LMFDB - Embedded newform 546.2.s.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(43,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.127
Dual form			546.2.s.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.732051i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.732051i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.00000 q^{12} +(1.59808 + 3.23205i) q^{13} -1.00000 q^{14} +(-0.633975 + 0.366025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.86603 - 3.23205i) q^{17} -1.00000i q^{18} +(0.866025 + 0.500000i) q^{19} +(-0.633975 - 0.366025i) q^{20} -1.00000i q^{21} +(-0.866025 + 1.50000i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(0.866025 - 0.500000i) q^{24} +4.46410 q^{25} +(-3.00000 - 2.00000i) q^{26} +1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(-3.23205 - 5.59808i) q^{29} +(0.366025 - 0.633975i) q^{30} -2.19615i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} +3.73205i q^{34} +(0.366025 - 0.633975i) q^{35} +(0.500000 + 0.866025i) q^{36} +(5.83013 - 3.36603i) q^{37} -1.00000 q^{38} +(2.00000 - 3.00000i) q^{39} +0.732051 q^{40} +(2.59808 - 1.50000i) q^{41} +(0.500000 + 0.866025i) q^{42} +(1.63397 - 2.83013i) q^{43} -1.73205i q^{44} +(0.633975 + 0.366025i) q^{45} +(3.00000 + 1.73205i) q^{46} -2.46410i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-3.86603 + 2.23205i) q^{50} -3.73205 q^{51} +(3.59808 + 0.232051i) q^{52} +7.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(-0.500000 + 0.866025i) q^{56} -1.00000i q^{57} +(5.59808 + 3.23205i) q^{58} +(0.803848 + 0.464102i) q^{59} +0.732051i q^{60} +(-2.59808 + 4.50000i) q^{61} +(1.09808 + 1.90192i) q^{62} +(-0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(2.36603 - 1.16987i) q^{65} +1.73205 q^{66} +(7.73205 - 4.46410i) q^{67} +(-1.86603 - 3.23205i) q^{68} +(-1.73205 + 3.00000i) q^{69} +0.732051i q^{70} +(-1.90192 - 1.09808i) q^{71} +(-0.866025 - 0.500000i) q^{72} +5.46410i q^{73} +(-3.36603 + 5.83013i) q^{74} +(-2.23205 - 3.86603i) q^{75} +(0.866025 - 0.500000i) q^{76} +1.73205 q^{77} +(-0.232051 + 3.59808i) q^{78} +2.07180 q^{79} +(-0.633975 + 0.366025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{82} -0.196152i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-2.36603 - 1.36603i) q^{85} +3.26795i q^{86} +(-3.23205 + 5.59808i) q^{87} +(0.866025 + 1.50000i) q^{88} +(-9.06218 + 5.23205i) q^{89} -0.732051 q^{90} +(-0.232051 + 3.59808i) q^{91} -3.46410 q^{92} +(-1.90192 + 1.09808i) q^{93} +(1.23205 + 2.13397i) q^{94} +(0.366025 - 0.633975i) q^{95} -1.00000i q^{96} +(13.5622 + 7.83013i) q^{97} +(-0.866025 - 0.500000i) q^{98} +1.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{20} + 4 q^{25} - 12 q^{26} + 4 q^{27} - 6 q^{29} - 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} + 6 q^{37} - 4 q^{38} + 8 q^{39} - 4 q^{40} + 2 q^{42} + 10 q^{43} + 6 q^{45} + 12 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{50} - 8 q^{51} + 4 q^{52} + 28 q^{53} - 6 q^{55} - 2 q^{56} + 12 q^{58} + 24 q^{59} - 6 q^{62} - 4 q^{64} + 6 q^{65} + 24 q^{67} - 4 q^{68} - 18 q^{71} - 10 q^{74} - 2 q^{75} + 6 q^{78} + 36 q^{79} - 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{85} - 6 q^{87} - 12 q^{89} + 4 q^{90} + 6 q^{91} - 18 q^{93} - 2 q^{94} - 2 q^{95} + 30 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^20 + 4 * q^25 - 12 * q^26 + 4 * q^27 - 6 * q^29 - 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 + 6 * q^37 - 4 * q^38 + 8 * q^39 - 4 * q^40 + 2 * q^42 + 10 * q^43 + 6 * q^45 + 12 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^50 - 8 * q^51 + 4 * q^52 + 28 * q^53 - 6 * q^55 - 2 * q^56 + 12 * q^58 + 24 * q^59 - 6 * q^62 - 4 * q^64 + 6 * q^65 + 24 * q^67 - 4 * q^68 - 18 * q^71 - 10 * q^74 - 2 * q^75 + 6 * q^78 + 36 * q^79 - 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^85 - 6 * q^87 - 12 * q^89 + 4 * q^90 + 6 * q^91 - 18 * q^93 - 2 * q^94 - 2 * q^95 + 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	0.732051i		−	0.327383i	−0.986512	−	0.163692i	$-0.947660\pi$
$5$		−	0.732051i		−	0.327383i	0.986512	−	0.163692i	$-0.0523402\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.366025	+	0.633975i	0.115747	+	0.200480i
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$	−1.00000			−0.288675
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$14$	−1.00000			−0.267261
$15$	−0.633975	+	0.366025i	−0.163692	+	0.0945074i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.86603	−	3.23205i	0.452578	−	0.783887i	−0.545968	−	0.837806i	$-0.683838\pi$
$17$	1.86603	−	3.23205i	0.452578	−	0.783887i	0.998545	+	0.0539188i	$0.0171712\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i	0.596040	−	0.802955i	$-0.296740\pi$
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	−0.633975	−	0.366025i	−0.141761	−	0.0818458i
$21$		−	1.00000i		−	0.218218i
$22$	−0.866025	+	1.50000i	−0.184637	+	0.319801i
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	0.626994	−	0.779024i	$-0.284285\pi$
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	−0.988152	+	0.153481i	$0.950952\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	4.46410			0.892820
$26$	−3.00000	−	2.00000i	−0.588348	−	0.392232i
$27$	1.00000			0.192450
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	−3.23205	−	5.59808i	−0.600177	−	1.03954i	−0.992794	−	0.119835i	$-0.961764\pi$
$29$	−3.23205	−	5.59808i	−0.600177	−	1.03954i	0.392617	−	0.919702i	$-0.371570\pi$
$30$	0.366025	−	0.633975i	0.0668268	−	0.115747i
$31$		−	2.19615i		−	0.394441i	−0.980359	−	0.197220i	$-0.936809\pi$
$31$		−	2.19615i		−	0.394441i	0.980359	−	0.197220i	$-0.0631914\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.50000	−	0.866025i	−0.261116	−	0.150756i
$34$			3.73205i			0.640041i
$35$	0.366025	−	0.633975i	0.0618696	−	0.107161i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	5.83013	−	3.36603i	0.958467	−	0.553371i	0.0627661	−	0.998028i	$-0.480008\pi$
$37$	5.83013	−	3.36603i	0.958467	−	0.553371i	0.895701	+	0.444657i	$0.146674\pi$
$38$	−1.00000			−0.162221
$39$	2.00000	−	3.00000i	0.320256	−	0.480384i
$40$	0.732051			0.115747
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	1.63397	−	2.83013i	0.249179	−	0.431590i	−0.714119	−	0.700024i	$-0.753173\pi$
$43$	1.63397	−	2.83013i	0.249179	−	0.431590i	0.963298	+	0.268434i	$0.0865060\pi$
$44$		−	1.73205i		−	0.261116i
$45$	0.633975	+	0.366025i	0.0945074	+	0.0545638i
$46$	3.00000	+	1.73205i	0.442326	+	0.255377i
$47$		−	2.46410i		−	0.359426i	−0.983719	−	0.179713i	$-0.942483\pi$
$47$		−	2.46410i		−	0.359426i	0.983719	−	0.179713i	$-0.0575169\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−3.86603	+	2.23205i	−0.546739	+	0.315660i
$51$	−3.73205			−0.522592
$52$	3.59808	+	0.232051i	0.498963	+	0.0321797i
$53$	7.00000			0.961524			0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000			0.961524			0.480762	+	0.876851i	$0.340360\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−0.633975	−	1.09808i	−0.0854851	−	0.148065i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		−	1.00000i		−	0.132453i
$58$	5.59808	+	3.23205i	0.735063	+	0.424389i
$59$	0.803848	+	0.464102i	0.104652	+	0.0604209i	0.551413	−	0.834233i	$-0.314089\pi$
$59$	0.803848	+	0.464102i	0.104652	+	0.0604209i	−0.446760	+	0.894654i	$0.647422\pi$
$60$			0.732051i			0.0945074i
$61$	−2.59808	+	4.50000i	−0.332650	+	0.576166i	−0.983030	−	0.183442i	$-0.941276\pi$
$61$	−2.59808	+	4.50000i	−0.332650	+	0.576166i	0.650381	+	0.759608i	$0.274609\pi$
$62$	1.09808	+	1.90192i	0.139456	+	0.241545i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	−1.00000			−0.125000
$65$	2.36603	−	1.16987i	0.293469	−	0.145105i
$66$	1.73205			0.213201
$67$	7.73205	−	4.46410i	0.944620	−	0.545377i	0.0532147	−	0.998583i	$-0.483053\pi$
$67$	7.73205	−	4.46410i	0.944620	−	0.545377i	0.891406	+	0.453206i	$0.149720\pi$
$68$	−1.86603	−	3.23205i	−0.226289	−	0.391944i
$69$	−1.73205	+	3.00000i	−0.208514	+	0.361158i
$70$			0.732051i			0.0874968i
$71$	−1.90192	−	1.09808i	−0.225717	−	0.130318i	0.382878	−	0.923799i	$-0.374933\pi$
$71$	−1.90192	−	1.09808i	−0.225717	−	0.130318i	−0.608595	+	0.793481i	$0.708266\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			5.46410i			0.639525i	0.947498	+	0.319762i	$0.103603\pi$
$73$			5.46410i			0.639525i	−0.947498	+	0.319762i	$0.896397\pi$
$74$	−3.36603	+	5.83013i	−0.391293	+	0.677738i
$75$	−2.23205	−	3.86603i	−0.257735	−	0.446410i
$76$	0.866025	−	0.500000i	0.0993399	−	0.0573539i
$77$	1.73205			0.197386
$78$	−0.232051	+	3.59808i	−0.0262746	+	0.407402i
$79$	2.07180			0.233095			0.116548	−	0.993185i	$-0.462817\pi$
$79$	2.07180			0.233095			0.116548	+	0.993185i	$0.462817\pi$
$80$	−0.633975	+	0.366025i	−0.0708805	+	0.0409229i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$		−	0.196152i		−	0.0215305i	−0.999942	−	0.0107653i	$-0.996573\pi$
$83$		−	0.196152i		−	0.0215305i	0.999942	−	0.0107653i	$-0.00342676\pi$
$84$	−0.866025	−	0.500000i	−0.0944911	−	0.0545545i
$85$	−2.36603	−	1.36603i	−0.256631	−	0.148166i
$86$			3.26795i			0.352392i
$87$	−3.23205	+	5.59808i	−0.346512	+	0.600177i
$88$	0.866025	+	1.50000i	0.0923186	+	0.159901i
$89$	−9.06218	+	5.23205i	−0.960589	+	0.554596i	−0.896354	−	0.443339i	$-0.853794\pi$
$89$	−9.06218	+	5.23205i	−0.960589	+	0.554596i	−0.0642347	+	0.997935i	$0.520461\pi$
$90$	−0.732051			−0.0771649
$91$	−0.232051	+	3.59808i	−0.0243255	+	0.377181i
$92$	−3.46410			−0.361158
$93$	−1.90192	+	1.09808i	−0.197220	+	0.113865i
$94$	1.23205	+	2.13397i	0.127076	+	0.220103i
$95$	0.366025	−	0.633975i	0.0375534	−	0.0650444i
$96$		−	1.00000i		−	0.102062i
$97$	13.5622	+	7.83013i	1.37703	+	0.795029i	0.991801	−	0.127792i	$-0.0407889\pi$
$97$	13.5622	+	7.83013i	1.37703	+	0.795029i	0.385230	+	0.922821i	$0.374122\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$			1.73205i			0.174078i
$100$	2.23205	−	3.86603i	0.223205	−	0.386603i
$101$	1.53590	+	2.66025i	0.152828	+	0.264705i	0.932266	−	0.361774i	$-0.117829\pi$
$101$	1.53590	+	2.66025i	0.152828	+	0.264705i	−0.779438	+	0.626479i	$0.784495\pi$
$102$	3.23205	−	1.86603i	0.320021	−	0.184764i
$103$	−14.7321			−1.45159			−0.725796	−	0.687910i	$-0.758528\pi$
$103$	−14.7321			−1.45159			−0.725796	+	0.687910i	$0.758528\pi$
$104$	−3.23205	+	1.59808i	−0.316929	+	0.156704i
$105$	−0.732051			−0.0714408
$106$	−6.06218	+	3.50000i	−0.588811	+	0.339950i
$107$	−5.42820	−	9.40192i	−0.524764	−	0.908918i	−0.999584	−	0.0288353i	$-0.990820\pi$
$107$	−5.42820	−	9.40192i	−0.524764	−	0.908918i	0.474820	−	0.880083i	$-0.342513\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	4.73205i		−	0.453248i	−0.973982	−	0.226624i	$-0.927231\pi$
$109$		−	4.73205i		−	0.453248i	0.973982	−	0.226624i	$-0.0727689\pi$
$110$	1.09808	+	0.633975i	0.104697	+	0.0604471i
$111$	−5.83013	−	3.36603i	−0.553371	−	0.319489i
$112$		−	1.00000i		−	0.0944911i
$113$	−7.63397	+	13.2224i	−0.718144	+	1.24386i	0.243590	+	0.969878i	$0.421675\pi$
$113$	−7.63397	+	13.2224i	−0.718144	+	1.24386i	−0.961734	+	0.273984i	$0.911659\pi$
$114$	0.500000	+	0.866025i	0.0468293	+	0.0811107i
$115$	−2.19615	+	1.26795i	−0.204792	+	0.118237i
$116$	−6.46410			−0.600177
$117$	−3.59808	−	0.232051i	−0.332642	−	0.0214531i
$118$	−0.928203			−0.0854480
$119$	3.23205	−	1.86603i	0.296282	−	0.171058i
$120$	−0.366025	−	0.633975i	−0.0334134	−	0.0578737i
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$		−	5.19615i		−	0.470438i
$123$	−2.59808	−	1.50000i	−0.234261	−	0.135250i
$124$	−1.90192	−	1.09808i	−0.170798	−	0.0986102i
$125$		−	6.92820i		−	0.619677i
$126$	0.500000	−	0.866025i	0.0445435	−	0.0771517i
$127$	−7.73205	−	13.3923i	−0.686109	−	1.18837i	−0.973087	−	0.230438i	$-0.925984\pi$
$127$	−7.73205	−	13.3923i	−0.686109	−	1.18837i	0.286978	−	0.957937i	$-0.407349\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.26795			−0.287727
$130$	−1.46410	+	2.19615i	−0.128410	+	0.192615i
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$	−1.50000	+	0.866025i	−0.130558	+	0.0753778i
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	−4.46410	+	7.73205i	−0.385640	+	0.667947i
$135$		−	0.732051i		−	0.0630049i
$136$	3.23205	+	1.86603i	0.277146	+	0.160010i
$137$	12.4641	+	7.19615i	1.06488	+	0.614809i	0.926778	−	0.375609i	$-0.122567\pi$
$137$	12.4641	+	7.19615i	1.06488	+	0.614809i	0.138102	+	0.990418i	$0.455900\pi$
$138$		−	3.46410i		−	0.294884i
$139$	−5.79423	+	10.0359i	−0.491460	+	0.851234i	−0.999952	−	0.00983316i	$-0.996870\pi$
$139$	−5.79423	+	10.0359i	−0.491460	+	0.851234i	0.508492	+	0.861067i	$0.330203\pi$
$140$	−0.366025	−	0.633975i	−0.0309348	−	0.0535806i
$141$	−2.13397	+	1.23205i	−0.179713	+	0.103757i
$142$	2.19615			0.184297
$143$	5.19615	+	3.46410i	0.434524	+	0.289683i
$144$	1.00000			0.0833333
$145$	−4.09808	+	2.36603i	−0.340327	+	0.196488i
$146$	−2.73205	−	4.73205i	−0.226106	−	0.391627i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		−	6.73205i		−	0.553371i
$149$	12.0000	+	6.92820i	0.983078	+	0.567581i	0.903198	−	0.429224i	$-0.141213\pi$
$149$	12.0000	+	6.92820i	0.983078	+	0.567581i	0.0798802	+	0.996804i	$0.474546\pi$
$150$	3.86603	+	2.23205i	0.315660	+	0.182246i
$151$		−	5.19615i		−	0.422857i	−0.977393	−	0.211428i	$-0.932188\pi$
$151$		−	5.19615i		−	0.422857i	0.977393	−	0.211428i	$-0.0678115\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	1.86603	+	3.23205i	0.150859	+	0.261296i
$154$	−1.50000	+	0.866025i	−0.120873	+	0.0697863i
$155$	−1.60770			−0.129133
$156$	−1.59808	−	3.23205i	−0.127948	−	0.258771i
$157$	−0.535898			−0.0427693			−0.0213847	−	0.999771i	$-0.506807\pi$
$157$	−0.535898			−0.0427693			−0.0213847	+	0.999771i	$0.506807\pi$
$158$	−1.79423	+	1.03590i	−0.142741	+	0.0824117i
$159$	−3.50000	−	6.06218i	−0.277568	−	0.480762i
$160$	0.366025	−	0.633975i	0.0289368	−	0.0501201i
$161$		−	3.46410i		−	0.273009i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	2.36603	+	1.36603i	0.185321	+	0.106995i	0.589790	−	0.807556i	$-0.299210\pi$
$163$	2.36603	+	1.36603i	0.185321	+	0.106995i	−0.404469	+	0.914552i	$0.632544\pi$
$164$		−	3.00000i		−	0.234261i
$165$	−0.633975	+	1.09808i	−0.0493549	+	0.0854851i
$166$	0.0980762	+	0.169873i	0.00761219	+	0.0131847i
$167$	−12.0000	+	6.92820i	−0.928588	+	0.536120i	−0.886365	−	0.462988i	$-0.846777\pi$
$167$	−12.0000	+	6.92820i	−0.928588	+	0.536120i	−0.0422232	+	0.999108i	$0.513444\pi$
$168$	1.00000			0.0771517
$169$	−7.89230	+	10.3301i	−0.607100	+	0.794625i
$170$	2.73205			0.209539
$171$	−0.866025	+	0.500000i	−0.0662266	+	0.0382360i
$172$	−1.63397	−	2.83013i	−0.124589	−	0.215795i
$173$	−4.56218	+	7.90192i	−0.346856	+	0.600772i	−0.985689	−	0.168573i	$-0.946084\pi$
$173$	−4.56218	+	7.90192i	−0.346856	+	0.600772i	0.638833	+	0.769345i	$0.279417\pi$
$174$		−	6.46410i		−	0.490042i
$175$	3.86603	+	2.23205i	0.292244	+	0.168727i
$176$	−1.50000	−	0.866025i	−0.113067	−	0.0652791i
$177$		−	0.928203i		−	0.0697680i
$178$	5.23205	−	9.06218i	0.392159	−	0.679239i
$179$	5.73205	+	9.92820i	0.428434	+	0.742069i	0.996734	−	0.0807523i	$-0.0257323\pi$
$179$	5.73205	+	9.92820i	0.428434	+	0.742069i	−0.568301	+	0.822821i	$0.692399\pi$
$180$	0.633975	−	0.366025i	0.0472537	−	0.0272819i
$181$	2.66025			0.197735			0.0988676	−	0.995101i	$-0.468478\pi$
$181$	2.66025			0.197735			0.0988676	+	0.995101i	$0.468478\pi$
$182$	−1.59808	−	3.23205i	−0.118457	−	0.239576i
$183$	5.19615			0.384111
$184$	3.00000	−	1.73205i	0.221163	−	0.127688i
$185$	−2.46410	−	4.26795i	−0.181164	−	0.313786i
$186$	1.09808	−	1.90192i	0.0805149	−	0.139456i
$187$		−	6.46410i		−	0.472702i
$188$	−2.13397	−	1.23205i	−0.155636	−	0.0898565i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$			0.732051i			0.0531085i
$191$	−11.5622	+	20.0263i	−0.836610	+	1.44905i	0.0561031	+	0.998425i	$0.482132\pi$
$191$	−11.5622	+	20.0263i	−0.836610	+	1.44905i	−0.892713	+	0.450626i	$0.851201\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−1.03590	+	0.598076i	−0.0745656	+	0.0430505i	−0.536819	−	0.843697i	$-0.680374\pi$
$193$	−1.03590	+	0.598076i	−0.0745656	+	0.0430505i	0.462254	+	0.886748i	$0.347041\pi$
$194$	−15.6603			−1.12434
$195$	−2.19615	−	1.46410i	−0.157270	−	0.104846i
$196$	1.00000			0.0714286
$197$	23.0885	−	13.3301i	1.64498	−	0.949732i	0.665961	−	0.745987i	$-0.268022\pi$
$197$	23.0885	−	13.3301i	1.64498	−	0.949732i	0.979024	−	0.203745i	$-0.0653114\pi$
$198$	−0.866025	−	1.50000i	−0.0615457	−	0.106600i
$199$	−8.09808	+	14.0263i	−0.574057	+	0.994297i	0.422086	+	0.906556i	$0.361298\pi$
$199$	−8.09808	+	14.0263i	−0.574057	+	0.994297i	−0.996143	+	0.0877408i	$0.972035\pi$
$200$			4.46410i			0.315660i
$201$	−7.73205	−	4.46410i	−0.545377	−	0.314873i
$202$	−2.66025	−	1.53590i	−0.187175	−	0.108065i
$203$		−	6.46410i		−	0.453691i
$204$	−1.86603	+	3.23205i	−0.130648	+	0.226289i
$205$	−1.09808	−	1.90192i	−0.0766930	−	0.132836i
$206$	12.7583	−	7.36603i	0.888915	−	0.513215i
$207$	3.46410			0.240772
$208$	2.00000	−	3.00000i	0.138675	−	0.208013i
$209$	1.73205			0.119808
$210$	0.633975	−	0.366025i	0.0437484	−	0.0252582i
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.833858	−	0.551979i	$-0.813873\pi$
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.0610990	−	0.998132i	$-0.519461\pi$
$212$	3.50000	−	6.06218i	0.240381	−	0.416352i
$213$			2.19615i			0.150478i
$214$	9.40192	+	5.42820i	0.642702	+	0.371064i
$215$	−2.07180	−	1.19615i	−0.141295	−	0.0815769i
$216$			1.00000i			0.0680414i
$217$	1.09808	−	1.90192i	0.0745423	−	0.129111i
$218$	2.36603	+	4.09808i	0.160247	+	0.277557i
$219$	4.73205	−	2.73205i	0.319762	−	0.184615i
$220$	−1.26795			−0.0854851
$221$	13.4282	+	0.866025i	0.903279	+	0.0582552i
$222$	6.73205			0.451826
$223$	21.1244	−	12.1962i	1.41459	−	0.816715i	0.418775	−	0.908090i	$-0.362460\pi$
$223$	21.1244	−	12.1962i	1.41459	−	0.816715i	0.995817	+	0.0913753i	$0.0291263\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	−2.23205	+	3.86603i	−0.148803	+	0.257735i
$226$		−	15.2679i		−	1.01561i
$227$	15.9282	+	9.19615i	1.05719	+	0.610370i	0.924654	−	0.380808i	$-0.124354\pi$
$227$	15.9282	+	9.19615i	1.05719	+	0.610370i	0.132538	+	0.991178i	$0.457687\pi$
$228$	−0.866025	−	0.500000i	−0.0573539	−	0.0331133i
$229$			19.9282i			1.31689i	0.752628	+	0.658446i	$0.228786\pi$
$229$			19.9282i			1.31689i	−0.752628	+	0.658446i	$0.771214\pi$
$230$	1.26795	−	2.19615i	0.0836061	−	0.144810i
$231$	−0.866025	−	1.50000i	−0.0569803	−	0.0986928i
$232$	5.59808	−	3.23205i	0.367532	−	0.212195i
$233$	9.12436			0.597756			0.298878	−	0.954291i	$-0.403388\pi$
$233$	9.12436			0.597756			0.298878	+	0.954291i	$0.403388\pi$
$234$	3.23205	−	1.59808i	0.211286	−	0.104470i
$235$	−1.80385			−0.117670
$236$	0.803848	−	0.464102i	0.0523260	−	0.0302104i
$237$	−1.03590	−	1.79423i	−0.0672888	−	0.116548i
$238$	−1.86603	+	3.23205i	−0.120956	+	0.209503i
$239$		−	0.732051i		−	0.0473524i	−0.999720	−	0.0236762i	$-0.992463\pi$
$239$		−	0.732051i		−	0.0473524i	0.999720	−	0.0236762i	$-0.00753708\pi$
$240$	0.633975	+	0.366025i	0.0409229	+	0.0236268i
$241$	−6.92820	−	4.00000i	−0.446285	−	0.257663i	0.259975	−	0.965615i	$-0.416286\pi$
$241$	−6.92820	−	4.00000i	−0.446285	−	0.257663i	−0.706260	+	0.707953i	$0.749619\pi$
$242$		−	8.00000i		−	0.514259i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.59808	+	4.50000i	0.166325	+	0.288083i
$245$	0.633975	−	0.366025i	0.0405032	−	0.0233845i
$246$	3.00000			0.191273
$247$	−0.232051	+	3.59808i	−0.0147650	+	0.228940i
$248$	2.19615			0.139456
$249$	−0.169873	+	0.0980762i	−0.0107653	+	0.00621533i
$250$	3.46410	+	6.00000i	0.219089	+	0.379473i
$251$	6.56218	−	11.3660i	0.414201	−	0.717417i	−0.581143	−	0.813801i	$-0.697394\pi$
$251$	6.56218	−	11.3660i	0.414201	−	0.717417i	0.995344	+	0.0963841i	$0.0307277\pi$
$252$			1.00000i			0.0629941i
$253$	−5.19615	−	3.00000i	−0.326679	−	0.188608i
$254$	13.3923	+	7.73205i	0.840308	+	0.485152i
$255$			2.73205i			0.171088i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.3301	+	17.8923i	0.644376	+	1.11609i	0.984445	+	0.175691i	$0.0562160\pi$
$257$	10.3301	+	17.8923i	0.644376	+	1.11609i	−0.340070	+	0.940400i	$0.610451\pi$
$258$	2.83013	−	1.63397i	0.176196	−	0.101727i
$259$	6.73205			0.418309
$260$	0.169873	−	2.63397i	0.0105351	−	0.163352i
$261$	6.46410			0.400118
$262$	12.0000	−	6.92820i	0.741362	−	0.428026i
$263$	7.56218	+	13.0981i	0.466304	+	0.807662i	0.999259	−	0.0384813i	$-0.0122520\pi$
$263$	7.56218	+	13.0981i	0.466304	+	0.807662i	−0.532955	+	0.846143i	$0.678919\pi$
$264$	0.866025	−	1.50000i	0.0533002	−	0.0923186i
$265$		−	5.12436i		−	0.314787i
$266$	−0.866025	−	0.500000i	−0.0530994	−	0.0306570i
$267$	9.06218	+	5.23205i	0.554596	+	0.320196i
$268$		−	8.92820i		−	0.545377i
$269$	4.92820	−	8.53590i	0.300478	−	0.520443i	−0.675766	−	0.737116i	$-0.736187\pi$
$269$	4.92820	−	8.53590i	0.300478	−	0.520443i	0.976244	+	0.216673i	$0.0695205\pi$
$270$	0.366025	+	0.633975i	0.0222756	+	0.0385825i
$271$	−24.2942	+	14.0263i	−1.47577	+	0.852036i	−0.999626	−	0.0273321i	$-0.991299\pi$
$271$	−24.2942	+	14.0263i	−1.47577	+	0.852036i	−0.476143	+	0.879368i	$0.657965\pi$
$272$	−3.73205			−0.226289
$273$	3.23205	−	1.59808i	0.195613	−	0.0967200i
$274$	−14.3923			−0.869471
$275$	6.69615	−	3.86603i	0.403793	−	0.233130i
$276$	1.73205	+	3.00000i	0.104257	+	0.180579i
$277$	4.66025	−	8.07180i	0.280008	−	0.484987i	−0.691379	−	0.722493i	$-0.742996\pi$
$277$	4.66025	−	8.07180i	0.280008	−	0.484987i	0.971386	+	0.237505i	$0.0763297\pi$
$278$		−	11.5885i		−	0.695029i
$279$	1.90192	+	1.09808i	0.113865	+	0.0657401i
$280$	0.633975	+	0.366025i	0.0378872	+	0.0218742i
$281$			0.339746i			0.0202675i	0.999949	+	0.0101338i	$0.00322574\pi$
$281$			0.339746i			0.0202675i	−0.999949	+	0.0101338i	$0.996774\pi$
$282$	1.23205	−	2.13397i	0.0733676	−	0.127076i
$283$	−4.92820	−	8.53590i	−0.292951	−	0.507406i	0.681555	−	0.731767i	$-0.261304\pi$
$283$	−4.92820	−	8.53590i	−0.292951	−	0.507406i	−0.974506	+	0.224360i	$0.927971\pi$
$284$	−1.90192	+	1.09808i	−0.112858	+	0.0651588i
$285$	−0.732051			−0.0433629
$286$	−6.23205	−	0.401924i	−0.368509	−	0.0237663i
$287$	3.00000			0.177084
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	1.53590	+	2.66025i	0.0903470	+	0.156486i
$290$	2.36603	−	4.09808i	0.138938	−	0.240647i
$291$		−	15.6603i		−	0.918020i
$292$	4.73205	+	2.73205i	0.276922	+	0.159881i
$293$	−14.7846	−	8.53590i	−0.863726	−	0.498673i	0.00153218	−	0.999999i	$-0.499512\pi$
$293$	−14.7846	−	8.53590i	−0.863726	−	0.498673i	−0.865258	+	0.501326i	$0.832846\pi$
$294$			1.00000i			0.0583212i
$295$	0.339746	−	0.588457i	0.0197808	−	0.0342613i
$296$	3.36603	+	5.83013i	0.195646	+	0.338869i
$297$	1.50000	−	0.866025i	0.0870388	−	0.0502519i
$298$	−13.8564			−0.802680
$299$	6.92820	−	10.3923i	0.400668	−	0.601003i
$300$	−4.46410			−0.257735
$301$	2.83013	−	1.63397i	0.163126	−	0.0941807i
$302$	2.59808	+	4.50000i	0.149502	+	0.258946i
$303$	1.53590	−	2.66025i	0.0882351	−	0.152828i
$304$		−	1.00000i		−	0.0573539i
$305$	3.29423	+	1.90192i	0.188627	+	0.108904i
$306$	−3.23205	−	1.86603i	−0.184764	−	0.106674i
$307$		−	8.60770i		−	0.491267i	−0.969363	−	0.245634i	$-0.921004\pi$
$307$		−	8.60770i		−	0.491267i	0.969363	−	0.245634i	$-0.0789960\pi$
$308$	0.866025	−	1.50000i	0.0493464	−	0.0854704i
$309$	7.36603	+	12.7583i	0.419039	+	0.725796i
$310$	1.39230	−	0.803848i	0.0790776	−	0.0456555i
$311$	−4.26795			−0.242013			−0.121007	−	0.992652i	$-0.538612\pi$
$311$	−4.26795			−0.242013			−0.121007	+	0.992652i	$0.538612\pi$
$312$	3.00000	+	2.00000i	0.169842	+	0.113228i
$313$	13.5167			0.764007			0.382003	−	0.924161i	$-0.375234\pi$
$313$	13.5167			0.764007			0.382003	+	0.924161i	$0.375234\pi$
$314$	0.464102	−	0.267949i	0.0261908	−	0.0151212i
$315$	0.366025	+	0.633975i	0.0206232	+	0.0357204i
$316$	1.03590	−	1.79423i	0.0582738	−	0.100933i
$317$		−	11.8564i		−	0.665922i	−0.942941	−	0.332961i	$-0.891952\pi$
$317$		−	11.8564i		−	0.665922i	0.942941	−	0.332961i	$-0.108048\pi$
$318$	6.06218	+	3.50000i	0.339950	+	0.196270i
$319$	−9.69615	−	5.59808i	−0.542880	−	0.313432i
$320$			0.732051i			0.0409229i
$321$	−5.42820	+	9.40192i	−0.302973	+	0.524764i
$322$	1.73205	+	3.00000i	0.0965234	+	0.167183i
$323$	3.23205	−	1.86603i	0.179836	−	0.103828i
$324$	−1.00000			−0.0555556
$325$	7.13397	+	14.4282i	0.395722	+	0.800333i
$326$	−2.73205			−0.151314
$327$	−4.09808	+	2.36603i	−0.226624	+	0.130842i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	1.23205	−	2.13397i	0.0679252	−	0.117650i
$330$		−	1.26795i		−	0.0697983i
$331$	24.1244	+	13.9282i	1.32599	+	0.765563i	0.984678	−	0.174385i	$-0.0557937\pi$
$331$	24.1244	+	13.9282i	1.32599	+	0.765563i	0.341317	+	0.939948i	$0.389127\pi$
$332$	−0.169873	−	0.0980762i	−0.00932299	−	0.00538263i
$333$			6.73205i			0.368914i
$334$	6.92820	−	12.0000i	0.379094	−	0.656611i
$335$	−3.26795	−	5.66025i	−0.178547	−	0.309253i
$336$	−0.866025	+	0.500000i	−0.0472456	+	0.0272772i
$337$	−19.0000			−1.03500			−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000			−1.03500			−0.517498	+	0.855684i	$0.673136\pi$
$338$	1.66987	−	12.8923i	0.0908291	−	0.701249i
$339$	15.2679			0.829241
$340$	−2.36603	+	1.36603i	−0.128316	+	0.0740831i
$341$	−1.90192	−	3.29423i	−0.102995	−	0.178392i
$342$	0.500000	−	0.866025i	0.0270369	−	0.0468293i
$343$			1.00000i			0.0539949i
$344$	2.83013	+	1.63397i	0.152590	+	0.0880980i
$345$	2.19615	+	1.26795i	0.118237	+	0.0682641i
$346$		−	9.12436i		−	0.490528i
$347$	−2.69615	+	4.66987i	−0.144737	+	0.250692i	−0.929275	−	0.369389i	$-0.879567\pi$
$347$	−2.69615	+	4.66987i	−0.144737	+	0.250692i	0.784538	+	0.620081i	$0.212900\pi$
$348$	3.23205	+	5.59808i	0.173256	+	0.300088i
$349$	−20.5359	+	11.8564i	−1.09926	+	0.634659i	−0.936027	−	0.351928i	$-0.885526\pi$
$349$	−20.5359	+	11.8564i	−1.09926	+	0.634659i	−0.163235	+	0.986587i	$0.552193\pi$
$350$	−4.46410			−0.238616
$351$	1.59808	+	3.23205i	0.0852990	+	0.172514i
$352$	1.73205			0.0923186
$353$	−8.19615	+	4.73205i	−0.436237	+	0.251862i	−0.702000	−	0.712177i	$-0.747709\pi$
$353$	−8.19615	+	4.73205i	−0.436237	+	0.251862i	0.265763	+	0.964038i	$0.414376\pi$
$354$	0.464102	+	0.803848i	0.0246667	+	0.0427240i
$355$	−0.803848	+	1.39230i	−0.0426638	+	0.0738959i
$356$			10.4641i			0.554596i
$357$	−3.23205	−	1.86603i	−0.171058	−	0.0987605i
$358$	−9.92820	−	5.73205i	−0.524722	−	0.302948i
$359$			3.80385i			0.200759i	0.994949	+	0.100380i	$0.0320058\pi$
$359$			3.80385i			0.200759i	−0.994949	+	0.100380i	$0.967994\pi$
$360$	−0.366025	+	0.633975i	−0.0192912	+	0.0334134i
$361$	−9.00000	−	15.5885i	−0.473684	−	0.820445i
$362$	−2.30385	+	1.33013i	−0.121088	+	0.0699099i
$363$	8.00000			0.419891
$364$	3.00000	+	2.00000i	0.157243	+	0.104828i
$365$	4.00000			0.209370
$366$	−4.50000	+	2.59808i	−0.235219	+	0.135804i
$367$	−12.6603	−	21.9282i	−0.660860	−	1.14464i	−0.980390	−	0.197067i	$-0.936858\pi$
$367$	−12.6603	−	21.9282i	−0.660860	−	1.14464i	0.319530	−	0.947576i	$-0.396475\pi$
$368$	−1.73205	+	3.00000i	−0.0902894	+	0.156386i
$369$			3.00000i			0.156174i
$370$	4.26795	+	2.46410i	0.221880	+	0.128103i
$371$	6.06218	+	3.50000i	0.314733	+	0.181711i
$372$			2.19615i			0.113865i
$373$	−4.83013	+	8.36603i	−0.250094	+	0.433176i	−0.963552	−	0.267523i	$-0.913795\pi$
$373$	−4.83013	+	8.36603i	−0.250094	+	0.433176i	0.713457	+	0.700699i	$0.247128\pi$
$374$	3.23205	+	5.59808i	0.167125	+	0.289470i
$375$	−6.00000	+	3.46410i	−0.309839	+	0.178885i
$376$	2.46410			0.127076
$377$	12.9282	−	19.3923i	0.665836	−	0.998755i
$378$	−1.00000			−0.0514344
$379$	24.6340	−	14.2224i	1.26536	−	0.730557i	0.291255	−	0.956645i	$-0.405927\pi$
$379$	24.6340	−	14.2224i	1.26536	−	0.730557i	0.974107	+	0.226088i	$0.0725937\pi$
$380$	−0.366025	−	0.633975i	−0.0187767	−	0.0325222i
$381$	−7.73205	+	13.3923i	−0.396125	+	0.686109i
$382$		−	23.1244i		−	1.18314i
$383$	−4.79423	−	2.76795i	−0.244974	−	0.141436i	0.372487	−	0.928037i	$-0.378505\pi$
$383$	−4.79423	−	2.76795i	−0.244974	−	0.141436i	−0.617461	+	0.786602i	$0.711838\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		−	1.26795i		−	0.0646207i
$386$	0.598076	−	1.03590i	0.0304413	−	0.0527258i
$387$	1.63397	+	2.83013i	0.0830596	+	0.143863i
$388$	13.5622	−	7.83013i	0.688515	−	0.397514i
$389$	−8.39230			−0.425507			−0.212753	−	0.977106i	$-0.568243\pi$
$389$	−8.39230			−0.425507			−0.212753	+	0.977106i	$0.568243\pi$
$390$	2.63397	+	0.169873i	0.133376	+	0.00860185i
$391$	−12.9282			−0.653807
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$	6.92820	+	12.0000i	0.349482	+	0.605320i
$394$	−13.3301	+	23.0885i	−0.671562	+	1.16318i
$395$		−	1.51666i		−	0.0763115i
$396$	1.50000	+	0.866025i	0.0753778	+	0.0435194i
$397$	6.99038	+	4.03590i	0.350837	+	0.202556i	0.665054	−	0.746795i	$-0.268409\pi$
$397$	6.99038	+	4.03590i	0.350837	+	0.202556i	−0.314217	+	0.949351i	$0.601742\pi$
$398$		−	16.1962i		−	0.811840i
$399$	0.500000	−	0.866025i	0.0250313	−	0.0433555i
$400$	−2.23205	−	3.86603i	−0.111603	−	0.193301i
$401$	−33.5885	+	19.3923i	−1.67733	+	0.968405i	−0.713973	+	0.700173i	$0.753106\pi$
$401$	−33.5885	+	19.3923i	−1.67733	+	0.968405i	−0.963354	+	0.268233i	$0.913560\pi$
$402$	8.92820			0.445298
$403$	7.09808	−	3.50962i	0.353580	−	0.174827i
$404$	3.07180			0.152828
$405$	−0.633975	+	0.366025i	−0.0315025	+	0.0181879i
$406$	3.23205	+	5.59808i	0.160404	+	0.277828i
$407$	5.83013	−	10.0981i	0.288989	−	0.500543i
$408$		−	3.73205i		−	0.184764i
$409$	−33.5429	−	19.3660i	−1.65859	−	0.957588i	−0.973366	−	0.229258i	$-0.926370\pi$
$409$	−33.5429	−	19.3660i	−1.65859	−	0.957588i	−0.685226	−	0.728331i	$-0.740297\pi$
$410$	1.90192	+	1.09808i	0.0939293	+	0.0542301i
$411$		−	14.3923i		−	0.709920i
$412$	−7.36603	+	12.7583i	−0.362898	+	0.628558i
$413$	0.464102	+	0.803848i	0.0228369	+	0.0395548i
$414$	−3.00000	+	1.73205i	−0.147442	+	0.0851257i
$415$	−0.143594			−0.00704873
$416$	−0.232051	+	3.59808i	−0.0113772	+	0.176410i
$417$	11.5885			0.567489
$418$	−1.50000	+	0.866025i	−0.0733674	+	0.0423587i
$419$	−0.366025	−	0.633975i	−0.0178815	−	0.0309717i	0.856946	−	0.515406i	$-0.172359\pi$
$419$	−0.366025	−	0.633975i	−0.0178815	−	0.0309717i	−0.874828	+	0.484434i	$0.839025\pi$
$420$	−0.366025	+	0.633975i	−0.0178602	+	0.0309348i
$421$		−	22.3923i		−	1.09133i	−0.838002	−	0.545667i	$-0.816276\pi$
$421$		−	22.3923i		−	1.09133i	0.838002	−	0.545667i	$-0.183724\pi$
$422$	22.5167	+	13.0000i	1.09609	+	0.632830i
$423$	2.13397	+	1.23205i	0.103757	+	0.0599044i
$424$			7.00000i			0.339950i
$425$	8.33013	−	14.4282i	0.404071	−	0.699871i
$426$	−1.09808	−	1.90192i	−0.0532020	−	0.0921485i
$427$	−4.50000	+	2.59808i	−0.217770	+	0.125730i
$428$	−10.8564			−0.524764
$429$	0.401924	−	6.23205i	0.0194051	−	0.300886i
$430$	2.39230			0.115367
$431$	−12.2942	+	7.09808i	−0.592192	+	0.341902i	−0.765964	−	0.642884i	$-0.777738\pi$
$431$	−12.2942	+	7.09808i	−0.592192	+	0.341902i	0.173772	+	0.984786i	$0.444405\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−13.5359	+	23.4449i	−0.650494	+	1.12669i	0.332509	+	0.943100i	$0.392105\pi$
$433$	−13.5359	+	23.4449i	−0.650494	+	1.12669i	−0.983003	+	0.183588i	$0.941229\pi$
$434$			2.19615i			0.105419i
$435$	4.09808	+	2.36603i	0.196488	+	0.113442i
$436$	−4.09808	−	2.36603i	−0.196262	−	0.113312i
$437$		−	3.46410i		−	0.165710i
$438$	−2.73205	+	4.73205i	−0.130542	+	0.226106i
$439$	−12.5885	−	21.8038i	−0.600814	−	1.04064i	−0.992698	−	0.120626i	$-0.961510\pi$
$439$	−12.5885	−	21.8038i	−0.600814	−	1.04064i	0.391884	−	0.920015i	$-0.371824\pi$
$440$	1.09808	−	0.633975i	0.0523487	−	0.0302236i
$441$	−1.00000			−0.0476190
$442$	−12.0622	+	5.96410i	−0.573739	+	0.283683i
$443$	−33.6410			−1.59833			−0.799166	−	0.601110i	$-0.794725\pi$
$443$	−33.6410			−1.59833			−0.799166	+	0.601110i	$0.794725\pi$
$444$	−5.83013	+	3.36603i	−0.276686	+	0.159744i
$445$	3.83013	+	6.63397i	0.181565	+	0.314481i
$446$	−12.1962	+	21.1244i	−0.577505	+	1.00027i
$447$		−	13.8564i		−	0.655386i
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	17.8301	+	10.2942i	0.841456	+	0.485815i	0.857759	−	0.514052i	$-0.171856\pi$
$449$	17.8301	+	10.2942i	0.841456	+	0.485815i	−0.0163031	+	0.999867i	$0.505190\pi$
$450$		−	4.46410i		−	0.210440i
$451$	2.59808	−	4.50000i	0.122339	−	0.211897i
$452$	7.63397	+	13.2224i	0.359072	+	0.621931i
$453$	−4.50000	+	2.59808i	−0.211428	+	0.122068i
$454$	−18.3923			−0.863194
$455$	2.63397	+	0.169873i	0.123483	+	0.00796377i
$456$	1.00000			0.0468293
$457$	10.2679	−	5.92820i	0.480314	−	0.277310i	−0.240233	−	0.970715i	$-0.577224\pi$
$457$	10.2679	−	5.92820i	0.480314	−	0.277310i	0.720548	+	0.693406i	$0.243891\pi$
$458$	−9.96410	−	17.2583i	−0.465592	−	0.806429i
$459$	1.86603	−	3.23205i	0.0870986	−	0.150859i
$460$			2.53590i			0.118237i
$461$	−23.3205	−	13.4641i	−1.08614	−	0.627086i	−0.153597	−	0.988134i	$-0.549086\pi$
$461$	−23.3205	−	13.4641i	−1.08614	−	0.627086i	−0.932547	+	0.361048i	$0.882419\pi$
$462$	1.50000	+	0.866025i	0.0697863	+	0.0402911i
$463$			6.26795i			0.291296i	0.989336	+	0.145648i	$0.0465267\pi$
$463$			6.26795i			0.291296i	−0.989336	+	0.145648i	$0.953473\pi$
$464$	−3.23205	+	5.59808i	−0.150044	+	0.259884i
$465$	0.803848	+	1.39230i	0.0372775	+	0.0645666i
$466$	−7.90192	+	4.56218i	−0.366050	+	0.211339i
$467$	13.8564			0.641198			0.320599	−	0.947215i	$-0.396116\pi$
$467$	13.8564			0.641198			0.320599	+	0.947215i	$0.396116\pi$
$468$	−2.00000	+	3.00000i	−0.0924500	+	0.138675i
$469$	8.92820			0.412266
$470$	1.56218	−	0.901924i	0.0720579	−	0.0416026i
$471$	0.267949	+	0.464102i	0.0123464	+	0.0213847i
$472$	−0.464102	+	0.803848i	−0.0213620	+	0.0370001i
$473$		−	5.66025i		−	0.260259i
$474$	1.79423	+	1.03590i	0.0824117	+	0.0475804i
$475$	3.86603	+	2.23205i	0.177385	+	0.102414i
$476$		−	3.73205i		−	0.171058i
$477$	−3.50000	+	6.06218i	−0.160254	+	0.277568i
$478$	0.366025	+	0.633975i	0.0167416	+	0.0289973i
$479$	−28.1147	+	16.2321i	−1.28460	+	0.741661i	−0.977685	−	0.210077i	$-0.932628\pi$
$479$	−28.1147	+	16.2321i	−1.28460	+	0.741661i	−0.306910	+	0.951738i	$0.599295\pi$
$480$	−0.732051			−0.0334134
$481$	20.1962	+	13.4641i	0.920865	+	0.613910i
$482$	8.00000			0.364390
$483$	−3.00000	+	1.73205i	−0.136505	+	0.0788110i
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	5.73205	−	9.92820i	0.260279	−	0.450816i
$486$		−	1.00000i		−	0.0453609i
$487$	−14.4282	−	8.33013i	−0.653804	−	0.377474i	0.136108	−	0.990694i	$-0.456541\pi$
$487$	−14.4282	−	8.33013i	−0.653804	−	0.377474i	−0.789912	+	0.613220i	$0.789874\pi$
$488$	−4.50000	−	2.59808i	−0.203705	−	0.117609i
$489$		−	2.73205i		−	0.123548i
$490$	−0.366025	+	0.633975i	−0.0165353	+	0.0286401i
$491$	17.7321	+	30.7128i	0.800236	+	1.38605i	0.919460	+	0.393182i	$0.128626\pi$
$491$	17.7321	+	30.7128i	0.800236	+	1.38605i	−0.119224	+	0.992867i	$0.538041\pi$
$492$	−2.59808	+	1.50000i	−0.117130	+	0.0676252i
$493$	−24.1244			−1.08651
$494$	−1.59808	−	3.23205i	−0.0719008	−	0.145417i
$495$	1.26795			0.0569901
$496$	−1.90192	+	1.09808i	−0.0853989	+	0.0493051i
$497$	−1.09808	−	1.90192i	−0.0492554	−	0.0853129i
$498$	0.0980762	−	0.169873i	0.00439490	−	0.00761219i
$499$			11.5167i			0.515557i	0.966204	+	0.257778i	$0.0829904\pi$
$499$			11.5167i			0.515557i	−0.966204	+	0.257778i	$0.917010\pi$
$500$	−6.00000	−	3.46410i	−0.268328	−	0.154919i
$501$	12.0000	+	6.92820i	0.536120	+	0.309529i
$502$			13.1244i			0.585769i
$503$	−3.46410	+	6.00000i	−0.154457	+	0.267527i	−0.932861	−	0.360236i	$-0.882696\pi$
$503$	−3.46410	+	6.00000i	−0.154457	+	0.267527i	0.778404	+	0.627763i	$0.216029\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$	1.94744	−	1.12436i	0.0866600	−	0.0500332i
$506$	6.00000			0.266733
$507$	12.8923	+	1.66987i	0.572567	+	0.0741617i
$508$	−15.4641			−0.686109
$509$	−19.3468	+	11.1699i	−0.857531	+	0.495096i	−0.863185	−	0.504888i	$-0.831534\pi$
$509$	−19.3468	+	11.1699i	−0.857531	+	0.495096i	0.00565352	+	0.999984i	$0.498200\pi$
$510$	−1.36603	−	2.36603i	−0.0604886	−	0.104769i
$511$	−2.73205	+	4.73205i	−0.120859	+	0.209334i
$512$		−	1.00000i		−	0.0441942i
$513$	0.866025	+	0.500000i	0.0382360	+	0.0220755i
$514$	−17.8923	−	10.3301i	−0.789196	−	0.455642i
$515$			10.7846i			0.475227i
$516$	−1.63397	+	2.83013i	−0.0719317	+	0.124589i
$517$	−2.13397	−	3.69615i	−0.0938521	−	0.162557i
$518$	−5.83013	+	3.36603i	−0.256161	+	0.147895i
$519$	9.12436			0.400515
$520$	1.16987	+	2.36603i	0.0513023	+	0.103757i
$521$	7.05256			0.308978			0.154489	−	0.987994i	$-0.450627\pi$
$521$	7.05256			0.308978			0.154489	+	0.987994i	$0.450627\pi$
$522$	−5.59808	+	3.23205i	−0.245021	+	0.141463i
$523$	6.93782	+	12.0167i	0.303370	+	0.525452i	0.976897	−	0.213711i	$-0.0685549\pi$
$523$	6.93782	+	12.0167i	0.303370	+	0.525452i	−0.673527	+	0.739162i	$0.735222\pi$
$524$	−6.92820	+	12.0000i	−0.302660	+	0.524222i
$525$		−	4.46410i		−	0.194829i
$526$	−13.0981	−	7.56218i	−0.571103	−	0.329727i
$527$	−7.09808	−	4.09808i	−0.309197	−	0.178515i
$528$			1.73205i			0.0753778i
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	2.56218	+	4.43782i	0.111294	+	0.192767i
$531$	−0.803848	+	0.464102i	−0.0348840	+	0.0201403i
$532$	1.00000			0.0433555
$533$	9.00000	+	6.00000i	0.389833	+	0.259889i
$534$	−10.4641			−0.452826
$535$	−6.88269	+	3.97372i	−0.297564	+	0.171799i
$536$	4.46410	+	7.73205i	0.192820	+	0.333974i
$537$	5.73205	−	9.92820i	0.247356	−	0.428434i
$538$			9.85641i			0.424940i
$539$	1.50000	+	0.866025i	0.0646096	+	0.0373024i
$540$	−0.633975	−	0.366025i	−0.0272819	−	0.0157512i
$541$			24.3397i			1.04645i	0.852195	+	0.523224i	$0.175271\pi$
$541$			24.3397i			1.04645i	−0.852195	+	0.523224i	$0.824729\pi$
$542$	14.0263	−	24.2942i	0.602480	−	1.04353i
$543$	−1.33013	−	2.30385i	−0.0570812	−	0.0988676i
$544$	3.23205	−	1.86603i	0.138573	−	0.0800052i
$545$	−3.46410			−0.148386
$546$	−2.00000	+	3.00000i	−0.0855921	+	0.128388i
$547$	−1.26795			−0.0542136			−0.0271068	−	0.999633i	$-0.508629\pi$
$547$	−1.26795			−0.0542136			−0.0271068	+	0.999633i	$0.508629\pi$
$548$	12.4641	−	7.19615i	0.532440	−	0.307404i
$549$	−2.59808	−	4.50000i	−0.110883	−	0.192055i
$550$	−3.86603	+	6.69615i	−0.164848	+	0.285525i
$551$		−	6.46410i		−	0.275380i
$552$	−3.00000	−	1.73205i	−0.127688	−	0.0737210i
$553$	1.79423	+	1.03590i	0.0762984	+	0.0440509i
$554$			9.32051i			0.395990i
$555$	−2.46410	+	4.26795i	−0.104595	+	0.181164i
$556$	5.79423	+	10.0359i	0.245730	+	0.425617i
$557$	11.3038	−	6.52628i	0.478959	−	0.276527i	−0.241023	−	0.970519i	$-0.577483\pi$
$557$	11.3038	−	6.52628i	0.478959	−	0.276527i	0.719983	+	0.693992i	$0.244150\pi$
$558$	−2.19615			−0.0929705
$559$	11.7583	+	0.758330i	0.497324	+	0.0320740i
$560$	−0.732051			−0.0309348
$561$	−5.59808	+	3.23205i	−0.236351	+	0.136457i
$562$	−0.169873	−	0.294229i	−0.00716566	−	0.0124113i
$563$	−18.0981	+	31.3468i	−0.762743	+	1.32111i	0.178689	+	0.983906i	$0.442815\pi$
$563$	−18.0981	+	31.3468i	−0.762743	+	1.32111i	−0.941432	+	0.337204i	$0.890519\pi$
$564$			2.46410i			0.103757i
$565$	9.67949	+	5.58846i	0.407219	+	0.235108i
$566$	8.53590	+	4.92820i	0.358791	+	0.207148i
$567$		−	1.00000i		−	0.0419961i
$568$	1.09808	−	1.90192i	0.0460743	−	0.0798029i
$569$	−19.2224	−	33.2942i	−0.805846	−	1.39577i	−0.915718	−	0.401821i	$-0.868377\pi$
$569$	−19.2224	−	33.2942i	−0.805846	−	1.39577i	0.109872	−	0.993946i	$-0.464956\pi$
$570$	0.633975	−	0.366025i	0.0265543	−	0.0153311i
$571$	−16.9808			−0.710623			−0.355311	−	0.934748i	$-0.615625\pi$
$571$	−16.9808			−0.710623			−0.355311	+	0.934748i	$0.615625\pi$
$572$	5.59808	−	2.76795i	0.234067	−	0.115734i
$573$	23.1244			0.966034
$574$	−2.59808	+	1.50000i	−0.108442	+	0.0626088i
$575$	−7.73205	−	13.3923i	−0.322449	−	0.558498i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			10.3397i			0.430449i	0.976565	+	0.215225i	$0.0690484\pi$
$577$			10.3397i			0.430449i	−0.976565	+	0.215225i	$0.930952\pi$
$578$	−2.66025	−	1.53590i	−0.110652	−	0.0638850i
$579$	1.03590	+	0.598076i	0.0430505	+	0.0248552i
$580$			4.73205i			0.196488i
$581$	0.0980762	−	0.169873i	0.00406889	−	0.00704752i
$582$	7.83013	+	13.5622i	0.324569	+	0.562170i
$583$	10.5000	−	6.06218i	0.434866	−	0.251070i
$584$	−5.46410			−0.226106
$585$	−0.169873	+	2.63397i	−0.00702338	+	0.108901i
$586$	17.0718			0.705229
$587$	10.6865	−	6.16987i	0.441080	−	0.254658i	−0.262975	−	0.964803i	$-0.584704\pi$
$587$	10.6865	−	6.16987i	0.441080	−	0.254658i	0.704056	+	0.710145i	$0.251370\pi$
$588$	−0.500000	−	0.866025i	−0.0206197	−	0.0357143i
$589$	1.09808	−	1.90192i	0.0452454	−	0.0783674i
$590$			0.679492i			0.0279742i
$591$	−23.0885	−	13.3301i	−0.949732	−	0.548328i
$592$	−5.83013	−	3.36603i	−0.239617	−	0.138343i
$593$		−	0.464102i		−	0.0190584i	−0.999955	−	0.00952918i	$-0.996967\pi$
$593$		−	0.464102i		−	0.0190584i	0.999955	−	0.00952918i	$-0.00303328\pi$
$594$	−0.866025	+	1.50000i	−0.0355335	+	0.0615457i
$595$	−1.36603	−	2.36603i	−0.0560016	−	0.0969976i
$596$	12.0000	−	6.92820i	0.491539	−	0.283790i
$597$	16.1962			0.662864
$598$	−0.803848	+	12.4641i	−0.0328718	+	0.509695i
$599$	−28.6410			−1.17024			−0.585120	−	0.810947i	$-0.698953\pi$
$599$	−28.6410			−1.17024			−0.585120	+	0.810947i	$0.698953\pi$
$600$	3.86603	−	2.23205i	0.157830	−	0.0911231i
$601$	11.3660	+	19.6865i	0.463630	+	0.803030i	0.999139	−	0.0414993i	$-0.0132134\pi$
$601$	11.3660	+	19.6865i	0.463630	+	0.803030i	−0.535509	+	0.844530i	$0.679880\pi$
$602$	−1.63397	+	2.83013i	−0.0665958	+	0.115347i
$603$			8.92820i			0.363585i
$604$	−4.50000	−	2.59808i	−0.183102	−	0.105714i
$605$	5.07180	+	2.92820i	0.206198	+	0.119048i
$606$			3.07180i			0.124783i
$607$	15.7583	−	27.2942i	0.639611	−	1.10784i	−0.345907	−	0.938269i	$-0.612429\pi$
$607$	15.7583	−	27.2942i	0.639611	−	1.10784i	0.985518	−	0.169570i	$-0.0542378\pi$
$608$	0.500000	+	0.866025i	0.0202777	+	0.0351220i
$609$	−5.59808	+	3.23205i	−0.226845	+	0.130969i
$610$	−3.80385			−0.154013
$611$	7.96410	−	3.93782i	0.322193	−	0.159307i
$612$	3.73205			0.150859
$613$	3.46410	−	2.00000i	0.139914	−	0.0807792i	−0.428409	−	0.903585i	$-0.640926\pi$
$613$	3.46410	−	2.00000i	0.139914	−	0.0807792i	0.568323	+	0.822806i	$0.307592\pi$
$614$	4.30385	+	7.45448i	0.173689	+	0.300838i
$615$	−1.09808	+	1.90192i	−0.0442787	+	0.0766930i
$616$			1.73205i			0.0697863i
$617$	1.90192	+	1.09808i	0.0765686	+	0.0442069i	0.537795	−	0.843075i	$-0.319257\pi$
$617$	1.90192	+	1.09808i	0.0765686	+	0.0442069i	−0.461227	+	0.887282i	$0.652591\pi$
$618$	−12.7583	−	7.36603i	−0.513215	−	0.296305i
$619$		−	22.0718i		−	0.887140i	−0.896240	−	0.443570i	$-0.853712\pi$
$619$		−	22.0718i		−	0.887140i	0.896240	−	0.443570i	$-0.146288\pi$
$620$	−0.803848	+	1.39230i	−0.0322833	+	0.0559163i
$621$	−1.73205	−	3.00000i	−0.0695048	−	0.120386i
$622$	3.69615	−	2.13397i	0.148202	−	0.0855646i
$623$	−10.4641			−0.419235
$624$	−3.59808	−	0.232051i	−0.144038	−	0.00928947i
$625$	17.2487			0.689948
$626$	−11.7058	+	6.75833i	−0.467857	+	0.270117i
$627$	−0.866025	−	1.50000i	−0.0345857	−	0.0599042i
$628$	−0.267949	+	0.464102i	−0.0106923	+	0.0185197i
$629$		−	25.1244i		−	1.00177i
$630$	−0.633975	−	0.366025i	−0.0252582	−	0.0145828i
$631$	14.5526	+	8.40192i	0.579328	+	0.334475i	0.760866	−	0.648909i	$-0.224774\pi$
$631$	14.5526	+	8.40192i	0.579328	+	0.334475i	−0.181538	+	0.983384i	$0.558108\pi$
$632$			2.07180i			0.0824117i
$633$	−13.0000	+	22.5167i	−0.516704	+	0.894957i
$634$	5.92820	+	10.2679i	0.235439	+	0.407792i
$635$	−9.80385	+	5.66025i	−0.389054	+	0.224620i
$636$	−7.00000			−0.277568
$637$	−2.00000	+	3.00000i	−0.0792429	+	0.118864i
$638$	11.1962			0.443260
$639$	1.90192	−	1.09808i	0.0752389	−	0.0434392i
$640$	−0.366025	−	0.633975i	−0.0144684	−	0.0250600i
$641$	15.5885	−	27.0000i	0.615707	−	1.06644i	−0.374553	−	0.927206i	$-0.622204\pi$
$641$	15.5885	−	27.0000i	0.615707	−	1.06644i	0.990260	−	0.139230i	$-0.0444629\pi$
$642$		−	10.8564i		−	0.428468i
$643$	28.4545	+	16.4282i	1.12214	+	0.647865i	0.941945	−	0.335767i	$-0.108995\pi$
$643$	28.4545	+	16.4282i	1.12214	+	0.647865i	0.180190	+	0.983632i	$0.442329\pi$
$644$	−3.00000	−	1.73205i	−0.118217	−	0.0682524i
$645$			2.39230i			0.0941969i
$646$	−1.86603	+	3.23205i	−0.0734178	+	0.127163i
$647$	17.9186	+	31.0359i	0.704452	+	1.22015i	0.966889	+	0.255198i	$0.0821406\pi$
$647$	17.9186	+	31.0359i	0.704452	+	1.22015i	−0.262437	+	0.964949i	$0.584526\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	1.60770			0.0631076
$650$	−13.3923	−	8.92820i	−0.525289	−	0.350193i
$651$	−2.19615			−0.0860740
$652$	2.36603	−	1.36603i	0.0926607	−	0.0534977i
$653$	−23.3564	−	40.4545i	−0.914007	−	1.58311i	−0.808349	−	0.588704i	$-0.799638\pi$
$653$	−23.3564	−	40.4545i	−0.914007	−	1.58311i	−0.105658	−	0.994403i	$-0.533695\pi$
$654$	2.36603	−	4.09808i	0.0925189	−	0.160247i
$655$			10.1436i			0.396343i
$656$	−2.59808	−	1.50000i	−0.101438	−	0.0585652i
$657$	−4.73205	−	2.73205i	−0.184615	−	0.106587i
$658$			2.46410i			0.0960607i
$659$	−9.30385	+	16.1147i	−0.362426	+	0.627741i	−0.988360	−	0.152136i	$-0.951385\pi$
$659$	−9.30385	+	16.1147i	−0.362426	+	0.627741i	0.625933	+	0.779877i	$0.284718\pi$
$660$	0.633975	+	1.09808i	0.0246774	+	0.0427426i
$661$	10.7321	−	6.19615i	0.417428	−	0.241002i	−0.276548	−	0.961000i	$-0.589190\pi$
$661$	10.7321	−	6.19615i	0.417428	−	0.241002i	0.693976	+	0.719998i	$0.255857\pi$
$662$	−27.8564			−1.08267
$663$	−5.96410	−	12.0622i	−0.231627	−	0.468456i
$664$	0.196152			0.00761219
$665$	0.633975	−	0.366025i	0.0245845	−	0.0141939i
$666$	−3.36603	−	5.83013i	−0.130431	−	0.225913i
$667$	−11.1962	+	19.3923i	−0.433517	+	0.750873i
$668$			13.8564i			0.536120i
$669$	−21.1244	−	12.1962i	−0.816715	−	0.471530i
$670$	5.66025	+	3.26795i	0.218675	+	0.126252i
$671$			9.00000i			0.347441i
$672$	0.500000	−	0.866025i	0.0192879	−	0.0334077i
$673$	−16.3564	−	28.3301i	−0.630493	−	1.09205i	−0.987451	−	0.157926i	$-0.949519\pi$
$673$	−16.3564	−	28.3301i	−0.630493	−	1.09205i	0.356958	−	0.934120i	$-0.383814\pi$
$674$	16.4545	−	9.50000i	0.633803	−	0.365926i
$675$	4.46410			0.171823
$676$	5.00000	+	12.0000i	0.192308	+	0.461538i
$677$	36.7321			1.41173			0.705864	−	0.708348i	$-0.250559\pi$
$677$	36.7321			1.41173			0.705864	+	0.708348i	$0.250559\pi$
$678$	−13.2224	+	7.63397i	−0.507804	+	0.293181i
$679$	7.83013	+	13.5622i	0.300493	+	0.520469i
$680$	1.36603	−	2.36603i	0.0523847	−	0.0907329i
$681$		−	18.3923i		−	0.704795i
$682$	3.29423	+	1.90192i	0.126143	+	0.0728284i
$683$	25.6410	+	14.8038i	0.981126	+	0.566453i	0.902610	−	0.430459i	$-0.141648\pi$
$683$	25.6410	+	14.8038i	0.981126	+	0.566453i	0.0785163	+	0.996913i	$0.474982\pi$
$684$			1.00000i			0.0382360i
$685$	5.26795	−	9.12436i	0.201278	−	0.348624i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	17.2583	−	9.96410i	0.658446	−	0.380154i
$688$	−3.26795			−0.124589
$689$	11.1865	+	22.6244i	0.426173	+	0.861919i
$690$	−2.53590			−0.0965400
$691$	37.8564	−	21.8564i	1.44013	−	0.831457i	0.442268	−	0.896883i	$-0.354174\pi$
$691$	37.8564	−	21.8564i	1.44013	−	0.831457i	0.997857	+	0.0654260i	$0.0208406\pi$
$692$	4.56218	+	7.90192i	0.173428	+	0.300386i
$693$	−0.866025	+	1.50000i	−0.0328976	+	0.0569803i
$694$		−	5.39230i		−	0.204689i
$695$	7.34679	+	4.24167i	0.278680	+	0.160896i
$696$	−5.59808	−	3.23205i	−0.212195	−	0.122511i
$697$		−	11.1962i		−	0.424085i
$698$	11.8564	−	20.5359i	0.448772	−	0.777295i
$699$	−4.56218	−	7.90192i	−0.172557	−	0.298878i
$700$	3.86603	−	2.23205i	0.146122	−	0.0843636i
$701$	−1.14359			−0.0431929			−0.0215965	−	0.999767i	$-0.506875\pi$
$701$	−1.14359			−0.0431929			−0.0215965	+	0.999767i	$0.506875\pi$
$702$	−3.00000	−	2.00000i	−0.113228	−	0.0754851i
$703$	6.73205			0.253904
$704$	−1.50000	+	0.866025i	−0.0565334	+	0.0326396i
$705$	0.901924	+	1.56218i	0.0339684	+	0.0588350i
$706$	4.73205	−	8.19615i	0.178093	−	0.308466i
$707$			3.07180i			0.115527i
$708$	−0.803848	−	0.464102i	−0.0302104	−	0.0174420i
$709$	−27.7583	−	16.0263i	−1.04249	−	0.601880i	−0.121950	−	0.992536i	$-0.538915\pi$
$709$	−27.7583	−	16.0263i	−1.04249	−	0.601880i	−0.920536	+	0.390657i	$0.872248\pi$
$710$		−	1.60770i		−	0.0603357i
$711$	−1.03590	+	1.79423i	−0.0388492	+	0.0672888i
$712$	−5.23205	−	9.06218i	−0.196079	−	0.339619i
$713$	−6.58846	+	3.80385i	−0.246740	+	0.142455i
$714$	3.73205			0.139668
$715$	2.53590	−	3.80385i	0.0948372	−	0.142256i
$716$	11.4641			0.428434
$717$	−0.633975	+	0.366025i	−0.0236762	+	0.0136695i
$718$	−1.90192	−	3.29423i	−0.0709792	−	0.122940i
$719$	13.2583	−	22.9641i	0.494452	−	0.856416i	−0.505527	−	0.862811i	$-0.668702\pi$
$719$	13.2583	−	22.9641i	0.494452	−	0.856416i	0.999980	+	0.00639415i	$0.00203533\pi$
$720$		−	0.732051i		−	0.0272819i
$721$	−12.7583	−	7.36603i	−0.475145	−	0.274325i
$722$	15.5885	+	9.00000i	0.580142	+	0.334945i
$723$			8.00000i			0.297523i
$724$	1.33013	−	2.30385i	0.0494338	−	0.0856218i
$725$	−14.4282	−	24.9904i	−0.535850	−	0.928119i
$726$	−6.92820	+	4.00000i	−0.257130	+	0.148454i
$727$	19.3205			0.716558			0.358279	−	0.933615i	$-0.383364\pi$
$727$	19.3205			0.716558			0.358279	+	0.933615i	$0.383364\pi$
$728$	−3.59808	−	0.232051i	−0.133354	−	0.00860038i
$729$	1.00000			0.0370370
$730$	−3.46410	+	2.00000i	−0.128212	+	0.0740233i
$731$	−6.09808	−	10.5622i	−0.225545	−	0.390656i
$732$	2.59808	−	4.50000i	0.0960277	−	0.166325i
$733$			48.1769i			1.77945i	0.456492	+	0.889727i	$0.349106\pi$
$733$			48.1769i			1.77945i	−0.456492	+	0.889727i	$0.650894\pi$
$734$	21.9282	+	12.6603i	0.809385	+	0.467299i
$735$	−0.633975	−	0.366025i	−0.0233845	−	0.0135011i
$736$		−	3.46410i		−	0.127688i
$737$	7.73205	−	13.3923i	0.284814	−	0.493312i
$738$	−1.50000	−	2.59808i	−0.0552158	−	0.0956365i
$739$	13.1436	−	7.58846i	0.483495	−	0.279146i	−0.238377	−	0.971173i	$-0.576615\pi$
$739$	13.1436	−	7.58846i	0.483495	−	0.279146i	0.721872	+	0.692027i	$0.243282\pi$
$740$	−4.92820			−0.181164
$741$	3.23205	−	1.59808i	0.118732	−	0.0587068i
$742$	−7.00000			−0.256978
$743$	−12.1699	+	7.02628i	−0.446469	+	0.257769i	−0.706338	−	0.707875i	$-0.749654\pi$
$743$	−12.1699	+	7.02628i	−0.446469	+	0.257769i	0.259869	+	0.965644i	$0.416321\pi$
$744$	−1.09808	−	1.90192i	−0.0402574	−	0.0697279i
$745$	5.07180	−	8.78461i	0.185816	−	0.321843i
$746$		−	9.66025i		−	0.353687i
$747$	0.169873	+	0.0980762i	0.00621533	+	0.00358842i
$748$	−5.59808	−	3.23205i	−0.204686	−	0.118175i
$749$		−	10.8564i		−	0.396684i
$750$	3.46410	−	6.00000i	0.126491	−	0.219089i
$751$	−9.57180	−	16.5788i	−0.349280	−	0.604970i	0.636842	−	0.770994i	$-0.280240\pi$
$751$	−9.57180	−	16.5788i	−0.349280	−	0.604970i	−0.986122	+	0.166024i	$0.946907\pi$
$752$	−2.13397	+	1.23205i	−0.0778180	+	0.0449283i
$753$	−13.1244			−0.478278
$754$	−1.50000	+	23.2583i	−0.0546268	+	0.847018i
$755$	−3.80385			−0.138436
$756$	0.866025	−	0.500000i	0.0314970	−	0.0181848i
$757$	0.294229	+	0.509619i	0.0106939	+	0.0185224i	0.871323	−	0.490710i	$-0.163263\pi$
$757$	0.294229	+	0.509619i	0.0106939	+	0.0185224i	−0.860629	+	0.509233i	$0.829929\pi$
$758$	−14.2224	+	24.6340i	−0.516582	+	0.894746i
$759$			6.00000i			0.217786i
$760$	0.633975	+	0.366025i	0.0229967	+	0.0132771i
$761$	13.2679	+	7.66025i	0.480963	+	0.277684i	0.720818	−	0.693125i	$-0.243767\pi$
$761$	13.2679	+	7.66025i	0.480963	+	0.277684i	−0.239855	+	0.970809i	$0.577100\pi$
$762$		−	15.4641i		−	0.560205i
$763$	2.36603	−	4.09808i	0.0856559	−	0.148360i
$764$	11.5622	+	20.0263i	0.418305	+	0.724525i
$765$	2.36603	−	1.36603i	0.0855438	−	0.0493888i
$766$	5.53590			0.200020
$767$	−0.215390	+	3.33975i	−0.00777729	+	0.120591i
$768$	1.00000			0.0360844
$769$	36.6340	−	21.1506i	1.32105	−	0.762711i	0.337158	−	0.941448i	$-0.390534\pi$
$769$	36.6340	−	21.1506i	1.32105	−	0.762711i	0.983897	+	0.178737i	$0.0572010\pi$
$770$	0.633975	+	1.09808i	0.0228469	+	0.0395719i
$771$	10.3301	−	17.8923i	0.372030	−	0.644376i
$772$			1.19615i			0.0430505i
$773$	−40.8564	−	23.5885i	−1.46950	−	0.848418i	−0.470088	−	0.882620i	$-0.655778\pi$
$773$	−40.8564	−	23.5885i	−1.46950	−	0.848418i	−0.999415	+	0.0342018i	$0.989111\pi$
$774$	−2.83013	−	1.63397i	−0.101727	−	0.0587320i
$775$		−	9.80385i		−	0.352165i
$776$	−7.83013	+	13.5622i	−0.281085	+	0.486854i
$777$	−3.36603	−	5.83013i	−0.120755	−	0.209155i
$778$	7.26795	−	4.19615i	0.260569	−	0.150439i
$779$	3.00000			0.107486
$780$	−2.36603	+	1.16987i	−0.0847173	+	0.0418882i
$781$	−3.80385			−0.136112
$782$	11.1962	−	6.46410i	0.400374	−	0.231156i
$783$	−3.23205	−	5.59808i	−0.115504	−	0.200059i
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$			0.392305i			0.0140020i
$786$	−12.0000	−	6.92820i	−0.428026	−	0.247121i
$787$	3.18653	+	1.83975i	0.113588	+	0.0655799i	0.555717	−	0.831371i	$-0.312444\pi$
$787$	3.18653	+	1.83975i	0.113588	+	0.0655799i	−0.442130	+	0.896951i	$0.645777\pi$
$788$		−	26.6603i		−	0.949732i
$789$	7.56218	−	13.0981i	0.269221	−	0.466304i
$790$	0.758330	+	1.31347i	0.0269802	+	0.0467310i
$791$	−13.2224	+	7.63397i	−0.470136	+	0.271433i
$792$	−1.73205			−0.0615457
$793$	−18.6962	−	1.20577i	−0.663920	−	0.0428182i
$794$	−8.07180			−0.286457
$795$	−4.43782	+	2.56218i	−0.157393	+	0.0908711i
$796$	8.09808	+	14.0263i	0.287029	+	0.497148i
$797$	−1.43782	+	2.49038i	−0.0509303	+	0.0882138i	−0.890367	−	0.455244i	$-0.849552\pi$
$797$	−1.43782	+	2.49038i	−0.0509303	+	0.0882138i	0.839436	+	0.543458i	$0.182885\pi$
$798$			1.00000i			0.0353996i
$799$	−7.96410	−	4.59808i	−0.281750	−	0.162668i
$800$	3.86603	+	2.23205i	0.136685	+	0.0789149i
$801$		−	10.4641i		−	0.369731i
$802$	19.3923	−	33.5885i	0.684766	−	1.18605i
$803$	4.73205	+	8.19615i	0.166990	+	0.289236i
$804$	−7.73205	+	4.46410i	−0.272688	+	0.157437i
$805$	−2.53590			−0.0893787
$806$	−4.39230	+	6.58846i	−0.154712	+	0.232069i
$807$	−9.85641			−0.346962
$808$	−2.66025	+	1.53590i	−0.0935874	+	0.0540327i
$809$	3.22243	+	5.58142i	0.113295	+	0.196232i	0.917097	−	0.398665i	$-0.130526\pi$
$809$	3.22243	+	5.58142i	0.113295	+	0.196232i	−0.803802	+	0.594897i	$0.797193\pi$
$810$	0.366025	−	0.633975i	0.0128608	−	0.0222756i
$811$			24.5359i			0.861572i	0.902454	+	0.430786i	$0.141764\pi$
$811$			24.5359i			0.861572i	−0.902454	+	0.430786i	$0.858236\pi$
$812$	−5.59808	−	3.23205i	−0.196454	−	0.113423i
$813$	24.2942	+	14.0263i	0.852036	+	0.491923i
$814$			11.6603i			0.408692i
$815$	1.00000	−	1.73205i	0.0350285	−	0.0606711i
$816$	1.86603	+	3.23205i	0.0653240	+	0.113144i
$817$	2.83013	−	1.63397i	0.0990136	−	0.0571655i
$818$	38.7321			1.35423
$819$	−3.00000	−	2.00000i	−0.104828	−	0.0698857i
$820$	−2.19615			−0.0766930
$821$	−44.8923	+	25.9186i	−1.56675	+	0.904565i	−0.570208	+	0.821500i	$0.693137\pi$
$821$	−44.8923	+	25.9186i	−1.56675	+	0.904565i	−0.996544	+	0.0830645i	$0.973529\pi$
$822$	7.19615	+	12.4641i	0.250995	+	0.434735i
$823$	−3.39230	+	5.87564i	−0.118248	+	0.204812i	−0.919074	−	0.394086i	$-0.871061\pi$
$823$	−3.39230	+	5.87564i	−0.118248	+	0.204812i	0.800825	+	0.598898i	$0.204395\pi$
$824$		−	14.7321i		−	0.513215i
$825$	−6.69615	−	3.86603i	−0.233130	−	0.134598i
$826$	−0.803848	−	0.464102i	−0.0279694	−	0.0161482i
$827$			7.32051i			0.254559i	0.991867	+	0.127280i	$0.0406245\pi$
$827$			7.32051i			0.254559i	−0.991867	+	0.127280i	$0.959375\pi$
$828$	1.73205	−	3.00000i	0.0601929	−	0.104257i
$829$	−8.66987	−	15.0167i	−0.301117	−	0.521550i	0.675272	−	0.737569i	$-0.264026\pi$
$829$	−8.66987	−	15.0167i	−0.301117	−	0.521550i	−0.976389	+	0.216018i	$0.930693\pi$
$830$	0.124356	−	0.0717968i	0.00431645	−	0.00249210i
$831$	−9.32051			−0.323325
$832$	−1.59808	−	3.23205i	−0.0554033	−	0.112051i
$833$	3.73205			0.129308
$834$	−10.0359	+	5.79423i	−0.347515	+	0.200638i
$835$	5.07180	+	8.78461i	0.175517	+	0.304004i
$836$	0.866025	−	1.50000i	0.0299521	−	0.0518786i
$837$		−	2.19615i		−	0.0759101i
$838$	0.633975	+	0.366025i	0.0219003	+	0.0126441i
$839$	−29.5359	−	17.0526i	−1.01969	−	0.588720i	−0.105678	−	0.994400i	$-0.533701\pi$
$839$	−29.5359	−	17.0526i	−1.01969	−	0.588720i	−0.914015	+	0.405681i	$0.867034\pi$
$840$		−	0.732051i		−	0.0252582i
$841$	−6.39230	+	11.0718i	−0.220424	+	0.381786i
$842$	11.1962	+	19.3923i	0.385845	+	0.668303i
$843$	0.294229	−	0.169873i	0.0101338	−	0.00585074i
$844$	−26.0000			−0.894957
$845$	7.56218	+	5.77757i	0.260147	+	0.198754i
$846$	−2.46410			−0.0847176
$847$	−6.92820	+	4.00000i	−0.238056	+	0.137442i
$848$	−3.50000	−	6.06218i	−0.120190	−	0.208176i
$849$	−4.92820	+	8.53590i	−0.169135	+	0.292951i
$850$			16.6603i			0.571442i
$851$	−20.1962	−	11.6603i	−0.692315	−	0.399708i
$852$	1.90192	+	1.09808i	0.0651588	+	0.0376195i
$853$			7.92820i			0.271457i	0.990746	+	0.135728i	$0.0433374\pi$
$853$			7.92820i			0.271457i	−0.990746	+	0.135728i	$0.956663\pi$
$854$	2.59808	−	4.50000i	0.0889043	−	0.153987i
$855$	0.366025	+	0.633975i	0.0125178	+	0.0216815i
$856$	9.40192	−	5.42820i	0.321351	−	0.185532i
$857$	32.5359			1.11141			0.555703	−	0.831381i	$-0.312449\pi$
$857$	32.5359			1.11141			0.555703	+	0.831381i	$0.312449\pi$
$858$	2.76795	+	5.59808i	0.0944962	+	0.191115i
$859$	42.7654			1.45914			0.729568	−	0.683908i	$-0.239721\pi$
$859$	42.7654			1.45914			0.729568	+	0.683908i	$0.239721\pi$
$860$	−2.07180	+	1.19615i	−0.0706477	+	0.0407885i
$861$	−1.50000	−	2.59808i	−0.0511199	−	0.0885422i
$862$	7.09808	−	12.2942i	0.241761	−	0.418743i
$863$		−	3.07180i		−	0.104565i	−0.998632	−	0.0522826i	$-0.983350\pi$
$863$		−	3.07180i		−	0.104565i	0.998632	−	0.0522826i	$-0.0166497\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	5.78461	+	3.33975i	0.196683	+	0.113555i
$866$		−	27.0718i		−	0.919937i
$867$	1.53590	−	2.66025i	0.0521618	−	0.0903470i
$868$	−1.09808	−	1.90192i	−0.0372711	−	0.0645555i
$869$	3.10770	−	1.79423i	0.105421	−	0.0608650i
$870$	−4.73205			−0.160432
$871$	26.7846	+	17.8564i	0.907562	+	0.605041i
$872$	4.73205			0.160247
$873$	−13.5622	+	7.83013i	−0.459010	+	0.265010i
$874$	1.73205	+	3.00000i	0.0585875	+	0.101477i
$875$	3.46410	−	6.00000i	0.117108	−	0.202837i
$876$		−	5.46410i		−	0.184615i
$877$	20.1506	+	11.6340i	0.680439	+	0.392851i	0.800020	−	0.599973i	$-0.204822\pi$
$877$	20.1506	+	11.6340i	0.680439	+	0.392851i	−0.119582	+	0.992824i	$0.538155\pi$
$878$	21.8038	+	12.5885i	0.735844	+	0.424840i
$879$			17.0718i			0.575817i
$880$	−0.633975	+	1.09808i	−0.0213713	+	0.0370161i
$881$	11.4641	+	19.8564i	0.386235	+	0.668979i	0.991940	−	0.126710i	$-0.0404419\pi$
$881$	11.4641	+	19.8564i	0.386235	+	0.668979i	−0.605704	+	0.795690i	$0.707109\pi$
$882$	0.866025	−	0.500000i	0.0291606	−	0.0168359i
$883$	8.05256			0.270990			0.135495	−	0.990778i	$-0.456738\pi$
$883$	8.05256			0.270990			0.135495	+	0.990778i	$0.456738\pi$
$884$	7.46410	−	11.1962i	0.251045	−	0.376567i
$885$	−0.679492			−0.0228409
$886$	29.1340	−	16.8205i	0.978775	−	0.565096i
$887$	7.72243	+	13.3756i	0.259294	+	0.449110i	0.966053	−	0.258344i	$-0.0831768\pi$
$887$	7.72243	+	13.3756i	0.259294	+	0.449110i	−0.706759	+	0.707454i	$0.749844\pi$
$888$	3.36603	−	5.83013i	0.112956	−	0.195646i
$889$		−	15.4641i		−	0.518649i
$890$	−6.63397	−	3.83013i	−0.222371	−	0.128386i
$891$	−1.50000	−	0.866025i	−0.0502519	−	0.0290129i
$892$		−	24.3923i		−	0.816715i
$893$	1.23205	−	2.13397i	0.0412290	−	0.0714107i
$894$	6.92820	+	12.0000i	0.231714	+	0.401340i
$895$	7.26795	−	4.19615i	0.242941	−	0.140262i
$896$	1.00000			0.0334077
$897$	−12.4641	−	0.803848i	−0.416164	−	0.0268397i
$898$	−20.5885			−0.687046
$899$	−12.2942	+	7.09808i	−0.410035	+	0.236734i
$900$	2.23205	+	3.86603i	0.0744017	+	0.128868i
$901$	13.0622	−	22.6244i	0.435164	−	0.753727i
$902$			5.19615i			0.173013i
$903$	−2.83013	−	1.63397i	−0.0941807	−	0.0543753i
$904$	−13.2224	−	7.63397i	−0.439772	−	0.253902i
$905$		−	1.94744i		−	0.0647351i
$906$	2.59808	−	4.50000i	0.0863153	−	0.149502i
$907$	−0.803848	−	1.39230i	−0.0266913	−	0.0462307i	0.852371	−	0.522937i	$-0.175164\pi$
$907$	−0.803848	−	1.39230i	−0.0266913	−	0.0462307i	−0.879063	+	0.476706i	$0.841830\pi$
$908$	15.9282	−	9.19615i	0.528596	−	0.305185i
$909$	−3.07180			−0.101885
$910$	−2.36603	+	1.16987i	−0.0784330	+	0.0387809i
$911$	−50.8372			−1.68431			−0.842155	−	0.539235i	$-0.818713\pi$
$911$	−50.8372			−1.68431			−0.842155	+	0.539235i	$0.818713\pi$
$912$	−0.866025	+	0.500000i	−0.0286770	+	0.0165567i
$913$	−0.169873	−	0.294229i	−0.00562198	−	0.00973755i
$914$	−5.92820	+	10.2679i	−0.196088	+	0.339634i
$915$		−	3.80385i		−	0.125751i
$916$	17.2583	+	9.96410i	0.570231	+	0.329223i
$917$	−12.0000	−	6.92820i	−0.396275	−	0.228789i
$918$			3.73205i			0.123176i
$919$	−16.4282	+	28.4545i	−0.541916	+	0.938627i	0.456878	+	0.889530i	$0.348968\pi$
$919$	−16.4282	+	28.4545i	−0.541916	+	0.938627i	−0.998794	+	0.0490972i	$0.984366\pi$
$920$	−1.26795	−	2.19615i	−0.0418030	−	0.0724050i
$921$	−7.45448	+	4.30385i	−0.245634	+	0.141817i
$922$	26.9282			0.886833
$923$	0.509619	−	7.90192i	0.0167743	−	0.260095i
$924$	−1.73205			−0.0569803
$925$	26.0263	−	15.0263i	0.855739	−	0.494061i
$926$	−3.13397	−	5.42820i	−0.102989	−	0.178382i
$927$	7.36603	−	12.7583i	0.241932	−	0.419039i
$928$		−	6.46410i		−	0.212195i
$929$	2.00962	+	1.16025i	0.0659335	+	0.0380667i	0.532604	−	0.846364i	$-0.321213\pi$
$929$	2.00962	+	1.16025i	0.0659335	+	0.0380667i	−0.466671	+	0.884431i	$0.654547\pi$
$930$	−1.39230	−	0.803848i	−0.0456555	−	0.0263592i
$931$			1.00000i			0.0327737i
$932$	4.56218	−	7.90192i	0.149439	−	0.258836i
$933$	2.13397	+	3.69615i	0.0698632	+	0.121007i
$934$	−12.0000	+	6.92820i	−0.392652	+	0.226698i
$935$	−4.73205			−0.154755
$936$	0.232051	−	3.59808i	0.00758482	−	0.117607i
$937$	1.07180			0.0350141			0.0175070	−	0.999847i	$-0.494427\pi$
$937$	1.07180			0.0350141			0.0175070	+	0.999847i	$0.494427\pi$
$938$	−7.73205	+	4.46410i	−0.252460	+	0.145758i
$939$	−6.75833	−	11.7058i	−0.220550	−	0.382003i
$940$	−0.901924	+	1.56218i	−0.0294175	+	0.0509526i
$941$			11.6077i			0.378400i	0.981939	+	0.189200i	$0.0605895\pi$
$941$			11.6077i			0.378400i	−0.981939	+	0.189200i	$0.939411\pi$
$942$	−0.464102	−	0.267949i	−0.0151212	−	0.00873026i
$943$	−9.00000	−	5.19615i	−0.293080	−	0.169210i
$944$		−	0.928203i		−	0.0302104i
$945$	0.366025	−	0.633975i	0.0119068	−	0.0206232i
$946$	2.83013	+	4.90192i	0.0920154	+	0.159375i
$947$	−28.1603	+	16.2583i	−0.915085	+	0.528325i	−0.882064	−	0.471130i	$-0.843846\pi$
$947$	−28.1603	+	16.2583i	−0.915085	+	0.528325i	−0.0330215	+	0.999455i	$0.510513\pi$
$948$	−2.07180			−0.0672888
$949$	−17.6603	+	8.73205i	−0.573276	+	0.283454i
$950$	−4.46410			−0.144835
$951$	−10.2679	+	5.92820i	−0.332961	+	0.192235i
$952$	1.86603	+	3.23205i	0.0604782	+	0.104751i
$953$	17.0981	−	29.6147i	0.553861	−	0.959315i	−0.444130	−	0.895962i	$-0.646487\pi$
$953$	17.0981	−	29.6147i	0.553861	−	0.959315i	0.997991	−	0.0633531i	$-0.0201794\pi$
$954$		−	7.00000i		−	0.226633i
$955$	14.6603	+	8.46410i	0.474395	+	0.273892i
$956$	−0.633975	−	0.366025i	−0.0205042	−	0.0118381i
$957$			11.1962i			0.361920i
$958$	16.2321	−	28.1147i	0.524434	−	0.908346i
$959$	7.19615	+	12.4641i	0.232376	+	0.402487i
$960$	0.633975	−	0.366025i	0.0204614	−	0.0118134i
$961$	26.1769			0.844417
$962$	−24.2224	−	1.56218i	−0.780963	−	0.0503666i
$963$	10.8564			0.349843
$964$	−6.92820	+	4.00000i	−0.223142	+	0.128831i
$965$	0.437822	+	0.758330i	0.0140940	+	0.0244115i
$966$	1.73205	−	3.00000i	0.0557278	−	0.0965234i
$967$		−	0.287187i		−	0.00923531i	−0.999989	−	0.00461766i	$-0.998530\pi$
$967$		−	0.287187i		−	0.00923531i	0.999989	−	0.00461766i	$-0.00146985\pi$
$968$	−6.92820	−	4.00000i	−0.222681	−	0.128565i
$969$	−3.23205	−	1.86603i	−0.103828	−	0.0599454i
$970$			11.4641i			0.368090i
$971$	27.0526	−	46.8564i	0.868158	−	1.50369i	0.00428092	−	0.999991i	$-0.498637\pi$
$971$	27.0526	−	46.8564i	0.868158	−	1.50369i	0.863877	−	0.503703i	$-0.168029\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−10.0359	+	5.79423i	−0.321736	+	0.185754i
$974$	16.6603			0.533829
$975$	8.92820	−	13.3923i	0.285931	−	0.428897i
$976$	5.19615			0.166325
$977$	−14.1962	+	8.19615i	−0.454175	+	0.262218i	−0.709592	−	0.704613i	$-0.751121\pi$
$977$	−14.1962	+	8.19615i	−0.454175	+	0.262218i	0.255417	+	0.966831i	$0.417787\pi$
$978$	1.36603	+	2.36603i	0.0436807	+	0.0756571i
$979$	−9.06218	+	15.6962i	−0.289628	+	0.501651i
$980$		−	0.732051i		−	0.0233845i
$981$	4.09808	+	2.36603i	0.130842	+	0.0755414i
$982$	−30.7128	−	17.7321i	−0.980085	−	0.565852i
$983$			35.8564i			1.14364i	0.820379	+	0.571821i	$0.193763\pi$
$983$			35.8564i			1.14364i	−0.820379	+	0.571821i	$0.806237\pi$
$984$	1.50000	−	2.59808i	0.0478183	−	0.0828236i
$985$	−9.75833	−	16.9019i	−0.310926	−	0.538540i
$986$	20.8923	−	12.0622i	0.665347	−	0.384138i
$987$	−2.46410			−0.0784332
$988$	3.00000	+	2.00000i	0.0954427	+	0.0636285i
$989$	−11.3205			−0.359971
$990$	−1.09808	+	0.633975i	−0.0348992	+	0.0201490i
$991$	29.6244	+	51.3109i	0.941049	+	1.62994i	0.763476	+	0.645836i	$0.223491\pi$
$991$	29.6244	+	51.3109i	0.941049	+	1.62994i	0.177573	+	0.984108i	$0.443175\pi$
$992$	1.09808	−	1.90192i	0.0348640	−	0.0603861i
$993$		−	27.8564i		−	0.883996i
$994$	1.90192	+	1.09808i	0.0603254	+	0.0348289i
$995$	10.2679	+	5.92820i	0.325516	+	0.187937i
$996$			0.196152i			0.00621533i
$997$	10.5263	−	18.2321i	0.333371	−	0.577415i	−0.649800	−	0.760105i	$-0.725147\pi$
$997$	10.5263	−	18.2321i	0.333371	−	0.577415i	0.983170	+	0.182691i	$0.0584806\pi$
$998$	−5.75833	−	9.97372i	−0.182277	−	0.315713i
$999$	5.83013	−	3.36603i	0.184457	−	0.106496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.s.a.127.1	yes	4
3.2	odd	2		1638.2.bj.b.127.2		4
13.2	odd	12		7098.2.a.bp.1.1		2
13.4	even	6	inner	546.2.s.a.43.1	✓	4
13.11	odd	12		7098.2.a.bx.1.2		2
39.17	odd	6		1638.2.bj.b.1135.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.a.43.1	✓	4	13.4	even	6	inner
546.2.s.a.127.1	yes	4	1.1	even	1	trivial
1638.2.bj.b.127.2		4	3.2	odd	2
1638.2.bj.b.1135.2		4	39.17	odd	6
7098.2.a.bp.1.1		2	13.2	odd	12
7098.2.a.bx.1.2		2	13.11	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.732051i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.732051i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.00000 q^{12} +(1.59808 + 3.23205i) q^{13} -1.00000 q^{14} +(-0.633975 + 0.366025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.86603 - 3.23205i) q^{17} -1.00000i q^{18} +(0.866025 + 0.500000i) q^{19} +(-0.633975 - 0.366025i) q^{20} -1.00000i q^{21} +(-0.866025 + 1.50000i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(0.866025 - 0.500000i) q^{24} +4.46410 q^{25} +(-3.00000 - 2.00000i) q^{26} +1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(-3.23205 - 5.59808i) q^{29} +(0.366025 - 0.633975i) q^{30} -2.19615i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} +3.73205i q^{34} +(0.366025 - 0.633975i) q^{35} +(0.500000 + 0.866025i) q^{36} +(5.83013 - 3.36603i) q^{37} -1.00000 q^{38} +(2.00000 - 3.00000i) q^{39} +0.732051 q^{40} +(2.59808 - 1.50000i) q^{41} +(0.500000 + 0.866025i) q^{42} +(1.63397 - 2.83013i) q^{43} -1.73205i q^{44} +(0.633975 + 0.366025i) q^{45} +(3.00000 + 1.73205i) q^{46} -2.46410i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-3.86603 + 2.23205i) q^{50} -3.73205 q^{51} +(3.59808 + 0.232051i) q^{52} +7.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(-0.500000 + 0.866025i) q^{56} -1.00000i q^{57} +(5.59808 + 3.23205i) q^{58} +(0.803848 + 0.464102i) q^{59} +0.732051i q^{60} +(-2.59808 + 4.50000i) q^{61} +(1.09808 + 1.90192i) q^{62} +(-0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(2.36603 - 1.16987i) q^{65} +1.73205 q^{66} +(7.73205 - 4.46410i) q^{67} +(-1.86603 - 3.23205i) q^{68} +(-1.73205 + 3.00000i) q^{69} +0.732051i q^{70} +(-1.90192 - 1.09808i) q^{71} +(-0.866025 - 0.500000i) q^{72} +5.46410i q^{73} +(-3.36603 + 5.83013i) q^{74} +(-2.23205 - 3.86603i) q^{75} +(0.866025 - 0.500000i) q^{76} +1.73205 q^{77} +(-0.232051 + 3.59808i) q^{78} +2.07180 q^{79} +(-0.633975 + 0.366025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{82} -0.196152i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-2.36603 - 1.36603i) q^{85} +3.26795i q^{86} +(-3.23205 + 5.59808i) q^{87} +(0.866025 + 1.50000i) q^{88} +(-9.06218 + 5.23205i) q^{89} -0.732051 q^{90} +(-0.232051 + 3.59808i) q^{91} -3.46410 q^{92} +(-1.90192 + 1.09808i) q^{93} +(1.23205 + 2.13397i) q^{94} +(0.366025 - 0.633975i) q^{95} -1.00000i q^{96} +(13.5622 + 7.83013i) q^{97} +(-0.866025 - 0.500000i) q^{98} +1.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{20} + 4 q^{25} - 12 q^{26} + 4 q^{27} - 6 q^{29} - 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} + 6 q^{37} - 4 q^{38} + 8 q^{39} - 4 q^{40} + 2 q^{42} + 10 q^{43} + 6 q^{45} + 12 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{50} - 8 q^{51} + 4 q^{52} + 28 q^{53} - 6 q^{55} - 2 q^{56} + 12 q^{58} + 24 q^{59} - 6 q^{62} - 4 q^{64} + 6 q^{65} + 24 q^{67} - 4 q^{68} - 18 q^{71} - 10 q^{74} - 2 q^{75} + 6 q^{78} + 36 q^{79} - 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{85} - 6 q^{87} - 12 q^{89} + 4 q^{90} + 6 q^{91} - 18 q^{93} - 2 q^{94} - 2 q^{95} + 30 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^20 + 4 * q^25 - 12 * q^26 + 4 * q^27 - 6 * q^29 - 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 + 6 * q^37 - 4 * q^38 + 8 * q^39 - 4 * q^40 + 2 * q^42 + 10 * q^43 + 6 * q^45 + 12 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^50 - 8 * q^51 + 4 * q^52 + 28 * q^53 - 6 * q^55 - 2 * q^56 + 12 * q^58 + 24 * q^59 - 6 * q^62 - 4 * q^64 + 6 * q^65 + 24 * q^67 - 4 * q^68 - 18 * q^71 - 10 * q^74 - 2 * q^75 + 6 * q^78 + 36 * q^79 - 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^85 - 6 * q^87 - 12 * q^89 + 4 * q^90 + 6 * q^91 - 18 * q^93 - 2 * q^94 - 2 * q^95 + 30 * q^97

Introduction

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