} +(-0.803048 - 2.89052i) q^{18} +(-0.591493 + 3.35452i) q^{19} +(-0.221089 + 3.79596i) q^{20} +(-5.04232 - 3.38874i) q^{21} +(-1.41437 - 3.27887i) q^{22} +(1.62119 + 0.814194i) q^{23} +(-0.317725 + 1.70266i) q^{24} +(9.20321 + 2.18120i) q^{25} +(-3.08522 + 5.34375i) q^{26} +(-5.19384 - 0.155090i) q^{27} +(1.75377 + 3.03762i) q^{28} +(-0.375745 - 1.25508i) q^{29} +(6.16603 + 2.31399i) q^{30} +(0.265030 - 0.174313i) q^{31} +(0.597159 - 0.802123i) q^{32} +(-6.15002 + 0.656872i) q^{33} +(0.114324 + 0.0751919i) q^{34} +(12.5327 - 4.56154i) q^{35} +(2.65357 + 1.39948i) q^{36} +(-7.16975 - 2.60958i) q^{37} +(-2.03408 - 2.73225i) q^{38} +(7.25649 + 7.84640i) q^{39} +(-2.60936 - 2.76576i) q^{40} +(4.36125 + 4.62265i) q^{41} +(5.92513 - 1.34216i) q^{42} +(1.92691 + 2.58828i) q^{43} +(3.35556 + 1.22132i) q^{44} +(6.99262 - 9.01259i) q^{45} +(-1.70475 + 0.620480i) q^{46} +(3.99017 + 2.62437i) q^{47} +(-1.02043 - 1.39954i) q^{48} +(3.16665 - 4.25355i) q^{49} +(-7.90218 + 5.19734i) q^{50} +(0.183063 - 0.150530i) q^{51} +(-1.76970 - 5.91121i) q^{52} +(-2.78294 - 4.82020i) q^{53} +(3.67704 - 3.67143i) q^{54} +(6.78900 - 11.7589i) q^{55} +(-3.41300 - 0.808895i) q^{56} +(-5.56384 + 1.96260i) q^{57} +(1.17076 + 0.587978i) q^{58} +(1.85601 + 4.30271i) q^{59} +(-5.91452 + 2.89705i) q^{60} +(-0.784513 + 13.4696i) q^{61} +(-0.0550839 + 0.312396i) q^{62} +(0.820759 - 10.4906i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-23.3037 + 2.72382i) q^{65} +(3.74261 - 4.92414i) q^{66} +(-2.79770 + 9.34496i) q^{67} +(-0.133146 + 0.0315562i) q^{68} +(0.151481 + 3.13857i) q^{69} +(-5.28253 + 12.2463i) q^{70} +(3.05189 - 2.56084i) q^{71} +(-2.83894 + 0.969758i) q^{72} +(-10.7055 - 8.98301i) q^{73} +(6.81832 - 3.42429i) q^{74} +(4.54202 + 15.7398i) q^{75} +(3.38324 + 0.395444i) q^{76} +(-0.728272 - 12.5039i) q^{77} +(-10.6870 - 0.106345i) q^{78} +(2.36891 - 2.51090i) q^{79} +3.80239 q^{80} +(-4.18629 - 7.96712i) q^{81} -6.35527 q^{82} +(0.597161 - 0.632954i) q^{83} +(-3.08982 + 5.23083i) q^{84} +(0.0302527 + 0.519418i) q^{85} +(-3.20497 - 0.374608i) q^{86} +(1.57355 - 1.63497i) q^{87} +(-3.19108 + 1.60262i) q^{88} +(6.42404 + 5.39041i) q^{89} +(1.75689 + 11.2711i) q^{90} +(-16.5795 + 13.9119i) q^{91} +(0.718553 - 1.66579i) q^{92} +(0.488514 + 0.251459i) q^{93} +(-4.64712 + 1.10139i) q^{94} +(3.71467 - 12.4078i) q^{95} +(1.71825 + 0.218187i) q^{96} +(-6.91065 + 0.807739i) q^{97} +(0.920833 + 5.22230i) q^{98} +(-6.22494 - 8.71853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more