N = 188, p = 19; cusp example -- Sage

p = 11 M = ModularSymbols(188,2,sign=1) S = M.cuspidal_submodule() N = S.new_subspace() D = N.decomposition()

e = M([0,oo]); e

-(1,0)

-(1,0)

D[0].rational_period_mapping()( e )

(0, 0)

(0, 0)

D[1].rational_period_mapping()( e )

(-1, 0)

(-1, 0)

A = D[0] phi = A.rational_period_mapping()

phi(e)

(0, 0)

(0, 0)

time v = A.dual_eigenvector() print v

Time: CPU 0.16 s, Wall: 0.17 s
(0, 1, 1, 0, 0, -1, 1/2*alpha - 2, -1, 0, -1, 0, -1, 1, -1, 1/2*alpha -
2, 0, 0, 1, -1/2*alpha + 3, 1, 0, 1, 0, 0, 0, 0, 0)

Time: CPU 0.16 s, Wall: 0.17 s
(0, 1, 1, 0, 0, -1, 1/2*alpha - 2, -1, 0, -1, 0, -1, 1, -1, 1/2*alpha - 2, 0, 0, 1, -1/2*alpha + 3, 1, 0, 1, 0, 0, 0, 0, 0)

def modsym(r): s = M([r, oo]) return v.dot_product(s.element())

z = [modsym(a/p^2) for a in [0..p^2-1]]

K_f = z[0].parent(); K_f

Number Field in alpha with defining polynomial x^2 - 6*x + 4

Number Field in alpha with defining polynomial x^2 - 6*x + 4

print K_f.factor(p) a_p = A.eigenvalue(p) print a_p

(Fractional ideal (3/2*alpha - 5)) * (Fractional ideal (3/2*alpha - 4))
-2*alpha + 4

(Fractional ideal (3/2*alpha - 5)) * (Fractional ideal (3/2*alpha - 4))
-2*alpha + 4

Q = Qp(p,prec=10); Q F = Q R.<x> = F[] (R(K_f.defining_polynomial())).roots() psi1 = K_f.hom([ (R(K_f.defining_polynomial())).roots()[0][0]]) psi2 = K_f.hom([ (R(K_f.defining_polynomial())).roots()[1][0]]) a_p = A.eigenvalue(p) a_p_padic1 = psi1(a_p) a_p_padic2 = psi2(a_p) f1 = x^2 - a_p_padic1*x + p f2 = x^2 - a_p_padic2*x + p padic_lseries_alpha1 =root01 = f1.roots()[0][0] padic_lseries_alpha2 = root02 = f2.roots()[0][0] print padic_lseries_alpha1, padic_lseries_alpha2

1 + 11 + 2*11^2 + 2*11^3 + 9*11^4 + 9*11^5 + 4*11^6 + 8*11^7 + 4*11^8 +
3*11^9 + O(11^10) 6 + 6*11 + 2*11^2 + 11^3 + 3*11^4 + 6*11^5 + 9*11^6 +
7*11^7 + 7*11^8 + 2*11^9 + O(11^10)

1 + 11 + 2*11^2 + 2*11^3 + 9*11^4 + 9*11^5 + 4*11^6 + 8*11^7 + 4*11^8 + 3*11^9 + O(11^10) 6 + 6*11 + 2*11^2 + 11^3 + 3*11^4 + 6*11^5 + 9*11^6 + 7*11^7 + 7*11^8 + 2*11^9 + O(11^10)

def modsym_padic(r): print "r = ",r s = M([r,oo]) return psi1(v.dot_product(s.element())) def tau(a): return F.teichmuller(a)

def mu(a, n): return 1/padic_lseries_alpha1^n *modsym_padic(a/p^n) - 1/padic_lseries_alpha1^(n+1)*modsym_padic(a/p^(n-1))

def P_n(n): R.<T> = F[] # F = the p-adic field P = R(0) for a in [1..p-1]: for j in [0..p^(n-1)-1]: P += mu(tau(a)*(1+p)^j, n) * (1+T)^j print P return P

P2 = P_n(2)

r =  11^-2 + O(11^8)
r =  11^-1 + O(11^9)
0
r =  11^-2 + 11^-1 + O(11^8)
r =  11^-1 + 1 + O(11^9)
(9 + 3*11 + 2*11^2 + 3*11^3 + 3*11^4 + 2*11^5 + 10*11^6 + 2*11^7 +
7*11^8 + 8*11^9 + O(11^10))*T + (9 + 3*11 + 2*11^2 + 3*11^3 + 3*11^4 +
2*11^5 + 10*11^6 + 2*11^7 + 7*11^8 + 8*11^9 + O(11^10))
r =  11^-2 + 2*11^-1 + 1 + O(11^8)
r =  11^-1 + 2 + 11 + O(11^9)
(3 + 8*11 + 11^2 + 6*11^4 + 6*11^5 + 10*11^6 + 6*11^7 + 4*11^8 + 5*11^9
+ O(11^10))*T^2 + (4 + 9*11 + 5*11^2 + 3*11^3 + 4*11^4 + 4*11^5 + 9*11^6
+ 5*11^7 + 5*11^8 + 8*11^9 + O(11^10))*T + (1 + 11 + 4*11^2 + 3*11^3 +
9*11^4 + 8*11^5 + 9*11^6 + 9*11^7 + 3*11^9 + O(11^10))
r =  11^-2 + 3*11^-1 + 3 + 11 + O(11^8)
r =  11^-1 + 3 + 3*11 + 11^2 + O(11^9)
(8 + 2*11 + 9*11^2 + 10*11^3 + 4*11^4 + 4*11^5 + 4*11^7 + 6*11^8 +
5*11^9 + O(11^10))*T^3 + (5 + 5*11 + 7*11^2 + 10*11^3 + 9*11^4 + 8*11^5
+ 8*11^7 + 11^8 + O(11^10))*T^2 + (6 + 6*11 + 3*11^3 + 8*11^4 + 6*11^5 +
10*11^6 + 6*11^7 + 2*11^8 + 3*11^9 + O(11^10))*T + (9 + 3*11 + 2*11^2 +
3*11^3 + 3*11^4 + 2*11^5 + 10*11^6 + 2*11^7 + 7*11^8 + 8*11^9 +
O(11^10))
r =  11^-2 + 4*11^-1 + 6 + 4*11 + 11^2 + O(11^8)
r =  11^-1 + 4 + 6*11 + 4*11^2 + 11^3 + O(11^9)
(2 + 7*11 + 8*11^2 + 7*11^3 + 7*11^4 + 8*11^5 + 8*11^7 + 3*11^8 + 2*11^9
+ O(11^10))*T^4 + (5 + 9*11 + 10*11^2 + 8*11^3 + 2*11^4 + 6*11^5 +
3*11^6 + 3*11^7 + 10*11^8 + 3*11^9 + O(11^10))*T^3 + (6 + 4*11 + 4*11^2
+ 2*11^3 + 11^4 + 6*11^5 + 5*11^6 + 11^7 + 2*11^8 + 3*11^9 +
O(11^10))*T^2 + (3 + 2*11 + 2*11^2 + 11^3 + 6*11^4 + 8*11^5 + 2*11^6 +
6*11^7 + 6*11^8 + 11^9 + O(11^10))*T + (O(11^10))
r =  11^-2 + 5*11^-1 + 10 + 10*11 + 5*11^2 + 11^3 + O(11^8)
r =  11^-1 + 5 + 10*11 + 10*11^2 + 5*11^3 + 11^4 + O(11^9)
(9 + 2*11^2 + 7*11^3 + 2*11^4 + 10*11^5 + 2*11^6 + 7*11^7 + 11^8 +
7*11^9 + O(11^10))*T^5 + (3 + 8*11^2 + 10*11^3 + 9*11^4 + 4*11^5 +
4*11^6 + 11^8 + 5*11^9 + O(11^10))*T^4 + (7 + 6*11 + 9*11^2 + 3*11^3 +
7*11^4 + 9*11^5 + 10*11^6 + 9*11^7 + 4*11^8 + 9*11^9 + O(11^10))*T^3 +
(8 + 11 + 3*11^2 + 8*11^3 + 5*11^4 + 9*11^5 + 11^6 + 8*11^7 + 7*11^8 +
8*11^9 + O(11^10))*T^2 + (4 + 6*11 + 11^2 + 4*11^3 + 8*11^4 + 4*11^5 +
6*11^6 + 9*11^7 + 3*11^8 + 4*11^9 + O(11^10))*T + (9 + 2*11^2 + 7*11^3 +
2*11^4 + 10*11^5 + 2*11^6 + 7*11^7 + 11^8 + 7*11^9 + O(11^10))
r =  11^-2 + 6*11^-1 + 4 + 10*11 + 5*11^2 + 7*11^3 + 11^4 + O(11^8)
Traceback (click to the left of this block for traceback)
...
TypeError: Unable to convert 11^-2 + 6*11^-1 + 4 + 10*11 + 5*11^2 +
7*11^3 + 11^4 + O(11^8) to a Cusp

r =  11^-2 + O(11^8)
r =  11^-1 + O(11^9)
0
r =  11^-2 + 11^-1 + O(11^8)
r =  11^-1 + 1 + O(11^9)
(9 + 3*11 + 2*11^2 + 3*11^3 + 3*11^4 + 2*11^5 + 10*11^6 + 2*11^7 + 7*11^8 + 8*11^9 + O(11^10))*T + (9 + 3*11 + 2*11^2 + 3*11^3 + 3*11^4 + 2*11^5 + 10*11^6 + 2*11^7 + 7*11^8 + 8*11^9 + O(11^10))
r =  11^-2 + 2*11^-1 + 1 + O(11^8)
r =  11^-1 + 2 + 11 + O(11^9)
(3 + 8*11 + 11^2 + 6*11^4 + 6*11^5 + 10*11^6 + 6*11^7 + 4*11^8 + 5*11^9 + O(11^10))*T^2 + (4 + 9*11 + 5*11^2 + 3*11^3 + 4*11^4 + 4*11^5 + 9*11^6 + 5*11^7 + 5*11^8 + 8*11^9 + O(11^10))*T + (1 + 11 + 4*11^2 + 3*11^3 + 9*11^4 + 8*11^5 + 9*11^6 + 9*11^7 + 3*11^9 + O(11^10))
r =  11^-2 + 3*11^-1 + 3 + 11 + O(11^8)
r =  11^-1 + 3 + 3*11 + 11^2 + O(11^9)
(8 + 2*11 + 9*11^2 + 10*11^3 + 4*11^4 + 4*11^5 + 4*11^7 + 6*11^8 + 5*11^9 + O(11^10))*T^3 + (5 + 5*11 + 7*11^2 + 10*11^3 + 9*11^4 + 8*11^5 + 8*11^7 + 11^8 + O(11^10))*T^2 + (6 + 6*11 + 3*11^3 + 8*11^4 + 6*11^5 + 10*11^6 + 6*11^7 + 2*11^8 + 3*11^9 + O(11^10))*T + (9 + 3*11 + 2*11^2 + 3*11^3 + 3*11^4 + 2*11^5 + 10*11^6 + 2*11^7 + 7*11^8 + 8*11^9 + O(11^10))
r =  11^-2 + 4*11^-1 + 6 + 4*11 + 11^2 + O(11^8)
r =  11^-1 + 4 + 6*11 + 4*11^2 + 11^3 + O(11^9)
(2 + 7*11 + 8*11^2 + 7*11^3 + 7*11^4 + 8*11^5 + 8*11^7 + 3*11^8 + 2*11^9 + O(11^10))*T^4 + (5 + 9*11 + 10*11^2 + 8*11^3 + 2*11^4 + 6*11^5 + 3*11^6 + 3*11^7 + 10*11^8 + 3*11^9 + O(11^10))*T^3 + (6 + 4*11 + 4*11^2 + 2*11^3 + 11^4 + 6*11^5 + 5*11^6 + 11^7 + 2*11^8 + 3*11^9 + O(11^10))*T^2 + (3 + 2*11 + 2*11^2 + 11^3 + 6*11^4 + 8*11^5 + 2*11^6 + 6*11^7 + 6*11^8 + 11^9 + O(11^10))*T + (O(11^10))
r =  11^-2 + 5*11^-1 + 10 + 10*11 + 5*11^2 + 11^3 + O(11^8)
r =  11^-1 + 5 + 10*11 + 10*11^2 + 5*11^3 + 11^4 + O(11^9)
(9 + 2*11^2 + 7*11^3 + 2*11^4 + 10*11^5 + 2*11^6 + 7*11^7 + 11^8 + 7*11^9 + O(11^10))*T^5 + (3 + 8*11^2 + 10*11^3 + 9*11^4 + 4*11^5 + 4*11^6 + 11^8 + 5*11^9 + O(11^10))*T^4 + (7 + 6*11 + 9*11^2 + 3*11^3 + 7*11^4 + 9*11^5 + 10*11^6 + 9*11^7 + 4*11^8 + 9*11^9 + O(11^10))*T^3 + (8 + 11 + 3*11^2 + 8*11^3 + 5*11^4 + 9*11^5 + 11^6 + 8*11^7 + 7*11^8 + 8*11^9 + O(11^10))*T^2 + (4 + 6*11 + 11^2 + 4*11^3 + 8*11^4 + 4*11^5 + 6*11^6 + 9*11^7 + 3*11^8 + 4*11^9 + O(11^10))*T + (9 + 2*11^2 + 7*11^3 + 2*11^4 + 10*11^5 + 2*11^6 + 7*11^7 + 11^8 + 7*11^9 + O(11^10))
r =  11^-2 + 6*11^-1 + 4 + 10*11 + 5*11^2 + 7*11^3 + 11^4 + O(11^8)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_18.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("UDIgPSBQX24oMik="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpM9_AFz/___code___.py", line 3, in <module>
    exec compile(u'P2 = P_n(_sage_const_2 )
  File "", line 1, in <module>
    
  File "/tmp/tmpJ6aPuL/___code___.py", line 8, in P_n
    P += mu(tau(a)*(_sage_const_1 +p)**j, n) * (_sage_const_1 +T)**j
  File "/tmp/tmppeSxeq/___code___.py", line 4, in mu
    return _sage_const_1 /padic_lseries_alpha1**n *modsym_padic(a/p**n) - _sage_const_1 /padic_lseries_alpha1**(n+_sage_const_1 )*modsym_padic(a/p**(n-_sage_const_1 ))
  File "/tmp/tmpxZ9zcy/___code___.py", line 4, in modsym_padic
    s = M([r,oo])
  File "/home/sage/sage_install/sage-4.3.5/local/lib/python2.6/site-packages/sage/modular/modsym/ambient.py", line 481, in __call__
    return self.modular_symbol(x)
  File "/home/sage/sage_install/sage-4.3.5/local/lib/python2.6/site-packages/sage/modular/modsym/ambient.py", line 776, in modular_symbol
    alpha = Cusp(x[1])
  File "/home/sage/sage_install/sage-4.3.5/local/lib/python2.6/site-packages/sage/modular/cusps.py", line 303, in __init__
    raise TypeError, "Unable to convert %s to a Cusp"%a
TypeError: Unable to convert 11^-2 + 6*11^-1 + 4 + 10*11 + 5*11^2 + 7*11^3 + 11^4 + O(11^8) to a Cusp

print P2

(8 + 2*11 + 10*11^2 + 4*11^3 + 10*11^4 + 8*11^5 + 4*11^6 + 10*11^7 +
4*11^8 + 9*11^9 + O(11^10))

(8 + 2*11 + 10*11^2 + 4*11^3 + 10*11^4 + 8*11^5 + 4*11^6 + 10*11^7 + 4*11^8 + 9*11^9 + O(11^10))

QQ(2*19^-2 + 10*19^-1 + 9 + 19 + 9*19^3 + 14*19^4 + 11*19^5 + 19^6 + 12*19^7 + 12*19^8 + 12*19^9 + 9*19^10 + 17*19^11 + 12*19^12 + 10*19^13 + 4*19^14 + 15*19^15 + 5*19^16 + 19^17 + 7*19^19 + 16*19^20 + 6*19^21 + 12*19^22 + 8*19^23 + 11*19^24 + 19^25 + 11*19^26 + 10*19^27 + 10*19^29 + 15*19^30 + 18*19^31 + 6*19^32 + 6*19^33 + 9*19^34 + 4*19^35 + 7*19^36 + 6*19^37 + 15*19^38 + 14*19^39 + 3*19^41 + 13*19^42 + O(19^43))

Traceback (click to the left of this block for traceback)
...
ValueError: Rational reconstruction of
397529252086698362540978975361450216964475331613570462 (mod
9691808871033067112824380501725664483616416540730367659) does not exist.

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_36.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("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"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpG_LDhl/___code___.py", line 8, in <module>
    _sage_const_6 *_sage_const_19 **_sage_const_37  + _sage_const_15 *_sage_const_19 **_sage_const_38  + _sage_const_14 *_sage_const_19 **_sage_const_39  + _sage_const_3 *_sage_const_19 **_sage_const_41  + _sage_const_13 *_sage_const_19 **_sage_const_42  + O(_sage_const_19 **_sage_const_43 ))
  File "parent.pyx", line 854, in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:6332)
  File "coerce_maps.pyx", line 82, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3108)
  File "coerce_maps.pyx", line 77, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3010)
  File "rational.pyx", line 367, in sage.rings.rational.Rational.__init__ (sage/rings/rational.c:5781)
  File "rational.pyx", line 513, in sage.rings.rational.Rational.__set_value (sage/rings/rational.c:6934)
  File "padic_generic_element.pyx", line 906, in sage.rings.padics.padic_generic_element.pAdicGenericElement.rational_reconstruction (sage/rings/padics/padic_generic_element.c:6666)
  File "/home/sage/sage_install/sage-4.3.5/local/lib/python2.6/site-packages/sage/rings/arith.py", line 1841, in rational_reconstruction
    return ZZ(a).rational_reconstruction(m)
  File "integer.pyx", line 2754, in sage.rings.integer.Integer.rational_reconstruction (sage/rings/integer.c:17269)
  File "rational.pyx", line 3212, in sage.rings.rational.pyrex_rational_reconstruction (sage/rings/rational.c:21253)
  File "gmp.pxi", line 144, in sage.rings.rational.mpq_rational_reconstruction (sage/rings/rational.c:3426)
ValueError: Rational reconstruction of 397529252086698362540978975361450216964475331613570462 (mod 9691808871033067112824380501725664483616416540730367659) does not exist.

for a in [1..p-1]: print tau(a)

1 + O(11^10)
2 + 10*11 + 4*11^2 + 9*11^3 + 11^4 + 2*11^5 + 3*11^6 + 9*11^7 + 7*11^8 +
8*11^9 + O(11^10)
3 + 11^2 + 2*11^3 + 3*11^4 + 6*11^5 + 10*11^6 + 8*11^7 + 7*11^8 +
O(11^10)
4 + 7*11 + 9*11^2 + 5*11^3 + 2*11^4 + 9*11^5 + 8*11^6 + 7*11^8 + 8*11^9
+ O(11^10)
5 + 2*11 + 5*11^2 + 11^3 + 7*11^4 + 8*11^5 + 5*11^6 + 10*11^7 + 3*11^8 +
10*11^9 + O(11^10)
6 + 8*11 + 5*11^2 + 9*11^3 + 3*11^4 + 2*11^5 + 5*11^6 + 7*11^8 +
O(11^10)
7 + 3*11 + 11^2 + 5*11^3 + 8*11^4 + 11^5 + 2*11^6 + 10*11^7 + 3*11^8 +
2*11^9 + O(11^10)
8 + 10*11 + 9*11^2 + 8*11^3 + 7*11^4 + 4*11^5 + 2*11^7 + 3*11^8 +
10*11^9 + O(11^10)
9 + 6*11^2 + 11^3 + 9*11^4 + 8*11^5 + 7*11^6 + 11^7 + 3*11^8 + 2*11^9 +
O(11^10)
10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 +
10*11^8 + 10*11^9 + O(11^10)

1 + O(11^10)
2 + 10*11 + 4*11^2 + 9*11^3 + 11^4 + 2*11^5 + 3*11^6 + 9*11^7 + 7*11^8 + 8*11^9 + O(11^10)
3 + 11^2 + 2*11^3 + 3*11^4 + 6*11^5 + 10*11^6 + 8*11^7 + 7*11^8 + O(11^10)
4 + 7*11 + 9*11^2 + 5*11^3 + 2*11^4 + 9*11^5 + 8*11^6 + 7*11^8 + 8*11^9 + O(11^10)
5 + 2*11 + 5*11^2 + 11^3 + 7*11^4 + 8*11^5 + 5*11^6 + 10*11^7 + 3*11^8 + 10*11^9 + O(11^10)
6 + 8*11 + 5*11^2 + 9*11^3 + 3*11^4 + 2*11^5 + 5*11^6 + 7*11^8 + O(11^10)
7 + 3*11 + 11^2 + 5*11^3 + 8*11^4 + 11^5 + 2*11^6 + 10*11^7 + 3*11^8 + 2*11^9 + O(11^10)
8 + 10*11 + 9*11^2 + 8*11^3 + 7*11^4 + 4*11^5 + 2*11^7 + 3*11^8 + 10*11^9 + O(11^10)
9 + 6*11^2 + 11^3 + 9*11^4 + 8*11^5 + 7*11^6 + 11^7 + 3*11^8 + 2*11^9 + O(11^10)
10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10)

z = [modsym(a/p^2) for a in [0..p^2-1]]

z

[0, 0, 1, 1/2*alpha + 2, 1, 0, -1, 1/2*alpha + 2, -1/2*alpha - 2,
-1/2*alpha - 2, -1/2*alpha - 4, 0, -2, 0, -1, -2, 1/2*alpha + 1, -1, -1,
-1, 1, -1/2*alpha - 3, -1, 1/2*alpha + 1, -1, -1, 1/2*alpha + 2, -1, -1,
-1/2*alpha - 3, 1, 1, 0, 0, -1/2*alpha - 1, -alpha - 4, 2, 1, 1,
1/2*alpha + 2, 0, -1, -1/2*alpha - 2, 1/2*alpha + 3, 0, 2, 1, 0, 1,
-1/2*alpha - 2, alpha + 4, 1, 1/2*alpha + 3, 1/2*alpha + 2, 1/2*alpha +
4, 1, 0, -1/2*alpha - 1, -1/2*alpha - 2, -1/2*alpha - 2, 1/2*alpha + 2,
1/2*alpha + 2, -1/2*alpha - 2, -1/2*alpha - 2, -1/2*alpha - 1, 0, 1,
1/2*alpha + 4, 1/2*alpha + 2, 1/2*alpha + 3, 1, alpha + 4, -1/2*alpha -
2, 1, 0, 1, 2, 0, 1/2*alpha + 3, -1/2*alpha - 2, -1, 0, 1/2*alpha + 2,
1, 1, 2, -alpha - 4, -1/2*alpha - 1, 0, 0, 1, 1, -1/2*alpha - 3, -1, -1,
1/2*alpha + 2, -1, -1, 1/2*alpha + 1, -1, -1/2*alpha - 3, 1, -1, -1, -1,
1/2*alpha + 1, -2, -1, 0, -2, 0, -1/2*alpha - 4, -1/2*alpha - 2,
-1/2*alpha - 2, 1/2*alpha + 2, -1, 0, 1, 1/2*alpha + 2, 1, 0]

[0, 0, 1, 1/2*alpha + 2, 1, 0, -1, 1/2*alpha + 2, -1/2*alpha - 2, -1/2*alpha - 2, -1/2*alpha - 4, 0, -2, 0, -1, -2, 1/2*alpha + 1, -1, -1, -1, 1, -1/2*alpha - 3, -1, 1/2*alpha + 1, -1, -1, 1/2*alpha + 2, -1, -1, -1/2*alpha - 3, 1, 1, 0, 0, -1/2*alpha - 1, -alpha - 4, 2, 1, 1, 1/2*alpha + 2, 0, -1, -1/2*alpha - 2, 1/2*alpha + 3, 0, 2, 1, 0, 1, -1/2*alpha - 2, alpha + 4, 1, 1/2*alpha + 3, 1/2*alpha + 2, 1/2*alpha + 4, 1, 0, -1/2*alpha - 1, -1/2*alpha - 2, -1/2*alpha - 2, 1/2*alpha + 2, 1/2*alpha + 2, -1/2*alpha - 2, -1/2*alpha - 2, -1/2*alpha - 1, 0, 1, 1/2*alpha + 4, 1/2*alpha + 2, 1/2*alpha + 3, 1, alpha + 4, -1/2*alpha - 2, 1, 0, 1, 2, 0, 1/2*alpha + 3, -1/2*alpha - 2, -1, 0, 1/2*alpha + 2, 1, 1, 2, -alpha - 4, -1/2*alpha - 1, 0, 0, 1, 1, -1/2*alpha - 3, -1, -1, 1/2*alpha + 2, -1, -1, 1/2*alpha + 1, -1, -1/2*alpha - 3, 1, -1, -1, -1, 1/2*alpha + 1, -2, -1, 0, -2, 0, -1/2*alpha - 4, -1/2*alpha - 2, -1/2*alpha - 2, 1/2*alpha + 2, -1, 0, 1, 1/2*alpha + 2, 1, 0]

z1 = [modsym_padic(a/p^2) for a in [0..p^2-1]] z1

WARNING: Output truncated!  
full_output.txt



r =  0
r =  1/121
r =  2/121
r =  3/121
r =  4/121
r =  5/121
r =  6/121
r =  7/121
r =  8/121
r =  9/121
r =  10/121
r =  1/11
r =  12/121
r =  13/121
r =  14/121
r =  15/121
r =  16/121
r =  17/121
r =  18/121
r =  19/121
r =  20/121
r =  21/121
r =  2/11
r =  23/121
r =  24/121
r =  25/121
r =  26/121
r =  27/121
r =  28/121
r =  29/121
r =  30/121
r =  31/121
r =  32/121
r =  3/11
r =  34/121
r =  35/121
r =  36/121
r =  37/121
r =  38/121
r =  39/121
r =  40/121
r =  41/121
r =  42/121
r =  43/121
r =  4/11
r =  45/121
r =  46/121
r =  47/121
r =  48/121
r =  49/121
r =  50/121
r =  51/121
r =  52/121
r =  53/121
r =  54/121
r =  5/11
r =  56/121
r =  57/121
r =  58/121

...

r =  62/121
r =  63/121
r =  64/121
r =  65/121
r =  6/11
r =  67/121
r =  68/121
r =  69/121
r =  70/121
r =  71/121
r =  72/121
r =  73/121
r =  74/121
r =  75/121
r =  76/121
r =  7/11
r =  78/121
r =  79/121
r =  80/121
r =  81/121
r =  82/121
r =  83/121
r =  84/121
r =  85/121
r =  86/121
r =  87/121
r =  8/11
r =  89/121
r =  90/121
r =  91/121
r =  92/121
r =  93/121
r =  94/121
r =  95/121
r =  96/121
r =  97/121
r =  98/121
r =  9/11
r =  100/121
r =  101/121
r =  102/121
r =  103/121
r =  104/121
r =  105/121
r =  106/121
r =  107/121
r =  108/121
r =  109/121
r =  10/11
r =  111/121
r =  112/121
r =  113/121
r =  114/121
r =  115/121
r =  116/121
r =  117/121
r =  118/121
r =  119/121
r =  120/121
[0, 0, 1 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 +
8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 1 + O(11^10), 0, 10 +
10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 +
10*11^8 + 10*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 +
4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 3 + 3*11 + 3*11^3
+ 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 +
3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 1 +
3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 +
O(11^10), 0, 9 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6
+ 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 0, 10 + 10*11 + 10*11^2 +
10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 +
O(11^10), 9 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 +
10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 7 + 7*11 + 10*11^2 + 7*11^3 +
5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 +
10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 +
10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 +
10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 +
10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 +
10*11^9 + O(11^10), 1 + O(11^10), 2 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 +
2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3
+ 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10),
7 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8
+ 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5
+ 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2
+ 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 +
O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 +
9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 +
10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10
+ 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 +
10*11^8 + 10*11^9 + O(11^10), 2 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 +
2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 1 + O(11^10), 1 + O(11^10), 0,
0, 4 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 +
O(11^10), 6 + 6*11 + 6*11^3 + 10*11^4 + 11^5 + 5*11^6 + 2*11^7 + 3*11^8
+ 3*11^9 + O(11^10), 2 + O(11^10), 1 + O(11^10), 1 + O(11^10), 8 + 7*11
+ 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9
+ O(11^10), 0, 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 +
10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 3 + 3*11 + 3*11^3 +
5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 9 + 7*11 +
10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 +
O(11^10), 0, 2 + O(11^10), 1 + O(11^10), 0, 1 + O(11^10), 3 + 3*11 +
3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 5 +
4*11 + 10*11^2 + 4*11^3 + 9*11^5 + 5*11^6 + 8*11^7 + 7*11^8 + 7*11^9 +
O(11^10), 1 + O(11^10), 9 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 +
8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 8 + 7*11 + 10*11^2 +
7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10),
10 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 +
3*11^8 + 9*11^9 + O(11^10), 1 + O(11^10), 0, 4 + 3*11 + 3*11^3 + 5*11^4
+ 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 +
5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 +
3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 8 +
7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 +
9*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 +
8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4
+ 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 +
5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 4 + 3*11 +
3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 0,
1 + O(11^10), 10 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 +
9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 +
5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 9 + 7*11
+ 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9
+ O(11^10), 1 + O(11^10), 5 + 4*11 + 10*11^2 + 4*11^3 + 9*11^5 + 5*11^6
+ 8*11^7 + 7*11^8 + 7*11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 +
6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 1 + O(11^10), 0, 1 +
O(11^10), 2 + O(11^10), 0, 9 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5
+ 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 3 + 3*11 + 3*11^3 +
5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 10 + 10*11 +
10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 +
10*11^9 + O(11^10), 0, 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 +
8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 1 + O(11^10), 1 +
O(11^10), 2 + O(11^10), 6 + 6*11 + 6*11^3 + 10*11^4 + 11^5 + 5*11^6 +
2*11^7 + 3*11^8 + 3*11^9 + O(11^10), 4 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5
+ 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 0, 0, 1 + O(11^10), 1 +
O(11^10), 2 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 +
11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 +
10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 +
10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 +
O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 +
9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 +
10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10
+ 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 +
10*11^8 + 10*11^9 + O(11^10), 7 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 +
4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 +
10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 +
10*11^9 + O(11^10), 2 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7
+ 7*11^8 + 11^9 + O(11^10), 1 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3
+ 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10),
10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 +
10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 +
10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 7 + 7*11 +
10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 +
O(11^10), 9 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 +
10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 +
10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 0,
9 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 +
10*11^8 + 10*11^9 + O(11^10), 0, 1 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 +
2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 +
6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 +
5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 8 + 7*11 +
10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 +
O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 +
10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 0, 1 + O(11^10), 8 + 7*11 +
10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 +
O(11^10), 1 + O(11^10), 0]

WARNING: Output truncated!  
full_output.txt



r =  0
r =  1/121
r =  2/121
r =  3/121
r =  4/121
r =  5/121
r =  6/121
r =  7/121
r =  8/121
r =  9/121
r =  10/121
r =  1/11
r =  12/121
r =  13/121
r =  14/121
r =  15/121
r =  16/121
r =  17/121
r =  18/121
r =  19/121
r =  20/121
r =  21/121
r =  2/11
r =  23/121
r =  24/121
r =  25/121
r =  26/121
r =  27/121
r =  28/121
r =  29/121
r =  30/121
r =  31/121
r =  32/121
r =  3/11
r =  34/121
r =  35/121
r =  36/121
r =  37/121
r =  38/121
r =  39/121
r =  40/121
r =  41/121
r =  42/121
r =  43/121
r =  4/11
r =  45/121
r =  46/121
r =  47/121
r =  48/121
r =  49/121
r =  50/121
r =  51/121
r =  52/121
r =  53/121
r =  54/121
r =  5/11
r =  56/121
r =  57/121
r =  58/121

...

r =  62/121
r =  63/121
r =  64/121
r =  65/121
r =  6/11
r =  67/121
r =  68/121
r =  69/121
r =  70/121
r =  71/121
r =  72/121
r =  73/121
r =  74/121
r =  75/121
r =  76/121
r =  7/11
r =  78/121
r =  79/121
r =  80/121
r =  81/121
r =  82/121
r =  83/121
r =  84/121
r =  85/121
r =  86/121
r =  87/121
r =  8/11
r =  89/121
r =  90/121
r =  91/121
r =  92/121
r =  93/121
r =  94/121
r =  95/121
r =  96/121
r =  97/121
r =  98/121
r =  9/11
r =  100/121
r =  101/121
r =  102/121
r =  103/121
r =  104/121
r =  105/121
r =  106/121
r =  107/121
r =  108/121
r =  109/121
r =  10/11
r =  111/121
r =  112/121
r =  113/121
r =  114/121
r =  115/121
r =  116/121
r =  117/121
r =  118/121
r =  119/121
r =  120/121
[0, 0, 1 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 1 + O(11^10), 0, 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 1 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 0, 9 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 0, 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 9 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 7 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 1 + O(11^10), 2 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 7 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 2 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 1 + O(11^10), 1 + O(11^10), 0, 0, 4 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 6 + 6*11 + 6*11^3 + 10*11^4 + 11^5 + 5*11^6 + 2*11^7 + 3*11^8 + 3*11^9 + O(11^10), 2 + O(11^10), 1 + O(11^10), 1 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 0, 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 9 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 0, 2 + O(11^10), 1 + O(11^10), 0, 1 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 5 + 4*11 + 10*11^2 + 4*11^3 + 9*11^5 + 5*11^6 + 8*11^7 + 7*11^8 + 7*11^9 + O(11^10), 1 + O(11^10), 9 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 1 + O(11^10), 0, 4 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 4 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 0, 1 + O(11^10), 10 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 9 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 1 + O(11^10), 5 + 4*11 + 10*11^2 + 4*11^3 + 9*11^5 + 5*11^6 + 8*11^7 + 7*11^8 + 7*11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 1 + O(11^10), 0, 1 + O(11^10), 2 + O(11^10), 0, 9 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 0, 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 1 + O(11^10), 1 + O(11^10), 2 + O(11^10), 6 + 6*11 + 6*11^3 + 10*11^4 + 11^5 + 5*11^6 + 2*11^7 + 3*11^8 + 3*11^9 + O(11^10), 4 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 0, 0, 1 + O(11^10), 1 + O(11^10), 2 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 7 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 2 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 1 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 7 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 9 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 0, 9 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 0, 1 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 3 + 3*11 + 3*11^3 + 5*11^4 + 6*11^5 + 2*11^6 + 11^7 + 7*11^8 + 11^9 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 10 + 10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + O(11^10), 0, 1 + O(11^10), 8 + 7*11 + 10*11^2 + 7*11^3 + 5*11^4 + 4*11^5 + 8*11^6 + 9*11^7 + 3*11^8 + 9*11^9 + O(11^10), 1 + O(11^10), 0]

full_output.txt

N = 188, p = 19; cusp example

558 days ago by jen