LMFDB - Embedded newform 546.2.s.e.43.1

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			43.1
Root			$0.560908 + 1.63871i$ of defining polynomial
Character	$\chi$	$=$	546.43
Dual form			546.2.s.e.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.332808i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.332808i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.166404 - 0.288220i) q^{10} +(2.26053 + 1.30512i) q^{11} +1.00000 q^{12} +(3.41140 + 1.16719i) q^{13} +1.00000 q^{14} +(0.288220 + 0.166404i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.94383 - 3.36681i) q^{17} +1.00000i q^{18} +(4.85997 - 2.80591i) q^{19} +(-0.288220 + 0.166404i) q^{20} +1.00000i q^{21} +(-1.30512 - 2.26053i) q^{22} +(2.10628 - 3.64819i) q^{23} +(-0.866025 - 0.500000i) q^{24} +4.88924 q^{25} +(-2.37076 - 2.71652i) q^{26} -1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(0.593337 - 1.02769i) q^{29} +(-0.166404 - 0.288220i) q^{30} +7.07434i q^{31} +(0.866025 - 0.500000i) q^{32} +(2.26053 - 1.30512i) q^{33} +3.88766i q^{34} +(-0.166404 - 0.288220i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.499211 + 0.288220i) q^{37} -5.61181 q^{38} +(2.71652 - 2.37076i) q^{39} +0.332808 q^{40} +(0.451251 + 0.260530i) q^{41} +(0.500000 - 0.866025i) q^{42} +(1.53717 + 2.66245i) q^{43} +2.61023i q^{44} +(0.288220 - 0.166404i) q^{45} +(-3.64819 + 2.10628i) q^{46} -12.0528i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-4.23421 - 2.44462i) q^{50} -3.88766 q^{51} +(0.694883 + 3.53796i) q^{52} -9.71047 q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.434353 + 0.752321i) q^{55} +(0.500000 + 0.866025i) q^{56} -5.61181i q^{57} +(-1.02769 + 0.593337i) q^{58} +(9.07175 - 5.23758i) q^{59} +0.332808i q^{60} +(-3.71989 - 6.44304i) q^{61} +(3.53717 - 6.12656i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-0.388451 + 1.13534i) q^{65} -2.61023 q^{66} +(10.3233 + 5.96015i) q^{67} +(1.94383 - 3.36681i) q^{68} +(-2.10628 - 3.64819i) q^{69} +0.332808i q^{70} +(-0.818065 + 0.472310i) q^{71} +(-0.866025 + 0.500000i) q^{72} -4.66562i q^{73} +(-0.288220 - 0.499211i) q^{74} +(2.44462 - 4.23421i) q^{75} +(4.85997 + 2.80591i) q^{76} -2.61023 q^{77} +(-3.53796 + 0.694883i) q^{78} -0.943042 q^{79} +(-0.288220 - 0.166404i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.260530 - 0.451251i) q^{82} +13.7172i q^{83} +(-0.866025 + 0.500000i) q^{84} +(1.12050 - 0.646922i) q^{85} -3.07434i q^{86} +(-0.593337 - 1.02769i) q^{87} +(1.30512 - 2.26053i) q^{88} +(2.92741 + 1.69014i) q^{89} -0.332808 q^{90} +(-3.53796 + 0.694883i) q^{91} +4.21257 q^{92} +(6.12656 + 3.53717i) q^{93} +(-6.02638 + 10.4380i) q^{94} +(0.933827 + 1.61744i) q^{95} -1.00000i q^{96} +(-5.03669 + 2.90793i) q^{97} +(-0.866025 + 0.500000i) q^{98} -2.61023i 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$5$			0.332808i			0.148836i	0.997227	+	0.0744180i	$0.0237099\pi$
$5$			0.332808i			0.148836i	−0.997227	+	0.0744180i	$0.976290\pi$
$6$	−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
$10$	0.166404	−	0.288220i	0.0526215	−	0.0911431i
$11$	2.26053	+	1.30512i	0.681575	+	0.393508i	0.800448	−	0.599402i	$-0.204595\pi$
$11$	2.26053	+	1.30512i	0.681575	+	0.393508i	−0.118873	+	0.992909i	$0.537928\pi$
$12$	1.00000			0.288675
$13$	3.41140	+	1.16719i	0.946153	+	0.323721i
$13$	3.41140	+	1.16719i	0.946153	+	0.323721i
$14$	1.00000			0.267261
$15$	0.288220	+	0.166404i	0.0744180	+	0.0429653i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.94383	−	3.36681i	−0.471448	−	0.816572i	0.528018	−	0.849233i	$-0.322935\pi$
$17$	−1.94383	−	3.36681i	−0.471448	−	0.816572i	−0.999466	+	0.0326607i	$0.989602\pi$
$18$			1.00000i			0.235702i
$19$	4.85997	−	2.80591i	1.11495	−	0.643719i	0.174846	−	0.984596i	$-0.444057\pi$
$19$	4.85997	−	2.80591i	1.11495	−	0.643719i	0.940108	+	0.340877i	$0.110724\pi$
$20$	−0.288220	+	0.166404i	−0.0644479	+	0.0372090i
$21$			1.00000i			0.218218i
$22$	−1.30512	−	2.26053i	−0.278252	−	0.481947i
$23$	2.10628	−	3.64819i	0.439191	−	0.760701i	−0.558437	−	0.829547i	$-0.688599\pi$
$23$	2.10628	−	3.64819i	0.439191	−	0.760701i	0.997627	+	0.0688467i	$0.0219319\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	4.88924			0.977848
$26$	−2.37076	−	2.71652i	−0.464945	−	0.532753i
$27$	−1.00000			−0.192450
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	0.593337	−	1.02769i	0.110180	−	0.190837i	−0.805663	−	0.592374i	$-0.798191\pi$
$29$	0.593337	−	1.02769i	0.110180	−	0.190837i	0.915843	+	0.401537i	$0.131524\pi$
$30$	−0.166404	−	0.288220i	−0.0303810	−	0.0526215i
$31$			7.07434i			1.27059i	0.772270	+	0.635294i	$0.219121\pi$
$31$			7.07434i			1.27059i	−0.772270	+	0.635294i	$0.780879\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.26053	−	1.30512i	0.393508	−	0.227192i
$34$			3.88766i			0.666729i
$35$	−0.166404	−	0.288220i	−0.0281274	−	0.0487180i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	0.499211	+	0.288220i	0.0820699	+	0.0473831i	0.540473	−	0.841361i	$-0.318245\pi$
$37$	0.499211	+	0.288220i	0.0820699	+	0.0473831i	−0.458403	+	0.888744i	$0.651579\pi$
$38$	−5.61181			−0.910356
$39$	2.71652	−	2.37076i	0.434991	−	0.379626i
$40$	0.332808			0.0526215
$41$	0.451251	+	0.260530i	0.0704735	+	0.0406879i	0.534823	−	0.844964i	$-0.320378\pi$
$41$	0.451251	+	0.260530i	0.0704735	+	0.0406879i	−0.464349	+	0.885652i	$0.653712\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	1.53717	+	2.66245i	0.234416	+	0.406020i	0.959103	−	0.283058i	$-0.0913489\pi$
$43$	1.53717	+	2.66245i	0.234416	+	0.406020i	−0.724687	+	0.689078i	$0.758016\pi$
$44$			2.61023i			0.393508i
$45$	0.288220	−	0.166404i	0.0429653	−	0.0248060i
$46$	−3.64819	+	2.10628i	−0.537896	+	0.310555i
$47$		−	12.0528i		−	1.75807i	−0.476753	−	0.879037i	$-0.658186\pi$
$47$		−	12.0528i		−	1.75807i	0.476753	−	0.879037i	$-0.341814\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−4.23421	−	2.44462i	−0.598807	−	0.345721i
$51$	−3.88766			−0.544382
$52$	0.694883	+	3.53796i	0.0963629	+	0.490626i
$53$	−9.71047			−1.33384			−0.666918	−	0.745132i	$-0.732387\pi$
$53$	−9.71047			−1.33384			−0.666918	+	0.745132i	$0.732387\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−0.434353	+	0.752321i	−0.0585681	+	0.101443i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		−	5.61181i		−	0.743303i
$58$	−1.02769	+	0.593337i	−0.134942	+	0.0779090i
$59$	9.07175	−	5.23758i	1.18104	−	0.681875i	0.224786	−	0.974408i	$-0.427832\pi$
$59$	9.07175	−	5.23758i	1.18104	−	0.681875i	0.956255	+	0.292533i	$0.0944983\pi$
$60$			0.332808i			0.0429653i
$61$	−3.71989	−	6.44304i	−0.476283	−	0.824947i	0.523347	−	0.852119i	$-0.324683\pi$
$61$	−3.71989	−	6.44304i	−0.476283	−	0.824947i	−0.999631	+	0.0271724i	$0.991350\pi$
$62$	3.53717	−	6.12656i	0.449221	−	0.778073i
$63$	0.866025	+	0.500000i	0.109109	+	0.0629941i
$64$	−1.00000			−0.125000
$65$	−0.388451	+	1.13534i	−0.0481814	+	0.140822i
$66$	−2.61023			−0.321298
$67$	10.3233	+	5.96015i	1.26119	+	0.728148i	0.973305	−	0.229517i	$-0.0737145\pi$
$67$	10.3233	+	5.96015i	1.26119	+	0.728148i	0.287885	+	0.957665i	$0.407048\pi$
$68$	1.94383	−	3.36681i	0.235724	−	0.408286i
$69$	−2.10628	−	3.64819i	−0.253567	−	0.439191i
$70$			0.332808i			0.0397781i
$71$	−0.818065	+	0.472310i	−0.0970864	+	0.0560529i	−0.547757	−	0.836637i	$-0.684518\pi$
$71$	−0.818065	+	0.472310i	−0.0970864	+	0.0560529i	0.450671	+	0.892690i	$0.351185\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$		−	4.66562i		−	0.546069i	−0.962004	−	0.273034i	$-0.911973\pi$
$73$		−	4.66562i		−	0.546069i	0.962004	−	0.273034i	$-0.0880273\pi$
$74$	−0.288220	−	0.499211i	−0.0335049	−	0.0580321i
$75$	2.44462	−	4.23421i	0.282280	−	0.488924i
$76$	4.85997	+	2.80591i	0.557477	+	0.321859i
$77$	−2.61023			−0.297464
$78$	−3.53796	+	0.694883i	−0.400595	+	0.0786800i
$79$	−0.943042			−0.106101			−0.0530503	−	0.998592i	$-0.516894\pi$
$79$	−0.943042			−0.106101			−0.0530503	+	0.998592i	$0.516894\pi$
$80$	−0.288220	−	0.166404i	−0.0322240	−	0.0186045i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.260530	−	0.451251i	−0.0287707	−	0.0498323i
$83$			13.7172i			1.50566i	0.658215	+	0.752830i	$0.271312\pi$
$83$			13.7172i			1.50566i	−0.658215	+	0.752830i	$0.728688\pi$
$84$	−0.866025	+	0.500000i	−0.0944911	+	0.0545545i
$85$	1.12050	−	0.646922i	0.121535	−	0.0701685i
$86$		−	3.07434i		−	0.331514i
$87$	−0.593337	−	1.02769i	−0.0636124	−	0.110180i
$88$	1.30512	−	2.26053i	0.139126	−	0.240973i
$89$	2.92741	+	1.69014i	0.310305	+	0.179155i	0.647063	−	0.762436i	$-0.275997\pi$
$89$	2.92741	+	1.69014i	0.310305	+	0.179155i	−0.336758	+	0.941591i	$0.609330\pi$
$90$	−0.332808			−0.0350810
$91$	−3.53796	+	0.694883i	−0.370879	+	0.0728435i
$92$	4.21257			0.439191
$93$	6.12656	+	3.53717i	0.635294	+	0.366787i
$94$	−6.02638	+	10.4380i	−0.621573	+	1.07660i
$95$	0.933827	+	1.61744i	0.0958086	+	0.165945i
$96$		−	1.00000i		−	0.102062i
$97$	−5.03669	+	2.90793i	−0.511398	+	0.295256i	−0.733408	−	0.679789i	$-0.762072\pi$
$97$	−5.03669	+	2.90793i	−0.511398	+	0.295256i	0.222010	+	0.975044i	$0.428738\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$		−	2.61023i		−	0.262338i
$100$	2.44462	+	4.23421i	0.244462	+	0.423421i
$101$	−7.98516	+	13.8307i	−0.794553	+	1.37621i	0.128569	+	0.991701i	$0.458962\pi$
$101$	−7.98516	+	13.8307i	−0.794553	+	1.37621i	−0.923122	+	0.384506i	$0.874372\pi$
$102$	3.36681	+	1.94383i	0.333364	+	0.192468i
$103$	−7.50641			−0.739629			−0.369814	−	0.929106i	$-0.620579\pi$
$103$	−7.50641			−0.739629			−0.369814	+	0.929106i	$0.620579\pi$
$104$	1.16719	−	3.41140i	0.114453	−	0.334515i
$105$	−0.332808			−0.0324787
$106$	8.40951	+	4.85523i	0.816804	+	0.471582i
$107$	−4.32539	+	7.49179i	−0.418151	+	0.724259i	−0.995754	−	0.0920593i	$-0.970655\pi$
$107$	−4.32539	+	7.49179i	−0.418151	+	0.724259i	0.577602	+	0.816318i	$0.303988\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			18.6144i			1.78293i	0.453088	+	0.891466i	$0.350322\pi$
$109$			18.6144i			1.78293i	−0.453088	+	0.891466i	$0.649678\pi$
$110$	0.752321	−	0.434353i	0.0717310	−	0.0414139i
$111$	0.499211	−	0.288220i	0.0473831	−	0.0273566i
$112$		−	1.00000i		−	0.0944911i
$113$	−4.57512	−	7.92435i	−0.430392	−	0.745460i	0.566515	−	0.824051i	$-0.308291\pi$
$113$	−4.57512	−	7.92435i	−0.430392	−	0.745460i	−0.996907	+	0.0785911i	$0.974958\pi$
$114$	−2.80591	+	4.85997i	−0.262797	+	0.455178i
$115$	1.21415	+	0.700987i	0.113220	+	0.0653674i
$116$	1.18667			0.110180
$117$	−0.694883	−	3.53796i	−0.0642419	−	0.327084i
$118$	−10.4752			−0.964316
$119$	3.36681	+	1.94383i	0.308635	+	0.178191i
$120$	0.166404	−	0.288220i	0.0151905	−	0.0263108i
$121$	−2.09334	−	3.62577i	−0.190303	−	0.329615i
$122$			7.43978i			0.673566i
$123$	0.451251	−	0.260530i	0.0406879	−	0.0234912i
$124$	−6.12656	+	3.53717i	−0.550181	+	0.317647i
$125$			3.29121i			0.294375i
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	3.38977	−	5.87125i	0.300793	−	0.520989i	−0.675523	−	0.737339i	$-0.736082\pi$
$127$	3.38977	−	5.87125i	0.300793	−	0.520989i	0.976316	+	0.216350i	$0.0694153\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	3.07434			0.270680
$130$	0.904078	−	0.789008i	0.0792929	−	0.0692006i
$131$	7.22879			0.631583			0.315791	−	0.948829i	$-0.397730\pi$
$131$	7.22879			0.631583			0.315791	+	0.948829i	$0.397730\pi$
$132$	2.26053	+	1.30512i	0.196754	+	0.113596i
$133$	−2.80591	+	4.85997i	−0.243303	+	0.421413i
$134$	−5.96015	−	10.3233i	−0.514879	−	0.891796i
$135$		−	0.332808i		−	0.0286435i
$136$	−3.36681	+	1.94383i	−0.288702	+	0.166682i
$137$	−10.2964	+	5.94462i	−0.879679	+	0.507883i	−0.870553	−	0.492075i	$-0.836238\pi$
$137$	−10.2964	+	5.94462i	−0.879679	+	0.507883i	−0.00912669	+	0.999958i	$0.502905\pi$
$138$			4.21257i			0.358598i
$139$	−7.16056	−	12.4025i	−0.607351	−	1.05196i	−0.991675	−	0.128764i	$-0.958899\pi$
$139$	−7.16056	−	12.4025i	−0.607351	−	1.05196i	0.384324	−	0.923198i	$-0.374434\pi$
$140$	0.166404	−	0.288220i	0.0140637	−	0.0243590i
$141$	−10.4380	−	6.02638i	−0.879037	−	0.507512i
$142$	0.944620			0.0792707
$143$	6.18825	+	7.09075i	0.517488	+	0.592959i
$144$	1.00000			0.0833333
$145$	0.342023	+	0.197467i	0.0284035	+	0.0163988i
$146$	−2.33281	+	4.04054i	−0.193065	+	0.334398i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$			0.576440i			0.0473831i
$149$	−5.24548	+	3.02848i	−0.429726	+	0.248103i	−0.699230	−	0.714897i	$-0.746474\pi$
$149$	−5.24548	+	3.02848i	−0.429726	+	0.248103i	0.269504	+	0.962999i	$0.413140\pi$
$150$	−4.23421	+	2.44462i	−0.345721	+	0.199602i
$151$			21.4953i			1.74926i	0.484791	+	0.874630i	$0.338896\pi$
$151$			21.4953i			1.74926i	−0.484791	+	0.874630i	$0.661104\pi$
$152$	−2.80591	−	4.85997i	−0.227589	−	0.394196i
$153$	−1.94383	+	3.36681i	−0.157149	+	0.272191i
$154$	2.26053	+	1.30512i	0.182159	+	0.105169i
$155$	−2.35439			−0.189109
$156$	3.41140	+	1.16719i	0.273131	+	0.0934502i
$157$	2.29227			0.182943			0.0914714	−	0.995808i	$-0.470843\pi$
$157$	2.29227			0.182943			0.0914714	+	0.995808i	$0.470843\pi$
$158$	0.816699	+	0.471521i	0.0649731	+	0.0375122i
$159$	−4.85523	+	8.40951i	−0.385045	+	0.666918i
$160$	0.166404	+	0.288220i	0.0131554	+	0.0227858i
$161$			4.21257i			0.331997i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	2.89314	−	1.67035i	0.226608	−	0.130832i	−0.382398	−	0.923998i	$-0.624902\pi$
$163$	2.89314	−	1.67035i	0.226608	−	0.130832i	0.609006	+	0.793165i	$0.291568\pi$
$164$			0.521059i			0.0406879i
$165$	0.434353	+	0.752321i	0.0338143	+	0.0585681i
$166$	6.85861	−	11.8795i	0.532331	−	0.922024i
$167$	5.57802	+	3.22047i	0.431640	+	0.249207i	0.700045	−	0.714099i	$-0.253163\pi$
$167$	5.57802	+	3.22047i	0.431640	+	0.249207i	−0.268405	+	0.963306i	$0.586497\pi$
$168$	1.00000			0.0771517
$169$	10.2753	+	7.96352i	0.790410	+	0.612579i
$170$	−1.29384			−0.0992333
$171$	−4.85997	−	2.80591i	−0.371651	−	0.214573i
$172$	−1.53717	+	2.66245i	−0.117208	+	0.203010i
$173$	−9.30718	−	16.1205i	−0.707611	−	1.22562i	−0.965741	−	0.259509i	$-0.916439\pi$
$173$	−9.30718	−	16.1205i	−0.707611	−	1.22562i	0.258129	−	0.966110i	$-0.416894\pi$
$174$			1.18667i			0.0899616i
$175$	−4.23421	+	2.44462i	−0.320076	+	0.184796i
$176$	−2.26053	+	1.30512i	−0.170394	+	0.0983769i
$177$		−	10.4752i		−	0.787361i
$178$	−1.69014	−	2.92741i	−0.126682	−	0.219419i
$179$	−11.1081	+	19.2398i	−0.830261	+	1.43805i	0.0675707	+	0.997714i	$0.478475\pi$
$179$	−11.1081	+	19.2398i	−0.830261	+	1.43805i	−0.897831	+	0.440339i	$0.854858\pi$
$180$	0.288220	+	0.166404i	0.0214826	+	0.0124030i
$181$	−4.05853			−0.301669			−0.150834	−	0.988559i	$-0.548196\pi$
$181$	−4.05853			−0.301669			−0.150834	+	0.988559i	$0.548196\pi$
$182$	3.41140	+	1.16719i	0.252870	+	0.0865181i
$183$	−7.43978			−0.549965
$184$	−3.64819	−	2.10628i	−0.268948	−	0.155277i
$185$	−0.0959218	+	0.166141i	−0.00705231	+	0.0122150i
$186$	−3.53717	−	6.12656i	−0.259358	−	0.449221i
$187$		−	10.1477i		−	0.742074i
$188$	10.4380	−	6.02638i	0.761269	−	0.439519i
$189$	0.866025	−	0.500000i	0.0629941	−	0.0363696i
$190$		−	1.86765i		−	0.135494i
$191$	5.86018	+	10.1501i	0.424028	+	0.734438i	0.996329	−	0.0856056i	$-0.0272825\pi$
$191$	5.86018	+	10.1501i	0.424028	+	0.734438i	−0.572301	+	0.820044i	$0.693949\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−20.6123	−	11.9005i	−1.48371	−	0.856618i	−0.483877	−	0.875136i	$-0.660772\pi$
$193$	−20.6123	−	11.9005i	−1.48371	−	0.856618i	−0.999829	+	0.0185185i	$0.994105\pi$
$194$	5.81587			0.417555
$195$	0.789008	+	0.904078i	0.0565021	+	0.0647424i
$196$	1.00000			0.0714286
$197$	8.73184	+	5.04133i	0.622118	+	0.359180i	0.777693	−	0.628644i	$-0.216390\pi$
$197$	8.73184	+	5.04133i	0.622118	+	0.359180i	−0.155575	+	0.987824i	$0.549723\pi$
$198$	−1.30512	+	2.26053i	−0.0927507	+	0.160649i
$199$	6.92504	+	11.9945i	0.490903	+	0.850269i	0.999945	−	0.0104725i	$-0.00333355\pi$
$199$	6.92504	+	11.9945i	0.490903	+	0.850269i	−0.509042	+	0.860742i	$0.670000\pi$
$200$		−	4.88924i		−	0.345721i
$201$	10.3233	−	5.96015i	0.728148	−	0.420397i
$202$	13.8307	−	7.98516i	0.973125	−	0.561834i
$203$			1.18667i			0.0832882i
$204$	−1.94383	−	3.36681i	−0.136095	−	0.235724i
$205$	−0.0867062	+	0.150180i	−0.00605583	+	0.0104890i
$206$	6.50074	+	3.75321i	0.452928	+	0.261498i
$207$	−4.21257			−0.292794
$208$	−2.71652	+	2.37076i	−0.188357	+	0.164383i
$209$	14.6481			1.01323
$210$	0.288220	+	0.166404i	0.0198891	+	0.0114830i
$211$	−2.27743	+	3.94462i	−0.156785	+	0.271559i	−0.933707	−	0.358037i	$-0.883446\pi$
$211$	−2.27743	+	3.94462i	−0.156785	+	0.271559i	0.776923	+	0.629596i	$0.216779\pi$
$212$	−4.85523	−	8.40951i	−0.333459	−	0.577568i
$213$			0.944620i			0.0647243i
$214$	7.49179	−	4.32539i	0.512128	−	0.295677i
$215$	−0.886085	+	0.511581i	−0.0604305	+	0.0348896i
$216$			1.00000i			0.0680414i
$217$	−3.53717	−	6.12656i	−0.240119	−	0.415898i
$218$	9.30718	−	16.1205i	0.630361	−	1.09182i
$219$	−4.04054	−	2.33281i	−0.273034	−	0.157637i
$220$	−0.868706			−0.0585681
$221$	−2.70147	−	13.7544i	−0.181720	−	0.925220i
$222$	−0.576440			−0.0386881
$223$	−7.30359	−	4.21673i	−0.489085	−	0.282373i	0.235110	−	0.971969i	$-0.424455\pi$
$223$	−7.30359	−	4.21673i	−0.489085	−	0.282373i	−0.724195	+	0.689596i	$0.757788\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−2.44462	−	4.23421i	−0.162975	−	0.282280i
$226$			9.15025i			0.608666i
$227$	24.2394	−	13.9946i	1.60883	−	0.928857i	0.619194	−	0.785238i	$-0.287459\pi$
$227$	24.2394	−	13.9946i	1.60883	−	0.928857i	0.989633	−	0.143619i	$-0.0458739\pi$
$228$	4.85997	−	2.80591i	0.321859	−	0.185826i
$229$		−	28.7785i		−	1.90174i	−0.309598	−	0.950868i	$-0.600194\pi$
$229$		−	28.7785i		−	1.90174i	0.309598	−	0.950868i	$-0.399806\pi$
$230$	−0.700987	−	1.21415i	−0.0462217	−	0.0800584i
$231$	−1.30512	+	2.26053i	−0.0858704	+	0.148732i
$232$	−1.02769	−	0.593337i	−0.0674712	−	0.0389545i
$233$	−18.8877			−1.23737			−0.618686	−	0.785638i	$-0.712335\pi$
$233$	−18.8877			−1.23737			−0.618686	+	0.785638i	$0.712335\pi$
$234$	−1.16719	+	3.41140i	−0.0763018	+	0.223010i
$235$	4.01125			0.261665
$236$	9.07175	+	5.23758i	0.590521	+	0.340937i
$237$	−0.471521	+	0.816699i	−0.0306286	+	0.0530503i
$238$	−1.94383	−	3.36681i	−0.126000	−	0.218238i
$239$			11.0933i			0.717565i	0.933421	+	0.358783i	$0.116808\pi$
$239$			11.0933i			0.717565i	−0.933421	+	0.358783i	$0.883192\pi$
$240$	−0.288220	+	0.166404i	−0.0186045	+	0.0107413i
$241$	−7.02686	+	4.05696i	−0.452640	+	0.261332i	−0.708944	−	0.705264i	$-0.750828\pi$
$241$	−7.02686	+	4.05696i	−0.452640	+	0.261332i	0.256305	+	0.966596i	$0.417495\pi$
$242$			4.18667i			0.269130i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.71989	−	6.44304i	0.238142	−	0.412474i
$245$	0.288220	+	0.166404i	0.0184137	+	0.0106311i
$246$	−0.521059			−0.0332215
$247$	19.8543	−	3.89955i	1.26330	−	0.248122i
$248$	7.07434			0.449221
$249$	11.8795	+	6.85861i	0.752830	+	0.434646i
$250$	1.64561	−	2.85027i	0.104077	−	0.180267i
$251$	−1.58465	−	2.74469i	−0.100022	−	0.173243i	0.811671	−	0.584114i	$-0.198558\pi$
$251$	−1.58465	−	2.74469i	−0.100022	−	0.173243i	−0.911694	+	0.410871i	$0.865225\pi$
$252$			1.00000i			0.0629941i
$253$	9.52264	−	5.49790i	0.598683	−	0.345650i
$254$	−5.87125	+	3.38977i	−0.368395	+	0.212693i
$255$		−	1.29384i		−	0.0810236i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.0967103	+	0.167507i	−0.00603263	+	0.0104488i	−0.869026	−	0.494766i	$-0.835254\pi$
$257$	−0.0967103	+	0.167507i	−0.00603263	+	0.0104488i	0.862993	+	0.505215i	$0.168587\pi$
$258$	−2.66245	−	1.53717i	−0.165757	−	0.0956999i
$259$	−0.576440			−0.0358182
$260$	−1.17746	+	0.231262i	−0.0730229	+	0.0143423i
$261$	−1.18667			−0.0734533
$262$	−6.26032	−	3.61440i	−0.386764	−	0.223298i
$263$	−6.02185	+	10.4301i	−0.371323	+	0.643150i	−0.989769	−	0.142677i	$-0.954429\pi$
$263$	−6.02185	+	10.4301i	−0.371323	+	0.643150i	0.618446	+	0.785827i	$0.287762\pi$
$264$	−1.30512	−	2.26053i	−0.0803244	−	0.139126i
$265$		−	3.23172i		−	0.198523i
$266$	4.85997	−	2.80591i	0.297984	−	0.172041i
$267$	2.92741	−	1.69014i	0.179155	−	0.103435i
$268$			11.9203i			0.728148i
$269$	−8.60487	−	14.9041i	−0.524648	−	0.908718i	−0.999588	−	0.0286993i	$-0.990863\pi$
$269$	−8.60487	−	14.9041i	−0.524648	−	0.908718i	0.474940	−	0.880018i	$-0.342470\pi$
$270$	−0.166404	+	0.288220i	−0.0101270	+	0.0175405i
$271$	−14.8453	−	8.57096i	−0.901790	−	0.520649i	−0.0240098	−	0.999712i	$-0.507643\pi$
$271$	−14.8453	−	8.57096i	−0.901790	−	0.520649i	−0.877781	+	0.479063i	$0.840977\pi$
$272$	3.88766			0.235724
$273$	−1.16719	+	3.41140i	−0.0706417	+	0.206467i
$274$	11.8892			0.718255
$275$	11.0523	+	6.38103i	0.666477	+	0.384791i
$276$	2.10628	−	3.64819i	0.126783	−	0.219595i
$277$	−7.85660	−	13.6080i	−0.472057	−	0.817627i	0.527432	−	0.849598i	$-0.323155\pi$
$277$	−7.85660	−	13.6080i	−0.472057	−	0.817627i	−0.999489	+	0.0319704i	$0.989822\pi$
$278$			14.3211i			0.858924i
$279$	6.12656	−	3.53717i	0.366787	−	0.211765i
$280$	−0.288220	+	0.166404i	−0.0172244	+	0.00994453i
$281$		−	4.07337i		−	0.242997i	−0.992592	−	0.121499i	$-0.961230\pi$
$281$		−	4.07337i		−	0.242997i	0.992592	−	0.121499i	$-0.0387700\pi$
$282$	6.02638	+	10.4380i	0.358865	+	0.621573i
$283$	10.7674	−	18.6497i	0.640057	−	1.10861i	−0.345363	−	0.938469i	$-0.612244\pi$
$283$	10.7674	−	18.6497i	0.640057	−	1.10861i	0.985420	−	0.170142i	$-0.0544226\pi$
$284$	−0.818065	−	0.472310i	−0.0485432	−	0.0280264i
$285$	1.86765			0.110630
$286$	−1.81381	−	9.23490i	−0.107253	−	0.546071i
$287$	−0.521059			−0.0307572
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	0.943042	−	1.63340i	0.0554731	−	0.0960822i
$290$	−0.197467	−	0.342023i	−0.0115957	−	0.0200843i
$291$			5.81587i			0.340932i
$292$	4.04054	−	2.33281i	0.236455	−	0.136517i
$293$	0.152457	−	0.0880210i	0.00890662	−	0.00514224i	−0.495540	−	0.868585i	$-0.665030\pi$
$293$	0.152457	−	0.0880210i	0.00890662	−	0.00514224i	0.504447	+	0.863443i	$0.331697\pi$
$294$			1.00000i			0.0583212i
$295$	1.74311	+	3.01915i	0.101488	+	0.175782i
$296$	0.288220	−	0.499211i	0.0167524	−	0.0290161i
$297$	−2.26053	−	1.30512i	−0.131169	−	0.0757306i
$298$	6.05696			0.350870
$299$	11.4435	−	9.98701i	0.661796	−	0.577564i
$300$	4.88924			0.282280
$301$	−2.66245	−	1.53717i	−0.153461	−	0.0886009i
$302$	10.7476	−	18.6154i	0.618457	−	1.07120i
$303$	7.98516	+	13.8307i	0.458736	+	0.794553i
$304$			5.61181i			0.321859i
$305$	2.14429	−	1.23801i	0.122782	−	0.0708882i
$306$	3.36681	−	1.94383i	0.192468	−	0.111121i
$307$		−	20.7405i		−	1.18372i	−0.806040	−	0.591861i	$-0.798394\pi$
$307$		−	20.7405i		−	1.18372i	0.806040	−	0.591861i	$-0.201606\pi$
$308$	−1.30512	−	2.26053i	−0.0743660	−	0.128806i
$309$	−3.75321	+	6.50074i	−0.213512	+	0.369814i
$310$	2.03896	+	1.17720i	0.115805	+	0.0668603i
$311$	10.9678			0.621926			0.310963	−	0.950422i	$-0.399348\pi$
$311$	10.9678			0.621926			0.310963	+	0.950422i	$0.399348\pi$
$312$	−2.37076	−	2.71652i	−0.134218	−	0.153793i
$313$	16.2189			0.916746			0.458373	−	0.888760i	$-0.348432\pi$
$313$	16.2189			0.916746			0.458373	+	0.888760i	$0.348432\pi$
$314$	−1.98516	−	1.14613i	−0.112029	−	0.0646800i
$315$	−0.166404	+	0.288220i	−0.00937579	+	0.0162393i
$316$	−0.471521	−	0.816699i	−0.0265251	−	0.0459429i
$317$			10.5358i			0.591750i	0.955227	+	0.295875i	$0.0956112\pi$
$317$			10.5358i			0.591750i	−0.955227	+	0.295875i	$0.904389\pi$
$318$	8.40951	−	4.85523i	0.471582	−	0.272268i
$319$	2.68251	−	1.54875i	0.150192	−	0.0867133i
$320$		−	0.332808i		−	0.0186045i
$321$	4.32539	+	7.49179i	0.241420	+	0.418151i
$322$	2.10628	−	3.64819i	0.117379	−	0.203306i
$323$	−18.8939	−	10.9084i	−1.05129	−	0.606960i
$324$	−1.00000			−0.0555556
$325$	16.6792	+	5.70668i	0.925193	+	0.316550i
$326$	−3.34071			−0.185025
$327$	16.1205	+	9.30718i	0.891466	+	0.514688i
$328$	0.260530	−	0.451251i	0.0143853	−	0.0249161i
$329$	6.02638	+	10.4380i	0.332245	+	0.575465i
$330$		−	0.868706i		−	0.0478207i
$331$	−13.9687	+	8.06486i	−0.767792	+	0.443285i	−0.832086	−	0.554646i	$-0.812854\pi$
$331$	−13.9687	+	8.06486i	−0.767792	+	0.443285i	0.0642946	+	0.997931i	$0.479520\pi$
$332$	−11.8795	+	6.85861i	−0.651970	+	0.376415i
$333$		−	0.576440i		−	0.0315887i
$334$	−3.22047	−	5.57802i	−0.176216	−	0.305216i
$335$	−1.98358	+	3.43567i	−0.108375	+	0.187711i
$336$	−0.866025	−	0.500000i	−0.0472456	−	0.0272772i
$337$	1.78785			0.0973906			0.0486953	−	0.998814i	$-0.484494\pi$
$337$	1.78785			0.0973906			0.0486953	+	0.998814i	$0.484494\pi$
$338$	−4.91693	−	12.0343i	−0.267446	−	0.654578i
$339$	−9.15025			−0.496973
$340$	1.12050	+	0.646922i	0.0607677	+	0.0350843i
$341$	−9.23284	+	15.9917i	−0.499986	+	0.866002i
$342$	2.80591	+	4.85997i	0.151726	+	0.262797i
$343$			1.00000i			0.0539949i
$344$	2.66245	−	1.53717i	0.143550	−	0.0828786i
$345$	1.21415	−	0.700987i	0.0653674	−	0.0377399i
$346$			18.6144i			1.00071i
$347$	−12.7030	−	22.0023i	−0.681935	−	1.18115i	−0.974389	−	0.224867i	$-0.927805\pi$
$347$	−12.7030	−	22.0023i	−0.681935	−	1.18115i	0.292454	−	0.956280i	$-0.405528\pi$
$348$	0.593337	−	1.02769i	0.0318062	−	0.0550900i
$349$	−24.5419	−	14.1693i	−1.31370	−	0.758463i	−0.330990	−	0.943634i	$-0.607383\pi$
$349$	−24.5419	−	14.1693i	−1.31370	−	0.758463i	−0.982706	+	0.185172i	$0.940716\pi$
$350$	4.88924			0.261341
$351$	−3.41140	−	1.16719i	−0.182087	−	0.0623001i
$352$	2.61023			0.139126
$353$	−1.69146	−	0.976568i	−0.0900276	−	0.0519774i	0.454310	−	0.890843i	$-0.349886\pi$
$353$	−1.69146	−	0.976568i	−0.0900276	−	0.0519774i	−0.544338	+	0.838866i	$0.683219\pi$
$354$	−5.23758	+	9.07175i	−0.278374	+	0.482158i
$355$	−0.157188	−	0.272258i	−0.00834269	−	0.0144500i
$356$			3.38029i			0.179155i
$357$	3.36681	−	1.94383i	0.178191	−	0.102878i
$358$	19.2398	−	11.1081i	1.01686	−	0.587083i
$359$			27.6565i			1.45965i	0.683633	+	0.729826i	$0.260399\pi$
$359$			27.6565i			1.45965i	−0.683633	+	0.729826i	$0.739601\pi$
$360$	−0.166404	−	0.288220i	−0.00877025	−	0.0151905i
$361$	6.24622	−	10.8188i	0.328748	−	0.569409i
$362$	3.51479	+	2.02927i	0.184733	+	0.106656i
$363$	−4.18667			−0.219743
$364$	−2.37076	−	2.71652i	−0.124262	−	0.142384i
$365$	1.55275			0.0812748
$366$	6.44304	+	3.71989i	0.336783	+	0.194442i
$367$	−2.87888	+	4.98636i	−0.150276	+	0.260286i	−0.931329	−	0.364179i	$-0.881350\pi$
$367$	−2.87888	+	4.98636i	−0.150276	+	0.260286i	0.781053	+	0.624465i	$0.214683\pi$
$368$	2.10628	+	3.64819i	0.109798	+	0.190175i
$369$		−	0.521059i		−	0.0271253i
$370$	0.166141	−	0.0959218i	0.00863728	−	0.00498673i
$371$	8.40951	−	4.85523i	0.436600	−	0.252071i
$372$			7.07434i			0.366787i
$373$	−13.9243	−	24.1177i	−0.720975	−	1.24877i	−0.960609	−	0.277903i	$-0.910361\pi$
$373$	−13.9243	−	24.1177i	−0.720975	−	1.24877i	0.239634	−	0.970863i	$-0.422973\pi$
$374$	−5.07386	+	8.78817i	−0.262363	+	0.454426i
$375$	2.85027	+	1.64561i	0.147188	+	0.0849788i
$376$	−12.0528			−0.621573
$377$	3.22362	−	2.81333i	0.166025	−	0.144894i
$378$	−1.00000			−0.0514344
$379$	−10.7836	−	6.22590i	−0.553915	−	0.319803i	0.196784	−	0.980447i	$-0.436950\pi$
$379$	−10.7836	−	6.22590i	−0.553915	−	0.319803i	−0.750700	+	0.660644i	$0.770283\pi$
$380$	−0.933827	+	1.61744i	−0.0479043	+	0.0829727i
$381$	−3.38977	−	5.87125i	−0.173663	−	0.300793i
$382$		−	11.7204i		−	0.599666i
$383$	−8.42273	+	4.86286i	−0.430381	+	0.248481i	−0.699509	−	0.714624i	$-0.746598\pi$
$383$	−8.42273	+	4.86286i	−0.430381	+	0.248481i	0.269128	+	0.963104i	$0.413265\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		−	0.868706i		−	0.0442734i
$386$	11.9005	+	20.6123i	0.605720	+	1.04914i
$387$	1.53717	−	2.66245i	0.0781387	−	0.135340i
$388$	−5.03669	−	2.90793i	−0.255699	−	0.147628i
$389$	−13.8910			−0.704302			−0.352151	−	0.935943i	$-0.614550\pi$
$389$	−13.8910			−0.704302			−0.352151	+	0.935943i	$0.614550\pi$
$390$	−0.231262	−	1.17746i	−0.0117104	−	0.0596230i
$391$	−16.3770			−0.828223
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$	3.61440	−	6.26032i	0.182322	−	0.315791i
$394$	−5.04133	−	8.73184i	−0.253979	−	0.439904i
$395$		−	0.313852i		−	0.0157916i
$396$	2.26053	−	1.30512i	0.113596	−	0.0655846i
$397$	5.87033	−	3.38924i	0.294624	−	0.170101i	−0.345401	−	0.938455i	$-0.612257\pi$
$397$	5.87033	−	3.38924i	0.294624	−	0.170101i	0.640025	+	0.768354i	$0.278924\pi$
$398$		−	13.8501i		−	0.694242i
$399$	2.80591	+	4.85997i	0.140471	+	0.243303i
$400$	−2.44462	+	4.23421i	−0.122231	+	0.211710i
$401$	12.5254	+	7.23152i	0.625487	+	0.361125i	0.779002	−	0.627021i	$-0.215726\pi$
$401$	12.5254	+	7.23152i	0.625487	+	0.361125i	−0.153515	+	0.988146i	$0.549059\pi$
$402$	−11.9203			−0.594531
$403$	−8.25711	+	24.1334i	−0.411316	+	1.20217i
$404$	−15.9703			−0.794553
$405$	−0.288220	−	0.166404i	−0.0143218	−	0.00826867i
$406$	0.593337	−	1.02769i	0.0294468	−	0.0510034i
$407$	0.752321	+	1.30306i	0.0372912	+	0.0645902i
$408$			3.88766i			0.192468i
$409$	20.2032	−	11.6643i	0.998982	−	0.576763i	0.0910351	−	0.995848i	$-0.470982\pi$
$409$	20.2032	−	11.6643i	0.998982	−	0.576763i	0.907947	+	0.419085i	$0.137649\pi$
$410$	0.150180	−	0.0867062i	0.00741684	−	0.00428212i
$411$			11.8892i			0.586453i
$412$	−3.75321	−	6.50074i	−0.184907	−	0.320269i
$413$	−5.23758	+	9.07175i	−0.257724	+	0.446392i
$414$	3.64819	+	2.10628i	0.179299	+	0.103518i
$415$	−4.56519			−0.224096
$416$	3.53796	−	0.694883i	0.173463	−	0.0340694i
$417$	−14.3211			−0.701308
$418$	−12.6857	−	7.32407i	−0.620476	−	0.358232i
$419$	11.2898	−	19.5544i	0.551540	−	0.955296i	−0.446623	−	0.894722i	$-0.647374\pi$
$419$	11.2898	−	19.5544i	0.551540	−	0.955296i	0.998164	−	0.0605740i	$-0.0192931\pi$
$420$	−0.166404	−	0.288220i	−0.00811967	−	0.0140637i
$421$			34.1708i			1.66538i	0.553738	+	0.832691i	$0.313201\pi$
$421$			34.1708i			1.66538i	−0.553738	+	0.832691i	$0.686799\pi$
$422$	3.94462	−	2.27743i	0.192021	−	0.110863i
$423$	−10.4380	+	6.02638i	−0.507512	+	0.293012i
$424$			9.71047i			0.471582i
$425$	−9.50385	−	16.4612i	−0.461005	−	0.798483i
$426$	0.472310	−	0.818065i	0.0228835	−	0.0396354i
$427$	6.44304	+	3.71989i	0.311801	+	0.180018i
$428$	−8.65078			−0.418151
$429$	9.23490	−	1.81381i	0.445865	−	0.0875714i
$430$	1.02316			0.0493413
$431$	4.53528	+	2.61844i	0.218457	+	0.126126i	0.605235	−	0.796047i	$-0.293079\pi$
$431$	4.53528	+	2.61844i	0.218457	+	0.126126i	−0.386779	+	0.922173i	$0.626412\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	8.41030	+	14.5671i	0.404173	+	0.700048i	0.994225	−	0.107317i	$-0.0342260\pi$
$433$	8.41030	+	14.5671i	0.404173	+	0.700048i	−0.590052	+	0.807365i	$0.700893\pi$
$434$			7.07434i			0.339579i
$435$	0.342023	−	0.197467i	0.0163988	−	0.00946782i
$436$	−16.1205	+	9.30718i	−0.772032	+	0.445733i
$437$		−	23.6401i		−	1.13086i
$438$	2.33281	+	4.04054i	0.111466	+	0.193065i
$439$	−7.36282	+	12.7528i	−0.351408	+	0.608657i	−0.986496	−	0.163783i	$-0.947630\pi$
$439$	−7.36282	+	12.7528i	−0.351408	+	0.608657i	0.635088	+	0.772440i	$0.280964\pi$
$440$	0.752321	+	0.434353i	0.0358655	+	0.0207070i
$441$	−1.00000			−0.0476190
$442$	−4.53765	+	13.2624i	−0.215834	+	0.630827i
$443$	36.2393			1.72178			0.860891	−	0.508789i	$-0.169907\pi$
$443$	36.2393			1.72178			0.860891	+	0.508789i	$0.169907\pi$
$444$	0.499211	+	0.288220i	0.0236915	+	0.0136783i
$445$	−0.562493	+	0.974266i	−0.0266647	+	0.0461846i
$446$	4.21673	+	7.30359i	0.199668	+	0.345835i
$447$			6.05696i			0.286484i
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	−21.0351	+	12.1446i	−0.992708	+	0.573140i	−0.906083	−	0.423101i	$-0.860942\pi$
$449$	−21.0351	+	12.1446i	−0.992708	+	0.573140i	−0.0866255	+	0.996241i	$0.527608\pi$
$450$			4.88924i			0.230481i
$451$	0.680043	+	1.17787i	0.0320220	+	0.0554637i
$452$	4.57512	−	7.92435i	0.215196	−	0.372730i
$453$	18.6154	+	10.7476i	0.874630	+	0.504968i
$454$	−27.9893			−1.31360
$455$	−0.231262	−	1.17746i	−0.0108417	−	0.0552001i
$456$	−5.61181			−0.262797
$457$	−28.8744	−	16.6706i	−1.35069	−	0.779819i	−0.362340	−	0.932046i	$-0.618022\pi$
$457$	−28.8744	−	16.6706i	−1.35069	−	0.779819i	−0.988345	+	0.152227i	$0.951355\pi$
$458$	−14.3892	+	24.9229i	−0.672365	+	1.16457i
$459$	1.94383	+	3.36681i	0.0907303	+	0.157149i
$460$			1.40197i			0.0653674i
$461$	−25.6317	+	14.7985i	−1.19379	+	0.689234i	−0.959164	−	0.282852i	$-0.908720\pi$
$461$	−25.6317	+	14.7985i	−1.19379	+	0.689234i	−0.234625	+	0.972086i	$0.575386\pi$
$462$	2.26053	−	1.30512i	0.105169	−	0.0607196i
$463$			36.6027i			1.70107i	0.525918	+	0.850535i	$0.323722\pi$
$463$			36.6027i			1.70107i	−0.525918	+	0.850535i	$0.676278\pi$
$464$	0.593337	+	1.02769i	0.0275450	+	0.0477093i
$465$	−1.17720	+	2.03896i	−0.0545912	+	0.0945547i
$466$	16.3572	+	9.44383i	0.757732	+	0.437477i
$467$	−6.21635			−0.287658			−0.143829	−	0.989603i	$-0.545942\pi$
$467$	−6.21635			−0.287658			−0.143829	+	0.989603i	$0.545942\pi$
$468$	2.71652	−	2.37076i	0.125571	−	0.109589i
$469$	−11.9203			−0.550428
$470$	−3.47384	−	2.00562i	−0.160236	−	0.0925125i
$471$	1.14613	−	1.98516i	0.0528110	−	0.0914714i
$472$	−5.23758	−	9.07175i	−0.241079	−	0.417561i
$473$			8.02474i			0.368978i
$474$	0.816699	−	0.471521i	0.0375122	−	0.0216577i
$475$	23.7616	−	13.7187i	1.09026	−	0.629459i
$476$			3.88766i			0.178191i
$477$	4.85523	+	8.40951i	0.222306	+	0.385045i
$478$	5.54665	−	9.60707i	0.253698	−	0.439417i
$479$	−29.0757	−	16.7869i	−1.32850	−	0.767011i	−0.343434	−	0.939177i	$-0.611590\pi$
$479$	−29.0757	−	16.7869i	−1.32850	−	0.767011i	−0.985068	+	0.172165i	$0.944924\pi$
$480$	0.332808			0.0151905
$481$	1.36660	+	1.56591i	0.0623117	+	0.0713993i
$482$	8.11392			0.369579
$483$	3.64819	+	2.10628i	0.165998	+	0.0958393i
$484$	2.09334	−	3.62577i	0.0951517	−	0.164808i
$485$	−0.967782	−	1.67625i	−0.0439447	−	0.0761145i
$486$		−	1.00000i		−	0.0453609i
$487$	17.5020	−	10.1048i	0.793089	−	0.457890i	−0.0479597	−	0.998849i	$-0.515272\pi$
$487$	17.5020	−	10.1048i	0.793089	−	0.457890i	0.841049	+	0.540959i	$0.181939\pi$
$488$	−6.44304	+	3.71989i	−0.291663	+	0.168392i
$489$		−	3.34071i		−	0.151072i
$490$	−0.166404	−	0.288220i	−0.00751736	−	0.0130204i
$491$	−3.38977	+	5.87125i	−0.152978	+	0.264966i	−0.932321	−	0.361632i	$-0.882220\pi$
$491$	−3.38977	+	5.87125i	−0.152978	+	0.264966i	0.779343	+	0.626598i	$0.215553\pi$
$492$	0.451251	+	0.260530i	0.0203439	+	0.0117456i
$493$	−4.61339			−0.207777
$494$	−19.1441	−	6.55006i	−0.861336	−	0.294701i
$495$	0.868706			0.0390454
$496$	−6.12656	−	3.53717i	−0.275090	−	0.158824i
$497$	0.472310	−	0.818065i	0.0211860	−	0.0366952i
$498$	−6.85861	−	11.8795i	−0.307341	−	0.532331i
$499$		−	11.0813i		−	0.496066i	−0.968752	−	0.248033i	$-0.920216\pi$
$499$		−	11.0813i		−	0.496066i	0.968752	−	0.248033i	$-0.0797841\pi$
$500$	−2.85027	+	1.64561i	−0.127468	+	0.0735938i
$501$	5.57802	−	3.22047i	0.249207	−	0.143880i
$502$			3.16930i			0.141453i
$503$	14.9958	+	25.9735i	0.668629	+	1.15810i	0.978288	+	0.207252i	$0.0664520\pi$
$503$	14.9958	+	25.9735i	0.668629	+	1.15810i	−0.309658	+	0.950848i	$0.600215\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	−4.60296	−	2.65752i	−0.204829	−	0.118258i
$506$	−10.9958			−0.488823
$507$	12.0343	−	4.91693i	0.534461	−	0.218368i
$508$	6.77953			0.300793
$509$	27.2629	+	15.7402i	1.20840	+	0.697673i	0.962411	−	0.271599i	$-0.0875523\pi$
$509$	27.2629	+	15.7402i	1.20840	+	0.697673i	0.245994	+	0.969271i	$0.420886\pi$
$510$	−0.646922	+	1.12050i	−0.0286462	+	0.0496166i
$511$	2.33281	+	4.04054i	0.103197	+	0.178743i
$512$			1.00000i			0.0441942i
$513$	−4.85997	+	2.80591i	−0.214573	+	0.123884i
$514$	0.167507	−	0.0967103i	0.00738843	−	0.00426571i
$515$		−	2.49819i		−	0.110083i
$516$	1.53717	+	2.66245i	0.0676701	+	0.117208i
$517$	15.7303	−	27.2456i	0.691816	−	1.19826i
$518$	0.499211	+	0.288220i	0.0219341	+	0.0126637i
$519$	−18.6144			−0.817079
$520$	1.13534	+	0.388451i	0.0497880	+	0.0170347i
$521$	17.8010			0.779877			0.389939	−	0.920841i	$-0.372496\pi$
$521$	17.8010			0.779877			0.389939	+	0.920841i	$0.372496\pi$
$522$	1.02769	+	0.593337i	0.0449808	+	0.0259697i
$523$	−16.4702	+	28.5272i	−0.720192	+	1.24741i	0.240731	+	0.970592i	$0.422613\pi$
$523$	−16.4702	+	28.5272i	−0.720192	+	1.24741i	−0.960923	+	0.276817i	$0.910720\pi$
$524$	3.61440	+	6.26032i	0.157896	+	0.273483i
$525$			4.88924i			0.213384i
$526$	10.4301	−	6.02185i	0.454776	−	0.262565i
$527$	23.8180	−	13.7513i	1.03753	−	0.599017i
$528$			2.61023i			0.113596i
$529$	2.62713	+	4.55033i	0.114223	+	0.197840i
$530$	−1.61586	+	2.79875i	−0.0701884	+	0.121570i
$531$	−9.07175	−	5.23758i	−0.393680	−	0.227292i
$532$	−5.61181			−0.243303
$533$	1.23531	+	1.41547i	0.0535072	+	0.0613107i
$534$	−3.38029			−0.146279
$535$	−2.49333	−	1.43952i	−0.107796	−	0.0622360i
$536$	5.96015	−	10.3233i	0.257439	−	0.445898i
$537$	11.1081	+	19.2398i	0.479351	+	0.830261i
$538$			17.2097i			0.741965i
$539$	2.26053	−	1.30512i	0.0973679	−	0.0562154i
$540$	0.288220	−	0.166404i	0.0124030	−	0.00716088i
$541$			15.5204i			0.667276i	0.942701	+	0.333638i	$0.108276\pi$
$541$			15.5204i			0.667276i	−0.942701	+	0.333638i	$0.891724\pi$
$542$	8.57096	+	14.8453i	0.368154	+	0.637662i
$543$	−2.02927	+	3.51479i	−0.0870842	+	0.150834i
$544$	−3.36681	−	1.94383i	−0.144351	−	0.0833411i
$545$	−6.19500			−0.265365
$546$	2.71652	−	2.37076i	0.116256	−	0.101459i
$547$	22.9529			0.981397			0.490698	−	0.871329i	$-0.336742\pi$
$547$	22.9529			0.981397			0.490698	+	0.871329i	$0.336742\pi$
$548$	−10.2964	−	5.94462i	−0.439840	−	0.253942i
$549$	−3.71989	+	6.44304i	−0.158761	+	0.274982i
$550$	−6.38103	−	11.0523i	−0.272088	−	0.471270i
$551$		−	6.65939i		−	0.283700i
$552$	−3.64819	+	2.10628i	−0.155277	+	0.0896494i
$553$	0.816699	−	0.471521i	0.0347296	−	0.0200511i
$554$			15.7132i			0.667590i
$555$	0.0959218	+	0.166141i	0.00407165	+	0.00705231i
$556$	7.16056	−	12.4025i	0.303675	−	0.525981i
$557$	−20.8161	−	12.0182i	−0.882005	−	0.509226i	−0.0106863	−	0.999943i	$-0.503402\pi$
$557$	−20.8161	−	12.0182i	−0.882005	−	0.509226i	−0.871319	+	0.490717i	$0.836735\pi$
$558$	−7.07434			−0.299481
$559$	2.13630	+	10.8769i	0.0903560	+	0.460043i
$560$	0.332808			0.0140637
$561$	−8.78817	−	5.07386i	−0.371037	−	0.214218i
$562$	−2.03669	+	3.52765i	−0.0859125	+	0.148805i
$563$	−18.9379	−	32.8015i	−0.798139	−	1.38242i	−0.920827	−	0.389972i	$-0.872485\pi$
$563$	−18.9379	−	32.8015i	−0.798139	−	1.38242i	0.122687	−	0.992445i	$-0.460849\pi$
$564$		−	12.0528i		−	0.507512i
$565$	2.63728	−	1.52264i	0.110951	−	0.0640578i
$566$	−18.6497	+	10.7674i	−0.783906	+	0.452589i
$567$		−	1.00000i		−	0.0419961i
$568$	0.472310	+	0.818065i	0.0198177	+	0.0343252i
$569$	−13.6833	+	23.7001i	−0.573632	+	0.993560i	0.422557	+	0.906336i	$0.361133\pi$
$569$	−13.6833	+	23.7001i	−0.573632	+	0.993560i	−0.996189	+	0.0872233i	$0.972201\pi$
$570$	−1.61744	−	0.933827i	−0.0677469	−	0.0391137i
$571$	17.6639			0.739213			0.369607	−	0.929188i	$-0.379492\pi$
$571$	17.6639			0.739213			0.369607	+	0.929188i	$0.379492\pi$
$572$	−3.04665	+	8.90456i	−0.127387	+	0.372318i
$573$	11.7204			0.489625
$574$	0.451251	+	0.260530i	0.0188348	+	0.0108743i
$575$	10.2981	−	17.8369i	0.429462	−	0.743849i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	11.3804i		−	0.473772i	−0.971537	−	0.236886i	$-0.923873\pi$
$577$		−	11.3804i		−	0.473772i	0.971537	−	0.236886i	$-0.0761268\pi$
$578$	−1.63340	+	0.943042i	−0.0679404	+	0.0392254i
$579$	−20.6123	+	11.9005i	−0.856618	+	0.494568i
$580$			0.394934i			0.0163988i
$581$	−6.85861	−	11.8795i	−0.284543	−	0.492843i
$582$	2.90793	−	5.03669i	0.120538	−	0.208777i
$583$	−21.9508	−	12.6733i	−0.909109	−	0.524874i
$584$	−4.66562			−0.193065
$585$	1.17746	−	0.231262i	0.0486819	−	0.00956152i
$586$	−0.176042			−0.00727222
$587$	15.9949	+	9.23469i	0.660182	+	0.381156i	0.792346	−	0.610072i	$-0.208859\pi$
$587$	15.9949	+	9.23469i	0.660182	+	0.381156i	−0.132164	+	0.991228i	$0.542193\pi$
$588$	0.500000	−	0.866025i	0.0206197	−	0.0357143i
$589$	19.8499	+	34.3811i	0.817902	+	1.41665i
$590$		−	3.48621i		−	0.143525i
$591$	8.73184	−	5.04133i	0.359180	−	0.207373i
$592$	−0.499211	+	0.288220i	−0.0205175	+	0.0118458i
$593$			19.3561i			0.794859i	0.917633	+	0.397429i	$0.130098\pi$
$593$			19.3561i			0.794859i	−0.917633	+	0.397429i	$0.869902\pi$
$594$	1.30512	+	2.26053i	0.0535496	+	0.0927507i
$595$	−0.646922	+	1.12050i	−0.0265212	+	0.0459361i
$596$	−5.24548	−	3.02848i	−0.214863	−	0.124051i
$597$	13.8501			0.566846
$598$	−14.9039	+	2.92724i	−0.609465	+	0.119704i
$599$	21.1818			0.865466			0.432733	−	0.901522i	$-0.357549\pi$
$599$	21.1818			0.865466			0.432733	+	0.901522i	$0.357549\pi$
$600$	−4.23421	−	2.44462i	−0.172861	−	0.0998012i
$601$	−11.0721	+	19.1774i	−0.451639	+	0.782261i	−0.998488	−	0.0549699i	$-0.982494\pi$
$601$	−11.0721	+	19.1774i	−0.451639	+	0.782261i	0.546849	+	0.837231i	$0.315827\pi$
$602$	1.53717	+	2.66245i	0.0626503	+	0.108513i
$603$		−	11.9203i		−	0.485432i
$604$	−18.6154	+	10.7476i	−0.757452	+	0.437315i
$605$	1.20668	−	0.696679i	0.0490586	−	0.0283240i
$606$		−	15.9703i		−	0.648750i
$607$	−17.1439	−	29.6942i	−0.695851	−	1.20525i	−0.969893	−	0.243531i	$-0.921694\pi$
$607$	−17.1439	−	29.6942i	−0.695851	−	1.20525i	0.274042	−	0.961718i	$-0.411639\pi$
$608$	2.80591	−	4.85997i	0.113795	−	0.197098i
$609$	1.02769	+	0.593337i	0.0416441	+	0.0240432i
$610$	−2.47602			−0.100251
$611$	14.0679	−	41.1168i	0.569125	−	1.66341i
$612$	−3.88766			−0.157149
$613$	14.7308	+	8.50484i	0.594972	+	0.343507i	0.767061	−	0.641574i	$-0.221718\pi$
$613$	14.7308	+	8.50484i	0.594972	+	0.343507i	−0.172089	+	0.985081i	$0.555052\pi$
$614$	−10.3702	+	17.9618i	−0.418509	+	0.724878i
$615$	0.0867062	+	0.150180i	0.00349633	+	0.00605583i
$616$			2.61023i			0.105169i
$617$	15.0005	−	8.66052i	0.603896	−	0.348659i	−0.166677	−	0.986012i	$-0.553304\pi$
$617$	15.0005	−	8.66052i	0.603896	−	0.348659i	0.770573	+	0.637352i	$0.219970\pi$
$618$	6.50074	−	3.75321i	0.261498	−	0.150976i
$619$		−	0.621482i		−	0.0249795i	−0.999922	−	0.0124897i	$-0.996024\pi$
$619$		−	0.621482i		−	0.0249795i	0.999922	−	0.0124897i	$-0.00397571\pi$
$620$	−1.17720	−	2.03896i	−0.0472773	−	0.0818868i
$621$	−2.10628	+	3.64819i	−0.0845223	+	0.146397i
$622$	−9.49838	−	5.48389i	−0.380850	−	0.219884i
$623$	−3.38029			−0.135428
$624$	0.694883	+	3.53796i	0.0278176	+	0.141632i
$625$	23.3509			0.934034
$626$	−14.0460	−	8.10945i	−0.561390	−	0.324119i
$627$	7.32407	−	12.6857i	0.292495	−	0.506617i
$628$	1.14613	+	1.98516i	0.0457357	+	0.0792165i
$629$		−	2.24100i		−	0.0893546i
$630$	0.288220	−	0.166404i	0.0114830	−	0.00662969i
$631$	11.7575	−	6.78817i	0.468057	−	0.270233i	−0.247369	−	0.968921i	$-0.579566\pi$
$631$	11.7575	−	6.78817i	0.468057	−	0.270233i	0.715426	+	0.698688i	$0.246233\pi$
$632$			0.943042i			0.0375122i
$633$	2.27743	+	3.94462i	0.0905196	+	0.156785i
$634$	5.26790	−	9.12428i	0.209215	−	0.362371i
$635$	1.95400	+	1.12814i	0.0775419	+	0.0447689i
$636$	−9.71047			−0.385045
$637$	2.71652	−	2.37076i	0.107632	−	0.0939331i
$638$	−3.09750			−0.122631
$639$	0.818065	+	0.472310i	0.0323621	+	0.0186843i
$640$	−0.166404	+	0.288220i	−0.00657769	+	0.0113929i
$641$	−10.2558	−	17.7636i	−0.405081	−	0.701622i	0.589250	−	0.807951i	$-0.299423\pi$
$641$	−10.2558	−	17.7636i	−0.405081	−	0.701622i	−0.994331	+	0.106330i	$0.966090\pi$
$642$		−	8.65078i		−	0.341419i
$643$	−37.0253	+	21.3766i	−1.46013	+	0.843009i	−0.999017	−	0.0443295i	$-0.985885\pi$
$643$	−37.0253	+	21.3766i	−1.46013	+	0.843009i	−0.461118	+	0.887339i	$0.652552\pi$
$644$	−3.64819	+	2.10628i	−0.143759	+	0.0829992i
$645$			1.02316i			0.0402870i
$646$	10.9084	+	18.8939i	0.429186	+	0.743372i
$647$	−13.1115	+	22.7098i	−0.515466	+	0.892814i	0.484372	+	0.874862i	$0.339048\pi$
$647$	−13.1115	+	22.7098i	−0.515466	+	0.892814i	−0.999839	+	0.0179521i	$0.994285\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	27.3426			1.07329
$650$	−11.5912	−	13.2817i	−0.454646	−	0.520952i
$651$	−7.07434			−0.277265
$652$	2.89314	+	1.67035i	0.113304	+	0.0654161i
$653$	4.36935	−	7.56794i	0.170986	−	0.296156i	−0.767779	−	0.640715i	$-0.778638\pi$
$653$	4.36935	−	7.56794i	0.170986	−	0.296156i	0.938765	+	0.344558i	$0.111971\pi$
$654$	−9.30718	−	16.1205i	−0.363939	−	0.630361i
$655$			2.40580i			0.0940023i
$656$	−0.451251	+	0.260530i	−0.0176184	+	0.0101720i
$657$	−4.04054	+	2.33281i	−0.157637	+	0.0910115i
$658$		−	12.0528i		−	0.469865i
$659$	−0.251052	−	0.434834i	−0.00977958	−	0.0169387i	0.861094	−	0.508445i	$-0.169780\pi$
$659$	−0.251052	−	0.434834i	−0.00977958	−	0.0169387i	−0.870874	+	0.491507i	$0.836446\pi$
$660$	−0.434353	+	0.752321i	−0.0169072	+	0.0292841i
$661$	27.1062	+	15.6498i	1.05431	+	0.608705i	0.923853	−	0.382749i	$-0.125022\pi$
$661$	27.1062	+	15.6498i	1.05431	+	0.608705i	0.130456	+	0.991454i	$0.458356\pi$
$662$	16.1297			0.626899
$663$	−13.2624	−	4.53765i	−0.515068	−	0.176228i
$664$	13.7172			0.532331
$665$	−1.61744	−	0.933827i	−0.0627215	−	0.0362123i
$666$	−0.288220	+	0.499211i	−0.0111683	+	0.0193440i
$667$	−2.49947	−	4.32922i	−0.0967800	−	0.167628i
$668$			6.44094i			0.249207i
$669$	−7.30359	+	4.21673i	−0.282373	+	0.163028i
$670$	3.43567	−	1.98358i	0.132731	−	0.0766325i
$671$		−	19.4196i		−	0.749685i
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	−11.8585	+	20.5395i	−0.457112	+	0.791741i	−0.998807	−	0.0488340i	$-0.984449\pi$
$673$	−11.8585	+	20.5395i	−0.457112	+	0.791741i	0.541695	+	0.840575i	$0.317783\pi$
$674$	−1.54833	−	0.893927i	−0.0596393	−	0.0344328i
$675$	−4.88924			−0.188187
$676$	−1.75895	+	12.8805i	−0.0676520	+	0.495402i
$677$	17.8136			0.684631			0.342315	−	0.939585i	$-0.388789\pi$
$677$	17.8136			0.684631			0.342315	+	0.939585i	$0.388789\pi$
$678$	7.92435	+	4.57512i	0.304333	+	0.175707i
$679$	2.90793	−	5.03669i	0.111596	−	0.193290i
$680$	−0.646922	−	1.12050i	−0.0248083	−	0.0429693i
$681$		−	27.9893i		−	1.07255i
$682$	15.9917	−	9.23284i	0.612356	−	0.353544i
$683$	10.3174	−	5.95673i	0.394783	−	0.227928i	−0.289448	−	0.957194i	$-0.593472\pi$
$683$	10.3174	−	5.95673i	0.394783	−	0.227928i	0.684230	+	0.729266i	$0.260138\pi$
$684$		−	5.61181i		−	0.214573i
$685$	−1.97841	−	3.42671i	−0.0755913	−	0.130928i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−24.9229	−	14.3892i	−0.950868	−	0.548984i
$688$	−3.07434			−0.117208
$689$	−33.1263	−	11.3340i	−1.26201	−	0.431790i
$690$	−1.40197			−0.0533723
$691$	−17.3085	−	9.99306i	−0.658446	−	0.380154i	0.133239	−	0.991084i	$-0.457462\pi$
$691$	−17.3085	−	9.99306i	−0.658446	−	0.380154i	−0.791685	+	0.610930i	$0.790796\pi$
$692$	9.30718	−	16.1205i	0.353806	−	0.612810i
$693$	1.30512	+	2.26053i	0.0495773	+	0.0858704i
$694$			25.4061i			0.964402i
$695$	4.12763	−	2.38309i	0.156570	−	0.0903957i
$696$	−1.02769	+	0.593337i	−0.0389545	+	0.0224904i
$697$		−	2.02570i		−	0.0767289i
$698$	14.1693	+	24.5419i	0.536314	+	0.928923i
$699$	−9.44383	+	16.3572i	−0.357198	+	0.618686i
$700$	−4.23421	−	2.44462i	−0.160038	−	0.0923979i
$701$	−23.9244			−0.903613			−0.451806	−	0.892116i	$-0.649220\pi$
$701$	−23.9244			−0.903613			−0.451806	+	0.892116i	$0.649220\pi$
$702$	2.37076	+	2.71652i	0.0894787	+	0.102528i
$703$	3.23487			0.122005
$704$	−2.26053	−	1.30512i	−0.0851969	−	0.0491885i
$705$	2.00562	−	3.47384i	0.0755362	−	0.130832i
$706$	0.976568	+	1.69146i	0.0367536	+	0.0636591i
$707$		−	15.9703i		−	0.600626i
$708$	9.07175	−	5.23758i	0.340937	−	0.196840i
$709$	30.7406	−	17.7481i	1.15449	−	0.666544i	0.204512	−	0.978864i	$-0.434439\pi$
$709$	30.7406	−	17.7481i	1.15449	−	0.666544i	0.949977	+	0.312320i	$0.101106\pi$
$710$			0.314377i			0.0117983i
$711$	0.471521	+	0.816699i	0.0176834	+	0.0306286i
$712$	1.69014	−	2.92741i	0.0633408	−	0.109710i
$713$	25.8085	+	14.9006i	0.966537	+	0.558031i
$714$	−3.88766			−0.145492
$715$	−2.35986	+	2.05950i	−0.0882536	+	0.0770208i
$716$	−22.2163			−0.830261
$717$	9.60707	+	5.54665i	0.358783	+	0.207143i
$718$	13.8282	−	23.9512i	0.516065	−	0.893851i
$719$	−3.09097	−	5.35372i	−0.115274	−	0.199660i	0.802615	−	0.596497i	$-0.203441\pi$
$719$	−3.09097	−	5.35372i	−0.115274	−	0.199660i	−0.917889	+	0.396837i	$0.870108\pi$
$720$			0.332808i			0.0124030i
$721$	6.50074	−	3.75321i	0.242100	−	0.139777i
$722$	−10.8188	+	6.24622i	−0.402633	+	0.232460i
$723$			8.11392i			0.301760i
$724$	−2.02927	−	3.51479i	−0.0754171	−	0.130626i
$725$	2.90097	−	5.02462i	0.107739	−	0.186610i
$726$	3.62577	+	2.09334i	0.134565	+	0.0776910i
$727$	−43.2387			−1.60363			−0.801817	−	0.597569i	$-0.796133\pi$
$727$	−43.2387			−1.60363			−0.801817	+	0.597569i	$0.796133\pi$
$728$	0.694883	+	3.53796i	0.0257541	+	0.131125i
$729$	1.00000			0.0370370
$730$	−1.34472	−	0.776376i	−0.0497704	−	0.0287350i
$731$	5.97599	−	10.3507i	0.221030	−	0.382835i
$732$	−3.71989	−	6.44304i	−0.137491	−	0.238142i
$733$			32.0306i			1.18308i	0.806277	+	0.591538i	$0.201479\pi$
$733$			32.0306i			1.18308i	−0.806277	+	0.591538i	$0.798521\pi$
$734$	4.98636	−	2.87888i	0.184050	−	0.106261i
$735$	0.288220	−	0.166404i	0.0106311	−	0.00613790i
$736$		−	4.21257i		−	0.155277i
$737$	15.5574	+	26.9462i	0.573064	+	0.992576i
$738$	−0.260530	+	0.451251i	−0.00959023	+	0.0166108i
$739$	−22.0558	−	12.7339i	−0.811334	−	0.468424i	0.0360848	−	0.999349i	$-0.488511\pi$
$739$	−22.0558	−	12.7339i	−0.811334	−	0.468424i	−0.847419	+	0.530925i	$0.821845\pi$
$740$	−0.191844			−0.00705231
$741$	6.55006	−	19.1441i	0.240623	−	0.703278i
$742$	−9.71047			−0.356482
$743$	−12.5533	−	7.24763i	−0.460535	−	0.265890i	0.251734	−	0.967796i	$-0.418999\pi$
$743$	−12.5533	−	7.24763i	−0.460535	−	0.265890i	−0.712269	+	0.701906i	$0.752332\pi$
$744$	3.53717	−	6.12656i	0.129679	−	0.224610i
$745$	−1.00790	−	1.74574i	−0.0369266	−	0.0639588i
$746$			27.8487i			1.01961i
$747$	11.8795	−	6.85861i	0.434646	−	0.250943i
$748$	8.78817	−	5.07386i	0.321327	−	0.185519i
$749$		−	8.65078i		−	0.316092i
$750$	−1.64561	−	2.85027i	−0.0600891	−	0.104077i
$751$	14.5632	−	25.2243i	0.531420	−	0.920447i	−0.467907	−	0.883777i	$-0.654992\pi$
$751$	14.5632	−	25.2243i	0.531420	−	0.920447i	0.999327	−	0.0366690i	$-0.0116747\pi$
$752$	10.4380	+	6.02638i	0.380634	+	0.219759i
$753$	−3.16930			−0.115496
$754$	−4.19840	+	0.824599i	−0.152897	+	0.0300301i
$755$	−7.15379			−0.260353
$756$	0.866025	+	0.500000i	0.0314970	+	0.0181848i
$757$	10.0230	−	17.3603i	0.364292	−	0.630973i	−0.624370	−	0.781129i	$-0.714644\pi$
$757$	10.0230	−	17.3603i	0.364292	−	0.630973i	0.988662	+	0.150156i	$0.0479776\pi$
$758$	6.22590	+	10.7836i	0.226135	+	0.391677i
$759$		−	10.9958i		−	0.399122i
$760$	1.61744	−	0.933827i	0.0586706	−	0.0338735i
$761$	16.4954	−	9.52360i	0.597956	−	0.345230i	−0.170281	−	0.985396i	$-0.554468\pi$
$761$	16.4954	−	9.52360i	0.597956	−	0.345230i	0.768237	+	0.640165i	$0.221134\pi$
$762$			6.77953i			0.245596i
$763$	−9.30718	−	16.1205i	−0.336942	−	0.583601i
$764$	−5.86018	+	10.1501i	−0.212014	+	0.367219i
$765$	−1.12050	−	0.646922i	−0.0405118	−	0.0233895i
$766$	9.72573			0.351405
$767$	37.0607	−	7.27900i	1.33818	−	0.262830i
$768$	−1.00000			−0.0360844
$769$	13.2055	+	7.62418i	0.476201	+	0.274935i	0.718832	−	0.695184i	$-0.244677\pi$
$769$	13.2055	+	7.62418i	0.476201	+	0.274935i	−0.242631	+	0.970119i	$0.578010\pi$

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.332808i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.332808i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.166404 - 0.288220i) q^{10} +(2.26053 + 1.30512i) q^{11} +1.00000 q^{12} +(3.41140 + 1.16719i) q^{13} +1.00000 q^{14} +(0.288220 + 0.166404i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.94383 - 3.36681i) q^{17} +1.00000i q^{18} +(4.85997 - 2.80591i) q^{19} +(-0.288220 + 0.166404i) q^{20} +1.00000i q^{21} +(-1.30512 - 2.26053i) q^{22} +(2.10628 - 3.64819i) q^{23} +(-0.866025 - 0.500000i) q^{24} +4.88924 q^{25} +(-2.37076 - 2.71652i) q^{26} -1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(0.593337 - 1.02769i) q^{29} +(-0.166404 - 0.288220i) q^{30} +7.07434i q^{31} +(0.866025 - 0.500000i) q^{32} +(2.26053 - 1.30512i) q^{33} +3.88766i q^{34} +(-0.166404 - 0.288220i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.499211 + 0.288220i) q^{37} -5.61181 q^{38} +(2.71652 - 2.37076i) q^{39} +0.332808 q^{40} +(0.451251 + 0.260530i) q^{41} +(0.500000 - 0.866025i) q^{42} +(1.53717 + 2.66245i) q^{43} +2.61023i q^{44} +(0.288220 - 0.166404i) q^{45} +(-3.64819 + 2.10628i) q^{46} -12.0528i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-4.23421 - 2.44462i) q^{50} -3.88766 q^{51} +(0.694883 + 3.53796i) q^{52} -9.71047 q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.434353 + 0.752321i) q^{55} +(0.500000 + 0.866025i) q^{56} -5.61181i q^{57} +(-1.02769 + 0.593337i) q^{58} +(9.07175 - 5.23758i) q^{59} +0.332808i q^{60} +(-3.71989 - 6.44304i) q^{61} +(3.53717 - 6.12656i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-0.388451 + 1.13534i) q^{65} -2.61023 q^{66} +(10.3233 + 5.96015i) q^{67} +(1.94383 - 3.36681i) q^{68} +(-2.10628 - 3.64819i) q^{69} +0.332808i q^{70} +(-0.818065 + 0.472310i) q^{71} +(-0.866025 + 0.500000i) q^{72} -4.66562i q^{73} +(-0.288220 - 0.499211i) q^{74} +(2.44462 - 4.23421i) q^{75} +(4.85997 + 2.80591i) q^{76} -2.61023 q^{77} +(-3.53796 + 0.694883i) q^{78} -0.943042 q^{79} +(-0.288220 - 0.166404i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.260530 - 0.451251i) q^{82} +13.7172i q^{83} +(-0.866025 + 0.500000i) q^{84} +(1.12050 - 0.646922i) q^{85} -3.07434i q^{86} +(-0.593337 - 1.02769i) q^{87} +(1.30512 - 2.26053i) q^{88} +(2.92741 + 1.69014i) q^{89} -0.332808 q^{90} +(-3.53796 + 0.694883i) q^{91} +4.21257 q^{92} +(6.12656 + 3.53717i) q^{93} +(-6.02638 + 10.4380i) q^{94} +(0.933827 + 1.61744i) q^{95} -1.00000i q^{96} +(-5.03669 + 2.90793i) q^{97} +(-0.866025 + 0.500000i) q^{98} -2.61023i 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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