LMFDB - Embedded newform 546.2.s.e.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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$1.30512 + 1.13871i$ of defining polynomial
Character	$\chi$	$=$	546.127
Dual form			546.2.s.e.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.39924i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.39924i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.19962 + 3.80986i) q^{10} +(0.971521 - 0.560908i) q^{11} +1.00000 q^{12} +(-2.14345 + 2.89924i) q^{13} +1.00000 q^{14} +(3.80986 - 2.19962i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.57781 - 2.73284i) q^{17} -1.00000i q^{18} +(-6.99395 - 4.03796i) q^{19} +(-3.80986 - 2.19962i) q^{20} -1.00000i q^{21} +(-0.560908 + 0.971521i) q^{22} +(-2.70436 - 4.68409i) q^{23} +(-0.866025 + 0.500000i) q^{24} -14.3533 q^{25} +(0.406663 - 3.58254i) q^{26} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(3.37076 + 5.83834i) q^{29} +(-2.19962 + 3.80986i) q^{30} -5.58592i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.971521 + 0.560908i) q^{33} +3.15561i q^{34} +(-2.19962 + 3.80986i) q^{35} +(0.500000 + 0.866025i) q^{36} +(6.59886 - 3.80986i) q^{37} +8.07591 q^{38} +(-3.58254 - 0.406663i) q^{39} +4.39924 q^{40} +(-1.78138 + 1.02848i) q^{41} +(0.500000 + 0.866025i) q^{42} +(0.792959 - 1.37344i) q^{43} -1.12182i q^{44} +(3.80986 + 2.19962i) q^{45} +(4.68409 + 2.70436i) q^{46} -7.58865i q^{47} +(0.500000 - 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(12.4304 - 7.17667i) q^{50} +3.15561 q^{51} +(1.43909 + 3.30591i) q^{52} +8.44252 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.46757 - 4.27396i) q^{55} +(0.500000 - 0.866025i) q^{56} -8.07591i q^{57} +(-5.83834 - 3.37076i) q^{58} +(-6.30380 - 3.63950i) q^{59} -4.39924i q^{60} +(-5.20831 + 9.02106i) q^{61} +(2.79296 + 4.83755i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(12.7545 + 9.42957i) q^{65} -1.12182 q^{66} +(4.56902 - 2.63792i) q^{67} +(-1.57781 - 2.73284i) q^{68} +(2.70436 - 4.68409i) q^{69} -4.39924i q^{70} +(7.51422 + 4.33834i) q^{71} +(-0.866025 - 0.500000i) q^{72} +12.7985i q^{73} +(-3.80986 + 6.59886i) q^{74} +(-7.17667 - 12.4304i) q^{75} +(-6.99395 + 4.03796i) q^{76} -1.12182 q^{77} +(3.30591 - 1.43909i) q^{78} -3.52106 q^{79} +(-3.80986 + 2.19962i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.02848 - 1.78138i) q^{82} -11.1392i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-12.0224 - 6.94115i) q^{85} +1.58592i q^{86} +(-3.37076 + 5.83834i) q^{87} +(0.560908 + 0.971521i) q^{88} +(9.02707 - 5.21178i) q^{89} -4.39924 q^{90} +(3.30591 - 1.43909i) q^{91} -5.40872 q^{92} +(4.83755 - 2.79296i) q^{93} +(3.79432 + 6.57196i) q^{94} +(-17.7640 + 30.7681i) q^{95} +1.00000i q^{96} +(1.06297 + 0.613704i) q^{97} +(-0.866025 - 0.500000i) q^{98} +1.12182i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{10} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 8 q^{14} + 6 q^{15} - 4 q^{16} + 2 q^{17} - 12 q^{19} - 6 q^{20} - 4 q^{22} + 8 q^{23} - 24 q^{25} + 6 q^{26} - 8 q^{27} + 2 q^{29} - 6 q^{30} + 6 q^{33} - 6 q^{35} + 4 q^{36} + 18 q^{37} - 4 q^{38} + 12 q^{40} + 12 q^{41} + 4 q^{42} - 8 q^{43} + 6 q^{45} + 18 q^{46} + 4 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} + 12 q^{52} - 12 q^{53} - 22 q^{55} + 4 q^{56} - 24 q^{58} + 18 q^{59} - 8 q^{61} + 8 q^{62} - 8 q^{64} + 46 q^{65} - 8 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} + 6 q^{71} - 6 q^{74} - 12 q^{75} - 12 q^{76} - 8 q^{77} + 6 q^{78} - 4 q^{79} - 6 q^{80} - 4 q^{81} + 10 q^{82} - 54 q^{85} - 2 q^{87} + 4 q^{88} - 18 q^{89} - 12 q^{90} + 6 q^{91} + 16 q^{92} + 30 q^{93} - 2 q^{94} - 50 q^{95} - 54 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^10 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 8 * q^14 + 6 * q^15 - 4 * q^16 + 2 * q^17 - 12 * q^19 - 6 * q^20 - 4 * q^22 + 8 * q^23 - 24 * q^25 + 6 * q^26 - 8 * q^27 + 2 * q^29 - 6 * q^30 + 6 * q^33 - 6 * q^35 + 4 * q^36 + 18 * q^37 - 4 * q^38 + 12 * q^40 + 12 * q^41 + 4 * q^42 - 8 * q^43 + 6 * q^45 + 18 * q^46 + 4 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 + 12 * q^52 - 12 * q^53 - 22 * q^55 + 4 * q^56 - 24 * q^58 + 18 * q^59 - 8 * q^61 + 8 * q^62 - 8 * q^64 + 46 * q^65 - 8 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 + 6 * q^71 - 6 * q^74 - 12 * q^75 - 12 * q^76 - 8 * q^77 + 6 * q^78 - 4 * q^79 - 6 * q^80 - 4 * q^81 + 10 * q^82 - 54 * q^85 - 2 * q^87 + 4 * q^88 - 18 * q^89 - 12 * q^90 + 6 * q^91 + 16 * q^92 + 30 * q^93 - 2 * q^94 - 50 * q^95 - 54 * 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
$5$		−	4.39924i		−	1.96740i	−0.179814	−	0.983701i	$-0.557549\pi$
$5$		−	4.39924i		−	1.96740i	0.179814	−	0.983701i	$-0.442451\pi$
$6$	−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
$10$	2.19962	+	3.80986i	0.695581	+	1.20478i
$11$	0.971521	−	0.560908i	0.292925	−	0.169120i	−0.346335	−	0.938111i	$-0.612574\pi$
$11$	0.971521	−	0.560908i	0.292925	−	0.169120i	0.639260	+	0.768991i	$0.279241\pi$
$12$	1.00000			0.288675
$13$	−2.14345	+	2.89924i	−0.594487	+	0.804105i
$13$	−2.14345	+	2.89924i	−0.594487	+	0.804105i
$14$	1.00000			0.267261
$15$	3.80986	−	2.19962i	0.983701	−	0.567940i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.57781	−	2.73284i	0.382674	−	0.662811i	−0.608769	−	0.793347i	$-0.708337\pi$
$17$	1.57781	−	2.73284i	0.382674	−	0.662811i	0.991444	+	0.130536i	$0.0416699\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−6.99395	−	4.03796i	−1.60452	−	0.926371i	−0.990567	−	0.137029i	$-0.956245\pi$
$19$	−6.99395	−	4.03796i	−1.60452	−	0.926371i	−0.613954	−	0.789342i	$-0.710422\pi$
$20$	−3.80986	−	2.19962i	−0.851910	−	0.491850i
$21$		−	1.00000i		−	0.218218i
$22$	−0.560908	+	0.971521i	−0.119586	+	0.207129i
$23$	−2.70436	−	4.68409i	−0.563898	−	0.976700i	−0.997151	−	0.0754280i	$-0.975968\pi$
$23$	−2.70436	−	4.68409i	−0.563898	−	0.976700i	0.433253	−	0.901272i	$-0.357366\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−14.3533			−2.87067
$26$	0.406663	−	3.58254i	0.0797531	−	0.702595i
$27$	−1.00000			−0.192450
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	3.37076	+	5.83834i	0.625935	+	1.08415i	0.988359	+	0.152138i	$0.0486159\pi$
$29$	3.37076	+	5.83834i	0.625935	+	1.08415i	−0.362424	+	0.932013i	$0.618051\pi$
$30$	−2.19962	+	3.80986i	−0.401594	+	0.695581i
$31$		−	5.58592i		−	1.00326i	−0.865082	−	0.501630i	$-0.832734\pi$
$31$		−	5.58592i		−	1.00326i	0.865082	−	0.501630i	$-0.167266\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.971521	+	0.560908i	0.169120	+	0.0976416i
$34$			3.15561i			0.541183i
$35$	−2.19962	+	3.80986i	−0.371804	+	0.643983i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	6.59886	−	3.80986i	1.08485	−	0.626337i	0.152647	−	0.988281i	$-0.451220\pi$
$37$	6.59886	−	3.80986i	1.08485	−	0.626337i	0.932200	+	0.361944i	$0.117887\pi$
$38$	8.07591			1.31009
$39$	−3.58254	−	0.406663i	−0.573666	−	0.0651182i
$40$	4.39924			0.695581
$41$	−1.78138	+	1.02848i	−0.278204	+	0.160621i	−0.632610	−	0.774470i	$-0.718016\pi$
$41$	−1.78138	+	1.02848i	−0.278204	+	0.160621i	0.354406	+	0.935092i	$0.384683\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	0.792959	−	1.37344i	0.120925	−	0.209448i	−0.799208	−	0.601055i	$-0.794747\pi$
$43$	0.792959	−	1.37344i	0.120925	−	0.209448i	0.920133	+	0.391607i	$0.128081\pi$
$44$		−	1.12182i		−	0.169120i
$45$	3.80986	+	2.19962i	0.567940	+	0.327900i
$46$	4.68409	+	2.70436i	0.690631	+	0.398736i
$47$		−	7.58865i		−	1.10692i	−0.832876	−	0.553459i	$-0.813308\pi$
$47$		−	7.58865i		−	1.10692i	0.832876	−	0.553459i	$-0.186692\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	12.4304	−	7.17667i	1.75792	−	1.01493i
$51$	3.15561			0.441874
$52$	1.43909	+	3.30591i	0.199566	+	0.458447i
$53$	8.44252			1.15967			0.579834	−	0.814734i	$-0.303117\pi$
$53$	8.44252			1.15967			0.579834	+	0.814734i	$0.303117\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−2.46757	−	4.27396i	−0.332727	−	0.576300i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		−	8.07591i		−	1.06968i
$58$	−5.83834	−	3.37076i	−0.766611	−	0.442603i
$59$	−6.30380	−	3.63950i	−0.820685	−	0.473823i	0.0299675	−	0.999551i	$-0.490460\pi$
$59$	−6.30380	−	3.63950i	−0.820685	−	0.473823i	−0.850653	+	0.525728i	$0.823793\pi$
$60$		−	4.39924i		−	0.567940i
$61$	−5.20831	+	9.02106i	−0.666856	+	1.15503i	0.311923	+	0.950107i	$0.399027\pi$
$61$	−5.20831	+	9.02106i	−0.666856	+	1.15503i	−0.978779	+	0.204921i	$0.934306\pi$
$62$	2.79296	+	4.83755i	0.354706	+	0.614369i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	−1.00000			−0.125000
$65$	12.7545	+	9.42957i	1.58200	+	1.16959i
$66$	−1.12182			−0.138086
$67$	4.56902	−	2.63792i	0.558195	−	0.322274i	−0.194226	−	0.980957i	$-0.562219\pi$
$67$	4.56902	−	2.63792i	0.558195	−	0.322274i	0.752421	+	0.658683i	$0.228886\pi$
$68$	−1.57781	−	2.73284i	−0.191337	−	0.331405i
$69$	2.70436	−	4.68409i	0.325567	−	0.563898i
$70$		−	4.39924i		−	0.525810i
$71$	7.51422	+	4.33834i	0.891773	+	0.514866i	0.874522	−	0.484986i	$-0.161175\pi$
$71$	7.51422	+	4.33834i	0.891773	+	0.514866i	0.0172513	+	0.999851i	$0.494508\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			12.7985i			1.49795i	0.662599	+	0.748975i	$0.269454\pi$
$73$			12.7985i			1.49795i	−0.662599	+	0.748975i	$0.730546\pi$
$74$	−3.80986	+	6.59886i	−0.442887	+	0.767102i
$75$	−7.17667	−	12.4304i	−0.828691	−	1.43533i
$76$	−6.99395	+	4.03796i	−0.802261	+	0.463185i
$77$	−1.12182			−0.127843
$78$	3.30591	−	1.43909i	0.374320	−	0.162945i
$79$	−3.52106			−0.396150			−0.198075	−	0.980187i	$-0.563469\pi$
$79$	−3.52106			−0.396150			−0.198075	+	0.980187i	$0.563469\pi$
$80$	−3.80986	+	2.19962i	−0.425955	+	0.245925i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.02848	−	1.78138i	0.113576	−	0.196720i
$83$		−	11.1392i		−	1.22269i	−0.791366	−	0.611343i	$-0.790630\pi$
$83$		−	11.1392i		−	1.22269i	0.791366	−	0.611343i	$-0.209370\pi$
$84$	−0.866025	−	0.500000i	−0.0944911	−	0.0545545i
$85$	−12.0224	−	6.94115i	−1.30402	−	0.752873i
$86$			1.58592i			0.171014i
$87$	−3.37076	+	5.83834i	−0.361384	+	0.625935i
$88$	0.560908	+	0.971521i	0.0597930	+	0.103565i
$89$	9.02707	−	5.21178i	0.956867	−	0.552448i	0.0616598	−	0.998097i	$-0.480361\pi$
$89$	9.02707	−	5.21178i	0.956867	−	0.552448i	0.895207	+	0.445650i	$0.147027\pi$
$90$	−4.39924			−0.463721
$91$	3.30591	−	1.43909i	0.346553	−	0.150858i
$92$	−5.40872			−0.563898
$93$	4.83755	−	2.79296i	0.501630	−	0.289616i
$94$	3.79432	+	6.57196i	0.391355	+	0.677846i
$95$	−17.7640	+	30.7681i	−1.82254	+	3.15674i
$96$			1.00000i			0.102062i
$97$	1.06297	+	0.613704i	0.107928	+	0.0623122i	0.552992	−	0.833186i	$-0.313486\pi$
$97$	1.06297	+	0.613704i	0.107928	+	0.0623122i	−0.445064	+	0.895499i	$0.646819\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$			1.12182i			0.112747i
$100$	−7.17667	+	12.4304i	−0.717667	+	1.24304i
$101$	−5.40714	−	9.36545i	−0.538031	−	0.931897i	−0.999010	−	0.0444859i	$-0.985835\pi$
$101$	−5.40714	−	9.36545i	−0.538031	−	0.931897i	0.460979	−	0.887411i	$-0.347498\pi$
$102$	−2.73284	+	1.57781i	−0.270591	+	0.156226i
$103$	17.2910			1.70374			0.851868	−	0.523757i	$-0.175470\pi$
$103$	17.2910			1.70374			0.851868	+	0.523757i	$0.175470\pi$
$104$	−2.89924	−	2.14345i	−0.284294	−	0.210183i
$105$	−4.39924			−0.429322
$106$	−7.31143	+	4.22126i	−0.710149	+	0.410005i
$107$	−7.10282	−	12.3024i	−0.686655	−	1.18932i	−0.972914	−	0.231169i	$-0.925745\pi$
$107$	−7.10282	−	12.3024i	−0.686655	−	1.18932i	0.286259	−	0.958152i	$-0.407588\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$		−	3.43821i		−	0.329321i	−0.986350	−	0.164660i	$-0.947347\pi$
$109$		−	3.43821i		−	0.329321i	0.986350	−	0.164660i	$-0.0526528\pi$
$110$	4.27396	+	2.46757i	0.407506	+	0.235274i
$111$	6.59886	+	3.80986i	0.626337	+	0.361616i
$112$			1.00000i			0.0944911i
$113$	3.01295	−	5.21858i	0.283434	−	0.490922i	−0.688794	−	0.724957i	$-0.741860\pi$
$113$	3.01295	−	5.21858i	0.283434	−	0.490922i	0.972228	+	0.234035i	$0.0751929\pi$
$114$	4.03796	+	6.99395i	0.378189	+	0.655043i
$115$	−20.6065	+	11.8971i	−1.92156	+	1.10941i
$116$	6.74153			0.625935
$117$	−1.43909	−	3.30591i	−0.133044	−	0.305631i
$118$	7.27900			0.670087
$119$	−2.73284	+	1.57781i	−0.250519	+	0.144637i
$120$	2.19962	+	3.80986i	0.200797	+	0.347791i
$121$	−4.87076	+	8.43641i	−0.442797	+	0.766946i
$122$		−	10.4166i		−	0.943077i
$123$	−1.78138	−	1.02848i	−0.160621	−	0.0927348i
$124$	−4.83755	−	2.79296i	−0.434425	−	0.250815i
$125$			41.1476i			3.68036i
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	4.87818	+	8.44926i	0.432869	+	0.749751i	0.997119	−	0.0758531i	$-0.0241680\pi$
$127$	4.87818	+	8.44926i	0.432869	+	0.749751i	−0.564250	+	0.825604i	$0.690835\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.58592			0.139632
$130$	−15.7605	−	1.78901i	−1.38229	−	0.156906i
$131$	7.62761			0.666428			0.333214	−	0.942851i	$-0.391867\pi$
$131$	7.62761			0.666428			0.333214	+	0.942851i	$0.391867\pi$
$132$	0.971521	−	0.560908i	0.0845601	−	0.0488208i
$133$	4.03796	+	6.99395i	0.350135	+	0.606452i
$134$	−2.63792	+	4.56902i	−0.227882	+	0.394703i
$135$			4.39924i			0.378627i
$136$	2.73284	+	1.57781i	0.234339	+	0.135296i
$137$	6.36818	+	3.67667i	0.544070	+	0.314119i	0.746727	−	0.665131i	$-0.231624\pi$
$137$	6.36818	+	3.67667i	0.544070	+	0.314119i	−0.202657	+	0.979250i	$0.564958\pi$
$138$			5.40872i			0.460421i
$139$	4.29454	−	7.43835i	0.364258	−	0.630913i	−0.624399	−	0.781106i	$-0.714656\pi$
$139$	4.29454	−	7.43835i	0.364258	−	0.630913i	0.988657	+	0.150193i	$0.0479894\pi$
$140$	2.19962	+	3.80986i	0.185902	+	0.321992i
$141$	6.57196	−	3.79432i	0.553459	−	0.319540i
$142$	−8.67667			−0.728130
$143$	−0.456201	+	4.01896i	−0.0381494	+	0.336082i
$144$	1.00000			0.0833333
$145$	25.6843	−	14.8288i	2.13296	−	1.23147i
$146$	−6.39924	−	11.0838i	−0.529605	−	0.917303i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$		−	7.61971i		−	0.626337i
$149$	−3.01285	−	1.73947i	−0.246822	−	0.142503i	0.371486	−	0.928439i	$-0.378848\pi$
$149$	−3.01285	−	1.73947i	−0.246822	−	0.142503i	−0.618308	+	0.785936i	$0.712182\pi$
$150$	12.4304	+	7.17667i	1.01493	+	0.585973i
$151$			16.2991i			1.32640i	0.748441	+	0.663202i	$0.230803\pi$
$151$			16.2991i			1.32640i	−0.748441	+	0.663202i	$0.769197\pi$
$152$	4.03796	−	6.99395i	0.327522	−	0.567284i
$153$	1.57781	+	2.73284i	0.127558	+	0.220937i
$154$	0.971521	−	0.560908i	0.0782874	−	0.0451993i
$155$	−24.5738			−1.97382
$156$	−2.14345	+	2.89924i	−0.171614	+	0.232125i
$157$	−0.684571			−0.0546347			−0.0273174	−	0.999627i	$-0.508696\pi$
$157$	−0.684571			−0.0546347			−0.0273174	+	0.999627i	$0.508696\pi$
$158$	3.04933	−	1.76053i	0.242591	−	0.140060i
$159$	4.22126	+	7.31143i	0.334768	+	0.579834i
$160$	2.19962	−	3.80986i	0.173895	−	0.301196i
$161$			5.40872i			0.426267i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	12.1690	+	7.02580i	0.953153	+	0.550303i	0.894059	−	0.447949i	$-0.147846\pi$
$163$	12.1690	+	7.02580i	0.953153	+	0.550303i	0.0590938	+	0.998252i	$0.481179\pi$
$164$			2.05696i			0.160621i
$165$	2.46757	−	4.27396i	0.192100	−	0.332727i
$166$	5.56960	+	9.64683i	0.432285	+	0.748739i
$167$	0.421983	−	0.243632i	0.0326540	−	0.0188528i	−0.483584	−	0.875298i	$-0.660665\pi$
$167$	0.421983	−	0.243632i	0.0326540	−	0.0188528i	0.516238	+	0.856445i	$0.327332\pi$
$168$	1.00000			0.0771517
$169$	−3.81122	−	12.4288i	−0.293171	−	0.956060i
$170$	13.8823			1.06472
$171$	6.99395	−	4.03796i	0.534840	−	0.308790i
$172$	−0.792959	−	1.37344i	−0.0604625	−	0.104724i
$173$	−1.71910	+	2.97757i	−0.130701	+	0.226381i	−0.923947	−	0.382521i	$-0.875056\pi$
$173$	−1.71910	+	2.97757i	−0.130701	+	0.226381i	0.793246	+	0.608901i	$0.208389\pi$
$174$		−	6.74153i		−	0.511074i
$175$	12.4304	+	7.17667i	0.939647	+	0.542505i
$176$	−0.971521	−	0.560908i	−0.0732312	−	0.0422800i
$177$		−	7.27900i		−	0.547123i
$178$	−5.21178	+	9.02707i	−0.390639	+	0.676607i
$179$	−1.08802	−	1.88451i	−0.0813225	−	0.140855i	0.822496	−	0.568771i	$-0.192581\pi$
$179$	−1.08802	−	1.88451i	−0.0813225	−	0.140855i	−0.903818	+	0.427917i	$0.859248\pi$
$180$	3.80986	−	2.19962i	0.283970	−	0.163950i
$181$	10.7188			0.796721			0.398361	−	0.917229i	$-0.369579\pi$
$181$	10.7188			0.796721			0.398361	+	0.917229i	$0.369579\pi$
$182$	−2.14345	+	2.89924i	−0.158883	+	0.214906i
$183$	−10.4166			−0.770019
$184$	4.68409	−	2.70436i	0.345316	−	0.199368i
$185$	−16.7605	−	29.0300i	−1.23226	−	2.13433i
$186$	−2.79296	+	4.83755i	−0.204790	+	0.354706i
$187$		−	3.54002i		−	0.258872i
$188$	−6.57196	−	3.79432i	−0.479310	−	0.276730i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$		−	35.5279i		−	2.57747i
$191$	−7.62813	+	13.2123i	−0.551952	+	0.956009i	0.446181	+	0.894943i	$0.352784\pi$
$191$	−7.62813	+	13.2123i	−0.551952	+	0.956009i	−0.998134	+	0.0610668i	$0.980550\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−12.2800	+	7.08987i	−0.883935	+	0.510340i	−0.871954	−	0.489588i	$-0.837147\pi$
$193$	−12.2800	+	7.08987i	−0.883935	+	0.510340i	−0.0119809	+	0.999928i	$0.503814\pi$
$194$	−1.22741			−0.0881228
$195$	−1.78901	+	15.7605i	−0.128114	+	1.12863i
$196$	1.00000			0.0714286
$197$	10.3662	−	5.98495i	0.738564	−	0.426410i	−0.0829831	−	0.996551i	$-0.526445\pi$
$197$	10.3662	−	5.98495i	0.738564	−	0.426410i	0.821547	+	0.570141i	$0.193111\pi$
$198$	−0.560908	−	0.971521i	−0.0398620	−	0.0690430i
$199$	−2.49684	+	4.32465i	−0.176996	+	0.306566i	−0.940850	−	0.338823i	$-0.889971\pi$
$199$	−2.49684	+	4.32465i	−0.176996	+	0.306566i	0.763854	+	0.645389i	$0.223305\pi$
$200$		−	14.3533i		−	1.01493i
$201$	4.56902	+	2.63792i	0.322274	+	0.186065i
$202$	9.36545	+	5.40714i	0.658951	+	0.380445i
$203$		−	6.74153i		−	0.473163i
$204$	1.57781	−	2.73284i	0.110468	−	0.191337i
$205$	4.52453	+	7.83671i	0.316007	+	0.547340i
$206$	−14.9745	+	8.64551i	−1.04332	+	0.602361i
$207$	5.40872			0.375932
$208$	3.58254	+	0.406663i	0.248405	+	0.0281970i
$209$	−9.05969			−0.626672
$210$	3.80986	−	2.19962i	0.262905	−	0.151788i
$211$	3.27743	+	5.67667i	0.225627	+	0.390798i	0.956507	−	0.291708i	$-0.0942235\pi$
$211$	3.27743	+	5.67667i	0.225627	+	0.390798i	−0.730880	+	0.682506i	$0.760890\pi$
$212$	4.22126	−	7.31143i	0.289917	−	0.502151i
$213$			8.67667i			0.594516i
$214$	12.3024	+	7.10282i	0.840977	+	0.485538i
$215$	−6.04212	−	3.48842i	−0.412069	−	0.237908i
$216$		−	1.00000i		−	0.0680414i
$217$	−2.79296	+	4.83755i	−0.189598	+	0.328394i
$218$	1.71910	+	2.97757i	0.116432	+	0.201667i
$219$	−11.0838	+	6.39924i	−0.748975	+	0.432421i
$220$	−4.93514			−0.332727
$221$	4.54121	+	10.4322i	0.305475	+	0.701743i
$222$	−7.61971			−0.511402
$223$	6.43757	−	3.71673i	0.431091	−	0.248891i	−0.268720	−	0.963218i	$-0.586601\pi$
$223$	6.43757	−	3.71673i	0.431091	−	0.248891i	0.699811	+	0.714328i	$0.253267\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	7.17667	−	12.4304i	0.478445	−	0.828691i
$226$			6.02589i			0.400837i
$227$	10.1529	+	5.86177i	0.673870	+	0.389059i	0.797542	−	0.603264i	$-0.206133\pi$
$227$	10.1529	+	5.86177i	0.673870	+	0.389059i	−0.123671	+	0.992323i	$0.539467\pi$
$228$	−6.99395	−	4.03796i	−0.463185	−	0.267420i
$229$		−	9.70668i		−	0.641436i	−0.947175	−	0.320718i	$-0.896076\pi$
$229$		−	9.70668i		−	0.641436i	0.947175	−	0.320718i	$-0.103924\pi$
$230$	11.8971	−	20.6065i	0.784474	−	1.35875i
$231$	−0.560908	−	0.971521i	−0.0369050	−	0.0639214i
$232$	−5.83834	+	3.37076i	−0.383305	+	0.221302i
$233$	−11.8444			−0.775952			−0.387976	−	0.921670i	$-0.626826\pi$
$233$	−11.8444			−0.775952			−0.387976	+	0.921670i	$0.626826\pi$
$234$	2.89924	+	2.14345i	0.189529	+	0.140122i
$235$	−33.3843			−2.17775
$236$	−6.30380	+	3.63950i	−0.410343	+	0.236911i
$237$	−1.76053	−	3.04933i	−0.114359	−	0.198075i
$238$	1.57781	−	2.73284i	0.102274	−	0.177144i
$239$			1.50484i			0.0973397i	0.998815	+	0.0486698i	$0.0154982\pi$
$239$			1.50484i			0.0973397i	−0.998815	+	0.0486698i	$0.984502\pi$
$240$	−3.80986	−	2.19962i	−0.245925	−	0.141985i
$241$	−2.56160	−	1.47894i	−0.165007	−	0.0952669i	0.415222	−	0.909720i	$-0.363704\pi$
$241$	−2.56160	−	1.47894i	−0.165007	−	0.0952669i	−0.580229	+	0.814453i	$0.697037\pi$
$242$		−	9.74153i		−	0.626209i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	5.20831	+	9.02106i	0.333428	+	0.577514i
$245$	3.80986	−	2.19962i	0.243403	−	0.140529i
$246$	2.05696			0.131147
$247$	26.6982	−	11.6220i	1.69877	−	0.739489i
$248$	5.58592			0.354706
$249$	9.64683	−	5.56960i	0.611343	−	0.352959i
$250$	−20.5738	−	35.6349i	−1.30120	−	2.25375i
$251$	−3.81728	+	6.61172i	−0.240944	+	0.417328i	−0.960984	−	0.276606i	$-0.910790\pi$
$251$	−3.81728	+	6.61172i	−0.240944	+	0.417328i	0.720039	+	0.693933i	$0.244124\pi$
$252$		−	1.00000i		−	0.0629941i
$253$	−5.25469	−	3.03380i	−0.330359	−	0.190733i
$254$	−8.44926	−	4.87818i	−0.530154	−	0.306084i
$255$		−	13.8823i		−	0.869343i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.6616	−	18.4665i	−0.665054	−	1.15191i	−0.979271	−	0.202555i	$-0.935075\pi$
$257$	−10.6616	−	18.4665i	−0.665054	−	1.15191i	0.314217	−	0.949351i	$-0.398258\pi$
$258$	−1.37344	+	0.792959i	−0.0855069	+	0.0493675i
$259$	−7.61971			−0.473466
$260$	14.5435	−	6.33092i	0.901949	−	0.392627i
$261$	−6.74153			−0.417290
$262$	−6.60571	+	3.81381i	−0.408102	+	0.235618i
$263$	2.65582	+	4.60002i	0.163765	+	0.283649i	0.936216	−	0.351425i	$-0.114303\pi$
$263$	2.65582	+	4.60002i	0.163765	+	0.283649i	−0.772451	+	0.635074i	$0.780969\pi$
$264$	−0.560908	+	0.971521i	−0.0345215	+	0.0597930i
$265$		−	37.1407i		−	2.28153i
$266$	−6.99395	−	4.03796i	−0.428826	−	0.247583i
$267$	9.02707	+	5.21178i	0.552448	+	0.318956i
$268$		−	5.27585i		−	0.322274i
$269$	1.01642	−	1.76048i	0.0619720	−	0.107339i	−0.833375	−	0.552708i	$-0.813594\pi$
$269$	1.01642	−	1.76048i	0.0619720	−	0.107339i	0.895347	+	0.445370i	$0.146928\pi$
$270$	−2.19962	−	3.80986i	−0.133865	−	0.231860i
$271$	1.22099	−	0.704938i	0.0741698	−	0.0428219i	−0.462456	−	0.886642i	$-0.653032\pi$
$271$	1.22099	−	0.704938i	0.0741698	−	0.0428219i	0.536626	+	0.843820i	$0.319699\pi$
$272$	−3.15561			−0.191337
$273$	2.89924	+	2.14345i	0.175470	+	0.129728i
$274$	−7.35334			−0.444232
$275$	−13.9446	+	8.05090i	−0.840889	+	0.485488i
$276$	−2.70436	−	4.68409i	−0.162783	−	0.281949i
$277$	11.7848	−	20.4119i	0.708080	−	1.22643i	−0.257488	−	0.966281i	$-0.582895\pi$
$277$	11.7848	−	20.4119i	0.708080	−	1.22643i	0.965568	−	0.260149i	$-0.0837718\pi$
$278$			8.58907i			0.515138i
$279$	4.83755	+	2.79296i	0.289616	+	0.167210i
$280$	−3.80986	−	2.19962i	−0.227682	−	0.131453i
$281$		−	8.12593i		−	0.484753i	−0.970182	−	0.242376i	$-0.922073\pi$
$281$		−	8.12593i		−	0.484753i	0.970182	−	0.242376i	$-0.0779268\pi$
$282$	−3.79432	+	6.57196i	−0.225949	+	0.391355i
$283$	−9.96358	−	17.2574i	−0.592273	−	1.02585i	−0.993926	−	0.110055i	$-0.964897\pi$
$283$	−9.96358	−	17.2574i	−0.592273	−	1.02585i	0.401652	−	0.915792i	$-0.368436\pi$
$284$	7.51422	−	4.33834i	0.445887	−	0.257433i
$285$	−35.5279			−2.10449
$286$	−1.61440	−	3.70862i	−0.0954613	−	0.219295i
$287$	2.05696			0.121418
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	3.52106	+	6.09865i	0.207121	+	0.358744i
$290$	−14.8288	+	25.6843i	−0.870778	+	1.50823i
$291$			1.22741i			0.0719519i
$292$	11.0838	+	6.39924i	0.648631	+	0.374487i
$293$	17.5078	+	10.1081i	1.02282	+	0.590523i	0.914918	−	0.403639i	$-0.132255\pi$
$293$	17.5078	+	10.1081i	1.02282	+	0.590523i	0.107898	+	0.994162i	$0.465588\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	−16.0111	+	27.7320i	−0.932200	+	1.61462i
$296$	3.80986	+	6.59886i	0.221443	+	0.383551i
$297$	−0.971521	+	0.560908i	−0.0563734	+	0.0325472i
$298$	3.47894			0.201530
$299$	19.3770	+	2.19953i	1.12060	+	0.127202i
$300$	−14.3533			−0.828691
$301$	−1.37344	+	0.792959i	−0.0791641	+	0.0457054i
$302$	−8.14956	−	14.1154i	−0.468954	−	0.812253i
$303$	5.40714	−	9.36545i	0.310632	−	0.538031i
$304$			8.07591i			0.463185i
$305$	39.6858	+	22.9126i	2.27240	+	1.31197i
$306$	−2.73284	−	1.57781i	−0.156226	−	0.0901971i
$307$		−	26.2764i		−	1.49967i	−0.661624	−	0.749836i	$-0.730132\pi$
$307$		−	26.2764i		−	1.49967i	0.661624	−	0.749836i	$-0.269868\pi$
$308$	−0.560908	+	0.971521i	−0.0319607	+	0.0553576i
$309$	8.64551	+	14.9745i	0.491826	+	0.851868i
$310$	21.2815	−	12.2869i	1.20871	−	0.697849i
$311$	7.30017			0.413954			0.206977	−	0.978346i	$-0.433637\pi$
$311$	7.30017			0.413954			0.206977	+	0.978346i	$0.433637\pi$
$312$	0.406663	−	3.58254i	0.0230227	−	0.202822i
$313$	25.4414			1.43803			0.719015	−	0.694994i	$-0.244593\pi$
$313$	25.4414			1.43803			0.719015	+	0.694994i	$0.244593\pi$
$314$	0.592856	−	0.342286i	0.0334568	−	0.0193163i
$315$	−2.19962	−	3.80986i	−0.123935	−	0.214661i
$316$	−1.76053	+	3.04933i	−0.0990375	+	0.171538i
$317$			20.2153i			1.13540i	0.823234	+	0.567702i	$0.192167\pi$
$317$			20.2153i			1.13540i	−0.823234	+	0.567702i	$0.807833\pi$
$318$	−7.31143	−	4.22126i	−0.410005	−	0.236716i
$319$	6.54954	+	3.78138i	0.366704	+	0.211716i
$320$			4.39924i			0.245925i
$321$	7.10282	−	12.3024i	0.396440	−	0.686655i
$322$	−2.70436	−	4.68409i	−0.150708	−	0.261034i
$323$	−22.0702	+	12.7422i	−1.22802	+	0.708996i
$324$	−1.00000			−0.0555556
$325$	30.7657	−	41.6138i	1.70657	−	2.30832i
$326$	−14.0516			−0.778246
$327$	2.97757	−	1.71910i	0.164660	−	0.0950666i
$328$	−1.02848	−	1.78138i	−0.0567882	−	0.0983601i
$329$	−3.79432	+	6.57196i	−0.209188	+	0.362324i
$330$			4.93514i			0.271671i
$331$	−21.0120	−	12.1313i	−1.15492	−	0.666796i	−0.204842	−	0.978795i	$-0.565668\pi$
$331$	−21.0120	−	12.1313i	−1.15492	−	0.666796i	−0.950083	+	0.311999i	$0.899002\pi$
$332$	−9.64683	−	5.56960i	−0.529438	−	0.305671i
$333$			7.61971i			0.417558i
$334$	−0.243632	+	0.421983i	−0.0133310	+	0.0230899i
$335$	−11.6049	−	20.1002i	−0.634042	−	1.09819i
$336$	−0.866025	+	0.500000i	−0.0472456	+	0.0272772i
$337$	8.14035			0.443433			0.221717	−	0.975111i	$-0.428834\pi$
$337$	8.14035			0.443433			0.221717	+	0.975111i	$0.428834\pi$
$338$	9.51501	+	8.85803i	0.517548	+	0.481813i
$339$	6.02589			0.327282
$340$	−12.0224	+	6.94115i	−0.652008	+	0.376437i
$341$	−3.13319	−	5.42684i	−0.169672	−	0.293880i
$342$	−4.03796	+	6.99395i	−0.218348	+	0.378189i
$343$		−	1.00000i		−	0.0539949i
$344$	1.37344	+	0.792959i	0.0740512	+	0.0427535i
$345$	−20.6065	−	11.8971i	−1.10941	−	0.640520i
$346$		−	3.43821i		−	0.184839i
$347$	6.73894	−	11.6722i	0.361765	−	0.626596i	−0.626486	−	0.779433i	$-0.715507\pi$
$347$	6.73894	−	11.6722i	0.361765	−	0.626596i	0.988251	+	0.152836i	$0.0488408\pi$
$348$	3.37076	+	5.83834i	0.180692	+	0.312968i
$349$	−5.64467	+	3.25895i	−0.302152	+	0.174448i	−0.643409	−	0.765522i	$-0.722481\pi$
$349$	−5.64467	+	3.25895i	−0.302152	+	0.174448i	0.341257	+	0.939970i	$0.389147\pi$
$350$	−14.3533			−0.767218
$351$	2.14345	−	2.89924i	0.114409	−	0.154750i
$352$	1.12182			0.0597930
$353$	20.7274	−	11.9669i	1.10321	−	0.636936i	0.166145	−	0.986101i	$-0.446868\pi$
$353$	20.7274	−	11.9669i	1.10321	−	0.636936i	0.937061	+	0.349165i	$0.113535\pi$
$354$	3.63950	+	6.30380i	0.193437	+	0.335043i
$355$	19.0854	−	33.0569i	1.01295	−	1.75448i
$356$		−	10.4236i		−	0.552448i
$357$	−2.73284	−	1.57781i	−0.144637	−	0.0835063i
$358$	1.88451	+	1.08802i	0.0995993	+	0.0575037i
$359$		−	7.32429i		−	0.386561i	−0.981144	−	0.193281i	$-0.938087\pi$
$359$		−	7.32429i		−	0.386561i	0.981144	−	0.193281i	$-0.0619128\pi$
$360$	−2.19962	+	3.80986i	−0.115930	+	0.200797i
$361$	23.1102	+	40.0280i	1.21633	+	2.10674i
$362$	−9.28274	+	5.35939i	−0.487890	+	0.281684i
$363$	−9.74153			−0.511298
$364$	0.406663	−	3.58254i	0.0213149	−	0.187776i
$365$	56.3037			2.94707
$366$	9.02106	−	5.20831i	0.471538	−	0.272243i
$367$	−5.11150	−	8.85339i	−0.266818	−	0.462143i	0.701220	−	0.712945i	$-0.252639\pi$
$367$	−5.11150	−	8.85339i	−0.266818	−	0.462143i	−0.968038	+	0.250802i	$0.919306\pi$
$368$	−2.70436	+	4.68409i	−0.140975	+	0.244175i
$369$		−	2.05696i		−	0.107081i
$370$	29.0300	+	16.7605i	1.50920	+	0.871336i
$371$	−7.31143	−	4.22126i	−0.379591	−	0.219157i
$372$		−	5.58592i		−	0.289616i
$373$	−0.781422	+	1.35346i	−0.0404605	+	0.0700797i	−0.885547	−	0.464551i	$-0.846216\pi$
$373$	−0.781422	+	1.35346i	−0.0404605	+	0.0700797i	0.845086	+	0.534630i	$0.179549\pi$
$374$	1.77001	+	3.06574i	0.0915249	+	0.158526i
$375$	−35.6349	+	20.5738i	−1.84018	+	1.06243i
$376$	7.58865			0.391355
$377$	−24.1518	−	2.74153i	−1.24388	−	0.141196i
$378$	−1.00000			−0.0514344
$379$	−7.26194	+	4.19268i	−0.373021	+	0.215364i	−0.674777	−	0.738021i	$-0.735760\pi$
$379$	−7.26194	+	4.19268i	−0.373021	+	0.215364i	0.301757	+	0.953385i	$0.402427\pi$
$380$	17.7640	+	30.7681i	0.911272	+	1.57837i
$381$	−4.87818	+	8.44926i	−0.249917	+	0.432869i
$382$		−	15.2563i		−	0.780578i
$383$	7.89645	+	4.55902i	0.403490	+	0.232955i	0.687989	−	0.725722i	$-0.258494\pi$
$383$	7.89645	+	4.55902i	0.403490	+	0.232955i	−0.284499	+	0.958676i	$0.591827\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$			4.93514i			0.251518i
$386$	7.08987	−	12.2800i	0.360865	−	0.625036i
$387$	0.792959	+	1.37344i	0.0403084	+	0.0698161i
$388$	1.06297	−	0.613704i	0.0539639	−	0.0311561i
$389$	37.1923			1.88572			0.942862	−	0.333184i	$-0.108123\pi$
$389$	37.1923			1.88572			0.942862	+	0.333184i	$0.108123\pi$
$390$	−6.33092	−	14.5435i	−0.320578	−	0.736438i
$391$	−17.0678			−0.863157
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$	3.81381	+	6.60571i	0.192381	+	0.333214i
$394$	−5.98495	+	10.3662i	−0.301517	+	0.522243i
$395$			15.4900i			0.779386i
$396$	0.971521	+	0.560908i	0.0488208	+	0.0281867i
$397$	−27.4588	−	15.8533i	−1.37812	−	0.795656i	−0.386184	−	0.922422i	$-0.626207\pi$
$397$	−27.4588	−	15.8533i	−1.37812	−	0.795656i	−0.991933	+	0.126765i	$0.959541\pi$
$398$		−	4.99368i		−	0.250310i
$399$	−4.03796	+	6.99395i	−0.202151	+	0.350135i
$400$	7.17667	+	12.4304i	0.358834	+	0.621518i
$401$	−23.3818	+	13.4995i	−1.16763	+	0.674132i	−0.953121	−	0.302590i	$-0.902149\pi$
$401$	−23.3818	+	13.4995i	−1.16763	+	0.674132i	−0.214509	+	0.976722i	$0.568815\pi$
$402$	−5.27585			−0.263135
$403$	16.1949	+	11.9731i	0.806727	+	0.596425i
$404$	−10.8143			−0.538031
$405$	−3.80986	+	2.19962i	−0.189313	+	0.109300i
$406$	3.37076	+	5.83834i	0.167288	+	0.289752i
$407$	4.27396	−	7.40271i	0.211852	−	0.366939i
$408$			3.15561i			0.156226i
$409$	8.94747	+	5.16583i	0.442424	+	0.255434i	0.704625	−	0.709580i	$-0.251115\pi$
$409$	8.94747	+	5.16583i	0.442424	+	0.255434i	−0.262201	+	0.965013i	$0.584448\pi$
$410$	−7.83671	−	4.52453i	−0.387028	−	0.223451i
$411$			7.35334i			0.362714i
$412$	8.64551	−	14.9745i	0.425934	−	0.737739i
$413$	3.63950	+	6.30380i	0.179088	+	0.310190i
$414$	−4.68409	+	2.70436i	−0.230210	+	0.132912i
$415$	−49.0040			−2.40551
$416$	−3.30591	+	1.43909i	−0.162085	+	0.0705573i
$417$	8.58907			0.420609
$418$	7.84592	−	4.52984i	0.383757	−	0.221562i
$419$	−12.7635	−	22.1070i	−0.623536	−	1.08000i	−0.988822	−	0.149101i	$-0.952362\pi$
$419$	−12.7635	−	22.1070i	−0.623536	−	1.08000i	0.365285	−	0.930896i	$-0.380971\pi$
$420$	−2.19962	+	3.80986i	−0.107331	+	0.185902i
$421$			4.31438i			0.210270i	0.994458	+	0.105135i	$0.0335274\pi$
$421$			4.31438i			0.210270i	−0.994458	+	0.105135i	$0.966473\pi$
$422$	−5.67667	−	3.27743i	−0.276336	−	0.159543i
$423$	6.57196	+	3.79432i	0.319540	+	0.184486i
$424$			8.44252i			0.410005i
$425$	−22.6468	+	39.2254i	−1.09853	+	1.90271i
$426$	−4.33834	−	7.51422i	−0.210193	−	0.364065i
$427$	9.02106	−	5.20831i	0.436560	−	0.252048i
$428$	−14.2056			−0.686655
$429$	−3.70862	+	1.61440i	−0.179054	+	0.0779438i
$430$	6.97684			0.336453
$431$	−6.37502	+	3.68062i	−0.307074	+	0.177289i	−0.645616	−	0.763662i	$-0.723399\pi$
$431$	−6.37502	+	3.68062i	−0.307074	+	0.177289i	0.338542	+	0.940951i	$0.390066\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−13.4103	+	23.2273i	−0.644458	+	1.11623i	0.339969	+	0.940437i	$0.389584\pi$
$433$	−13.4103	+	23.2273i	−0.644458	+	1.11623i	−0.984426	+	0.175797i	$0.943750\pi$
$434$		−	5.58592i		−	0.268133i
$435$	25.6843	+	14.8288i	1.23147	+	0.710987i
$436$	−2.97757	−	1.71910i	−0.142600	−	0.0823301i
$437$			43.6804i			2.08952i
$438$	6.39924	−	11.0838i	0.305768	−	0.529605i
$439$	17.4346	+	30.1976i	0.832109	+	1.44125i	0.896363	+	0.443321i	$0.146200\pi$
$439$	17.4346	+	30.1976i	0.832109	+	1.44125i	−0.0642541	+	0.997934i	$0.520467\pi$
$440$	4.27396	−	2.46757i	0.203753	−	0.117637i
$441$	−1.00000			−0.0476190
$442$	−9.14888	−	6.76390i	−0.435168	−	0.321726i
$443$	−8.59832			−0.408518			−0.204259	−	0.978917i	$-0.565479\pi$
$443$	−8.59832			−0.408518			−0.204259	+	0.978917i	$0.565479\pi$
$444$	6.59886	−	3.80986i	0.313168	−	0.180808i
$445$	−22.9279	−	39.7123i	−1.08689	−	1.88254i
$446$	−3.71673	+	6.43757i	−0.175992	+	0.304828i
$447$		−	3.47894i		−	0.164548i
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	−27.1348	−	15.6663i	−1.28057	−	0.739337i	−0.303616	−	0.952794i	$-0.598194\pi$
$449$	−27.1348	−	15.6663i	−1.28057	−	0.739337i	−0.976952	+	0.213458i	$0.931527\pi$
$450$			14.3533i			0.676623i
$451$	−1.15376	+	1.99838i	−0.0543286	+	0.0940999i
$452$	−3.01295	−	5.21858i	−0.141717	−	0.245461i
$453$	−14.1154	+	8.14956i	−0.663202	+	0.382900i
$454$	−11.7235			−0.550213
$455$	−6.33092	−	14.5435i	−0.296798	−	0.681809i
$456$	8.07591			0.378189
$457$	8.32180	−	4.80459i	0.389277	−	0.224749i	−0.292570	−	0.956244i	$-0.594510\pi$
$457$	8.32180	−	4.80459i	0.389277	−	0.224749i	0.681847	+	0.731495i	$0.261177\pi$
$458$	4.85334	+	8.40623i	0.226782	+	0.392797i
$459$	−1.57781	+	2.73284i	−0.0736457	+	0.127558i
$460$			23.7943i			1.10941i
$461$	−11.5452	−	6.66562i	−0.537713	−	0.310449i	0.206439	−	0.978460i	$-0.433813\pi$
$461$	−11.5452	−	6.66562i	−0.537713	−	0.310449i	−0.744151	+	0.668011i	$0.767146\pi$
$462$	0.971521	+	0.560908i	0.0451993	+	0.0260958i
$463$			5.55011i			0.257935i	0.991649	+	0.128968i	$0.0411664\pi$
$463$			5.55011i			0.257935i	−0.991649	+	0.128968i	$0.958834\pi$
$464$	3.37076	−	5.83834i	0.156484	−	0.271038i
$465$	−12.2869	−	21.2815i	−0.569792	−	0.986908i
$466$	10.2575	−	5.92219i	0.475171	−	0.274340i
$467$	−16.9272			−0.783299			−0.391650	−	0.920114i	$-0.628095\pi$
$467$	−16.9272			−0.783299			−0.391650	+	0.920114i	$0.628095\pi$
$468$	−3.58254	−	0.406663i	−0.165603	−	0.0187980i
$469$	−5.27585			−0.243616
$470$	28.9117	−	16.6922i	1.33360	−	0.769952i
$471$	−0.342286	−	0.592856i	−0.0157717	−	0.0273174i
$472$	3.63950	−	6.30380i	0.167522	−	0.290156i
$473$		−	1.77911i		−	0.0818035i
$474$	3.04933	+	1.76053i	0.140060	+	0.0808638i
$475$	100.386	+	57.9582i	4.60605	+	2.65930i
$476$			3.15561i			0.144637i
$477$	−4.22126	+	7.31143i	−0.193278	+	0.334768i
$478$	−0.752418	−	1.30323i	−0.0344148	−	0.0596081i
$479$	16.7981	−	9.69840i	0.767526	−	0.443131i	−0.0644654	−	0.997920i	$-0.520534\pi$
$479$	16.7981	−	9.69840i	0.767526	−	0.443131i	0.831991	+	0.554789i	$0.187201\pi$
$480$	4.39924			0.200797
$481$	−3.09865	+	27.2980i	−0.141286	+	1.24468i
$482$	2.95788			0.134728
$483$	−4.68409	+	2.70436i	−0.213133	+	0.123053i
$484$	4.87076	+	8.43641i	0.221398	+	0.383473i
$485$	2.69983	−	4.67625i	0.122593	−	0.212337i
$486$			1.00000i			0.0453609i
$487$	−13.3417	−	7.70283i	−0.604570	−	0.349049i	0.166267	−	0.986081i	$-0.446829\pi$
$487$	−13.3417	−	7.70283i	−0.604570	−	0.349049i	−0.770837	+	0.637032i	$0.780162\pi$
$488$	−9.02106	−	5.20831i	−0.408364	−	0.235769i
$489$			14.0516i			0.635435i
$490$	−2.19962	+	3.80986i	−0.0993688	+	0.172112i
$491$	−4.87818	−	8.44926i	−0.220149	−	0.381310i	0.734704	−	0.678388i	$-0.237321\pi$
$491$	−4.87818	−	8.44926i	−0.220149	−	0.381310i	−0.954853	+	0.297078i	$0.903988\pi$
$492$	−1.78138	+	1.02848i	−0.0803107	+	0.0463674i
$493$	21.2736			0.958117
$494$	−17.3103	+	23.4140i	−0.778829	+	1.05345i
$495$	4.93514			0.221818
$496$	−4.83755	+	2.79296i	−0.217212	+	0.125408i
$497$	−4.33834	−	7.51422i	−0.194601	−	0.337059i
$498$	−5.56960	+	9.64683i	−0.249580	+	0.432285i
$499$			5.52642i			0.247397i	0.992320	+	0.123698i	$0.0394755\pi$
$499$			5.52642i			0.247397i	−0.992320	+	0.123698i	$0.960525\pi$
$500$	35.6349	+	20.5738i	1.59364	+	0.920089i
$501$	0.421983	+	0.243632i	0.0188528	+	0.0108847i
$502$		−	7.63455i		−	0.340747i
$503$	−2.06759	+	3.58117i	−0.0921893	+	0.159677i	−0.908432	−	0.418032i	$-0.862720\pi$
$503$	−2.06759	+	3.58117i	−0.0921893	+	0.159677i	0.816243	+	0.577709i	$0.196053\pi$
$504$	0.500000	+	0.866025i	0.0222718	+	0.0385758i
$505$	−41.2009	+	23.7873i	−1.83342	+	1.05852i
$506$	6.06759			0.269737
$507$	8.85803	−	9.51501i	0.393399	−	0.422576i
$508$	9.75637			0.432869
$509$	−7.70067	+	4.44599i	−0.341326	+	0.197065i	−0.660858	−	0.750511i	$-0.729808\pi$
$509$	−7.70067	+	4.44599i	−0.341326	+	0.197065i	0.319532	+	0.947575i	$0.396474\pi$
$510$	6.94115	+	12.0224i	0.307359	+	0.532362i
$511$	6.39924	−	11.0838i	0.283086	−	0.490319i
$512$		−	1.00000i		−	0.0441942i
$513$	6.99395	+	4.03796i	0.308790	+	0.178280i
$514$	18.4665	+	10.6616i	0.814521	+	0.470264i
$515$		−	76.0674i		−	3.35193i
$516$	0.792959	−	1.37344i	0.0349081	−	0.0604625i
$517$	−4.25653	−	7.37253i	−0.187202	−	0.324244i
$518$	6.59886	−	3.80986i	0.289937	−	0.167395i
$519$	−3.43821			−0.150921
$520$	−9.42957	+	12.7545i	−0.413514	+	0.559321i
$521$	8.17974			0.358361			0.179180	−	0.983816i	$-0.442655\pi$
$521$	8.17974			0.358361			0.179180	+	0.983816i	$0.442655\pi$
$522$	5.83834	−	3.37076i	0.255537	−	0.147534i
$523$	−3.12787	−	5.41763i	−0.136772	−	0.236896i	0.789501	−	0.613749i	$-0.210339\pi$
$523$	−3.12787	−	5.41763i	−0.136772	−	0.236896i	−0.926273	+	0.376853i	$0.877006\pi$
$524$	3.81381	−	6.60571i	0.166607	−	0.288572i
$525$			14.3533i			0.626431i
$526$	−4.60002	−	2.65582i	−0.200570	−	0.115799i
$527$	−15.2654	−	8.81349i	−0.664972	−	0.383922i
$528$		−	1.12182i		−	0.0488208i
$529$	−3.12713	+	5.41635i	−0.135962	+	0.235494i
$530$	18.5703	+	32.1648i	0.806644	+	1.39715i
$531$	6.30380	−	3.63950i	0.273562	−	0.157941i
$532$	8.07591			0.350135
$533$	0.836488	−	7.36914i	0.0362323	−	0.319193i
$534$	−10.4236			−0.451072
$535$	−54.1214	+	31.2470i	−2.33987	+	1.35093i
$536$	2.63792	+	4.56902i	0.113941	+	0.197352i
$537$	1.08802	−	1.88451i	0.0469516	−	0.0813225i
$538$			2.03283i			0.0876416i
$539$	0.971521	+	0.560908i	0.0418464	+	0.0241600i
$540$	3.80986	+	2.19962i	0.163950	+	0.0946566i
$541$		−	35.8526i		−	1.54142i	−0.637183	−	0.770712i	$-0.719901\pi$
$541$		−	35.8526i		−	1.54142i	0.637183	−	0.770712i	$-0.280099\pi$
$542$	−0.704938	+	1.22099i	−0.0302797	+	0.0524459i
$543$	5.35939	+	9.28274i	0.229994	+	0.398361i
$544$	2.73284	−	1.57781i	0.117170	−	0.0676479i
$545$	−15.1255			−0.647906
$546$	−3.58254	−	0.406663i	−0.153319	−	0.0174036i
$547$	16.7073			0.714353			0.357177	−	0.934037i	$-0.383739\pi$
$547$	16.7073			0.714353			0.357177	+	0.934037i	$0.383739\pi$
$548$	6.36818	−	3.67667i	0.272035	−	0.157060i
$549$	−5.20831	−	9.02106i	−0.222285	−	0.385009i
$550$	8.05090	−	13.9446i	0.343292	−	0.594599i
$551$		−	54.4440i		−	2.31939i
$552$	4.68409	+	2.70436i	0.199368	+	0.115105i
$553$	3.04933	+	1.76053i	0.129671	+	0.0748653i
$554$			23.5696i			1.00138i
$555$	16.7605	−	29.0300i	0.711443	−	1.23226i
$556$	−4.29454	−	7.43835i	−0.182129	−	0.315456i
$557$	−12.1384	+	7.00811i	−0.514321	+	0.296943i	−0.734608	−	0.678492i	$-0.762634\pi$
$557$	−12.1384	+	7.00811i	−0.514321	+	0.296943i	0.220287	+	0.975435i	$0.429301\pi$
$558$	−5.58592			−0.236471
$559$	2.28228	+	5.24289i	0.0965302	+	0.221751i
$560$	4.39924			0.185902
$561$	3.06574	−	1.77001i	0.129436	−	0.0747298i
$562$	4.06297	+	7.03726i	0.171386	+	0.296849i
$563$	13.4476	−	23.2919i	0.566747	−	0.981635i	−0.430138	−	0.902763i	$-0.641535\pi$
$563$	13.4476	−	23.2919i	0.566747	−	0.981635i	0.996885	−	0.0788716i	$-0.0251317\pi$
$564$		−	7.58865i		−	0.319540i
$565$	−22.9578	−	13.2547i	−0.965842	−	0.557629i
$566$	17.2574	+	9.96358i	0.725383	+	0.418800i
$567$			1.00000i			0.0419961i
$568$	−4.33834	+	7.51422i	−0.182033	+	0.315290i
$569$	3.92493	+	6.79817i	0.164541	+	0.284994i	0.936492	−	0.350688i	$-0.114052\pi$
$569$	3.92493	+	6.79817i	0.164541	+	0.284994i	−0.771951	+	0.635682i	$0.780719\pi$
$570$	30.7681	−	17.7640i	1.28873	−	0.744050i
$571$	7.24502			0.303195			0.151597	−	0.988442i	$-0.451558\pi$
$571$	7.24502			0.303195			0.151597	+	0.988442i	$0.451558\pi$
$572$	3.25242	+	2.40456i	0.135990	+	0.100540i
$573$	−15.2563			−0.637340
$574$	−1.78138	+	1.02848i	−0.0743533	+	0.0429279i
$575$	38.8166	+	67.2323i	1.61876	+	2.80378i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	31.9688i		−	1.33088i	−0.746451	−	0.665440i	$-0.768244\pi$
$577$		−	31.9688i		−	1.33088i	0.746451	−	0.665440i	$-0.231756\pi$
$578$	−6.09865	−	3.52106i	−0.253671	−	0.146457i
$579$	−12.2800	−	7.08987i	−0.510340	−	0.294645i
$580$		−	29.6576i		−	1.23147i
$581$	−5.56960	+	9.64683i	−0.231066	+	0.400218i
$582$	−0.613704	−	1.06297i	−0.0254388	−	0.0440614i
$583$	8.20208	−	4.73548i	0.339696	−	0.196123i
$584$	−12.7985			−0.529605
$585$	−14.5435	+	6.33092i	−0.601299	+	0.261751i
$586$	−20.2163			−0.835126
$587$	−3.59302	+	2.07443i	−0.148300	+	0.0856210i	−0.572314	−	0.820035i	$-0.693954\pi$
$587$	−3.59302	+	2.07443i	−0.148300	+	0.0856210i	0.424014	+	0.905656i	$0.360621\pi$
$588$	0.500000	+	0.866025i	0.0206197	+	0.0357143i
$589$	−22.5557	+	39.0676i	−0.929391	+	1.60975i
$590$		−	32.0221i		−	1.31833i
$591$	10.3662	+	5.98495i	0.426410	+	0.246188i
$592$	−6.59886	−	3.80986i	−0.271212	−	0.156584i
$593$			21.0163i			0.863037i	0.902104	+	0.431519i	$0.142022\pi$
$593$			21.0163i			0.863037i	−0.902104	+	0.431519i	$0.857978\pi$
$594$	0.560908	−	0.971521i	0.0230143	−	0.0398620i
$595$	6.94115	+	12.0224i	0.284559	+	0.492871i
$596$	−3.01285	+	1.73947i	−0.123411	+	0.0712515i
$597$	−4.99368			−0.204378
$598$	−17.8807	+	7.78365i	−0.731197	+	0.318297i
$599$	−35.0575			−1.43241			−0.716205	−	0.697890i	$-0.754122\pi$
$599$	−35.0575			−1.43241			−0.716205	+	0.697890i	$0.754122\pi$
$600$	12.4304	−	7.17667i	0.507467	−	0.292986i
$601$	15.7586	+	27.2947i	0.642806	+	1.11337i	0.984803	+	0.173672i	$0.0555634\pi$
$601$	15.7586	+	27.2947i	0.642806	+	1.11337i	−0.341997	+	0.939701i	$0.611103\pi$
$602$	0.792959	−	1.37344i	0.0323186	−	0.0559774i
$603$			5.27585i			0.214849i
$604$	14.1154	+	8.14956i	0.574349	+	0.331601i
$605$	37.1138	+	21.4277i	1.50889	+	0.871159i
$606$			10.8143i			0.439300i
$607$	−16.9445	+	29.3488i	−0.687757	+	1.19123i	0.284805	+	0.958586i	$0.408071\pi$
$607$	−16.9445	+	29.3488i	−0.687757	+	1.19123i	−0.972562	+	0.232645i	$0.925262\pi$
$608$	−4.03796	−	6.99395i	−0.163761	−	0.283642i
$609$	5.83834	−	3.37076i	0.236581	−	0.136590i
$610$	−45.8253			−1.85541
$611$	22.0013	+	16.2659i	0.890079	+	0.658048i
$612$	3.15561			0.127558
$613$	−7.08979	+	4.09329i	−0.286354	+	0.165327i	−0.636296	−	0.771445i	$-0.719534\pi$
$613$	−7.08979	+	4.09329i	−0.286354	+	0.165327i	0.349942	+	0.936771i	$0.386201\pi$
$614$	13.1382	+	22.7560i	0.530214	+	0.918358i
$615$	−4.52453	+	7.83671i	−0.182447	+	0.316007i
$616$		−	1.12182i		−	0.0451993i
$617$	−31.4716	−	18.1701i	−1.26700	−	0.731502i	−0.292580	−	0.956241i	$-0.594514\pi$
$617$	−31.4716	−	18.1701i	−1.26700	−	0.731502i	−0.974419	+	0.224739i	$0.927847\pi$
$618$	−14.9745	−	8.64551i	−0.602361	−	0.347773i
$619$		−	38.2625i		−	1.53790i	−0.639309	−	0.768950i	$-0.720780\pi$
$619$		−	38.2625i		−	1.53790i	0.639309	−	0.768950i	$-0.279220\pi$
$620$	−12.2869	+	21.2815i	−0.493454	+	0.854687i
$621$	2.70436	+	4.68409i	0.108522	+	0.187966i
$622$	−6.32213	+	3.65008i	−0.253494	+	0.146355i
$623$	−10.4236			−0.417611
$624$	1.43909	+	3.30591i	0.0576098	+	0.132342i
$625$	109.252			4.37007
$626$	−22.0329	+	12.7207i	−0.880610	+	0.508421i
$627$	−4.52984	−	7.84592i	−0.180905	−	0.313336i
$628$	−0.342286	+	0.592856i	−0.0136587	+	0.0236575i
$629$		−	24.0449i		−	0.958731i
$630$	3.80986	+	2.19962i	0.151788	+	0.0876350i
$631$	−8.77412	−	5.06574i	−0.349292	−	0.201664i	0.315081	−	0.949065i	$-0.397968\pi$
$631$	−8.77412	−	5.06574i	−0.349292	−	0.201664i	−0.664374	+	0.747401i	$0.731302\pi$
$632$		−	3.52106i		−	0.140060i
$633$	−3.27743	+	5.67667i	−0.130266	+	0.225627i
$634$	−10.1077	−	17.5070i	−0.401426	−	0.695290i
$635$	37.1704	−	21.4603i	1.47506	−	0.851627i
$636$	8.44252			0.334768
$637$	−3.58254	−	0.406663i	−0.141946	−	0.0161126i
$638$	−7.56276			−0.299412
$639$	−7.51422	+	4.33834i	−0.297258	+	0.171622i
$640$	−2.19962	−	3.80986i	−0.0869477	−	0.150598i
$641$	13.4520	−	23.2995i	0.531322	−	0.920276i	−0.468010	−	0.883723i	$-0.655029\pi$
$641$	13.4520	−	23.2995i	0.531322	−	0.920276i	0.999332	−	0.0365532i	$-0.0116378\pi$
$642$			14.2056i			0.560652i
$643$	−28.9459	−	16.7119i	−1.14151	−	0.659053i	−0.194708	−	0.980861i	$-0.562376\pi$
$643$	−28.9459	−	16.7119i	−1.14151	−	0.659053i	−0.946805	+	0.321808i	$0.895709\pi$
$644$	4.68409	+	2.70436i	0.184579	+	0.106567i
$645$		−	6.97684i		−	0.274713i
$646$	12.7422	−	22.0702i	0.501336	−	0.868339i
$647$	−10.8789	−	18.8428i	−0.427693	−	0.740786i	0.568975	−	0.822355i	$-0.307340\pi$
$647$	−10.8789	−	18.8428i	−0.427693	−	0.740786i	−0.996668	+	0.0815693i	$0.974007\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−8.16570			−0.320532
$650$	−5.83697	+	51.4215i	−0.228945	+	2.01692i
$651$	−5.58592			−0.218929
$652$	12.1690	−	7.02580i	0.476576	−	0.275151i
$653$	−3.21872	−	5.57498i	−0.125958	−	0.218166i	0.796149	−	0.605101i	$-0.206867\pi$
$653$	−3.21872	−	5.57498i	−0.125958	−	0.218166i	−0.922107	+	0.386935i	$0.873534\pi$
$654$	−1.71910	+	2.97757i	−0.0672223	+	0.116432i
$655$		−	33.5557i		−	1.31113i
$656$	1.78138	+	1.02848i	0.0695511	+	0.0401554i
$657$	−11.0838	−	6.39924i	−0.432421	−	0.249658i
$658$		−	7.58865i		−	0.295836i
$659$	−4.51690	+	7.82350i	−0.175953	+	0.304760i	−0.940491	−	0.339819i	$-0.889634\pi$
$659$	−4.51690	+	7.82350i	−0.175953	+	0.304760i	0.764537	+	0.644579i	$0.222967\pi$
$660$	−2.46757	−	4.27396i	−0.0960501	−	0.166364i
$661$	−8.45556	+	4.88182i	−0.328883	+	0.189881i	−0.655345	−	0.755330i	$-0.727477\pi$
$661$	−8.45556	+	4.88182i	−0.328883	+	0.189881i	0.326462	+	0.945210i	$0.394143\pi$
$662$	24.2626			0.942992
$663$	−6.76390	+	9.14888i	−0.262688	+	0.355313i
$664$	11.1392			0.432285
$665$	30.7681	−	17.7640i	1.19313	−	0.688857i
$666$	−3.80986	−	6.59886i	−0.147629	−	0.255701i
$667$	18.2315	−	31.5779i	0.705927	−	1.22270i
$668$		−	0.487264i		−	0.0188528i
$669$	6.43757	+	3.71673i	0.248891	+	0.143697i
$670$	20.1002	+	11.6049i	0.776540	+	0.448335i
$671$			11.6855i			0.451115i
$672$	0.500000	−	0.866025i	0.0192879	−	0.0334077i
$673$	−20.3902	−	35.3169i	−0.785985	−	1.36137i	−0.928409	−	0.371559i	$-0.878823\pi$
$673$	−20.3902	−	35.3169i	−0.785985	−	1.36137i	0.142425	−	0.989806i	$-0.454510\pi$
$674$	−7.04975	+	4.07017i	−0.271546	+	0.156777i
$675$	14.3533			0.552460
$676$	−12.6693	−	2.91377i	−0.487279	−	0.112068i
$677$	28.6313			1.10039			0.550195	−	0.835036i	$-0.314553\pi$
$677$	28.6313			1.10039			0.550195	+	0.835036i	$0.314553\pi$
$678$	−5.21858	+	3.01295i	−0.200418	+	0.115712i
$679$	−0.613704	−	1.06297i	−0.0235518	−	0.0407929i
$680$	6.94115	−	12.0224i	0.266181	−	0.461039i
$681$			11.7235i			0.449247i
$682$	5.42684	+	3.13319i	0.207804	+	0.119976i
$683$	34.7160	+	20.0433i	1.32837	+	0.766935i	0.985047	−	0.172283i	$-0.0551144\pi$
$683$	34.7160	+	20.0433i	1.32837	+	0.766935i	0.343322	+	0.939218i	$0.388448\pi$
$684$		−	8.07591i		−	0.308790i
$685$	16.1746	−	28.0152i	0.617998	−	1.07040i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	8.40623	−	4.85334i	0.320718	−	0.185166i
$688$	−1.58592			−0.0604625
$689$	−18.0961	+	24.4769i	−0.689408	+	0.932496i
$690$	23.7943			0.905833
$691$	−24.3518	+	14.0595i	−0.926385	+	0.534848i	−0.885666	−	0.464322i	$-0.846298\pi$
$691$	−24.3518	+	14.0595i	−0.926385	+	0.534848i	−0.0407184	+	0.999171i	$0.512965\pi$
$692$	1.71910	+	2.97757i	0.0653505	+	0.113190i
$693$	0.560908	−	0.971521i	0.0213071	−	0.0369050i
$694$			13.4779i			0.511614i
$695$	−32.7231	−	18.8927i	−1.24126	−	0.716641i
$696$	−5.83834	−	3.37076i	−0.221302	−	0.127768i
$697$			6.49096i			0.245863i
$698$	3.25895	−	5.64467i	0.123353	−	0.213654i
$699$	−5.92219	−	10.2575i	−0.223998	−	0.387976i
$700$	12.4304	−	7.17667i	0.469823	−	0.271253i
$701$	−3.59224			−0.135677			−0.0678385	−	0.997696i	$-0.521610\pi$
$701$	−3.59224			−0.135677			−0.0678385	+	0.997696i	$0.521610\pi$
$702$	−0.406663	+	3.58254i	−0.0153485	+	0.135214i
$703$	−61.5361			−2.32088
$704$	−0.971521	+	0.560908i	−0.0366156	+	0.0211400i
$705$	−16.6922	−	28.9117i	−0.628663	−	1.08888i
$706$	−11.9669	+	20.7274i	−0.450382	+	0.780085i
$707$			10.8143i			0.406713i
$708$	−6.30380	−	3.63950i	−0.236911	−	0.136781i
$709$	7.28564	+	4.20637i	0.273618	+	0.157973i	0.630531	−	0.776164i	$-0.282837\pi$
$709$	7.28564	+	4.20637i	0.273618	+	0.157973i	−0.356913	+	0.934138i	$0.616171\pi$
$710$			38.1708i			1.43252i
$711$	1.76053	−	3.04933i	0.0660250	−	0.114359i
$712$	5.21178	+	9.02707i	0.195320	+	0.338304i
$713$	−26.1649	+	15.1063i	−0.979885	+	0.565737i
$714$	3.15561			0.118096
$715$	17.6804	+	2.00694i	0.661208	+	0.0750552i
$716$	−2.17604			−0.0813225
$717$	−1.30323	+	0.752418i	−0.0486698	+	0.0280995i
$718$	3.66215	+	6.34302i	0.136670	+	0.236720i
$719$	−24.1674	+	41.8591i	−0.901290	+	1.56108i	−0.0754696	+	0.997148i	$0.524046\pi$
$719$	−24.1674	+	41.8591i	−0.901290	+	1.56108i	−0.825821	+	0.563933i	$0.809288\pi$
$720$		−	4.39924i		−	0.163950i
$721$	−14.9745	−	8.64551i	−0.557678	−	0.321976i
$722$	−40.0280	−	23.1102i	−1.48969	−	0.860072i
$723$		−	2.95788i		−	0.110005i
$724$	5.35939	−	9.28274i	0.199180	−	0.344990i
$725$	−48.3817	−	83.7996i	−1.79685	−	3.11224i
$726$	8.43641	−	4.87076i	0.313105	−	0.180771i
$727$	46.3297			1.71827			0.859137	−	0.511745i	$-0.171001\pi$
$727$	46.3297			1.71827			0.859137	+	0.511745i	$0.171001\pi$
$728$	1.43909	+	3.30591i	0.0533363	+	0.122525i
$729$	1.00000			0.0370370
$730$	−48.7604	+	28.1518i	−1.80470	+	1.04195i
$731$	−2.50227	−	4.33406i	−0.0925498	−	0.160301i
$732$	−5.20831	+	9.02106i	−0.192505	+	0.333428i
$733$		−	17.1464i		−	0.633315i	−0.948540	−	0.316658i	$-0.897439\pi$
$733$		−	17.1464i		−	0.633315i	0.948540	−	0.316658i	$-0.102561\pi$
$734$	8.85339	+	5.11150i	0.326784	+	0.188669i
$735$	3.80986	+	2.19962i	0.140529	+	0.0811343i
$736$		−	5.40872i		−	0.199368i
$737$	2.95927	−	5.12560i	0.109006	−	0.188804i
$738$	1.02848	+	1.78138i	0.0378588	+	0.0655734i
$739$	−13.0327	+	7.52443i	−0.479416	+	0.276791i	−0.720173	−	0.693795i	$-0.755938\pi$
$739$	−13.0327	+	7.52443i	−0.479416	+	0.276791i	0.240757	+	0.970585i	$0.422604\pi$
$740$	−33.5210			−1.23226
$741$	23.4140	+	17.3103i	0.860136	+	0.635911i
$742$	8.44252			0.309935
$743$	20.1776	−	11.6496i	0.740245	−	0.427381i	−0.0819132	−	0.996639i	$-0.526103\pi$
$743$	20.1776	−	11.6496i	0.740245	−	0.427381i	0.822158	+	0.569259i	$0.192770\pi$
$744$	2.79296	+	4.83755i	0.102395	+	0.177353i
$745$	−7.65235	+	13.2543i	−0.280361	+	0.485599i
$746$		−	1.56284i		−	0.0572198i
$747$	9.64683	+	5.56960i	0.352959	+	0.203781i
$748$	−3.06574	−	1.77001i	−0.112095	−	0.0647179i
$749$			14.2056i			0.519062i
$750$	20.5738	−	35.6349i	0.751249	−	1.30120i
$751$	15.4534	+	26.7661i	0.563903	+	0.976709i	0.997151	+	0.0754344i	$0.0240343\pi$
$751$	15.4534	+	26.7661i	0.563903	+	0.976709i	−0.433247	+	0.901275i	$0.642632\pi$
$752$	−6.57196	+	3.79432i	−0.239655	+	0.138365i
$753$	−7.63455			−0.278219
$754$	22.2869	−	9.70168i	0.811640	−	0.353314i
$755$	71.7038			2.60957
$756$	0.866025	−	0.500000i	0.0314970	−	0.0181848i
$757$	−7.58518	−	13.1379i	−0.275688	−	0.477506i	0.694620	−	0.719376i	$-0.255572\pi$
$757$	−7.58518	−	13.1379i	−0.275688	−	0.477506i	−0.970308	+	0.241871i	$0.922239\pi$
$758$	4.19268	−	7.26194i	0.152285	−	0.263766i
$759$		−	6.06759i		−	0.220240i
$760$	−30.7681	−	17.7640i	−1.11608	−	0.644366i
$761$	9.45208	+	5.45716i	0.342638	+	0.197822i	0.661438	−	0.750000i	$-0.269947\pi$
$761$	9.45208	+	5.45716i	0.342638	+	0.197822i	−0.318800	+	0.947822i	$0.603280\pi$
$762$		−	9.75637i		−	0.353436i
$763$	−1.71910	+	2.97757i	−0.0622357	+	0.107795i
$764$	7.62813	+	13.2123i	0.275976	+	0.478005i
$765$	12.0224	−	6.94115i	0.434672	−	0.250958i
$766$	−9.11803			−0.329448
$767$	24.0637	−	10.4752i	0.868890	−	0.378236i
$768$	−1.00000			−0.0360844
$769$	−15.9112	+	9.18636i	−0.573774	+	0.331269i	−0.758655	−	0.651492i	$-0.774143\pi$
$769$	−15.9112	+	9.18636i	−0.573774	+	0.331269i	0.184881	+	0.982761i	$0.440810\pi$
$770$	−2.46757	−	4.27396i	−0.0889251	−	0.154023i
$771$	10.6616	−	18.4665i	0.383969	−

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.39924i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.39924i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.19962 + 3.80986i) q^{10} +(0.971521 - 0.560908i) q^{11} +1.00000 q^{12} +(-2.14345 + 2.89924i) q^{13} +1.00000 q^{14} +(3.80986 - 2.19962i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.57781 - 2.73284i) q^{17} -1.00000i q^{18} +(-6.99395 - 4.03796i) q^{19} +(-3.80986 - 2.19962i) q^{20} -1.00000i q^{21} +(-0.560908 + 0.971521i) q^{22} +(-2.70436 - 4.68409i) q^{23} +(-0.866025 + 0.500000i) q^{24} -14.3533 q^{25} +(0.406663 - 3.58254i) q^{26} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(3.37076 + 5.83834i) q^{29} +(-2.19962 + 3.80986i) q^{30} -5.58592i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.971521 + 0.560908i) q^{33} +3.15561i q^{34} +(-2.19962 + 3.80986i) q^{35} +(0.500000 + 0.866025i) q^{36} +(6.59886 - 3.80986i) q^{37} +8.07591 q^{38} +(-3.58254 - 0.406663i) q^{39} +4.39924 q^{40} +(-1.78138 + 1.02848i) q^{41} +(0.500000 + 0.866025i) q^{42} +(0.792959 - 1.37344i) q^{43} -1.12182i q^{44} +(3.80986 + 2.19962i) q^{45} +(4.68409 + 2.70436i) q^{46} -7.58865i q^{47} +(0.500000 - 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(12.4304 - 7.17667i) q^{50} +3.15561 q^{51} +(1.43909 + 3.30591i) q^{52} +8.44252 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.46757 - 4.27396i) q^{55} +(0.500000 - 0.866025i) q^{56} -8.07591i q^{57} +(-5.83834 - 3.37076i) q^{58} +(-6.30380 - 3.63950i) q^{59} -4.39924i q^{60} +(-5.20831 + 9.02106i) q^{61} +(2.79296 + 4.83755i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(12.7545 + 9.42957i) q^{65} -1.12182 q^{66} +(4.56902 - 2.63792i) q^{67} +(-1.57781 - 2.73284i) q^{68} +(2.70436 - 4.68409i) q^{69} -4.39924i q^{70} +(7.51422 + 4.33834i) q^{71} +(-0.866025 - 0.500000i) q^{72} +12.7985i q^{73} +(-3.80986 + 6.59886i) q^{74} +(-7.17667 - 12.4304i) q^{75} +(-6.99395 + 4.03796i) q^{76} -1.12182 q^{77} +(3.30591 - 1.43909i) q^{78} -3.52106 q^{79} +(-3.80986 + 2.19962i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.02848 - 1.78138i) q^{82} -11.1392i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-12.0224 - 6.94115i) q^{85} +1.58592i q^{86} +(-3.37076 + 5.83834i) q^{87} +(0.560908 + 0.971521i) q^{88} +(9.02707 - 5.21178i) q^{89} -4.39924 q^{90} +(3.30591 - 1.43909i) q^{91} -5.40872 q^{92} +(4.83755 - 2.79296i) q^{93} +(3.79432 + 6.57196i) q^{94} +(-17.7640 + 30.7681i) q^{95} +1.00000i q^{96} +(1.06297 + 0.613704i) q^{97} +(-0.866025 - 0.500000i) q^{98} +1.12182i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{10} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 8 q^{14} + 6 q^{15} - 4 q^{16} + 2 q^{17} - 12 q^{19} - 6 q^{20} - 4 q^{22} + 8 q^{23} - 24 q^{25} + 6 q^{26} - 8 q^{27} + 2 q^{29} - 6 q^{30} + 6 q^{33} - 6 q^{35} + 4 q^{36} + 18 q^{37} - 4 q^{38} + 12 q^{40} + 12 q^{41} + 4 q^{42} - 8 q^{43} + 6 q^{45} + 18 q^{46} + 4 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} + 12 q^{52} - 12 q^{53} - 22 q^{55} + 4 q^{56} - 24 q^{58} + 18 q^{59} - 8 q^{61} + 8 q^{62} - 8 q^{64} + 46 q^{65} - 8 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} + 6 q^{71} - 6 q^{74} - 12 q^{75} - 12 q^{76} - 8 q^{77} + 6 q^{78} - 4 q^{79} - 6 q^{80} - 4 q^{81} + 10 q^{82} - 54 q^{85} - 2 q^{87} + 4 q^{88} - 18 q^{89} - 12 q^{90} + 6 q^{91} + 16 q^{92} + 30 q^{93} - 2 q^{94} - 50 q^{95} - 54 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^10 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 8 * q^14 + 6 * q^15 - 4 * q^16 + 2 * q^17 - 12 * q^19 - 6 * q^20 - 4 * q^22 + 8 * q^23 - 24 * q^25 + 6 * q^26 - 8 * q^27 + 2 * q^29 - 6 * q^30 + 6 * q^33 - 6 * q^35 + 4 * q^36 + 18 * q^37 - 4 * q^38 + 12 * q^40 + 12 * q^41 + 4 * q^42 - 8 * q^43 + 6 * q^45 + 18 * q^46 + 4 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 + 12 * q^52 - 12 * q^53 - 22 * q^55 + 4 * q^56 - 24 * q^58 + 18 * q^59 - 8 * q^61 + 8 * q^62 - 8 * q^64 + 46 * q^65 - 8 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 + 6 * q^71 - 6 * q^74 - 12 * q^75 - 12 * q^76 - 8 * q^77 + 6 * q^78 - 4 * q^79 - 6 * q^80 - 4 * q^81 + 10 * q^82 - 54 * q^85 - 2 * q^87 + 4 * q^88 - 18 * q^89 - 12 * q^90 + 6 * q^91 + 16 * q^92 + 30 * q^93 - 2 * q^94 - 50 * q^95 - 54 * q^97

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