Asymptotics of norms.sagews

113da9e-6020-4f35-b3de-d4541446f30s︠

abs(-3)

3

from tqdm import tqdm

  

(q, x, y)

var('q,x,y')
#Produces tables that indicate distributions of gamma_S(r1,l1,r2,l2,n) for varying r1 and r2
#first prime ranges from l1start to l1stop, second prime ranges from l2start to l2stop
#lists n from N0 to N in table. probably limit range to 10 for the sake of visualization
#For N greater than 20, this will take more than a few minutes. for N around 30, this might take around 15 minutes. 
def Cnormstatistic(l1start,l1stop,l2start,l2stop,N0,N,h10,h20,h11):
    sig = 2*h20 + 2 -h11
    eul = 2-4*h10+2*h20+h11
    print "Hodge numbers are {}, {}, and {}. Euler is {} and Signature is {}.".format(h10,h20,h11,eul,sig)
    
#     if eul < 0:
#         print
#         return "The Euler Characteristic must be nonnegative"
    
#     if eul < sig:
#         print
#         return "The Euler Characteristic must be greater than or equal to the signature"
    
    def OnePrimes(n):
        lst = [1]
        for i in range(2,n+1):
            if i in Primes():
                lst.append(i)
        return lst
    
    SPrimes = OnePrimes(l1stop * l2stop + 1)

    def generatingFunctionWithPrecision(M):

        def numerator(NN):
            return prod(((1-x*q^n)*(1-x^(-1)*q^n)*(1-y*q^n)*(1-y^(-1)*q^n))^h10 for n in range (1,NN))

        def Denominator1(NN):
            return prod((sum((x*y*q^n)^k for k in range(0,NN))) for n in range(1,NN))
    
        def Denominator2(NN):
            return prod((sum((x^(-1)*y^(-1)*q^n)^k for k in range(0,NN))) for n in range(1,NN))

        def Denominator3(NN):
            if h20 == 0:
                return 1
            else:
                return prod((sum(binomial(k,h20-1)*(x^(-1)*y*q^n)^(k-h20+1) for k in range(h20-1,NN+h20-1))) for n in range(1,NN))
    
        def Denominator4(NN):
            if h20 == 0:
                return 1
            else:
                return prod((sum(binomial(k,h20-1)*(x*y^(-1)*q^n)^(k-h20+1) for k in range(h20-1,NN+h20-1))) for n in range(1,NN))

        def Denominator5(NN):
            if h11 == 0:
                return 1
            else:
                return prod((sum(binomial(k,h11-1)*(q^n)^(k-h11+1) for k in range(h11-1,NN+h11-1))) for n in range(1,NN))

        def genFxnHelper(NN):
            return numerator(NN) * Denominator1(NN) * Denominator2(NN) * Denominator3(NN) * Denominator4(NN) * Denominator5(NN)
    
        def genFxnUpTo(NN):
            return taylor(genFxnHelper(NN),q,0,NN)
        
        


        theFxn = genFxnUpTo(M+1)
        
        #print theFxn

        lstOfDumbCoeffs = [(k,theFxn.coefficient(q^k)) for k in range(1,M+1)]
        return lstOfDumbCoeffs
    
    theFxn = generatingFunctionWithPrecision(2*N)
    
   
    
    def Cfunction(r1,l1,r2,l2):

        def ComputeMatrix(m,theFxn1):
            #print "m={}".format(m)
            #print len(theFxn1)

            scaledFxn = x^m*y^m*theFxn1[m-1][1]
            #print "scaledFxn is {}".format(scaledFxn)

            # creates 2m+1 x 2m+1 list of zeros
            matrix = []
            for i in range(0,2*m+1):
                matrix.append([])
                for j in range(0,2*m+1):
                    matrix[i].append(0)

            # top left quadrant
            for i in range(0,m+1):
                for j in range(0,m+1):
                    matrix[i][j] = scaledFxn.coefficient(x^(i+m)*y^(j+m)).coefficient(x,0).coefficient(y,0)

            # top right quadrant
            for i in range(0,m+1):
                for j in range(m+1,2*m+1):
                    matrix[i][j] = scaledFxn.coefficient(x^(i+m)*y^(j-(m+1))).coefficient(x,0).coefficient(y,0)

            # bottom left quadrant
            for i in range(m+1,2*m+1):
                for j in range(0,m+1):
                    matrix[i][j] = scaledFxn.coefficient(x^(i-m-1)*y^(j+m)).coefficient(x,0).coefficient(y,0)

            # bottom right quadrant
            for i in range(m+1,2*m+1):
                for j in range(m+1,2*m+1):
                    matrix[i][j] = scaledFxn.coefficient(x,(i-m-1)).coefficient(y,(j-m-1))
    
            return matrix

        def natefunction(m):

            matrix = ComputeMatrix(m,theFxn)

            sum = 0
        
        
            for n in range(-m,m+1):
                if (n % l1) == r1:
                    for t in range(-m,m+1):
                        if (t % l2) == r2:
                            #print "about to input ({},{})".format(n,t)
                            #print "matrix size is {}".format(len(matrix))
                            sum = sum + matrix[n][t]
                        
        

            return sum
    
        lst = []
        for n in range(0,N+1):
            lst.append(natefunction(n))
        return lst
    
    for l1 in range(l1start,l1stop):
#         if l1 in SPrimes:
        for l2 in range(l2start,l2stop):
#                 if l2 in SPrimes:
            if (l1,l2) != (2,1) and (l1,l2) != (1,1):
                print
                print "l1 is {}, l2 is {}".format(l1,l2)


                header= ["(r1,r2)"]

                for n in range(N0,N+1):
                    header.append("n={}".format(n))

                rows = [header]


                for a in range(0,l1):
                    for b in range(0,l2):
                        lst = [(a,b)]
                        for n in range(N0,N+1):
                            lst.append(Cfunction(a,l1,b,l2)[n])
                        rows.append(lst)


                #return table(rows)

                print

                print "Exact values"

                print table(rows)

                print

                #stats = rows

                total = []

                for a in range(0,N+1-N0):
                    colsum = 0
                    for t in range(1,l1*l2+1):
                        colsum = colsum + abs(rows[t][a+1])
                    total.append(colsum)

                for a in range(0,N+1-N0):
                    #total = 0
                    #for t in range(1,l1*l2+1):
                        #total = total + rows[t][a+1]
                    #print total
                    for b in range(0,l1*l2):
                        if total[a] == 0:
                            rows[b+1][a+1] = "N/A"
                        else:
                            rows[b+1][a+1] = float(rows[b+1][a+1] / total[a])

                print "Proportions"

                print table(rows)


Cnormstatistic(3,4,9,10,1,10, 0,0,1)
# Cnormstatistic(5,6,11,12,15,20,1,9,8)
# Cnormstatistic(5,6,11,12,25,30,1,9,8)
# Cnormstatistic(5,6,11,12,25,30,1,9,8)
# Cnormstatistic(4,5,6,7,15,20,1,2,3)
# Cnormstatistic(4,5,6,7,25,30,1,2,3)


# for i in range(100):
#     h10 = random.randint(3,100)
#     h20 = random.randint(0,100)
#     h11 = random.randint(1,100)
#     sig = 2*h20 + 2 -h11
#     eul = 2-4*h10+2*h20+h11
#     if eul < 0 or eul < sig:
#         if h10 > 2*h20:
#             Cnormstatistic(2,6,3,5,25,30,h10,h20,h11)
    

(q, x, y) Hodge numbers are 0, 0, and 1. Euler is 3 and Signature is 1. l1 is 3, l2 is 9 Exact values (r1,r2) n=1 n=2 n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 (0, 0) 1 3 6 13 24 47 83 150 259 444 (0, 1) 0 0 0 0 0 0 0 0 0 0 (0, 2) 0 0 0 0 0 0 0 0 0 0 (0, 3) 0 0 1 2 6 14 30 60 118 218 (0, 4) 0 0 0 0 0 0 0 0 0 0 (0, 5) 0 0 0 0 0 0 0 0 0 0 (0, 6) 0 0 1 2 6 14 30 60 118 218 (0, 7) 0 0 0 0 0 0 0 0 0 0 (0, 8) 0 0 0 0 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 0 0 0 0 (1, 1) 1 2 5 10 21 39 74 132 234 402 (1, 2) 0 0 0 0 0 0 0 0 0 0 (1, 3) 0 0 0 0 0 0 0 0 0 0 (1, 4) 0 0 0 1 3 8 19 42 85 167 (1, 5) 0 0 0 0 0 0 0 0 0 0 (1, 6) 0 0 0 0 0 0 0 0 0 0 (1, 7) 0 1 2 6 12 26 50 96 173 311 (1, 8) 0 0 0 0 0 0 0 0 0 0 (2, 0) 0 0 0 0 0 0 0 0 0 0 (2, 1) 0 0 0 0 0 0 0 0 0 0 (2, 2) 0 1 2 6 12 26 50 96 173 311 (2, 3) 0 0 0 0 0 0 0 0 0 0 (2, 4) 0 0 0 0 0 0 0 0 0 0 (2, 5) 0 0 0 1 3 8 19 42 85 167 (2, 6) 0 0 0 0 0 0 0 0 0 0 (2, 7) 0 0 0 0 0 0 0 0 0 0 (2, 8) 1 2 5 10 21 39 74 132 234 402 Proportions (r1,r2) n=1 n=2 n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 (0, 0) 0.333333333333 0.333333333333 0.272727272727 0.254901960784 0.222222222222 0.212669683258 0.193473193473 0.185185185185 0.175118323191 0.168181818182 (0, 1) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (0, 2) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (0, 3) 0.0 0.0 0.0454545454545 0.0392156862745 0.0555555555556 0.0633484162896 0.0699300699301 0.0740740740741 0.079783637593 0.0825757575758 (0, 4) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (0, 5) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (0, 6) 0.0 0.0 0.0454545454545 0.0392156862745 0.0555555555556 0.0633484162896 0.0699300699301 0.0740740740741 0.079783637593 0.0825757575758 (0, 7) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (0, 8) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (1, 0) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (1, 1) 0.333333333333 0.222222222222 0.227272727273 0.196078431373 0.194444444444 0.176470588235 0.172494172494 0.162962962963 0.158215010142 0.152272727273 (1, 2) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (1, 3) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (1, 4) 0.0 0.0 0.0 0.0196078431373 0.0277777777778 0.0361990950226 0.044289044289 0.0518518518519 0.0574712643678 0.0632575757576 (1, 5) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (1, 6) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (1, 7) 0.0 0.111111111111 0.0909090909091 0.117647058824 0.111111111111 0.117647058824 0.11655011655 0.118518518519 0.116970926302 0.117803030303 (1, 8) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (2, 0) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (2, 1) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (2, 2) 0.0 0.111111111111 0.0909090909091 0.117647058824 0.111111111111 0.117647058824 0.11655011655 0.118518518519 0.116970926302 0.117803030303 (2, 3) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (2, 4) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (2, 5) 0.0 0.0 0.0 0.0196078431373 0.0277777777778 0.0361990950226 0.044289044289 0.0518518518519 0.0574712643678 0.0632575757576 (2, 6) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (2, 7) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (2, 8) 0.333333333333 0.222222222222 0.227272727273 0.196078431373 0.194444444444 0.176470588235 0.172494172494 0.162962962963 0.158215010142 0.152272727273

print "Euler is greater than zero, other is greater than zero"
print 
Cnormstatistic(2,6,1,5,25,30,0,4,1)
print
Cnormstatistic(2,6,1,5,25,30,0,8,2)
print
Cnormstatistic(2,6,1,5,25,30,3,12,1)
print



print "Euler is greater than zero, other equals zero"
print
Cnormstatistic(2,6,1,5,25,30,0,-1,2)
print
Cnormstatistic(2,6,1,5,25,30,1,1,4)
print
Cnormstatistic(2,6,1,5,25,30,2,3,8)
print



print "Euler is greater than zero, other is less than zero"
print
Cnormstatistic(2,6,1,5,25,30,2,0,8)
print
Cnormstatistic(2,6,1,5,25,30,4,0,20)
print
Cnormstatistic(2,6,1,5,25,30,8,0,40)
print



print "Euler equals zero, other equals zero"
print
Cnormstatistic(2,6,1,5,25,30,0,-1,0)
print
Cnormstatistic(2,6,1,5,25,30,2,3,0)
print
Cnormstatistic(2,6,1,5,25,30,8,15,0)
print



print "Euler equals zero, other is less than zero"
print
Cnormstatistic(2,6,1,5,25,30,1,0,2)
print
Cnormstatistic(2,6,1,5,25,30,3,0,10)
print
Cnormstatistic(2,6,1,5,25,30,6,0,22)
print



print "Euler is less than zero, other is less than zero"
print
Cnormstatistic(2,6,1,5,25,30,1,0,0)
print
Cnormstatistic(2,6,1,5,25,30,5,0,0)
print
Cnormstatistic(2,6,1,5,25,30,8,0,2)
print

Euler is greater than zero, other is greater than zero Hodge numbers are 0, 4, and 1. Euler is 11 and Signature is 9. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 565422690809 1162033979741 2360296117046 4741370245964 9424010892260 18543591602455 (0, 1) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (1, 1) 565441326474 1162006561620 2360336182260 4741312074752 9424094842440 18543471148052 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.499991760431 0.500005898804 0.499995756372 0.500003067234 0.499997772981 0.500001623941 (0, 1) 0.0 0.0 0.0 0.0 0.0 0.0 (1, 0) 0.0 0.0 0.0 0.0 0.0 0.0 (1, 1) 0.500008239569 0.499994101196 0.500004243628 0.499996932766 0.500002227019 0.499998376059 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 188477355037 387349241499 786772033148 1580466326886 3141350730900 6181216851501 (0, 1) 188472667886 387342369121 786762041949 1580451959539 3141330080680 6181187375477 (0, 2) 188472667886 387342369121 786762041949 1580451959539 3141330080680 6181187375477 (1, 0) 188477300844 387330942870 786772088556 1580427745934 3141351188610 6181137442818 (1, 1) 188482012815 387337809375 786782046852 1580442164409 3141371826915 6181166852617 (1, 2) 188482012815 387337809375 786782046852 1580442164409 3141371826915 6181166852617 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.166666683312 0.166670604323 0.166666663121 0.166668699154 0.166666654735 0.166667737833 (0, 1) 0.16666253856 0.166667647241 0.166664546625 0.16666718404 0.166665559123 0.166666943054 (0, 2) 0.16666253856 0.166667647241 0.166664546625 0.16666718404 0.166665559123 0.166666943054 (1, 0) 0.16666663539 0.166662730695 0.166666674859 0.166664630585 0.166666679019 0.166665596691 (1, 1) 0.16667080209 0.16666568525 0.166668784385 0.166666151091 0.166667774 0.166666389684 (1, 2) 0.16667080209 0.16666568525 0.166668784385 0.166666151091 0.166667774 0.166666389684 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 376954655881 774680184369 1573544121704 3160894072820 6282701919510 12362354294319 (1, 0) 376954680701 774680178496 1573544088801 3160894123948 6282701907595 12362354228094 (2, 0) 376954680701 774680178496 1573544088801 3160894123948 6282701907595 12362354228094 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.333333318701 0.333333335018 0.33333333798 0.333333329739 0.333333333755 0.333333334524 (1, 0) 0.333333340649 0.333333332491 0.33333333101 0.333333335131 0.333333333123 0.333333332738 (2, 0) 0.333333340649 0.333333332491 0.33333333101 0.333333335131 0.333333333123 0.333333332738 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 188477355037 387349241499 786772033148 1580466326886 3141350730900 6181216851501 (0, 1) 188477300844 387330942870 786772088556 1580427745934 3141351188610 6181137442818 (1, 0) 188472667886 387342369121 786762041949 1580451959539 3141330080680 6181187375477 (1, 1) 188482012815 387337809375 786782046852 1580442164409 3141371826915 6181166852617 (2, 0) 188472667886 387342369121 786762041949 1580451959539 3141330080680 6181187375477 (2, 1) 188482012815 387337809375 786782046852 1580442164409 3141371826915 6181166852617 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.166666683312 0.166670604323 0.166666663121 0.166668699154 0.166666654735 0.166667737833 (0, 1) 0.16666663539 0.166662730695 0.166666674859 0.166664630585 0.166666679019 0.166665596691 (1, 0) 0.16666253856 0.166667647241 0.166664546625 0.16666718404 0.166665559123 0.166666943054 (1, 1) 0.16667080209 0.16666568525 0.166668784385 0.166666151091 0.166667774 0.166666389684 (2, 0) 0.16666253856 0.166667647241 0.166664546625 0.16666718404 0.166665559123 0.166666943054 (2, 1) 0.16667080209 0.16666568525 0.166668784385 0.166666151091 0.166667774 0.166666389684 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 133033549131 272064380109 550189813766 1100809780812 2180127173430 4275789188207 (0, 1) 121960553375 251307902130 511677153969 1030042146004 2051287373040 4043282553056 (0, 2) 121960553375 251307902130 511677153969 1030042146004 2051287373040 4043282553056 (1, 0) 121960553375 251307902130 511677153969 1030042146004 2051287373040 4043282553056 (1, 1) 121960560981 251307899726 511677144609 1030042161738 2051287368203 4043282534075 (1, 2) 133033566345 272064376640 550189790223 1100809816206 2180127166352 4275789140963 (2, 0) 121960553375 251307902130 511677153969 1030042146004 2051287373040 4043282553056 (2, 1) 133033566345 272064376640 550189790223 1100809816206 2180127166352 4275789140963 (2, 2) 121960560981 251307899726 511677144609 1030042161738 2051287368203 4043282534075 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.117638855864 0.117065247042 0.116550025268 0.116086329119 0.115668237653 0.115290585749 (0, 1) 0.107847231419 0.108134043988 0.108391656356 0.10862350031 0.108832548051 0.109021374388 (0, 2) 0.107847231419 0.108134043988 0.108391656356 0.10862350031 0.108832548051 0.109021374388 (1, 0) 0.107847231419 0.108134043988 0.108391656356 0.10862350031 0.108832548051 0.109021374388 (1, 1) 0.107847238145 0.108134042954 0.108391654373 0.108623501969 0.108832547794 0.109021373876 (1, 2) 0.117638871086 0.117065245549 0.116550020281 0.116086332851 0.115668237277 0.115290584475 (2, 0) 0.107847231419 0.108134043988 0.108391656356 0.10862350031 0.108832548051 0.109021374388 (2, 1) 0.117638871086 0.117065245549 0.116550020281 0.116086332851 0.115668237277 0.115290584475 (2, 2) 0.107847238145 0.108134042954 0.108391654373 0.108623501969 0.108832547794 0.109021373876 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 226172823113 464808133941 944126493616 1896536506986 3769621202570 7417412621347 (1, 0) 226172809630 464808116320 944126469940 1896536477740 3769621163970 7417412572015 (2, 0) 226172787455 464808087390 944126432905 1896536429125 3769621102095 7417412492565 (3, 0) 226172787455 464808087390 944126432905 1896536429125 3769621102095 7417412492565 (4, 0) 226172809630 464808116320 944126469940 1896536477740 3769621163970 7417412572015 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.200000017382 0.200000011045 0.20000000715 0.200000004518 0.200000002951 0.200000001921 (1, 0) 0.200000005459 0.200000003463 0.200000002135 0.200000001434 0.200000000904 0.200000000591 (2, 0) 0.19999998585 0.199999991015 0.19999999429 0.199999996307 0.199999997621 0.199999998449 (3, 0) 0.19999998585 0.199999991015 0.19999999429 0.199999996307 0.199999997621 0.199999998449 (4, 0) 0.200000005459 0.200000003463 0.200000002135 0.200000001434 0.200000000904 0.200000000591 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 115875601479 237327089201 480644924846 963111471564 1910209195390 3751846243015 (0, 1) 110297221634 227481044740 463481568770 933425035422 1859412007180 3665566378332 (1, 0) 110826532195 228426208785 465113263640 936270347550 1864247499880 3673827137810 (1, 1) 115346277435 236381907535 479013206300 960266130190 1905373664090 3743585434205 (2, 0) 113947012470 233927236485 474712332460 952859039650 1892653348555 3722045541910 (2, 1) 112225774985 230880850905 469414100445 943677389475 1876967753540 3695366950655 (3, 0) 113947012470 233927236485 474712332460 952859039650 1892653348555 3722045541910 (3, 1) 112225774985 230880850905 469414100445 943677389475 1876967753540 3695366950655 (4, 0) 110826532195 228426208785 465113263640 936270347550 1864247499880 3673827137810 (4, 1) 115346277435 236381907535 479013206300 960266130190 1905373664090 3743585434205 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.102466432487 0.1021183086 0.101817912172 0.101565299668 0.101347542415 0.101163207997 (0, 1) 0.0975335848947 0.0978817024452 0.0981820949787 0.0984347048496 0.0986524605365 0.0988367939244 (1, 0) 0.0980016434348 0.098288392444 0.0985277467403 0.098734758361 0.0989090111293 0.0990595335771 (1, 1) 0.101998362024 0.101711611019 0.101472255395 0.101265243073 0.101090989774 0.100940467014 (2, 0) 0.100761020537 0.100655402658 0.10056117536 0.100484125422 0.100416104154 0.100359674395 (2, 1) 0.0992389653131 0.0993445883564 0.0994388189298 0.0995158708853 0.099583893467 0.0996403240536 (3, 0) 0.100761020537 0.100655402658 0.10056117536 0.100484125422 0.100416104154 0.100359674395 (3, 1) 0.0992389653131 0.0993445883564 0.0994388189298 0.0995158708853 0.099583893467 0.0996403240536 (4, 0) 0.0980016434348 0.098288392444 0.0985277467403 0.098734758361 0.0989090111293 0.0990595335771 (4, 1) 0.101998362024 0.101711611019 0.101472255395 0.101265243073 0.101090989774 0.100940467014 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 76528159241 156942883729 318214581446 638245578964 1266943914562 2490159285445 (0, 1) 74822331936 153932625106 312955956085 629145464011 1251338644004 2463626667951 (0, 2) 74822331936 153932625106 312955956085 629145464011 1251338644004 2463626667951 (1, 0) 74471385738 153313296289 311873629137 627272368697 1248125821441 2458163900370 (1, 1) 75271620638 154725713346 314341464275 631543544653 1255451120026 2470619633675 (1, 2) 76429803254 156769106685 317911376528 637720564390 1266044222503 2488629037970 (2, 0) 75741862582 155555354031 315791140992 634051878231 1259753181033 2477933604067 (2, 1) 76151503562 156278351136 317053838633 636237212378 1263500130519 2484304589365 (2, 2) 74279421311 152974382223 311281453280 626247338516 1246367790543 2455174299133 (3, 0) 75741862582 155555354031 315791140992 634051878231 1259753181033 2477933604067 (3, 1) 74279421311 152974382223 311281453280 626247338516 1246367790543 2455174299133 (3, 2) 76151503562 156278351136 317053838633 636237212378 1263500130519 2484304589365 (4, 0) 74471385738 153313296289 311873629137 627272368697 1248125821441 2458163900370 (4, 1) 76429803254 156769106685 317911376528 637720564390 1266044222503 2488629037970 (4, 2) 75271620638 154725713346 314341464275 631543544653 1255451120026 2470619633675 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.0676722913378 0.0675301832889 0.0674093132593 0.0673064389777 0.0672186336598 0.0671436102179 (0, 1) 0.066163863022 0.066234913878 0.0662953469456 0.0663467827702 0.0663906846458 0.0664281958516 (0, 2) 0.066163863022 0.066234913878 0.0662953469456 0.0663467827702 0.0663906846458 0.0664281958516 (1, 0) 0.0658535284525 0.0659684259205 0.066066071103 0.0661492547659 0.0662202260009 0.0662809000785 (1, 1) 0.0665611598633 0.0665761679249 0.0665888474985 0.066599673309 0.0666088750614 0.0666167512455 (1, 2) 0.0675853171433 0.0674554096174 0.0673450835336 0.0672510733589 0.0671708998413 0.067102349267 (2, 0) 0.0669769852294 0.0669331499441 0.0668959412574 0.0668641906147 0.0668371240466 0.0668139620745 (2, 1) 0.0673392223983 0.0672442448205 0.0671634261113 0.0670946458881 0.0670359211851 0.0669857466491 (2, 2) 0.0656837782225 0.0658225962502 0.0659406269211 0.0660411598043 0.0661269523891 0.066200289725 (3, 0) 0.0669769852294 0.0669331499441 0.0668959412574 0.0668641906147 0.0668371240466 0.0668139620745 (3, 1) 0.0656837782225 0.0658225962502 0.0659406269211 0.0660411598043 0.0661269523891 0.066200289725 (3, 2) 0.0673392223983 0.0672442448205 0.0671634261113 0.0670946458881 0.0670359211851 0.0669857466491 (4, 0) 0.0658535284525 0.0659684259205 0.066066071103 0.0661492547659 0.0662202260009 0.0662809000785 (4, 1) 0.0675853171433 0.0674554096174 0.0673450835336 0.0672510733589 0.0671708998413 0.067102349267 (4, 2) 0.0665611598633 0.0665761679249 0.0665888474985 0.066599673309 0.0666088750614 0.0666167512455 Hodge numbers are 0, 8, and 2. Euler is 20 and Signature is 16. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 1595657423097920 4099017222427512 10373999895451516 25885863677399086 63725498523586990 154870580400964876 (0, 1) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (1, 1) 1595670814240832 4098994513496358 10374038042770204 25885800167982404 63725603361665630 154870408732409998 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.499997901948 0.500001385027 0.499999080701 0.500000613361 0.499999588713 0.500000277116 (0, 1) 0.0 0.0 0.0 0.0 0.0 0.0 (1, 0) 0.0 0.0 0.0 0.0 0.0 0.0 (1, 1) 0.500002098052 0.499998614973 0.500000919299 0.499999386639 0.500000411287 0.499999722884 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 531888038983262 1366342859492994 3458006323426912 8628631809150772 21241850315603194 51623555412772558 (0, 1) 531884692057329 1366337181467259 3457996786012302 8628615934124157 21241824103991898 51623512494096159 (0, 2) 531884692057329 1366337181467259 3457996786012302 8628615934124157 21241824103991898 51623512494096159 (1, 0) 531888038981318 1366327720197564 3458006323424044 8628589469545232 21241850315599076 51623440967049856 (1, 1) 531891387629757 1366333396649397 3458015859673080 8628605349218586 21241876523033277 51623483882680071 (1, 2) 531891387629757 1366333396649397 3458015859673080 8628605349218586 21241876523033277 51623483882680071 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.166666666487 0.166667590082 0.166666666685 0.166667075544 0.166666666678 0.166666851414 (0, 1) 0.166665617731 0.166666897472 0.166666207008 0.166666768908 0.166666461017 0.166666712851 (0, 2) 0.166665617731 0.166666897472 0.166666207008 0.166666768908 0.166666461017 0.166666712851 (1, 0) 0.166666666486 0.166665743379 0.166666666685 0.16666625773 0.166666666678 0.166666481926 (1, 1) 0.166667715783 0.166666435797 0.166667126307 0.166666564455 0.166666872305 0.166666620479 (1, 2) 0.166667715783 0.166666435797 0.166667126307 0.166666564455 0.166666872305 0.166666620479 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 1063776077964580 2732670579690558 6916012646850956 17257221278696004 42483700631202270 103246996379822414 (1, 0) 1063776079687086 2732670578116656 6916012645685382 17257221283342743 42483700627025175 103246996376776230 (2, 0) 1063776079687086 2732670578116656 6916012645685382 17257221283342743 42483700627025175 103246996376776230 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.333333332974 0.333333333461 0.333333333371 0.333333333273 0.333333333355 0.33333333334 (1, 0) 0.333333333513 0.333333333269 0.333333333315 0.333333333363 0.333333333322 0.33333333333 (2, 0) 0.333333333513 0.333333333269 0.333333333315 0.333333333363 0.333333333322 0.33333333333 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 531888038983262 1366342859492994 3458006323426912 8628631809150772 21241850315603194 51623555412772558 (0, 1) 531888038981318 1366327720197564 3458006323424044 8628589469545232 21241850315599076 51623440967049856 (1, 0) 531884692057329 1366337181467259 3457996786012302 8628615934124157 21241824103991898 51623512494096159 (1, 1) 531891387629757 1366333396649397 3458015859673080 8628605349218586 21241876523033277 51623483882680071 (2, 0) 531884692057329 1366337181467259 3457996786012302 8628615934124157 21241824103991898 51623512494096159 (2, 1) 531891387629757 1366333396649397 3458015859673080 8628605349218586 21241876523033277 51623483882680071 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.166666666487 0.166667590082 0.166666666685 0.166667075544 0.166666666678 0.166666851414 (0, 1) 0.166666666486 0.166665743379 0.166666666685 0.16666625773 0.166666666678 0.166666481926 (1, 0) 0.166665617731 0.166666897472 0.166666207008 0.166666768908 0.166666461017 0.166666712851 (1, 1) 0.166667715783 0.166666435797 0.166667126307 0.166666564455 0.166666872305 0.166666620479 (2, 0) 0.166665617731 0.166666897472 0.166666207008 0.166666768908 0.166666461017 0.166666712851 (2, 1) 0.166667715783 0.166666435797 0.166667126307 0.166666564455 0.166666872305 0.166666620479 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 431595198857256 1096829275213870 2748091783740552 6792761657179906 16575022751558118 39948759248966646 (0, 1) 316090439553662 817920652238344 2083960431555202 5232229810758049 12954338939822076 31649118565427884 (0, 2) 316090439553662 817920652238344 2083960431555202 5232229810758049 12954338939822076 31649118565427884 (1, 0) 316090439553662 817920652238344 2083960431555202 5232229810758049 12954338939822076 31649118565427884 (1, 1) 316090440039052 817920651736282 2083960431302944 5232229812079300 12954338938486743 31649118564752116 (1, 2) 431595200094372 1096829274142030 2748091782827236 6792761660505394 16575022748716356 39948759246596230 (2, 0) 316090439553662 817920652238344 2083960431555202 5232229810758049 12954338939822076 31649118565427884 (2, 1) 431595200094372 1096829274142030 2748091782827236 6792761660505394 16575022748716356 39948759246596230 (2, 2) 316090440039052 817920651736282 2083960431302944 5232229812079300 12954338938486743 31649118564752116 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.135239989985 0.133792108446 0.132450682417 0.131206168638 0.130050054542 0.128974726144 (0, 1) 0.0990466714941 0.0997706125077 0.100441325477 0.101063582318 0.101641639407 0.102179303598 (0, 2) 0.0990466714941 0.0997706125077 0.100441325477 0.101063582318 0.101641639407 0.102179303598 (1, 0) 0.0990466714941 0.0997706125077 0.100441325477 0.101063582318 0.101641639407 0.102179303598 (1, 1) 0.0990466716462 0.0997706124464 0.100441325465 0.101063582343 0.101641639396 0.102179303596 (1, 2) 0.135239990373 0.133792108315 0.132450682373 0.131206168702 0.130050054519 0.128974726136 (2, 0) 0.0990466714941 0.0997706125077 0.100441325477 0.101063582318 0.101641639407 0.102179303598 (2, 1) 0.135239990373 0.133792108315 0.132450682373 0.131206168702 0.130050054519 0.128974726136 (2, 2) 0.0990466716462 0.0997706124464 0.100441325465 0.101063582343 0.101641639396 0.102179303596 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 638265651780232 1639602353532692 4149607596799754 10354332782260276 25490220395963834 61948197853519818 (1, 0) 638265648829570 1639602349121904 4149607590483658 10354332773162213 25490220382863152 61948197835007461 (2, 0) 638265643949690 1639602342073685 4149607580227325 10354332758398394 25490220361781241 61948197804920067 (3, 0) 638265643949690 1639602342073685 4149607580227325 10354332758398394 25490220361781241 61948197804920067 (4, 0) 638265648829570 1639602349121904 4149607590483658 10354332773162213 25490220382863152 61948197835007461 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.200000001351 0.200000000774 0.200000000441 0.200000000255 0.200000000148 0.200000000087 (1, 0) 0.200000000427 0.200000000236 0.200000000137 0.200000000079 0.200000000046 0.200000000027 (2, 0) 0.199999998898 0.199999999377 0.199999999643 0.199999999794 0.19999999988 0.19999999993 (3, 0) 0.199999998898 0.199999999377 0.199999999643 0.199999999794 0.19999999988 0.19999999993 (4, 0) 0.200000000427 0.200000000236 0.200000000137 0.200000000079 0.200000000046 0.200000000027 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 325788252736000 834234133793264 2105652590485988 5242273881382096 12880762958093774 31253483014778952 (0, 1) 312477399044232 805368219739428 2043955006313766 5112058900878180 12609457437870060 30694714838740866 (1, 0) 313746048558117 808128775103520 2049839697228324 5124504809565579 12635345837739378 30748103497363032 (1, 1) 324519600271453 831473574018384 2099767893255334 5229827963596634 12854874545123774 31200094337644429 (2, 0) 321188536622843 824262769213604 2084333955254440 5197290088442916 12787021945007230 31060445195729930 (2, 1) 317077107326847 815339572860081 2065273624972885 5157042669955478 12703198416774011 30887752609190137 (3, 0) 321188536622843 824262769213604 2084333955254440 5197290088442916 12787021945007230 31060445195729930 (3, 1) 317077107326847 815339572860081 2065273624972885 5157042669955478 12703198416774011 30887752609190137 (4, 0) 313746048558117 808128775103520 2049839697228324 5124504809565579 12635345837739378 30748103497363032 (4, 1) 324519600271453 831473574018384 2099767893255334 5229827963596634 12854874545123774 31200094337644429 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.10208547304 0.101760543979 0.101486829586 0.101257589423 0.101064351485 0.100901992669 (0, 1) 0.0979145283109 0.0982394567954 0.098513170855 0.098742410832 0.0989356486633 0.0990980074178 (1, 0) 0.0983120585615 0.0985761915371 0.098796797236 0.0989828108455 0.0991387728379 0.0992703729119 (1, 1) 0.101687941865 0.101423808699 0.101203202901 0.101017189233 0.100861227208 0.100729627115 (2, 0) 0.100644155892 0.100544228987 0.100459328321 0.100388701124 0.100328845776 0.100278769312 (2, 1) 0.0993558430051 0.0994557703897 0.0995406713214 0.0996112986702 0.0996711541043 0.0997212306179 (3, 0) 0.100644155892 0.100544228987 0.100459328321 0.100388701124 0.100328845776 0.100278769312 (3, 1) 0.0993558430051 0.0994557703897 0.0995406713214 0.0996112986702 0.0996711541043 0.0997212306179 (4, 0) 0.0983120585615 0.0985761915371 0.098796797236 0.0989828108455 0.0991387728379 0.0992703729119 (4, 1) 0.101687941865 0.101423808699 0.101203202901 0.101017189233 0.100861227208 0.100729627115 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 222159507666774 567740971076180 1430363170518448 3554946426797500 8721051139993450 21129733608469464 (0, 1) 208053072056729 535930691228256 1359622213140653 3399693177731388 8384584627985192 20409232122525177 (0, 2) 208053072056729 535930691228256 1359622213140653 3399693177731388 8384584627985192 20409232122525177 (1, 0) 205152126915924 529386825429187 1345065024195198 3367738214000874 8315318035964235 20260886572073262 (1, 1) 211768076434911 544310205271375 1378259950370240 3440603082987072 8473254122191717 20599124395898707 (1, 2) 221345445478735 565905318421342 1426282615918220 3545991476174267 8701648224707200 21088186867035492 (2, 0) 215656158232979 553077978878002 1397759713971056 3483399211948378 8566006709640175 20797744813603213 (2, 1) 219044289814029 560717855987006 1414747751563165 3520680911670044 8646798991401652 20970746742959166 (2, 2) 203565195902682 525806507208677 1337100114693104 3350252634779972 8277414660739414 20179706248357688 (3, 0) 215656158232979 553077978878002 1397759713971056 3483399211948378 8566006709640175 20797744813603213 (3, 1) 203565195902682 525806507208677 1337100114693104 3350252634779972 8277414660739414 20179706248357688 (3, 2) 219044289814029 560717855987006 1414747751563165 3520680911670044 8646798991401652 20970746742959166 (4, 0) 205152126915924 529386825429187 1345065024195198 3367738214000874 8315318035964235 20260886572073262 (4, 1) 221345445478735 565905318421342 1426282615918220 3545991476174267 8701648224707200 21088186867035492 (4, 2) 211768076434911 544310205271375 1378259950370240 3440603082987072 8473254122191717 20599124395898707 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.0696134935503 0.06925349577 0.0689396835873 0.0686658716902 0.0684266437166 0.0682174279471 (0, 1) 0.0651932539005 0.0653732525022 0.065530158427 0.0656670642822 0.0657866782159 0.0658912860698 (0, 2) 0.0651932539005 0.0653732525022 0.065530158427 0.0656670642822 0.0657866782159 0.0658912860698 (1, 0) 0.0642842451979 0.0645750265408 0.0648285408095 0.0650498354478 0.0652432023966 0.0654123518775 (1, 1) 0.0663573473757 0.0663953922981 0.0664284475705 0.0664572630554 0.0664823920457 0.0665043540202 (1, 2) 0.0693584078532 0.0690295813973 0.0687430117568 0.0684929015757 0.0682744056033 0.0680832941292 (2, 0) 0.0675756745138 0.0674648923049 0.0673682840822 0.0672838953438 0.0672101424227 0.0671456008189 (2, 1) 0.0686373426748 0.0683968105986 0.0681870621104 0.0680040132028 0.0678440504907 0.0677041382273 (2, 2) 0.063786981709 0.0641382964731 0.0644446534499 0.0647120912472 0.0649458069668 0.0651502608835 (3, 0) 0.0675756745138 0.0674648923049 0.0673682840822 0.0672838953438 0.0672101424227 0.0671456008189 (3, 1) 0.063786981709 0.0641382964731 0.0644446534499 0.0647120912472 0.0649458069668 0.0651502608835 (3, 2) 0.0686373426748 0.0683968105986 0.0681870621104 0.0680040132028 0.0678440504907 0.0677041382273 (4, 0) 0.0642842451979 0.0645750265408 0.0648285408095 0.0650498354478 0.0652432023966 0.0654123518775 (4, 1) 0.0693584078532 0.0690295813973 0.0687430117568 0.0684929015757 0.0682744056033 0.0680832941292 (4, 2) 0.0663573473757 0.0663953922981 0.0664284475705 0.0664572630554 0.0664823920457 0.0665043540202 Hodge numbers are 3, 12, and 1. Euler is 15 and Signature is 25. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 9401392478982422250 31357519642752177427 102639300516816105104 329991712568927581359 1042973138954521593038 3243092065658540961034 (0, 1) -9401362996994391444 -31357451703184830132 -102639147346588697884 -329991369421113224064 -1042972382931088083168 -3243090413342360116096 (1, 0) -9401362996994391444 -31357451703184830132 -102639147346588697884 -329991369421113224064 -1042972382931088083168 -3243090413342360116096 (1, 1) 9401392648471067436 31357519357964752652 102639300990312201124 329991711789463188864 1042973140225693636768 3243092063603799250304 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250000390864 0.250000271394 0.250000186251 0.250000130131 0.250000090533 0.250000063726 (0, 1) -0.249999606883 -0.249999729741 -0.249999813172 -0.249999870164 -0.249999909315 -0.249999936354 (1, 0) -0.249999606883 -0.249999729741 -0.249999813172 -0.249999870164 -0.249999909315 -0.249999936354 (1, 1) 0.250000395371 0.250000269124 0.250000187405 0.250000129541 0.250000090838 0.250000063567 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 81186314235300 179365296678501 390265410221728 838533519894555 1777885524978366 3726366947037490 (0, 1) -25852163102247 -55712864665603 -118547591407254 -247692852768630 -510931045734248 -1037025383096276 (0, 2) -25852163102247 -55712864665603 -118547591407254 -247692852768630 -510931045734248 -1037025383096276 (1, 0) -61475159332674 -134167118199216 -287994181937838 -610028131786830 -1273446005004696 -2625507980984806 (1, 1) 45563318004333 100910949060868 220818952720539 476198240875815 1015370305279148 2137884710059507 (1, 2) 45563318004333 100910949060868 220818952720539 476198240875815 1015370305279148 2137884710059507 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.284372908211 0.286169444725 0.287595810835 0.289514493622 0.291268787867 0.293375562356 (0, 1) -0.0905528828864 -0.0888874260553 -0.0873605238394 -0.0855191463927 -0.0837052016476 -0.0816446445739 (0, 2) -0.0905528828864 -0.0888874260553 -0.0873605238394 -0.0855191463927 -0.0837052016476 -0.0816446445739 (1, 0) -0.215330256175 -0.214057738182 -0.212229723929 -0.210620066436 -0.208627084861 -0.206705322191 (1, 1) 0.159595534921 0.160998982491 0.162726708779 0.164413573578 0.166346861989 0.168314913153 (1, 2) 0.159595534921 0.160998982491 0.162726708779 0.164413573578 0.166346861989 0.168314913153 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 19711154902626 45198178479285 102271228283890 228505388107725 504439519973670 1100858966052684 (1, 0) 19711154902086 45198084395265 102271361313285 228505388107185 504439259544900 1100859326963231 (2, 0) 19711154902086 45198084395265 102271361313285 228505388107185 504439259544900 1100859326963231 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.333333333339 0.333333795909 0.333333044278 0.333333333334 0.333333448061 0.333333260479 (1, 0) 0.33333333333 0.333333102045 0.333333477861 0.333333333333 0.33333327597 0.33333336976 (2, 0) 0.33333333333 0.333333102045 0.333333477861 0.333333333333 0.33333327597 0.33333336976 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 81186314235300 179365296678501 390265410221728 838533519894555 1777885524978366 3726366947037490 (0, 1) -61475159332674 -134167118199216 -287994181937838 -610028131786830 -1273446005004696 -2625507980984806 (1, 0) -25852163102247 -55712864665603 -118547591407254 -247692852768630 -510931045734248 -1037025383096276 (1, 1) 45563318004333 100910949060868 220818952720539 476198240875815 1015370305279148 2137884710059507 (2, 0) -25852163102247 -55712864665603 -118547591407254 -247692852768630 -510931045734248 -1037025383096276 (2, 1) 45563318004333 100910949060868 220818952720539 476198240875815 1015370305279148 2137884710059507 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.284372908211 0.286169444725 0.287595810835 0.289514493622 0.291268787867 0.293375562356 (0, 1) -0.215330256175 -0.214057738182 -0.212229723929 -0.210620066436 -0.208627084861 -0.206705322191 (1, 0) -0.0905528828864 -0.0888874260553 -0.0873605238394 -0.0855191463927 -0.0837052016476 -0.0816446445739 (1, 1) 0.159595534921 0.160998982491 0.162726708779 0.164413573578 0.166346861989 0.168314913153 (2, 0) -0.0905528828864 -0.0888874260553 -0.0873605238394 -0.0855191463927 -0.0837052016476 -0.0816446445739 (2, 1) 0.159595534921 0.160998982491 0.162726708779 0.164413573578 0.166346861989 0.168314913153 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 282240294433872246 860214165306746115 2576583372479226796 7590943908941476689 22013864547243062490 62886128652521318982 (0, 1) -141110291639484810 -430084483564133415 -1288240550625471453 -3795357701776684482 -11006680053861544410 -31442513896777633149 (0, 2) -141110291639484810 -430084483564133415 -1288240550625471453 -3795357701776684482 -11006680053861544410 -31442513896777633149 (1, 0) -141110291639484810 -430084483564133415 -1288240550625471453 -3795357701776684482 -11006680053861544410 -31442513896777633149 (1, 1) -141110291639497761 -430084483595494755 -1288240550581106259 -3795357701776713471 -11006680053948354000 -31442513896657281061 (1, 2) 282240294433884657 860214165244023435 2576583372567890997 7590943908941505138 22013864547069443310 62886128652761877441 (2, 0) -141110291639484810 -430084483564133415 -1288240550625471453 -3795357701776684482 -11006680053861544410 -31442513896777633149 (2, 1) 282240294433884657 860214165244023435 2576583372567890997 7590943908941505138 22013864547069443310 62886128652761877441 (2, 2) -141110291639497761 -430084483595494755 -1288240550581106259 -3795357701776713471 -11006680053948354000 -31442513896657281061 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.16667248672 0.166671045362 0.166669974446 0.166669175235 0.166668576241 0.166668125479 (0, 1) -0.0833304233066 -0.0833311439878 -0.0833316794427 -0.0833320790491 -0.0833323785463 -0.0833326039272 (0, 2) -0.0833304233066 -0.0833311439878 -0.0833316794427 -0.0833320790491 -0.0833323785463 -0.0833326039272 (1, 0) -0.0833304233066 -0.0833311439878 -0.0833316794427 -0.0833320790491 -0.0833323785463 -0.0833326039272 (1, 1) -0.0833304233066 -0.0833311439939 -0.0833316794399 -0.0833320790491 -0.083332378547 -0.0833326039269 (1, 2) 0.16667248672 0.16667104535 0.166669974452 0.166669175235 0.16666857624 0.166668125479 (2, 0) -0.0833304233066 -0.0833311439878 -0.0833316794427 -0.0833320790491 -0.0833323785463 -0.0833326039272 (2, 1) 0.16667248672 0.16667104535 0.166669974452 0.166669175235 0.16666857624 0.166668125479 (2, 2) -0.0833304233066 -0.0833311439939 -0.0833316794399 -0.0833320790491 -0.083332378547 -0.0833326039269 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 11826689006878 27118873529645 61362788161580 137103230398485 302663615545310 660515512516796 (1, 0) 11826696160455 27118866170910 61362791770710 137103234802635 302663601584325 660515533387810 (2, 0) 11826691689505 27118870699175 61362789603730 137103232159170 302663610174755 660515520343365 (3, 0) 11826691689505 27118870699175 61362789603730 137103232159170 302663610174755 660515520343365 (4, 0) 11826696160455 27118866170910 61362791770710 137103234802635 302663601584325 660515533387810 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.199999933464 0.200000030058 0.199999993415 0.199999996403 0.20000000511 0.199999996524 (1, 0) 0.200000054438 0.199999975788 0.200000005178 0.200000002827 0.199999995884 0.200000002844 (2, 0) 0.19999997883 0.200000009183 0.199999998115 0.199999998971 0.200000001561 0.199999998894 (3, 0) 0.19999997883 0.200000009183 0.199999998115 0.199999998971 0.200000001561 0.199999998894 (4, 0) 0.200000054438 0.199999975788 0.200000005178 0.200000002827 0.199999995884 0.200000002844 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 124736850887214560 355671000072750593 995807169775243868 2740121354308479663 7416427295933648068 19759902260558811728 (0, 1) -124725024198207682 -355643881199220948 -995745806987082288 -2739984251078081178 -7416124632318102758 -19759241745046294932 (1, 0) -100903565506481575 -287719302698799759 -805569505965308489 -2216680590232511552 -5999742188106350281 -15985498922387541454 (1, 1) 100915392202642030 287746421564970669 805630868757079199 2216817693467314187 6000044851707934606 15986159437920929264 (2, 0) 38549881056889698 109917772446098110 307742506191390165 846791486985450368 2291906551856281182 6106373950198558059 (2, 1) -38538054365200193 -109890653575398935 -307681143401786435 -846654383753291198 -2291603888246106427 -6105713434678214694 (3, 0) 38549881056889698 109917772446098110 307742506191390165 846791486985450368 2291906551856281182 6106373950198558059 (3, 1) -38538054365200193 -109890653575398935 -307681143401786435 -846654383753291198 -2291603888246106427 -6105713434678214694 (4, 0) -100903565506481575 -287719302698799759 -805569505965308489 -2216680590232511552 -5999742188106350281 -15985498922387541454 (4, 1) 100915392202642030 287746421564970669 805630868757079199 2216817693467314187 6000044851707934606 15986159437920929264 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.154515807746 0.154514396372 0.154513252752 0.154512365774 0.15451164816 0.154511080723 (0, 1) -0.154501157622 -0.154502615101 -0.154503731467 -0.154504634676 -0.154505342556 -0.154505915872 (1, 0) -0.124992701177 -0.124994093901 -0.124995248541 -0.124996128957 -0.124996850509 -0.124997415566 (1, 1) 0.125007351311 0.125005875169 0.125004769827 0.125003860055 0.125003156112 0.125002580418 (2, 0) 0.0477530574779 0.0477516532317 0.0477505054041 0.0477496209302 0.0477489018128 0.0477483352855 (2, 1) -0.04773840735 -0.0477398719621 -0.0477409841187 -0.047741889833 -0.0477425962088 -0.0477431704337 (3, 0) 0.0477530574779 0.0477516532317 0.0477505054041 0.0477496209302 0.0477489018128 0.0477483352855 (3, 1) -0.04773840735 -0.0477398719621 -0.0477409841187 -0.047741889833 -0.0477425962088 -0.0477431704337 (4, 0) -0.124992701177 -0.124994093901 -0.124995248541 -0.124996128957 -0.124996850509 -0.124997415566 (4, 1) 0.125007351311 0.125005875169 0.125004769827 0.125003860055 0.125003156112 0.125002580418 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 76953802292633424 223831705475426727 639605073098218460 1797122534262861363 4968928917622346646 13529642406679750790 (0, 1) -38470987801813273 -111902293300948541 -319771855155028440 -898492715516231439 -2484313127003400668 -6764490945583616997 (0, 2) -38470987801813273 -111902293300948541 -319771855155028440 -898492715516231439 -2484313127003400668 -6764490945583616997 (1, 0) -62247723750709541 -181062625174503114 -517405338654285739 -1453800536618799111 -4019728221922034265 -10945235048235983762 (1, 1) -8041257743984334 -23390223559838909 -66841817294747875 -187814440009063779 -519313464525019730 -1414047622938023210 (1, 2) 70300808190854330 204479967600512933 584308518740804324 1641752079862665525 4539344350048638320 12359943186707394782 (2, 0) 23780678181844142 69169371526029393 197653937719318454 555353522181422292 1535515982870847777 4180964274379134709 (2, 1) 51491933058517971 149772542188434213 427979590334700620 1202511806163564501 3324869236945315308 9053118621883450298 (2, 2) -75260784548672608 -218914794843764431 -625572165264415344 -1757728225112827623 -4860082556205988330 -13233422380742241642 (3, 0) 23780678181844142 69169371526029393 197653937719318454 555353522181422292 1535515982870847777 4180964274379134709 (3, 1) -75260784548672608 -218914794843764431 -625572165264415344 -1757728225112827623 -4860082556205988330 -13233422380742241642 (3, 2) 51491933058517971 149772542188434213 427979590334700620 1202511806163564501 3324869236945315308 9053118621883450298 (4, 0) -62247723750709541 -181062625174503114 -517405338654285739 -1453800536618799111 -4019728221922034265 -10945235048235983762 (4, 1) 70300808190854330 204479967600512933 584308518740804324 1641752079862665525 4539344350048638320 12359943186707394782 (4, 2) -8041257743984334 -23390223559838909 -66841817294747875 -187814440009063779 -519313464525019730 -1414047622938023210 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.104536606705 0.10453488778 0.104533324116 0.104532310579 0.10453142836 0.104530822035 (0, 1) -0.0522602704683 -0.0522611113012 -0.0522616476697 -0.0522621678824 -0.0522625306108 -0.0522628594267 (0, 2) -0.0522602704683 -0.0522611113012 -0.0522616476697 -0.0522621678824 -0.0522625306108 -0.0522628594267 (1, 0) -0.0845593800713 -0.0845606799253 -0.0845617119683 -0.0845624749097 -0.0845630798154 -0.0845635370524 (1, 1) -0.0109235122002 -0.0109238071961 -0.0109242369169 -0.0109245068157 -0.0109248047444 -0.0109250160485 (1, 2) 0.0954989580492 0.095497152296 0.0954959776621 0.0954949565393 0.0954942516983 0.0954936562832 (2, 0) 0.0323044648634 0.0323037903632 0.032303407217 0.0323029652986 0.0323026715859 0.0323023786856 (2, 1) 0.0699483559517 0.0699474449207 0.0699464890338 0.0699458913901 0.0699453214589 0.0699449329912 (2, 2) -0.102236755043 -0.102238570107 -0.102239867474 -0.102240881875 -0.102241625906 -0.102242208495 (3, 0) 0.0323044648634 0.0323037903632 0.032303407217 0.0323029652986 0.0323026715859 0.0323023786856 (3, 1) -0.102236755043 -0.102238570107 -0.102239867474 -0.102240881875 -0.102241625906 -0.102242208495 (3, 2) 0.0699483559517 0.0699474449207 0.0699464890338 0.0699458913901 0.0699453214589 0.0699449329912 (4, 0) -0.0845593800713 -0.0845606799253 -0.0845617119683 -0.0845624749097 -0.0845630798154 -0.0845635370524 (4, 1) 0.0954989580492 0.095497152296 0.0954959776621 0.0954949565393 0.0954942516983 0.0954936562832 (4, 2) -0.0109235122002 -0.0109238071961 -0.0109242369169 -0.0109245068157 -0.0109248047444 -0.0109250160485 Euler is greater than zero, other equals zero Hodge numbers are 0, -1, and 2. Euler is 2 and Signature is -2. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0 0 0 0 0 0 (0, 1) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (1, 1) 0 0 0 0 0 0 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) N/A N/A N/A N/A N/A N/A (0, 1) N/A N/A N/A N/A N/A N/A (1, 0) N/A N/A N/A N/A N/A N/A (1, 1) N/A N/A N/A N/A N/A N/A l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0 0 0 0 0 0 (0, 1) 0 0 0 0 0 0 (0, 2) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (1, 1) 0 0 0 0 0 0 (1, 2) 0 0 0 0 0 0 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) N/A N/A N/A N/A N/A N/A (0, 1) N/A N/A N/A N/A N/A N/A (0, 2) N/A N/A N/A N/A N/A N/A (1, 0) N/A N/A N/A N/A N/A N/A (1, 1) N/A N/A N/A N/A N/A N/A (1, 2) N/A N/A N/A N/A N/A N/A l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (2, 0) 0 0 0 0 0 0 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) N/A N/A N/A N/A N/A N/A (1, 0) N/A N/A N/A N/A N/A N/A (2, 0) N/A N/A N/A N/A N/A N/A l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0 0 0 0 0 0 (0, 1) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (1, 1) 0 0 0 0 0 0 (2, 0) 0 0 0 0 0 0 (2, 1) 0 0 0 0 0 0 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) N/A N/A N/A N/A N/A N/A (0, 1) N/A N/A N/A N/A N/A N/A (1, 0) N/A N/A N/A N/A N/A N/A (1, 1) N/A N/A N/A N/A N/A N/A (2, 0) N/A N/A N/A N/A N/A N/A (2, 1) N/A N/A N/A N/A N/A N/A l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0 0 0 0 0 0 (0, 1) 0 0 0 0 0 0 (0, 2) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (1, 1) 0 0 0 0 0 0 (1, 2) 0 0 0 0 0 0 (2, 0) 0 0 0 0 0 0 (2, 1) 0 0 0 0 0 0 (2, 2) 0 0 0 0 0 0 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) N/A N/A N/A N/A N/A N/A (0, 1) N/A N/A N/A N/A N/A N/A (0, 2) N/A N/A N/A N/A N/A N/A (1, 0) N/A N/A N/A N/A N/A N/A (1, 1) N/A N/A N/A N/A N/A N/A (1, 2) N/A N/A N/A N/A N/A N/A (2, 0) N/A N/A N/A N/A N/A N/A (2, 1) N/A N/A N/A N/A N/A N/A (2, 2) N/A N/A N/A N/A N/A N/A l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (2, 0) 0 0 0 0 0 0 (3, 0) 0 0 0 0 0 0 (4, 0) 0 0 0 0 0 0 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) N/A N/A N/A N/A N/A N/A (1, 0) N/A N/A N/A N/A N/A N/A (2, 0) N/A N/A N/A N/A N/A N/A (3, 0) N/A N/A N/A N/A N/A N/A (4, 0) N/A N/A N/A N/A N/A N/A l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0 0 0 0 0 0 (0, 1) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (1, 1) 0 0 0 0 0 0 (2, 0) 0 0 0 0 0 0 (2, 1) 0 0 0 0 0 0 (3, 0) 0 0 0 0 0 0 (3, 1) 0 0 0 0 0 0 (4, 0) 0 0 0 0 0 0 (4, 1) 0 0 0 0 0 0 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) N/A N/A N/A N/A N/A N/A (0, 1) N/A N/A N/A N/A N/A N/A (1, 0) N/A N/A N/A N/A N/A N/A (1, 1) N/A N/A N/A N/A N/A N/A (2, 0) N/A N/A N/A N/A N/A N/A (2, 1) N/A N/A N/A N/A N/A N/A (3, 0) N/A N/A N/A N/A N/A N/A (3, 1) N/A N/A N/A N/A N/A N/A (4, 0) N/A N/A N/A N/A N/A N/A (4, 1) N/A N/A N/A N/A N/A N/A l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0 0 0 0 0 0 (0, 1) 0 0 0 0 0 0 (0, 2) 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 (1, 1) 0 0 0 0 0 0 (1, 2) 0 0 0 0 0 0 (2, 0) 0 0 0 0 0 0 (2, 1) 0 0 0 0 0 0 (2, 2) 0 0 0 0 0 0 (3, 0) 0 0 0 0 0 0 (3, 1) 0 0 0 0 0 0 (3, 2) 0 0 0 0 0 0 (4, 0) 0 0 0 0 0 0 (4, 1) 0 0 0 0 0 0 (4, 2) 0 0 0 0 0 0 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) N/A N/A N/A N/A N/A N/A (0, 1) N/A N/A N/A N/A N/A N/A (0, 2) N/A N/A N/A N/A N/A N/A (1, 0) N/A N/A N/A N/A N/A N/A (1, 1) N/A N/A N/A N/A N/A N/A (1, 2) N/A N/A N/A N/A N/A N/A (2, 0) N/A N/A N/A N/A N/A N/A (2, 1) N/A N/A N/A N/A N/A N/A (2, 2) N/A N/A N/A N/A N/A N/A (3, 0) N/A N/A N/A N/A N/A N/A (3, 1) N/A N/A N/A N/A N/A N/A (3, 2) N/A N/A N/A N/A N/A N/A (4, 0) N/A N/A N/A N/A N/A N/A (4, 1) N/A N/A N/A N/A N/A N/A (4, 2) N/A N/A N/A N/A N/A N/A Hodge numbers are 1, 1, and 4. Euler is 4 and Signature is 0. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 236758531300 478386729986 955395169792 1886998933521 3687893381292 7135394863508 (0, 1) -236744023450 -478364111394 -955360167104 -1886945139266 -3687811258602 -7135270280220 (1, 0) -236744023450 -478364111394 -955360167104 -1886945139266 -3687811258602 -7135270280220 (1, 1) 236758531300 478386728216 955395169792 1886998930856 3687893381292 7135394859552 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250007659858 0.250005910493 0.250004579693 0.250003563618 0.250002783554 0.250002182541 (0, 1) -0.249992340142 -0.249994089969 -0.249995420307 -0.249996436558 -0.249997216446 -0.249997817528 (1, 0) -0.249992340142 -0.249994089969 -0.249995420307 -0.249996436558 -0.249997216446 -0.249997817528 (1, 1) 0.250007659858 0.250005909568 0.250004579693 0.250003563265 0.250002783554 0.250002182403 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3798891018 6749771064 11875780916 20701104031 35766970722 61278954632 (0, 1) -1892191584 -3363576236 -5920389114 -10323654888 -17842424016 -30577185672 (0, 2) -1892191584 -3363576236 -5920389114 -10323654888 -17842424016 -30577185672 (1, 0) -3789215322 -6734687730 -11852439568 -20665234190 -35712212274 -61195887780 (1, 1) 1901861586 3378652276 5943721128 10359512890 17897167482 30660233556 (1, 2) 1901861586 3378652276 5943721128 10359512890 17897167482 30660233556 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250318778348 0.250279659351 0.25024592392 0.250216789642 0.250191518865 0.25016956305 (0, 1) -0.124681409249 -0.124720484082 -0.124754174423 -0.124783285934 -0.124808533535 -0.124830477687 (0, 2) -0.124681409249 -0.124720484082 -0.124754174423 -0.124783285934 -0.124808533535 -0.124830477687 (1, 0) -0.249681221652 -0.249720373464 -0.24975407608 -0.249783226464 -0.249808481135 -0.249830445025 (1, 1) 0.125318590751 0.12527949951 0.125245825577 0.125216706013 0.125191466465 0.125169518276 (1, 2) 0.125318590751 0.12527949951 0.125245825577 0.125216706013 0.125191466465 0.125169518276 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 9675696 15083334 23341348 35869841 54758448 83066852 (1, 0) 9670002 15076040 23332014 35858002 54743466 83047884 (2, 0) 9670002 15076040 23332014 35858002 54743466 83047884 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.333464159059 0.333440830231 0.333422221745 0.333406694905 0.333394144785 0.333384084659 (1, 0) 0.333267920471 0.333279584885 0.333288889128 0.333296652548 0.333302927607 0.33330795767 (2, 0) 0.333267920471 0.333279584885 0.333288889128 0.333296652548 0.333302927607 0.33330795767 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3798891018 6749771064 11875780916 20701104031 35766970722 61278954632 (0, 1) -3789215322 -6734687730 -11852439568 -20665234190 -35712212274 -61195887780 (1, 0) -1892191584 -3363576236 -5920389114 -10323654888 -17842424016 -30577185672 (1, 1) 1901861586 3378652276 5943721128 10359512890 17897167482 30660233556 (2, 0) -1892191584 -3363576236 -5920389114 -10323654888 -17842424016 -30577185672 (2, 1) 1901861586 3378652276 5943721128 10359512890 17897167482 30660233556 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250318778348 0.250279659351 0.25024592392 0.250216789642 0.250191518865 0.25016956305 (0, 1) -0.249681221652 -0.249720373464 -0.24975407608 -0.249783226464 -0.249808481135 -0.249830445025 (1, 0) -0.124681409249 -0.124720484082 -0.124754174423 -0.124783285934 -0.124808533535 -0.124830477687 (1, 1) 0.125318590751 0.12527949951 0.125245825577 0.125216706013 0.125191466465 0.125169518276 (2, 0) -0.124681409249 -0.124720484082 -0.124754174423 -0.124783285934 -0.124808533535 -0.124830477687 (2, 1) 0.125318590751 0.12527949951 0.125245825577 0.125216706013 0.125191466465 0.125169518276 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 2374857064 4215222018 7411070352 12912926033 22306964064 38221030480 (0, 1) -1182590684 -2100069342 -3693864502 -6438528096 -11126102808 -19068981814 (0, 2) -1182590684 -2100069342 -3693864502 -6438528096 -11126102808 -19068981814 (1, 0) -1182590684 -2100069342 -3693864502 -6438528096 -11126102808 -19068981814 (1, 1) 596130343 1057572691 1858598258 3237193049 5590423137 9576014849 (1, 2) 596130343 1057572691 1858598258 3237193049 5590423137 9576014849 (2, 0) -1182590684 -2100069342 -3693864502 -6438528096 -11126102808 -19068981814 (2, 1) 596130343 1057572691 1858598258 3237193049 5590423137 9576014849 (2, 2) 596130343 1057572691 1858598258 3237193049 5590423137 9576014849 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250255198846 0.250224060757 0.25019715808 0.25017384944 0.250153601343 0.250135968971 (0, 1) -0.124617801747 -0.12466434185 -0.124704577995 -0.124739455208 -0.124769765996 -0.124796170679 (0, 2) -0.124617801747 -0.12466434185 -0.124704577995 -0.124739455208 -0.124769765996 -0.124796170679 (1, 0) -0.124617801747 -0.12466434185 -0.124704577995 -0.124739455208 -0.124769765996 -0.124796170679 (1, 1) 0.0628183985417 0.0627796429602 0.0627461324853 0.0627170824318 0.0626918336687 0.0626698370779 (1, 2) 0.0628183985417 0.0627796429602 0.0627461324853 0.0627170824318 0.0626918336687 0.0626698370779 (2, 0) -0.124617801747 -0.12466434185 -0.124704577995 -0.124739455208 -0.124769765996 -0.124796170679 (2, 1) 0.0628183985417 0.0627796429602 0.0627461324853 0.0627170824318 0.0626918336687 0.0626698370779 (2, 2) 0.0628183985417 0.0627796429602 0.0627461324853 0.0627170824318 0.0626918336687 0.0626698370779 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 5891344 9168526 14167356 21743777 33156368 50247438 (1, 0) 5829699 9083715 14051369 21585812 32942358 49958628 (2, 0) 5732479 8949729 13867641 21335222 32602148 49498963 (3, 0) 5732479 8949729 13867641 21335222 32602148 49498963 (4, 0) 5829699 9083715 14051369 21585812 32942358 49958628 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.203039871518 0.202684693015 0.20237525758 0.202106299393 0.201870932382 0.201665233734 (1, 0) 0.200915332044 0.200809812418 0.200718427682 0.200638030031 0.200567942916 0.20050611123 (2, 0) 0.197564732197 0.197847841074 0.198093943528 0.198308820273 0.198496590893 0.198661271903 (3, 0) 0.197564732197 0.197847841074 0.198093943528 0.198308820273 0.198496590893 0.198661271903 (4, 0) 0.200915332044 0.200809812418 0.200718427682 0.200638030031 0.200567942916 0.20050611123 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 29308137534 55640728608 104472522524 194116028139 357104875738 650747062482 (0, 1) -29302246190 -55631560082 -104458355168 -194094284362 -357071719370 -650696815044 (1, 0) -23700770515 -44998752773 -84496090067 -157006491252 -288848134720 -526381121974 (1, 1) 23706600214 45007836488 84510141436 157028077064 288881077078 526431080602 (2, 0) 9053955673 17189697765 32277330149 59975374310 110336758196 201069882377 (2, 1) -9048223194 -17180748036 -32263462508 -59954039088 -110304156048 -201020383414 (3, 0) 9053955673 17189697765 32277330149 59975374310 110336758196 201069882377 (3, 1) -9048223194 -17180748036 -32263462508 -59954039088 -110304156048 -201020383414 (4, 0) -23700770515 -44998752773 -84496090067 -157006491252 -288848134720 -526381121974 (4, 1) 23706600214 45007836488 84510141436 157028077064 288881077078 526431080602 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.154554751104 0.154546263755 0.154539453361 0.154533964818 0.154529521983 0.154525911715 (0, 1) -0.154523683445 -0.154520797492 -0.154518496506 -0.154516654799 -0.154515174271 -0.154513979996 (1, 0) -0.124984628711 -0.124987384038 -0.124989607359 -0.124991407603 -0.124992872448 -0.124994068313 (1, 1) 0.125015371289 0.125012614733 0.125010392641 0.125008591867 0.125007127552 0.125005931452 (2, 0) 0.0477455063093 0.047745664572 0.0477457692861 0.0477458377468 0.0477458798788 0.0477459041831 (2, 1) -0.0477152764162 -0.0477208060337 -0.0477252557806 -0.0477288529749 -0.0477317719943 -0.0477341501963 (3, 0) 0.0477455063093 0.047745664572 0.0477457692861 0.0477458377468 0.0477458798788 0.0477459041831 (3, 1) -0.0477152764162 -0.0477208060337 -0.0477252557806 -0.0477288529749 -0.0477317719943 -0.0477341501963 (4, 0) -0.124984628711 -0.124987384038 -0.124989607359 -0.124991407603 -0.124992872448 -0.124994068313 (4, 1) 0.125015371289 0.125012614733 0.125010392641 0.125008591867 0.125007127552 0.125005931452 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 2778509788 4960519690 8769855280 15361031013 26668939732 45912264198 (0, 1) -1386309222 -2475675582 -4377843962 -7669643618 -13317891682 -22931008380 (0, 2) -1386309222 -2475675582 -4377843962 -7669643618 -13317891682 -22931008380 (1, 0) -2229886153 -3984823509 -7050678837 -12358577986 -21469597938 -36981342774 (1, 1) 1117857926 1996953612 3532365103 6190081899 10751270148 18515650701 (1, 2) 1117857926 1996953612 3532365103 6190081899 10751270148 18515650701 (2, 0) 845469107 1512105331 2677421871 4695997400 8162507296 14066744101 (2, 1) -419868314 -751577801 -1331777115 -2337331089 -4064952574 -7008622569 (2, 2) -419868314 -751577801 -1331777115 -2337331089 -4064952574 -7008622569 (3, 0) 845469107 1512105331 2677421871 4695997400 8162507296 14066744101 (3, 1) -419868314 -751577801 -1331777115 -2337331089 -4064952574 -7008622569 (3, 2) -419868314 -751577801 -1331777115 -2337331089 -4064952574 -7008622569 (4, 0) -2229886153 -3984823509 -7050678837 -12358577986 -21469597938 -36981342774 (4, 1) 1117857926 1996953612 3532365103 6190081899 10751270148 18515650701 (4, 2) 1117857926 1996953612 3532365103 6190081899 10751270148 18515650701 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.155634889114 0.155502895439 0.155388329973 0.155288794137 0.15520192149 0.155126008041 (0, 1) -0.0776524462774 -0.0776077397585 -0.0775686531211 -0.0775344902235 -0.0775044827436 -0.0774781172848 (0, 2) -0.0776524462774 -0.0776077397585 -0.0775686531211 -0.0775344902235 -0.0775044827436 -0.0774781172848 (1, 0) -0.124904395032 -0.124916668451 -0.124927170937 -0.124936188923 -0.124943956794 -0.124950667904 (1, 1) 0.0626154693101 0.0626007128546 0.0625880697782 0.0625772028513 0.0625678336747 0.0625597327794 (1, 2) 0.0626154693101 0.0626007128546 0.0625880697782 0.0625772028513 0.0625678336747 0.0625597327794 (2, 0) 0.0473579367205 0.047401637706 0.0474397923209 0.0474731007899 0.0475023315231 0.0475279948972 (2, 1) -0.0235184193967 -0.0235605403278 -0.0235970395393 -0.0236287086461 -0.0236563004226 -0.0236803751674 (2, 2) -0.0235184193967 -0.0235605403278 -0.0235970395393 -0.0236287086461 -0.0236563004226 -0.0236803751674 (3, 0) 0.0473579367205 0.047401637706 0.0474397923209 0.0474731007899 0.0475023315231 0.0475279948972 (3, 1) -0.0235184193967 -0.0235605403278 -0.0235970395393 -0.0236287086461 -0.0236563004226 -0.0236803751674 (3, 2) -0.0235184193967 -0.0235605403278 -0.0235970395393 -0.0236287086461 -0.0236563004226 -0.0236803751674 (4, 0) -0.124904395032 -0.124916668451 -0.124927170937 -0.124936188923 -0.124943956794 -0.124950667904 (4, 1) 0.0626154693101 0.0626007128546 0.0625880697782 0.0625772028513 0.0625678336747 0.0625597327794 (4, 2) 0.0626154693101 0.0626007128546 0.0625880697782 0.0625772028513 0.0625678336747 0.0625597327794 Hodge numbers are 2, 3, and 8. Euler is 8 and Signature is 0. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3371152552543568 8881651453796800 23036244436719616 58866403670997234 148309597796889216 368638611223322288 (0, 1) -3371138599022872 -8881625494969920 -23036196632393728 -58866316483915076 -148309440238877088 -368638328982827312 (1, 0) -3371138599022872 -8881625494969920 -23036196632393728 -58866316483915076 -148309440238877088 -368638328982827312 (1, 1) 3371152552543568 8881651453731840 23036244436719616 58866403670881144 148309597796889216 368638611223118304 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250000517388 0.250000365344 0.250000259398 0.250000185138 0.250000132795 0.250000095704 (0, 1) -0.249999482612 -0.249999634656 -0.249999740602 -0.249999814862 -0.249999867205 -0.249999904296 (1, 0) -0.249999482612 -0.249999634656 -0.249999740602 -0.249999814862 -0.249999867205 -0.249999904296 (1, 1) 0.250000517388 0.250000365343 0.250000259398 0.250000185137 0.250000132795 0.250000095704 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 25842248025452 57859575297514 127785415444320 278580574221558 599875572844320 1276636920314100 (0, 1) -12914147252378 -28916808235317 -63868805559216 -139246693569700 -299859007416096 -638177339909562 (0, 2) -12914147252378 -28916808235317 -63868805559216 -139246693569700 -299859007416096 -638177339909562 (1, 0) -25832945387896 -57842269021528 -127753545309408 -278522448716940 -599770533019392 -1276448758449944 (1, 1) 12923449454296 28934113891724 63900674817648 139304817841504 299964045515760 638365499370468 (1, 2) 12923449454296 28934113891724 63900674817648 139304817841504 299964045515760 638365499370468 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250045005335 0.250037394193 0.250031179331 0.250026083848 0.250021889752 0.250018424956 (0, 1) -0.124954996773 -0.124962607181 -0.124968821527 -0.124973916718 -0.124978110607 -0.124981575284 (0, 2) -0.124954996773 -0.124962607181 -0.124968821527 -0.124973916718 -0.124978110607 -0.124981575284 (1, 0) -0.249954994665 -0.249962605947 -0.249968820669 -0.249973916204 -0.249978110248 -0.249981575064 (1, 1) 0.125045003227 0.125037392749 0.125031178473 0.125026083256 0.125021889393 0.125018424706 (1, 2) 0.125045003227 0.125037392749 0.125031178473 0.125026083256 0.125021889393 0.125018424706 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 9302637556 17306275986 31870134912 58125504618 105039824928 188161864156 (1, 0) 9302201918 17305656407 31869258432 58124271804 105038099664 188159460906 (2, 0) 9302201918 17305656407 31869258432 58124271804 105038099664 188159460906 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.333343740217 0.333341289263 0.333339444914 0.333338046626 0.333336983341 0.333336171635 (1, 0) 0.333328129891 0.333329355369 0.333330277543 0.333330976687 0.333331508329 0.333331914183 (2, 0) 0.333328129891 0.333329355369 0.333330277543 0.333330976687 0.333331508329 0.333331914183 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 25842248025452 57859575297514 127785415444320 278580574221558 599875572844320 1276636920314100 (0, 1) -25832945387896 -57842269021528 -127753545309408 -278522448716940 -599770533019392 -1276448758449944 (1, 0) -12914147252378 -28916808235317 -63868805559216 -139246693569700 -299859007416096 -638177339909562 (1, 1) 12923449454296 28934113891724 63900674817648 139304817841504 299964045515760 638365499370468 (2, 0) -12914147252378 -28916808235317 -63868805559216 -139246693569700 -299859007416096 -638177339909562 (2, 1) 12923449454296 28934113891724 63900674817648 139304817841504 299964045515760 638365499370468 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250045005335 0.250037394193 0.250031179331 0.250026083848 0.250021889752 0.250018424956 (0, 1) -0.249954994665 -0.249962605947 -0.249968820669 -0.249973916204 -0.249978110248 -0.249981575064 (1, 0) -0.124954996773 -0.124962607181 -0.124968821527 -0.124973916718 -0.124978110607 -0.124981575284 (1, 1) 0.125045003227 0.125037392749 0.125031178473 0.125026083256 0.125021889393 0.125018424706 (2, 0) -0.124954996773 -0.124962607181 -0.124968821527 -0.124973916718 -0.124978110607 -0.124981575284 (2, 1) 0.125045003227 0.125037392749 0.125031178473 0.125026083256 0.125021889393 0.125018424706 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 57919210058174 137656544392534 322650528397920 746315596454346 1704658734404580 3847039651755844 (0, 1) -28954953710309 -68819619058274 -161309329131504 -373128735474864 -852276847289826 -1923425744945844 (0, 2) -28954953710309 -68819619058274 -161309329131504 -373128735474864 -852276847289826 -1923425744945844 (1, 0) -28954953710309 -68819619058274 -161309329131504 -373128735474864 -852276847289826 -1923425744945844 (1, 1) -28621979132984 -68139311546204 -159935502732240 -370384997461020 -846854730620040 -1912817989370802 (1, 2) 57586235045211 136976236260885 321276701122176 743571857207688 1699236616009530 3836431893777552 (2, 0) -28954953710309 -68819619058274 -161309329131504 -373128735474864 -852276847289826 -1923425744945844 (2, 1) 57586235045211 136976236260885 321276701122176 743571857207688 1699236616009530 3836431893777552 (2, 2) -28621979132984 -68139311546204 -159935502732240 -370384997461020 -846854730620040 -1912817989370802 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.167321385561 0.167228147122 0.167149396663 0.167082679256 0.167025992879 0.166977697675 (0, 1) -0.0836472556996 -0.0836035615419 -0.0835664431552 -0.0835348331545 -0.0835078504298 -0.0834847653292 (0, 2) -0.0836472556996 -0.0836035615419 -0.0835664431552 -0.0835348331545 -0.0835078504298 -0.0834847653292 (1, 0) -0.0836472556996 -0.0836035615419 -0.0835664431552 -0.0835348331545 -0.0835078504298 -0.0834847653292 (1, 1) -0.0826853336089 -0.0827771092638 -0.0828547311525 -0.0829205741189 -0.0829765802102 -0.0830243441317 (1, 2) 0.166359462211 0.166401694091 0.166437684206 0.166468419944 0.166494722491 0.166517276373 (2, 0) -0.0836472556996 -0.0836035615419 -0.0835664431552 -0.0835348331545 -0.0835078504298 -0.0834847653292 (2, 1) 0.166359462211 0.166401694091 0.166437684206 0.166468419944 0.166494722491 0.166517276373 (2, 2) -0.0826853336089 -0.0827771092638 -0.0828547311525 -0.0829205741189 -0.0829765802102 -0.0830243441317 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 5607418824 10424523960 19185888560 34974471998 63176960568 113131823442 (1, 0) 5589413472 10396144435 19141495208 34905523443 63070605250 112968829444 (2, 0) 5560397812 10350387985 19069886400 34794264671 62898926594 112705651819 (3, 0) 5560397812 10350387985 19069886400 34794264671 62898926594 112705651819 (4, 0) 5589413472 10396144435 19141495208 34905523443 63070605250 112968829444 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.200932042392 0.20078983252 0.200671050199 0.200571543494 0.200487933666 0.200417492064 (1, 0) 0.200286852106 0.200243206114 0.200206726613 0.200176137436 0.200150422051 0.200128741761 (2, 0) 0.199247126698 0.199361877626 0.199457748287 0.199538090817 0.199605611116 0.199662512207 (3, 0) 0.199247126698 0.199361877626 0.199457748287 0.199538090817 0.199605611116 0.199662512207 (4, 0) 0.200286852106 0.200243206114 0.200206726613 0.200176137436 0.200150422051 0.200128741761 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 352199921024672 863431087080520 2084897843042416 4962389453829250 11650625122377048 26998481165631522 (0, 1) -352194313605848 -863420662556560 -2084878657153856 -4962354479357252 -11650561945416480 -26998368033808080 (1, 0) -284926490249112 -698513336846965 -1686686477309884 -4014600572078277 -9425451501508874 -21842047810385220 (1, 1) 284932079662584 698523732991400 1686705618805092 4014635477601720 9425514572114124 21842160779214664 (2, 0) 108833506497124 266810772720145 644261457951620 1533449438704731 3600217719326414 8342948347816947 (2, 1) -108827946099312 -266800422332160 -644242388065220 -1533414644440060 -3600154820399820 -8342835642165128 (3, 0) 108833506497124 266810772720145 644261457951620 1533449438704731 3600217719326414 8342948347816947 (3, 1) -108827946099312 -266800422332160 -644242388065220 -1533414644440060 -3600154820399820 -8342835642165128 (4, 0) -284926490249112 -698513336846965 -1686686477309884 -4014600572078277 -9425451501508874 -21842047810385220 (4, 1) 284932079662584 698523732991400 1686705618805092 4014635477601720 9425514572114124 21842160779214664 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.154511987544 0.154511126747 0.154510488526 0.154510012631 0.154509655856 0.154509387015 (0, 1) -0.15450952754 -0.154509261277 -0.154509066672 -0.154508923658 -0.154508818009 -0.154508739573 (1, 0) -0.124998773947 -0.124999069803 -0.124999290718 -0.124999456587 -0.124999581781 -0.124999676746 (1, 1) 0.125001226053 0.125000930194 0.125000709282 0.125000543412 0.125000418219 0.125000323254 (2, 0) 0.0477458409172 0.0477458290974 0.0477458178293 0.0477458076089 0.0477457986141 0.0477457908542 (2, 1) -0.0477434015409 -0.0477439768939 -0.0477444045718 -0.0477447242473 -0.0477449644535 -0.047745145852 (3, 0) 0.0477458409172 0.0477458290974 0.0477458178293 0.0477458076089 0.0477457986141 0.0477457908542 (3, 1) -0.0477434015409 -0.0477439768939 -0.0477444045718 -0.0477447242473 -0.0477449644535 -0.047745145852 (4, 0) -0.124998773947 -0.124999069803 -0.124999290718 -0.124999456587 -0.124999581781 -0.124999676746 (4, 1) 0.125001226053 0.125000930194 0.125000709282 0.125000543412 0.125000418219 0.125000323254 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 48089024286388 113559658138870 264426321585166 607547107881910 1378223084952758 3088679240710452 (0, 1) -24041708433782 -56774616807455 -132203567848303 -303756066704956 -689079953996095 -1544283054443505 (0, 2) -24041708433782 -56774616807455 -132203567848303 -303756066704956 -689079953996095 -1544283054443505 (1, 0) -38763469856708 -91585843270113 -213354028913925 -490386373912044 -1112796035385155 -2494513595731325 (1, 1) -4112330817284 -9915935582652 -23516698770989 -54912017739775 -126359686437274 -286787069609832 (1, 2) 42881390087464 101512174997200 236889869180122 545333297175262 1239218792427679 2781413634170601 (2, 0) 14723609032292 34814667338671 81156803188798 186641882723398 423737012821240 950268056308177 (2, 1) 30433304421657 72286166781851 169185154465829 390484026875215 889370000735080 2000224457341535 (2, 2) -45151353056137 -107090483732537 -250322887768227 -577091115333942 -1313044114629726 -2950379807997893 (3, 0) 14723609032292 34814667338671 81156803188798 186641882723398 423737012821240 950268056308177 (3, 1) -45151353056137 -107090483732537 -250322887768227 -577091115333942 -1313044114629726 -2950379807997893 (3, 2) 30433304421657 72286166781851 169185154465829 390484026875215 889370000735080 2000224457341535 (4, 0) -38763469856708 -91585843270113 -213354028913925 -490386373912044 -1112796035385155 -2494513595731325 (4, 1) 42881390087464 101512174997200 236889869180122 545333297175262 1239218792427679 2781413634170601 (4, 2) -4112330817284 -9915935582652 -23516698770989 -54912017739775 -126359686437274 -286787069609832 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.107268936704 0.106978406968 0.106723167725 0.106498338694 0.106299801104 0.10612406604 (0, 1) -0.0536282143068 -0.0534842932941 -0.0533577121245 -0.0532461039689 -0.0531474641906 -0.0530600894695 (0, 2) -0.0536282143068 -0.0534842932941 -0.0533577121245 -0.0532461039689 -0.0531474641906 -0.0530600894695 (1, 0) -0.0864670526421 -0.0862780654189 -0.0861102543652 -0.0859609624707 -0.0858279029873 -0.0857091024805 (1, 1) -0.00917309845002 -0.00934126616453 -0.00949140226368 -0.00962565468217 -0.00974588924132 -0.00985372955327 (1, 2) 0.0956526190191 0.0956291252283 0.0956093821873 0.0955927358228 0.095578656748 0.0955667135348 (2, 0) 0.0328429596727 0.0327970135878 0.0327551019384 0.0327168876008 0.0326820531994 0.0326503019913 (2, 1) 0.0678855155441 0.0680968848874 0.0682835789885 0.068448848837 0.0685954655801 0.0687258002088 (2, 2) -0.100716072013 -0.100884147935 -0.10103098427 -0.101159637271 -0.101272667501 -0.101372229742 (3, 0) 0.0328429596727 0.0327970135878 0.0327551019384 0.0327168876008 0.0326820531994 0.0326503019913 (3, 1) -0.100716072013 -0.100884147935 -0.10103098427 -0.101159637271 -0.101272667501 -0.101372229742 (3, 2) 0.0678855155441 0.0680968848874 0.0682835789885 0.068448848837 0.0685954655801 0.0687258002088 (4, 0) -0.0864670526421 -0.0862780654189 -0.0861102543652 -0.0859609624707 -0.0858279029873 -0.0857091024805 (4, 1) 0.0956526190191 0.0956291252283 0.0956093821873 0.0955927358228 0.095578656748 0.0955667135348 (4, 2) -0.00917309845002 -0.00934126616453 -0.00949140226368 -0.00962565468217 -0.00974588924132 -0.00985372955327 Euler is greater than zero, other is less than zero Hodge numbers are 2, 0, and 8. Euler is 2 and Signature is -6. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 31906046986736 73275145596665 165981752883840 371093520126731 819408786698064 1787990224816560 (0, 1) -31905838599504 -73274800977460 -165981187756400 -371092600786712 -819407302479324 -1787987845964704 (1, 0) -31905838599504 -73274800977460 -165981187756400 -371092600786712 -819407302479324 -1787987845964704 (1, 1) 31905630341784 73274456535342 165980622869800 371091681772708 819405818699774 1787985467701976 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250001632576 0.250001175626 0.250000851101 0.250000619292 0.2500004528 0.250000332595 (0, 1) -0.249999999746 -0.249999999849 -0.249999999909 -0.249999999945 -0.249999999967 -0.249999999979 (1, 0) -0.249999999746 -0.249999999849 -0.249999999909 -0.249999999945 -0.249999999967 -0.249999999979 (1, 1) 0.249998367931 0.249998824676 0.24999914908 0.249999380818 0.249999547267 0.249999667446 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 4144224497192 8918127623135 18946711919956 39765324633377 82497988762162 169272906842108 (0, 1) -2072008054980 -4458891501965 -9473073396258 -19882202646679 -41248252271711 -84635263995126 (0, 2) -2072008054980 -4458891501965 -9473073396258 -19882202646679 -41248252271711 -84635263995126 (1, 0) -4144113623752 -8917947750902 -18946422454996 -39764862358480 -82497255874732 -169271752973606 (1, 1) 2071952683016 4458801654392 9472928784198 19881971672238 41247886047591 84634687355439 (1, 2) 2071952683016 4458801654392 9472928784198 19881971672238 41247886047591 84634687355439 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250009628104 0.250007350454 0.250005637464 0.25000434259 0.250003359046 0.250002608556 (0, 1) -0.124998528339 -0.124998844766 -0.124999090247 -0.124999281352 -0.124999430622 -0.124999547591 (0, 2) -0.124998528339 -0.124998844766 -0.124999090247 -0.124999281352 -0.124999430622 -0.124999547591 (1, 0) -0.250002939416 -0.250002307985 -0.250001817916 -0.25000143627 -0.250001138091 -0.250000904384 (1, 1) 0.124995187901 0.124996326014 0.124997182062 0.124997829218 0.12499832081 0.12499869594 (1, 2) 0.124995187901 0.124996326014 0.124997182062 0.124997829218 0.12499832081 0.12499869594 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 110873440 179872233 289464960 462274897 732887430 1153868502 (1, 0) -55371964 -89847573 -144612060 -230974441 -366224120 -576639687 (2, 0) -55371964 -89847573 -144612060 -230974441 -366224120 -576639687 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.500292197316 0.500246250092 0.500208091018 0.500176372329 0.500149859861 0.500127674521 (1, 0) -0.249853901342 -0.249876874954 -0.249895954491 -0.249911813836 -0.249925070069 -0.249936162739 (2, 0) -0.249853901342 -0.249876874954 -0.249895954491 -0.249911813836 -0.249925070069 -0.249936162739 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 4144224497192 8918127623135 18946711919956 39765324633377 82497988762162 169272906842108 (0, 1) -4144113623752 -8917947750902 -18946422454996 -39764862358480 -82497255874732 -169271752973606 (1, 0) -2072008054980 -4458891501965 -9473073396258 -19882202646679 -41248252271711 -84635263995126 (1, 1) 2071952683016 4458801654392 9472928784198 19881971672238 41247886047591 84634687355439 (2, 0) -2072008054980 -4458891501965 -9473073396258 -19882202646679 -41248252271711 -84635263995126 (2, 1) 2071952683016 4458801654392 9472928784198 19881971672238 41247886047591 84634687355439 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250009628104 0.250007350454 0.250005637464 0.25000434259 0.250003359046 0.250002608556 (0, 1) -0.250002939416 -0.250002307985 -0.250001817916 -0.25000143627 -0.250001138091 -0.250000904384 (1, 0) -0.124998528339 -0.124998844766 -0.124999090247 -0.124999281352 -0.124999430622 -0.124999547591 (1, 1) 0.124995187901 0.124996326014 0.124997182062 0.124997829218 0.12499832081 0.12499869594 (2, 0) -0.124998528339 -0.124998844766 -0.124999090247 -0.124999281352 -0.124999430622 -0.124999547591 (2, 1) 0.124995187901 0.124996326014 0.124997182062 0.124997829218 0.12499832081 0.12499869594 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3794655749018 8292283980711 17894264712756 38155372024373 80434597764800 167725840336578 (0, 1) -1897272437789 -4146052054239 -8946987623898 -19077454874738 -40216932438685 -83862343234038 (0, 2) -1897272437789 -4146052054239 -8946987623898 -19077454874738 -40216932438685 -83862343234038 (1, 0) -1897272437789 -4146052054239 -8946987623898 -19077454874738 -40216932438685 -83862343234038 (1, 1) 3536755059673 7771737398112 16855717894104 36106084601776 76433118283493 159990280347174 (1, 2) -1639537993848 -3625775191446 -7908874882266 -17028860701479 -36216552068928 -76128513752823 (2, 0) -1897272437789 -4146052054239 -8946987623898 -19077454874738 -40216932438685 -83862343234038 (2, 1) -1639537993848 -3625775191446 -7908874882266 -17028860701479 -36216552068928 -76128513752823 (2, 2) 3536755059673 7771737398112 16855717894104 36106084601776 76433118283493 159990280347174 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.174576640511 0.173946298272 0.173374884759 0.172855948661 0.172383862387 0.171953700098 (0, 1) -0.087285769838 -0.0869712625564 -0.0866860400878 -0.0864269272046 -0.0861911458477 -0.0859762585722 (0, 2) -0.087285769838 -0.0869712625564 -0.0866860400878 -0.0864269272046 -0.0861911458477 -0.0859762585722 (1, 0) -0.087285769838 -0.0869712625564 -0.0866860400878 -0.0864269272046 -0.0861911458477 -0.0859762585722 (1, 1) 0.162711681234 0.163026851793 0.163312558204 0.163572026039 0.163808069042 0.164023150102 (1, 2) -0.0754284588345 -0.0760574739585 -0.076627919241 -0.0771461452215 -0.0776177080694 -0.0780474827046 (2, 0) -0.087285769838 -0.0869712625564 -0.0866860400878 -0.0864269272046 -0.0861911458477 -0.0859762585722 (2, 1) -0.0754284588345 -0.0760574739585 -0.076627919241 -0.0771461452215 -0.0776177080694 -0.0780474827046 (2, 2) 0.162711681234 0.163026851793 0.163312558204 0.163572026039 0.163808069042 0.164023150102 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 127818554 209232101 339749480 547468789 875763940 1391197942 (1, 0) -94739363 -155844114 -254209205 -411357821 -660613990 -1053252756 (2, 0) 30894842 51316607 84454885 137786434 222951615 357948349 (3, 0) 30894842 51316607 84454885 137786434 222951615 357948349 (4, 0) -94739363 -155844114 -254209205 -411357821 -660613990 -1053252756 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.337174754445 0.335547930645 0.334044776876 0.332654632206 0.331365374067 0.330168476318 (1, 0) -0.249914589519 -0.249929000885 -0.249940800981 -0.249950476446 -0.249958455597 -0.249965046043 (2, 0) 0.0814980332587 0.082297033793 0.0830368105814 0.0837222074505 0.084358857369 0.0849507157982 (3, 0) 0.0814980332587 0.082297033793 0.0830368105814 0.0837222074505 0.084358857369 0.0849507157982 (4, 0) -0.249914589519 -0.249929000885 -0.249940800981 -0.249950476446 -0.249958455597 -0.249965046043 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 10099668124580 22521643881511 49554028259918 107654725800019 231061993144062 490241923277658 (0, 1) -10099540306026 -22521434649410 -49553688510438 -107654178331230 -231061117380122 -490240532079716 (1, 0) -8116033755838 -18112872942191 -39881297843188 -86693442054827 -186170232828271 -395176853439747 (1, 1) 8115939016475 18112717098077 39881043633983 86693030697006 186169572214281 395175800186991 (2, 0) 3066303887164 6852223311038 15104566276949 32866538824827 70639978365610 150057081226846 (2, 1) -3066272992322 -6852171994431 -15104481822064 -32866401038393 -70639755413995 -150056723278497 (3, 0) 3066303887164 6852223311038 15104566276949 32866538824827 70639978365610 150057081226846 (3, 1) -3066272992322 -6852171994431 -15104481822064 -32866401038393 -70639755413995 -150056723278497 (4, 0) -8116033755838 -18112872942191 -39881297843188 -86693442054827 -186170232828271 -395176853439747 (4, 1) 8115939016475 18112717098077 39881043633983 86693030697006 186169572214281 395175800186991 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.155551075902 0.155425603549 0.155317195532 0.155223240222 0.155141573339 0.155070392736 (0, 1) -0.155549107292 -0.155424159604 -0.155316130656 -0.155222450848 -0.155140985326 -0.15506995268 (1, 0) -0.124999927444 -0.124999943337 -0.124999955659 -0.124999965229 -0.124999972678 -0.124999978487 (1, 1) 0.124998468306 0.124998867831 0.124999158891 0.124999372108 0.124999529123 0.124999645328 (2, 0) 0.0472259942415 0.0472883306998 0.0473422435319 0.0473890078987 0.0474296842815 0.0474651583509 (2, 1) -0.0472255184114 -0.0472879765554 -0.047341978825 -0.0473888092297 -0.0474295345854 -0.0474650451268 (3, 0) 0.0472259942415 0.0472883306998 0.0473422435319 0.0473890078987 0.0474296842815 0.0474651583509 (3, 1) -0.0472255184114 -0.0472879765554 -0.047341978825 -0.0473888092297 -0.0474295345854 -0.0474650451268 (4, 0) -0.124999927444 -0.124999943337 -0.124999955659 -0.124999965229 -0.124999972678 -0.124999978487 (4, 1) 0.124998468306 0.124998867831 0.124999158891 0.124999372108 0.124999529123 0.124999645328 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3629004361496 7927762159083 17102258527536 36455162284215 76826215982554 160150477775152 (0, 1) -1814438271471 -3963776463491 -8550959389028 -18227307407713 -38412670109307 -80074543288605 (0, 2) -1814438271471 -3963776463491 -8550959389028 -18227307407713 -38412670109307 -80074543288605 (1, 0) -2859819357278 -6261888485801 -13536586427726 -28908478350493 -61024772202627 -127404453154497 (1, 1) 2901135767232 6384182232214 13866333899978 29745377374656 63057693423040 132177141040207 (1, 2) -41411149317 -122449590527 -330001681457 -837310381984 -2033581834403 -4773741138466 (2, 0) 1045372613250 2298097342376 4985601896438 10681128345834 22612030655065 47329791201172 (2, 1) -2790315967012 -6186196247245 -13527644710919 -29198719029607 -62249529225577 -131160310462855 (2, 2) 1744974248604 3888150221476 8542127269366 18517728470207 39637721522127 83830877210032 (3, 0) 1045372613250 2298097342376 4985601896438 10681128345834 22612030655065 47329791201172 (3, 1) 1744974248604 3888150221476 8542127269366 18517728470207 39637721522127 83830877210032 (3, 2) -2790315967012 -6186196247245 -13527644710919 -29198719029607 -62249529225577 -131160310462855 (4, 0) -2859819357278 -6261888485801 -13536586427726 -28908478350493 -61024772202627 -127404453154497 (4, 1) -41411149317 -122449590527 -330001681457 -837310381984 -2033581834403 -4773741138466 (4, 2) 2901135767232 6384182232214 13866333899978 29745377374656 63057693423040 132177141040207 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.120870361088 0.119868348913 0.118946773183 0.118097397883 0.117313028738 0.116587356405 (0, 1) -0.0604330519335 -0.0599325926542 -0.0594722051071 -0.059047812172 -0.0586558457268 -0.0582931718162 (0, 2) -0.0604330519335 -0.0599325926542 -0.0594722051071 -0.059047812172 -0.0586558457268 -0.0582931718162 (1, 0) -0.0952513041949 -0.0946802160319 -0.0941474059055 -0.0936497290376 -0.0931843481238 -0.0927486985609 (1, 1) 0.0966274197606 0.096529306503 0.0964408104711 0.0963608840799 0.0962886028694 0.0962231500348 (1, 2) -0.00137927102655 -0.00185144684553 -0.00229517259905 -0.0027124876461 -0.00310526349801 -0.00347521822744 (2, 0) 0.034817970068 0.034747401416 0.0346750259331 0.0346017788718 0.0345283933113 0.0344554403585 (2, 1) -0.0929363717667 -0.0935357437989 -0.0940852159696 -0.0945899708803 -0.0950545424838 -0.0954829112882 (2, 2) 0.0581194307056 0.0587891182937 0.059410777423 0.0599886383711 0.0605264896178 0.0610277315113 (3, 0) 0.034817970068 0.034747401416 0.0346750259331 0.0346017788718 0.0345283933113 0.0344554403585 (3, 1) 0.0581194307056 0.0587891182937 0.059410777423 0.0599886383711 0.0605264896178 0.0610277315113 (3, 2) -0.0929363717667 -0.0935357437989 -0.0940852159696 -0.0945899708803 -0.0950545424838 -0.0954829112882 (4, 0) -0.0952513041949 -0.0946802160319 -0.0941474059055 -0.0936497290376 -0.0931843481238 -0.0927486985609 (4, 1) -0.00137927102655 -0.00185144684553 -0.00229517259905 -0.0027124876461 -0.00310526349801 -0.00347521822744 (4, 2) 0.0966274197606 0.096529306503 0.0964408104711 0.0963608840799 0.0962886028694 0.0962231500348 Hodge numbers are 4, 0, and 20. Euler is 6 and Signature is -18. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3920511133755483660 12641965341150480869 40013387316985054552 124425192388764009121 380439447204200201696 1144645091393902190855 (0, 1) -3920410069105239288 -12641728918407934136 -40012841890155041832 -124423950617576356528 -380436655428480938720 -1144638889739282880792 (1, 0) -3920410069105239288 -12641728918407934136 -40012841890155041832 -124423950617576356528 -380436655428480938720 -1144638889739282880792 (1, 1) 3920309005787439246 12641492497954600898 40012296467223093338 124422708852970295092 380433863663784923624 1144632688102984552298 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250006444754 0.250004675432 0.250003407818 0.250002495037 0.250001834585 0.250001354499 (0, 1) -0.249999999979 -0.249999999989 -0.249999999994 -0.249999999997 -0.249999999998 -0.249999999999 (1, 0) -0.249999999979 -0.249999999989 -0.249999999994 -0.249999999997 -0.249999999998 -0.249999999999 (1, 1) 0.249993555288 0.249995324591 0.249996592195 0.249997504969 0.249998165419 0.249998645503 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 742617091984962438 2267651589329439647 6802153665417811012 20061008631386342723 58216028562681531626 166355137288030492989 (0, 1) -371258013667359033 -1133707583293446457 -3400804119293899146 -10029883430099345065 -29106618393481134325 -83174467816705591463 (0, 2) -371258013667359033 -1133707583293446457 -3400804119293899146 -10029883430099345065 -29106618393481134325 -83174467816705591463 (1, 0) -742586605386793506 -2267582598478420712 -6801999600792813580 -20060668905224543402 -58215288391456007936 -166353543045415136456 (1, 1) 371242771034496732 1133673089012543737 3400727088930432543 10029713570309240983 29106248313379996420 83173670704558403981 (1, 2) 371242771034496732 1133673089012543737 3400727088930432543 10029713570309240983 29106248313379996420 83173670704558403981 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250022145032 0.250016836417 0.250012854853 0.250009854667 0.250007583926 0.250005858003 (0, 1) -0.124994059441 -0.124995384975 -0.124996403857 -0.124997189561 -0.12499779735 -0.124998268941 (0, 2) -0.124994059441 -0.124995384975 -0.124996403857 -0.124997189561 -0.12499779735 -0.124998268941 (1, 0) -0.250011880894 -0.250009229924 -0.250007192214 -0.250005620837 -0.250004405276 -0.250003462104 (1, 1) 0.124988927596 0.124991581855 0.124993572609 0.124995072687 0.124996208049 0.124997071006 (1, 2) 0.124988927596 0.124991581855 0.124993572609 0.124995072687 0.124996208049 0.124997071006 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 30486598168932 68990851018935 154064624997432 339726161799321 740171225523690 1594242615356533 (1, 0) -15242632862301 -34494280902720 -77030363466603 -169859790104082 -370080101137905 -797112147187482 (2, 0) -15242632862301 -34494280902720 -77030363466603 -169859790104082 -370080101137905 -797112147187482 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.500010926715 0.500008295489 0.500006325452 0.500004843353 0.500003723236 0.500002873008 (1, 0) -0.249994536643 -0.249995852255 -0.249996837274 -0.249997578323 -0.249998138382 -0.249998563496 (2, 0) -0.249994536643 -0.249995852255 -0.249996837274 -0.249997578323 -0.249998138382 -0.249998563496 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 742617091984962438 2267651589329439647 6802153665417811012 20061008631386342723 58216028562681531626 166355137288030492989 (0, 1) -742586605386793506 -2267582598478420712 -6801999600792813580 -20060668905224543402 -58215288391456007936 -166353543045415136456 (1, 0) -371258013667359033 -1133707583293446457 -3400804119293899146 -10029883430099345065 -29106618393481134325 -83174467816705591463 (1, 1) 371242771034496732 1133673089012543737 3400727088930432543 10029713570309240983 29106248313379996420 83173670704558403981 (2, 0) -371258013667359033 -1133707583293446457 -3400804119293899146 -10029883430099345065 -29106618393481134325 -83174467816705591463 (2, 1) 371242771034496732 1133673089012543737 3400727088930432543 10029713570309240983 29106248313379996420 83173670704558403981 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250022145032 0.250016836417 0.250012854853 0.250009854667 0.250007583926 0.250005858003 (0, 1) -0.250011880894 -0.250009229924 -0.250007192214 -0.250005620837 -0.250004405276 -0.250003462104 (1, 0) -0.124994059441 -0.124995384975 -0.124996403857 -0.124997189561 -0.12499779735 -0.124998268941 (1, 1) 0.124988927596 0.124991581855 0.124993572609 0.124995072687 0.124996208049 0.124997071006 (2, 0) -0.124994059441 -0.124995384975 -0.124996403857 -0.124997189561 -0.12499779735 -0.124998268941 (2, 1) 0.124988927596 0.124991581855 0.124993572609 0.124995072687 0.124996208049 0.124997071006 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 304015583478884976 913744068040550505 2699976190587672702 7849757494776837445 22471889321197914156 63388569788563567473 (0, 1) -151992548440358022 -456837538594765785 -1349911062981337635 -3924708884307519062 -11235574574986195233 -31693487772974105470 (0, 2) -151992548440358022 -456837538594765785 -1349911062981337635 -3924708884307519062 -11235574574986195233 -31693487772974105470 (1, 0) -151992548440358022 -456837538594765785 -1349911062981337635 -3924708884307519062 -11235574574986195233 -31693487772974105470 (1, 1) 231347957256504189 704269956398010915 2106171626085832680 6193101037220169908 17919690251827747842 51060100945941544104 (1, 2) -79370651449008468 -247466912084147850 -756337593467961648 -2268562012702754928 -6684485756942690514 -19367410285114626116 (2, 0) -151992548440358022 -456837538594765785 -1349911062981337635 -3924708884307519062 -11235574574986195233 -31693487772974105470 (2, 1) -79370651449008468 -247466912084147850 -756337593467961648 -2268562012702754928 -6684485756942690514 -19367410285114626116 (2, 2) 231347957256504189 704269956398010915 2106171626085832680 6193101037220169908 17919690251827747842 51060100945941544104 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.198259439528 0.196733921439 0.195301751728 0.193955652787 0.192689075292 0.191496103646 (0, 1) -0.0991197790633 -0.0983595336724 -0.097645303761 -0.0969736293335 -0.0963413642834 -0.0957456437291 (0, 2) -0.0991197790633 -0.0983595336724 -0.097645303761 -0.0969736293335 -0.0963413642834 -0.0957456437291 (1, 0) -0.0991197790633 -0.0983595336724 -0.097645303761 -0.0969736293335 -0.0963413642834 -0.0957456437291 (1, 1) 0.150870280453 0.151633039404 0.152349124206 0.153022173647 0.153655462378 0.154251948191 (1, 2) -0.0517604416563 -0.053280932532 -0.0547093924076 -0.0560527412924 -0.0573172714096 -0.0585087125279 (2, 0) -0.0991197790633 -0.0983595336724 -0.097645303761 -0.0969736293335 -0.0963413642834 -0.0957456437291 (2, 1) -0.0517604416563 -0.053280932532 -0.0547093924076 -0.0560527412924 -0.0573172714096 -0.0585087125279 (2, 2) 0.150870280453 0.151633039404 0.152349124206 0.153022173647 0.153655462378 0.154251948191 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 48119826328980 111116233881285 253128377128852 569248874087829 1264522854033354 2776252467626435 (1, 0) -38271894523740 -88519160291715 -201941792179547 -454720978256337 -1011270583973766 -2222518218313789 (2, 0) 14212647581415 32962187957820 75379552647234 170099832008001 379014668581029 834401144991356 (3, 0) 14212647581415 32962187957820 75379552647234 170099832008001 379014668581029 834401144991356 (4, 0) -38271894523740 -88519160291715 -201941792179547 -454720978256337 -1011270583973766 -2222518218313789 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.314326009372 0.313817695286 0.313366481591 0.312964895783 0.312606593164 0.312286162984 (1, 0) -0.249997824068 -0.249998383684 -0.249998793574 -0.249999095384 -0.249999318727 -0.249999484792 (2, 0) 0.092839171246 0.0930927686728 0.0933179656304 0.0935184567248 0.0936973846906 0.0938574337159 (3, 0) 0.092839171246 0.0930927686728 0.0933179656304 0.0935184567248 0.0936973846906 0.0938574337159 (4, 0) -0.249997824068 -0.249998383684 -0.249998793574 -0.249999095384 -0.249999318727 -0.249999484792 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 1513402078818394732 4771572420202434465 14772173704074890314 44945285556162075253 134503008492144607614 396198224919315611715 (0, 1) -1513353958992065752 -4771461303968553180 -14771920575697761462 -44944716307287987424 -134501743969290574260 -396195448666847985280 (1, 0) -1212579724882279712 -3827600809243862241 -11861766813387356687 -36121871341865370693 -108180563495720716089 -318873361007469700269 (1, 1) 1212541452987755972 3827512290083570526 11861564871595177140 36121416620887114356 108179552225136742323 318871138489251386480 (2, 0) 455929217798204532 1441932810513918375 4475952674764917890 13649849449378159363 40930455137508043770 120777349375121549443 (2, 1) -455915005150623117 -1441899848325960555 -4475877295212270656 -13649679349546151362 -40930076122839462741 -120776514973976558087 (3, 0) 455929217798204532 1441932810513918375 4475952674764917890 13649849449378159363 40930455137508043770 120777349375121549443 (3, 1) -455915005150623117 -1441899848325960555 -4475877295212270656 -13649679349546151362 -40930076122839462741 -120776514973976558087 (4, 0) -1212579724882279712 -3827600809243862241 -11861766813387356687 -36121871341865370693 -108180563495720716089 -318873361007469700269 (4, 1) 1212541452987755972 3827512290083570526 11861564871595177140 36121416620887114356 108179552225136742323 318871138489251386480 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.156009786097 0.155827179706 0.155669575506 0.155533131698 0.155414666284 0.155311531051 (0, 1) -0.156004825642 -0.155823550938 -0.155666908032 -0.155531161813 -0.155413205162 -0.155310442747 (1, 0) -0.124999368081 -0.124999515174 -0.124999627108 -0.124999712497 -0.124999777794 -0.12499982785 (1, 1) 0.124995422804 0.124996624368 0.12499749904 0.124998138935 0.124998609298 0.124998956613 (2, 0) 0.0469996841816 0.0470897857981 0.047167713217 0.0472352952217 0.0472940575633 0.0473452778633 (2, 1) -0.0469982190639 -0.0470887093385 -0.0471669188652 -0.0472347065914 -0.0472936196219 -0.0473449507742 (3, 0) 0.0469996841816 0.0470897857981 0.047167713217 0.0472352952217 0.0472940575633 0.0473452778633 (3, 1) -0.0469982190639 -0.0470887093385 -0.0471669188652 -0.0472347065914 -0.0472936196219 -0.0473449507742 (4, 0) -0.124999368081 -0.124999515174 -0.124999627108 -0.124999712497 -0.124999777794 -0.12499982785 (4, 1) 0.124995422804 0.124996624368 0.12499749904 0.124998138935 0.124998609298 0.124998956613 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 418052055053353242 1272934171917067203 3809402936520225020 11213523199039650673 32493176130508695324 92749746649423254561 (0, 1) -209001967613512131 -636411527841592959 -1904574904071548084 -5606476975082781422 -16245955803827330985 -46373485198477814063 (0, 2) -209001967613512131 -636411527841592959 -1904574904071548084 -5606476975082781422 -16245955803827330985 -46373485198477814063 (1, 0) -332124639181723522 -1013150807590343407 -3036894868702546948 -8952395871910099712 -25974299345614356081 -74226324678677214673 (1, 1) 278129938548098625 855560996629396255 2585358889080712828 7681246393522446590 22455770418475383586 64643876311852593429 (1, 2) 53956428739101157 157501291800655437 451334037829654573 1270694757409396785 3517517656554998729 9580225848606307455 (2, 0) 123113854954131367 376718217057319273 1132270432754933154 3345804135471174036 9728081365972770264 27852248475273265659 (2, 1) -236005851405535061 -733864790942487646 -2239932838287650965 -6717210071211053881 -19808547696825583213 -57487098451678267504 (2, 2) 112906209098985109 357179536073126193 1107737785085365045 3371576035571887846 10080845345521393978 29635684377549993201 (3, 0) 123113854954131367 376718217057319273 1132270432754933154 3345804135471174036 9728081365972770264 27852248475273265659 (3, 1) 112906209098985109 357179536073126193 1107737785085365045 3371576035571887846 10080845345521393978 29635684377549993201 (3, 2) -236005851405535061 -733864790942487646 -2239932838287650965 -6717210071211053881 -19808547696825583213 -57487098451678267504 (4, 0) -332124639181723522 -1013150807590343407 -3036894868702546948 -8952395871910099712 -25974299345614356081 -74226324678677214673 (4, 1) 53956428739101157 157501291800655437 451334037829654573 1270694757409396785 3517517656554998729 9580225848606307455 (4, 2) 278129938548098625 855560996629396255 2585358889080712828 7681246393522446590 22455770418475383586 64643876311852593429 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.134485456907 0.133519308974 0.132613471989 0.131762073419 0.130960032429 0.130202926646 (0, 1) -0.0672349884883 -0.0667538269417 -0.0663023300239 -0.0658776922919 -0.065477467957 -0.065099514659 (0, 2) -0.0672349884883 -0.0667538269417 -0.0663023300239 -0.0658776922919 -0.065477467957 -0.065099514659 (1, 0) -0.106842995533 -0.106270378076 -0.105720812241 -0.105193186942 -0.104686444654 -0.104199580662 (1, 1) 0.0894731443443 0.0897406288362 0.0900018780714 0.090256820563 0.0905054159804 0.0907476536552 (1, 2) 0.0173575392929 0.0165204643788 0.0157119041437 0.0149310232785 0.014176952863 0.0134488070154 (2, 0) 0.0396051707795 0.0395143418482 0.0394167579066 0.0393141461715 0.0392079200273 0.0390992363447 (2, 1) -0.0759220158719 -0.0769757949221 -0.0779768577009 -0.0789291207469 -0.079836087378 -0.080700904673 (2, 2) 0.0363214172369 0.03746491051 0.0385627239179 0.0396169732966 0.040629694926 0.0416028396681 (3, 0) 0.0396051707795 0.0395143418482 0.0394167579066 0.0393141461715 0.0392079200273 0.0390992363447 (3, 1) 0.0363214172369 0.03746491051 0.0385627239179 0.0396169732966 0.040629694926 0.0416028396681 (3, 2) -0.0759220158719 -0.0769757949221 -0.0779768577009 -0.0789291207469 -0.079836087378 -0.080700904673 (4, 0) -0.106842995533 -0.106270378076 -0.105720812241 -0.105193186942 -0.104686444654 -0.104199580662 (4, 1) 0.0173575392929 0.0165204643788 0.0157119041437 0.0149310232785 0.014176952863 0.0134488070154 (4, 2) 0.0894731443443 0.0897406288362 0.0900018780714 0.090256820563 0.0905054159804 0.0907476536552 Hodge numbers are 8, 0, and 40. Euler is 10 and Signature is -38. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 768346379737650928958016 3623598452350100268286896 16694895743560450296043664 75225213558153133761710273 331831562037523452043721616 1434339480192508090287341565 (0, 1) -768336772760447526222720 -3623567175190622383790208 -16694795795011577056489024 -75224899776822454507638688 -331830593446490248600175712 -1434336538143899285573089200 (1, 0) -768336772760447526222720 -3623567175190622383790208 -16694795795011577056489024 -75224899776822454507638688 -331830593446490248600175712 -1434336538143899285573089200 (1, 1) 768327165783603742260080 3623535898031860908746840 16694695846464115076309384 75224585995494525811090388 331829624855462351862913788 1434333596095300620541319050 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.2500031259 0.250002157898 0.250001496702 0.250001042811 0.250000729733 0.250000512789 (0, 1) -0.25 -0.25 -0.25 -0.25 -0.25 -0.25 (1, 0) -0.25 -0.25 -0.25 -0.25 -0.25 -0.25 (1, 1) 0.2499968741 0.249997842102 0.249998503298 0.249998957189 0.249999270267 0.249999487211 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 134365903706242185477292 598211224596490286054664 2604108281751709157780754 11095830135555972812321561 46321069959772154778692592 189629278733408025964481863 (0, 1) -67178148364519391370998 -299089973718506200778988 -1302004166601417959113057 -5547758177112646779124988 -23160050684369475667573344 -94813168342399610625114749 (0, 2) -67178148364519391370998 -299089973718506200778988 -1302004166601417959113057 -5547758177112646779124988 -23160050684369475667573344 -94813168342399610625114749 (1, 0) -134364549711021186213250 -598207047186302953398710 -2604095618585948419794340 -11095792387736891757515906 -46320959222035140690846690 -189628958794369490630500710 (1, 1) 67177471367088701125305 299087885013770739177671 1301997835019243219807350 5547739303204481530483803 23159995315503621976792383 94813008372885412799365280 (1, 2) 67177471367088701125305 299087885013770739177671 1301997835019243219807350 5547739303204481530483803 23159995315503621976792383 94813008372885412799365280 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250010197359 0.250007408675 0.2500054056 0.250003960212 0.250002912663 0.250002150258 (0, 1) -0.124996160987 -0.124997168584 -0.124997905059 -0.124998445149 -0.124998842504 -0.12499913577 (0, 2) -0.124996160987 -0.124997168584 -0.124997905059 -0.124998445149 -0.124998842504 -0.12499913577 (1, 0) -0.250007678025 -0.250005662831 -0.250004189883 -0.250003109703 -0.250002314992 -0.250001728459 (1, 1) 0.12499490132 0.124996295663 0.1249972972 0.124998019894 0.124998543668 0.124998924871 (1, 2) 0.12499490132 0.124996295663 0.1249972972 0.124998019894 0.124998543668 0.124998924871 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 1353995220999264042 4177410187332655954 12663165760737986414 37747819081054805655 110737737014087845902 319939038535333981153 (1, 0) -676997430690245693 -2088704735461601317 -6331582174739305707 -18873908165248641185 -55368865853690780961 -159969514197825749469 (2, 0) -676997430690245693 -2088704735461601317 -6331582174739305707 -18873908165248641185 -55368865853690780961 -159969514197825749469 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.5000000664 0.500000042874 0.500000027862 0.500000018217 0.50000001198 0.500000007923 (1, 0) -0.2499999668 -0.249999978563 -0.249999986069 -0.249999990892 -0.24999999401 -0.249999996038 (2, 0) -0.2499999668 -0.249999978563 -0.249999986069 -0.249999990892 -0.24999999401 -0.249999996038 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 134365903706242185477292 598211224596490286054664 2604108281751709157780754 11095830135555972812321561 46321069959772154778692592 189629278733408025964481863 (0, 1) -134364549711021186213250 -598207047186302953398710 -2604095618585948419794340 -11095792387736891757515906 -46320959222035140690846690 -189628958794369490630500710 (1, 0) -67178148364519391370998 -299089973718506200778988 -1302004166601417959113057 -5547758177112646779124988 -23160050684369475667573344 -94813168342399610625114749 (1, 1) 67177471367088701125305 299087885013770739177671 1301997835019243219807350 5547739303204481530483803 23159995315503621976792383 94813008372885412799365280 (2, 0) -67178148364519391370998 -299089973718506200778988 -1302004166601417959113057 -5547758177112646779124988 -23160050684369475667573344 -94813168342399610625114749 (2, 1) 67177471367088701125305 299087885013770739177671 1301997835019243219807350 5547739303204481530483803 23159995315503621976792383 94813008372885412799365280 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250010197359 0.250007408675 0.2500054056 0.250003960212 0.250002912663 0.250002150258 (0, 1) -0.250007678025 -0.250005662831 -0.250004189883 -0.250003109703 -0.250002314992 -0.250001728459 (1, 0) -0.124996160987 -0.124997168584 -0.124997905059 -0.124998445149 -0.124998842504 -0.12499913577 (1, 1) 0.12499490132 0.124996295663 0.1249972972 0.124998019894 0.124998543668 0.124998924871 (2, 0) -0.124996160987 -0.124997168584 -0.124997905059 -0.124998445149 -0.124998842504 -0.12499913577 (2, 1) 0.12499490132 0.124996295663 0.1249972972 0.124998019894 0.124998543668 0.124998924871 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 30773001304486223575202 131620924991437114039148 551017930778456230479134 2260092112018196597996651 9090889126142863428134784 35890250972546329287417511 (0, 1) -15385823654632612155580 -65808373790624890691597 -275502633806347746246360 -1130027182099557771595498 -4545389194202924670144441 -17944965516753896976718179 (0, 2) -15385823654632612155580 -65808373790624890691597 -275502633806347746246360 -1130027182099557771595498 -4545389194202924670144441 -17944965516753896976718179 (1, 0) -15385823654632612155580 -65808373790624890691597 -275502633806347746246360 -1130027182099557771595498 -4545389194202924670144441 -17944965516753896976718179 (1, 1) 18106255579525831312961 78657460023606749760964 334244679982816238932095 1390759502371307943056876 5671750170652361744712792 22690443159910200587948040 (1, 2) -2721108922323909403074 -12851174937717320670684 -58748377758643231991442 -260751194179915420102563 -1126416345315290765349312 -4745637612670501436979330 (2, 0) -15385823654632612155580 -65808373790624890691597 -275502633806347746246360 -1130027182099557771595498 -4545389194202924670144441 -17944965516753896976718179 (2, 1) -2721108922323909403074 -12851174937717320670684 -58748377758643231991442 -260751194179915420102563 -1126416345315290765349312 -4745637612670501436979330 (2, 2) 18106255579525831312961 78657460023606749760964 334244679982816238932095 1390759502371307943056876 5671750170652361744712792 22690443159910200587948040 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.2296989317 0.227768425503 0.22591826017 0.224143836135 0.222440928334 0.220805640036 (0, 1) -0.114844412537 -0.113880598272 -0.112956534126 -0.112070046254 -0.111219109371 -0.110401835846 (0, 2) -0.114844412537 -0.113880598272 -0.112956534126 -0.112070046254 -0.111219109371 -0.110401835846 (1, 0) -0.114844412537 -0.113880598272 -0.112956534126 -0.112070046254 -0.111219109371 -0.110401835846 (1, 1) 0.13515053415 0.136115787249 0.137040869915 0.137928081933 0.138779535833 0.139597179982 (1, 2) -0.0203111749262 -0.0222388034548 -0.0240869317488 -0.025859907492 -0.0275617812587 -0.0291963283078 (2, 0) -0.114844412537 -0.113880598272 -0.112956534126 -0.112070046254 -0.111219109371 -0.110401835846 (2, 1) -0.0203111749262 -0.0222388034548 -0.0240869317488 -0.025859907492 -0.0275617812587 -0.0291963283078 (2, 2) 0.13515053415 0.136115787249 0.137040869915 0.137928081933 0.138779535833 0.139597179982 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3447608549280894764 11009504759787437038 34521985960611340580 106385822601400499593 322465566380914470026 962097726086774221775 (1, 0) -2784156642319388782 -8893263345667095679 -27892496824924379070 -85972136794240934035 -260631292765098296836 -777715615936070906070 (2, 0) 1060352547488327728 3388511323978103820 10631504550248396280 32779226868819445881 99398512227994203813 296666757962525036290 (3, 0) 1060352547488327728 3388511323978103820 10631504550248396280 32779226868819445881 99398512227994203813 296666757962525036290 (4, 0) -2784156642319388782 -8893263345667095679 -27892496824924379070 -85972136794240934035 -260631292765098296836 -777715615936070906070 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.309573856725 0.309490006934 0.309420000481 0.309361339957 0.309312018252 0.309270414287 (1, 0) -0.249999991927 -0.249999994965 -0.249999996838 -0.249999998 -0.249999998727 -0.249999999185 (2, 0) 0.0952130797106 0.0952550015678 0.0952900029218 0.0953193320212 0.0953439921464 0.0953647936716 (3, 0) 0.0952130797106 0.0952550015678 0.0952900029218 0.0953193320212 0.0953439921464 0.0953647936716 (4, 0) -0.249999991927 -0.249999994965 -0.249999996838 -0.249999998 -0.249999998727 -0.249999999185 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 292882391605037978059344 1351111144814891578655324 6091442672324407382601744 26868447380598012293049639 116060697813657486933053264 491409243816621989176569751 (0, 1) -292878943996488697164580 -1351100135310131791218286 -6091408150338446771261164 -26868340994775410892550046 -116060375348091106018583238 -491408281718895902402347976 (1, 0) -235509528975886809311887 -1087384369998468116617867 -4906030259953289551626546 -21653192086230765652920720 -93582192218750815133877600 -396411354442373069140920754 (1, 1) 235506744819244489923105 1087375476735122449522188 4906002367456464627247476 21653106114093971411986685 93581931587458050035580764 396410576726757133070014684 (2, 0) 89073136661969521649863 411844436170761269538549 1860358898065522480102994 8219125286597099133431693 35552327607438673389123920 150708203558366476909762061 (2, 1) -89072076309422033322135 -411841047659437291434729 -1860348266560972231706714 -8219092507370230313985812 -35552228208926445394920107 -150707906891608514384725771 (3, 0) 89073136661969521649863 411844436170761269538549 1860358898065522480102994 8219125286597099133431693 35552327607438673389123920 150708203558366476909762061 (3, 1) -89072076309422033322135 -411841047659437291434729 -1860348266560972231706714 -8219092507370230313985812 -35552228208926445394920107 -150707906891608514384725771 (4, 0) -235509528975886809311887 -1087384369998468116617867 -4906030259953289551626546 -21653192086230765652920720 -93582192218750815133877600 -396411354442373069140920754 (4, 1) 235506744819244489923105 1087375476735122449522188 4906002367456464627247476 21653106114093971411986685 93581931587458050035580764 396410576726757133070014684 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.155450788579 0.155316164121 0.155202593568 0.155106480801 0.155024898926 0.154955454915 (0, 1) -0.15544895872 -0.15531489853 -0.155201713989 -0.155105866656 -0.155024468201 -0.154955151538 (1, 0) -0.124999464108 -0.124999612298 -0.124999718692 -0.1249997953 -0.124999850623 -0.12499989069 (1, 1) 0.124997986384 0.124998589978 0.124999008024 0.124999298999 0.124999502492 0.124999645454 (2, 0) 0.0472766193265 0.047343327961 0.0473996951918 0.0474474605999 0.047488048045 0.0475226270886 (2, 1) -0.0472760565319 -0.0473429384367 -0.0473994243139 -0.0474472713716 -0.0474879152762 -0.0475225335411 (3, 0) 0.0472766193265 0.047343327961 0.0473996951918 0.0474474605999 0.047488048045 0.0475226270886 (3, 1) -0.0472760565319 -0.0473429384367 -0.0473994243139 -0.0474472713716 -0.0474879152762 -0.0475225335411 (4, 0) -0.124999464108 -0.124999612298 -0.124999718692 -0.1249997953 -0.124999850623 -0.12499989069 (4, 1) 0.124997986384 0.124998589978 0.124999008024 0.124999298999 0.124999502492 0.124999645454 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 58221902352250189827314 255710444577937196196020 1098677085502782175103010 4622665788482989455730905 19064411943254391059843728 77133020238142832973034843 (0, 1) -29109227371850454466275 -127849717536588704379491 -549321281758410781881215 -2311279701330194027615656 -9532044738844005072686851 -38566029070208373099406534 (0, 2) -29109227371850454466275 -127849717536588704379491 -549321281758410781881215 -2311279701330194027615656 -9532044738844005072686851 -38566029070208373099406534 (1, 0) -46763460730099884470731 -205580701449043766553970 -884010088113617818243750 -3722050775360705752557161 -15359363341317540000202051 -62174758864976930913154896 (1, 1) 32919568029602715938788 145923207315898808981566 632587028907077266881437 2684684201434475319792610 11165016058843390038090497 45541109842280322717243677 (1, 2) 13841108543854849143161 59648600869799290476725 251395166709715626983243 1037280601789436191830516 4194086651181384863814718 16632871307080672125005149 (2, 0) 17653186551585289189095 77727567865168834783937 334677876945107099685452 1410736755028751552094536 5827212738558851514203138 23608408715424782093628051 (2, 1) -23989470175268941626701 -107600861361995572312921 -471678062236685869666850 -2022969971443107575805670 -8497421509210408867011449 -34990050394843659571539605 (2, 2) 6337343976231140765334 29876682008150715632804 137010816796129018377678 612265995641224843157015 2670308169163785347012124 11381938346176840002947844 (3, 0) 17653186551585289189095 77727567865168834783937 334677876945107099685452 1410736755028751552094536 5827212738558851514203138 23608408715424782093628051 (3, 1) 6337343976231140765334 29876682008150715632804 137010816796129018377678 612265995641224843157015 2670308169163785347012124 11381938346176840002947844 (3, 2) -23989470175268941626701 -107600861361995572312921 -471678062236685869666850 -2022969971443107575805670 -8497421509210408867011449 -34990050394843659571539605 (4, 0) -46763460730099884470731 -205580701449043766553970 -884010088113617818243750 -3722050775360705752557161 -15359363341317540000202051 -62174758864976930913154896 (4, 1) 13841108543854849143161 59648600869799290476725 251395166709715626983243 1037280601789436191830516 4194086651181384863814718 16632871307080672125005149 (4, 2) 32919568029602715938788 145923207315898808981566 632587028907077266881437 2684684201434475319792610 11165016058843390038090497 45541109842280322717243677 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.145755668004 0.144950288093 0.144182630672 0.143448777086 0.142745434459 0.142069814766 (0, 1) -0.072873518543 -0.07247202366 -0.0720890501248 -0.071722737881 -0.0713715099936 -0.0710340213483 (0, 2) -0.072873518543 -0.07247202366 -0.0720890501248 -0.071722737881 -0.0713715099936 -0.0710340213483 (1, 0) -0.117070023162 -0.11653408194 -0.116011248188 -0.115501240282 -0.115003756722 -0.114518483106 (1, 1) 0.0824125189098 0.0827170394812 0.083016259427 0.0833100819265 0.083598438431 0.0838812874115 (1, 2) 0.034650534253 0.0338120012841 0.0329913283463 0.0321884905009 0.0314033668053 0.030635763235 (2, 0) 0.04419388399 0.0440601218829 0.0439207637642 0.0437774374265 0.0436314540688 0.0434838703678 (2, 1) -0.0600564582949 -0.0609938943997 -0.0618997016874 -0.0627760218374 -0.0636247332844 -0.0644474955459 (2, 2) 0.0158652288453 0.0169356933054 0.0179803331268 0.0189996016032 0.0199940234654 0.0209641716028 (3, 0) 0.04419388399 0.0440601218829 0.0439207637642 0.0437774374265 0.0436314540688 0.0434838703678 (3, 1) 0.0158652288453 0.0169356933054 0.0179803331268 0.0189996016032 0.0199940234654 0.0209641716028 (3, 2) -0.0600564582949 -0.0609938943997 -0.0618997016874 -0.0627760218374 -0.0636247332844 -0.0644474955459 (4, 0) -0.117070023162 -0.11653408194 -0.116011248188 -0.115501240282 -0.115003756722 -0.114518483106 (4, 1) 0.034650534253 0.0338120012841 0.0329913283463 0.0321884905009 0.0314033668053 0.030635763235 (4, 2) 0.0824125189098 0.0827170394812 0.083016259427 0.0833100819265 0.083598438431 0.0838812874115

Output too long: 150676 -- MAX_OUTPUT (=150000) exceeded (type 'smc?' to learn how to raise this limit): attempting to terminate...

Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 10099668124580 22521643881511 49554028259918 107654725800019 231061993144062 490241923277658 (0, 1) -10099540306026 -22521434649410 -49553688510438 -107654178331230 -231061117380122 -490240532079716 (1, 0) -8116033755838 -18112872942191 -39881297843188 -86693442054827 -186170232828271 -395176853439747 (1, 1) 8115939016475 18112717098077 39881043633983 86693030697006 186169572214281 395175800186991 (2, 0) 3066303887164 6852223311038 15104566276949 32866538824827 70639978365610 150057081226846 (2, 1) -3066272992322 -6852171994431 -15104481822064 -32866401038393 -70639755413995 -150056723278497 (3, 0) 3066303887164 6852223311038 15104566276949 32866538824827 70639978365610 150057081226846 (3, 1) -3066272992322 -6852171994431 -15104481822064 -32866401038393 -70639755413995 -150056723278497 (4, 0) -8116033755838 -18112872942191 -39881297843188 -86693442054827 -186170232828271 -395176853439747 (4, 1) 8115939016475 18112717098077 39881043633983 86693030697006 186169572214281 395175800186991 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.155551075902 0.155425603549 0.155317195532 0.155223240222 0.155141573339 0.155070392736 (0, 1) -0.155549107292 -0.155424159604 -0.155316130656 -0.155222450848 -0.155140985326 -0.15506995268 (1, 0) -0.124999927444 -0.124999943337 -0.124999955659 -0.124999965229 -0.124999972678 -0.124999978487 (1, 1) 0.124998468306 0.124998867831 0.124999158891 0.124999372108 0.124999529123 0.124999645328 (2, 0) 0.0472259942415 0.0472883306998 0.0473422435319 0.0473890078987 0.0474296842815 0.0474651583509 (2, 1) -0.0472255184114 -0.0472879765554 -0.047341978825 -0.0473888092297 -0.0474295345854 -0.0474650451268 (3, 0) 0.0472259942415 0.0472883306998 0.0473422435319 0.0473890078987 0.0474296842815 0.0474651583509 (3, 1) -0.0472255184114 -0.0472879765554 -0.047341978825 -0.0473888092297 -0.0474295345854 -0.0474650451268 (4, 0) -0.124999927444 -0.124999943337 -0.124999955659 -0.124999965229 -0.124999972678 -0.124999978487 (4, 1) 0.124998468306 0.124998867831 0.124999158891 0.124999372108 0.124999529123 0.124999645328 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3629004361496 7927762159083 17102258527536 36455162284215 76826215982554 160150477775152 (0, 1) -1814438271471 -3963776463491 -8550959389028 -18227307407713 -38412670109307 -80074543288605 (0, 2) -1814438271471 -3963776463491 -8550959389028 -18227307407713 -38412670109307 -80074543288605 (1, 0) -2859819357278 -6261888485801 -13536586427726 -28908478350493 -61024772202627 -127404453154497 (1, 1) 2901135767232 6384182232214 13866333899978 29745377374656 63057693423040 132177141040207 (1, 2) -41411149317 -122449590527 -330001681457 -837310381984 -2033581834403 -4773741138466 (2, 0) 1045372613250 2298097342376 4985601896438 10681128345834 22612030655065 47329791201172 (2, 1) -2790315967012 -6186196247245 -13527644710919 -29198719029607 -62249529225577 -131160310462855 (2, 2) 1744974248604 3888150221476 8542127269366 18517728470207 39637721522127 83830877210032 (3, 0) 1045372613250 2298097342376 4985601896438 10681128345834 22612030655065 47329791201172 (3, 1) 1744974248604 3888150221476 8542127269366 18517728470207 39637721522127 83830877210032 (3, 2) -2790315967012 -6186196247245 -13527644710919 -29198719029607 -62249529225577 -131160310462855 (4, 0) -2859819357278 -6261888485801 -13536586427726 -28908478350493 -61024772202627 -127404453154497 (4, 1) -41411149317 -122449590527 -330001681457 -837310381984 -2033581834403 -4773741138466 (4, 2) 2901135767232 6384182232214 13866333899978 29745377374656 63057693423040 132177141040207 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.120870361088 0.119868348913 0.118946773183 0.118097397883 0.117313028738 0.116587356405 (0, 1) -0.0604330519335 -0.0599325926542 -0.0594722051071 -0.059047812172 -0.0586558457268 -0.0582931718162 (0, 2) -0.0604330519335 -0.0599325926542 -0.0594722051071 -0.059047812172 -0.0586558457268 -0.0582931718162 (1, 0) -0.0952513041949 -0.0946802160319 -0.0941474059055 -0.0936497290376 -0.0931843481238 -0.0927486985609 (1, 1) 0.0966274197606 0.096529306503 0.0964408104711 0.0963608840799 0.0962886028694 0.0962231500348 (1, 2) -0.00137927102655 -0.00185144684553 -0.00229517259905 -0.0027124876461 -0.00310526349801 -0.00347521822744 (2, 0) 0.034817970068 0.034747401416 0.0346750259331 0.0346017788718 0.0345283933113 0.0344554403585 (2, 1) -0.0929363717667 -0.0935357437989 -0.0940852159696 -0.0945899708803 -0.0950545424838 -0.0954829112882 (2, 2) 0.0581194307056 0.0587891182937 0.059410777423 0.0599886383711 0.0605264896178 0.0610277315113 (3, 0) 0.034817970068 0.034747401416 0.0346750259331 0.0346017788718 0.0345283933113 0.0344554403585 (3, 1) 0.0581194307056 0.0587891182937 0.059410777423 0.0599886383711 0.0605264896178 0.0610277315113 (3, 2) -0.0929363717667 -0.0935357437989 -0.0940852159696 -0.0945899708803 -0.0950545424838 -0.0954829112882 (4, 0) -0.0952513041949 -0.0946802160319 -0.0941474059055 -0.0936497290376 -0.0931843481238 -0.0927486985609 (4, 1) -0.00137927102655 -0.00185144684553 -0.00229517259905 -0.0027124876461 -0.00310526349801 -0.00347521822744 (4, 2) 0.0966274197606 0.096529306503 0.0964408104711 0.0963608840799 0.0962886028694 0.0962231500348 Hodge numbers are 4, 0, and 20. Euler is 6 and Signature is -18. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3920511133755483660 12641965341150480869 40013387316985054552 124425192388764009121 380439447204200201696 1144645091393902190855 (0, 1) -3920410069105239288 -12641728918407934136 -40012841890155041832 -124423950617576356528 -380436655428480938720 -1144638889739282880792 (1, 0) -3920410069105239288 -12641728918407934136 -40012841890155041832 -124423950617576356528 -380436655428480938720 -1144638889739282880792 (1, 1) 3920309005787439246 12641492497954600898 40012296467223093338 124422708852970295092 380433863663784923624 1144632688102984552298 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250006444754 0.250004675432 0.250003407818 0.250002495037 0.250001834585 0.250001354499 (0, 1) -0.249999999979 -0.249999999989 -0.249999999994 -0.249999999997 -0.249999999998 -0.249999999999 (1, 0) -0.249999999979 -0.249999999989 -0.249999999994 -0.249999999997 -0.249999999998 -0.249999999999 (1, 1) 0.249993555288 0.249995324591 0.249996592195 0.249997504969 0.249998165419 0.249998645503 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 742617091984962438 2267651589329439647 6802153665417811012 20061008631386342723 58216028562681531626 166355137288030492989 (0, 1) -371258013667359033 -1133707583293446457 -3400804119293899146 -10029883430099345065 -29106618393481134325 -83174467816705591463 (0, 2) -371258013667359033 -1133707583293446457 -3400804119293899146 -10029883430099345065 -29106618393481134325 -83174467816705591463 (1, 0) -742586605386793506 -2267582598478420712 -6801999600792813580 -20060668905224543402 -58215288391456007936 -166353543045415136456 (1, 1) 371242771034496732 1133673089012543737 3400727088930432543 10029713570309240983 29106248313379996420 83173670704558403981 (1, 2) 371242771034496732 1133673089012543737 3400727088930432543 10029713570309240983 29106248313379996420 83173670704558403981 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250022145032 0.250016836417 0.250012854853 0.250009854667 0.250007583926 0.250005858003 (0, 1) -0.124994059441 -0.124995384975 -0.124996403857 -0.124997189561 -0.12499779735 -0.124998268941 (0, 2) -0.124994059441 -0.124995384975 -0.124996403857 -0.124997189561 -0.12499779735 -0.124998268941 (1, 0) -0.250011880894 -0.250009229924 -0.250007192214 -0.250005620837 -0.250004405276 -0.250003462104 (1, 1) 0.124988927596 0.124991581855 0.124993572609 0.124995072687 0.124996208049 0.124997071006 (1, 2) 0.124988927596 0.124991581855 0.124993572609 0.124995072687 0.124996208049 0.124997071006 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 30486598168932 68990851018935 154064624997432 339726161799321 740171225523690 1594242615356533 (1, 0) -15242632862301 -34494280902720 -77030363466603 -169859790104082 -370080101137905 -797112147187482 (2, 0) -15242632862301 -34494280902720 -77030363466603 -169859790104082 -370080101137905 -797112147187482 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.500010926715 0.500008295489 0.500006325452 0.500004843353 0.500003723236 0.500002873008 (1, 0) -0.249994536643 -0.249995852255 -0.249996837274 -0.249997578323 -0.249998138382 -0.249998563496 (2, 0) -0.249994536643 -0.249995852255 -0.249996837274 -0.249997578323 -0.249998138382 -0.249998563496 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 742617091984962438 2267651589329439647 6802153665417811012 20061008631386342723 58216028562681531626 166355137288030492989 (0, 1) -742586605386793506 -2267582598478420712 -6801999600792813580 -20060668905224543402 -58215288391456007936 -166353543045415136456 (1, 0) -371258013667359033 -1133707583293446457 -3400804119293899146 -10029883430099345065 -29106618393481134325 -83174467816705591463 (1, 1) 371242771034496732 1133673089012543737 3400727088930432543 10029713570309240983 29106248313379996420 83173670704558403981 (2, 0) -371258013667359033 -1133707583293446457 -3400804119293899146 -10029883430099345065 -29106618393481134325 -83174467816705591463 (2, 1) 371242771034496732 1133673089012543737 3400727088930432543 10029713570309240983 29106248313379996420 83173670704558403981 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250022145032 0.250016836417 0.250012854853 0.250009854667 0.250007583926 0.250005858003 (0, 1) -0.250011880894 -0.250009229924 -0.250007192214 -0.250005620837 -0.250004405276 -0.250003462104 (1, 0) -0.124994059441 -0.124995384975 -0.124996403857 -0.124997189561 -0.12499779735 -0.124998268941 (1, 1) 0.124988927596 0.124991581855 0.124993572609 0.124995072687 0.124996208049 0.124997071006 (2, 0) -0.124994059441 -0.124995384975 -0.124996403857 -0.124997189561 -0.12499779735 -0.124998268941 (2, 1) 0.124988927596 0.124991581855 0.124993572609 0.124995072687 0.124996208049 0.124997071006 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 304015583478884976 913744068040550505 2699976190587672702 7849757494776837445 22471889321197914156 63388569788563567473 (0, 1) -151992548440358022 -456837538594765785 -1349911062981337635 -3924708884307519062 -11235574574986195233 -31693487772974105470 (0, 2) -151992548440358022 -456837538594765785 -1349911062981337635 -3924708884307519062 -11235574574986195233 -31693487772974105470 (1, 0) -151992548440358022 -456837538594765785 -1349911062981337635 -3924708884307519062 -11235574574986195233 -31693487772974105470 (1, 1) 231347957256504189 704269956398010915 2106171626085832680 6193101037220169908 17919690251827747842 51060100945941544104 (1, 2) -79370651449008468 -247466912084147850 -756337593467961648 -2268562012702754928 -6684485756942690514 -19367410285114626116 (2, 0) -151992548440358022 -456837538594765785 -1349911062981337635 -3924708884307519062 -11235574574986195233 -31693487772974105470 (2, 1) -79370651449008468 -247466912084147850 -756337593467961648 -2268562012702754928 -6684485756942690514 -19367410285114626116 (2, 2) 231347957256504189 704269956398010915 2106171626085832680 6193101037220169908 17919690251827747842 51060100945941544104 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.198259439528 0.196733921439 0.195301751728 0.193955652787 0.192689075292 0.191496103646 (0, 1) -0.0991197790633 -0.0983595336724 -0.097645303761 -0.0969736293335 -0.0963413642834 -0.0957456437291 (0, 2) -0.0991197790633 -0.0983595336724 -0.097645303761 -0.0969736293335 -0.0963413642834 -0.0957456437291 (1, 0) -0.0991197790633 -0.0983595336724 -0.097645303761 -0.0969736293335 -0.0963413642834 -0.0957456437291 (1, 1) 0.150870280453 0.151633039404 0.152349124206 0.153022173647 0.153655462378 0.154251948191 (1, 2) -0.0517604416563 -0.053280932532 -0.0547093924076 -0.0560527412924 -0.0573172714096 -0.0585087125279 (2, 0) -0.0991197790633 -0.0983595336724 -0.097645303761 -0.0969736293335 -0.0963413642834 -0.0957456437291 (2, 1) -0.0517604416563 -0.053280932532 -0.0547093924076 -0.0560527412924 -0.0573172714096 -0.0585087125279 (2, 2) 0.150870280453 0.151633039404 0.152349124206 0.153022173647 0.153655462378 0.154251948191 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 48119826328980 111116233881285 253128377128852 569248874087829 1264522854033354 2776252467626435 (1, 0) -38271894523740 -88519160291715 -201941792179547 -454720978256337 -1011270583973766 -2222518218313789 (2, 0) 14212647581415 32962187957820 75379552647234 170099832008001 379014668581029 834401144991356 (3, 0) 14212647581415 32962187957820 75379552647234 170099832008001 379014668581029 834401144991356 (4, 0) -38271894523740 -88519160291715 -201941792179547 -454720978256337 -1011270583973766 -2222518218313789 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.314326009372 0.313817695286 0.313366481591 0.312964895783 0.312606593164 0.312286162984 (1, 0) -0.249997824068 -0.249998383684 -0.249998793574 -0.249999095384 -0.249999318727 -0.249999484792 (2, 0) 0.092839171246 0.0930927686728 0.0933179656304 0.0935184567248 0.0936973846906 0.0938574337159 (3, 0) 0.092839171246 0.0930927686728 0.0933179656304 0.0935184567248 0.0936973846906 0.0938574337159 (4, 0) -0.249997824068 -0.249998383684 -0.249998793574 -0.249999095384 -0.249999318727 -0.249999484792 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 1513402078818394732 4771572420202434465 14772173704074890314 44945285556162075253 134503008492144607614 396198224919315611715 (0, 1) -1513353958992065752 -4771461303968553180 -14771920575697761462 -44944716307287987424 -134501743969290574260 -396195448666847985280 (1, 0) -1212579724882279712 -3827600809243862241 -11861766813387356687 -36121871341865370693 -108180563495720716089 -318873361007469700269 (1, 1) 1212541452987755972 3827512290083570526 11861564871595177140 36121416620887114356 108179552225136742323 318871138489251386480 (2, 0) 455929217798204532 1441932810513918375 4475952674764917890 13649849449378159363 40930455137508043770 120777349375121549443 (2, 1) -455915005150623117 -1441899848325960555 -4475877295212270656 -13649679349546151362 -40930076122839462741 -120776514973976558087 (3, 0) 455929217798204532 1441932810513918375 4475952674764917890 13649849449378159363 40930455137508043770 120777349375121549443 (3, 1) -455915005150623117 -1441899848325960555 -4475877295212270656 -13649679349546151362 -40930076122839462741 -120776514973976558087 (4, 0) -1212579724882279712 -3827600809243862241 -11861766813387356687 -36121871341865370693 -108180563495720716089 -318873361007469700269 (4, 1) 1212541452987755972 3827512290083570526 11861564871595177140 36121416620887114356 108179552225136742323 318871138489251386480 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.156009786097 0.155827179706 0.155669575506 0.155533131698 0.155414666284 0.155311531051 (0, 1) -0.156004825642 -0.155823550938 -0.155666908032 -0.155531161813 -0.155413205162 -0.155310442747 (1, 0) -0.124999368081 -0.124999515174 -0.124999627108 -0.124999712497 -0.124999777794 -0.12499982785 (1, 1) 0.124995422804 0.124996624368 0.12499749904 0.124998138935 0.124998609298 0.124998956613 (2, 0) 0.0469996841816 0.0470897857981 0.047167713217 0.0472352952217 0.0472940575633 0.0473452778633 (2, 1) -0.0469982190639 -0.0470887093385 -0.0471669188652 -0.0472347065914 -0.0472936196219 -0.0473449507742 (3, 0) 0.0469996841816 0.0470897857981 0.047167713217 0.0472352952217 0.0472940575633 0.0473452778633 (3, 1) -0.0469982190639 -0.0470887093385 -0.0471669188652 -0.0472347065914 -0.0472936196219 -0.0473449507742 (4, 0) -0.124999368081 -0.124999515174 -0.124999627108 -0.124999712497 -0.124999777794 -0.12499982785 (4, 1) 0.124995422804 0.124996624368 0.12499749904 0.124998138935 0.124998609298 0.124998956613 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 418052055053353242 1272934171917067203 3809402936520225020 11213523199039650673 32493176130508695324 92749746649423254561 (0, 1) -209001967613512131 -636411527841592959 -1904574904071548084 -5606476975082781422 -16245955803827330985 -46373485198477814063 (0, 2) -209001967613512131 -636411527841592959 -1904574904071548084 -5606476975082781422 -16245955803827330985 -46373485198477814063 (1, 0) -332124639181723522 -1013150807590343407 -3036894868702546948 -8952395871910099712 -25974299345614356081 -74226324678677214673 (1, 1) 278129938548098625 855560996629396255 2585358889080712828 7681246393522446590 22455770418475383586 64643876311852593429 (1, 2) 53956428739101157 157501291800655437 451334037829654573 1270694757409396785 3517517656554998729 9580225848606307455 (2, 0) 123113854954131367 376718217057319273 1132270432754933154 3345804135471174036 9728081365972770264 27852248475273265659 (2, 1) -236005851405535061 -733864790942487646 -2239932838287650965 -6717210071211053881 -19808547696825583213 -57487098451678267504 (2, 2) 112906209098985109 357179536073126193 1107737785085365045 3371576035571887846 10080845345521393978 29635684377549993201 (3, 0) 123113854954131367 376718217057319273 1132270432754933154 3345804135471174036 9728081365972770264 27852248475273265659 (3, 1) 112906209098985109 357179536073126193 1107737785085365045 3371576035571887846 10080845345521393978 29635684377549993201 (3, 2) -236005851405535061 -733864790942487646 -2239932838287650965 -6717210071211053881 -19808547696825583213 -57487098451678267504 (4, 0) -332124639181723522 -1013150807590343407 -3036894868702546948 -8952395871910099712 -25974299345614356081 -74226324678677214673 (4, 1) 53956428739101157 157501291800655437 451334037829654573 1270694757409396785 3517517656554998729 9580225848606307455 (4, 2) 278129938548098625 855560996629396255 2585358889080712828 7681246393522446590 22455770418475383586 64643876311852593429 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.134485456907 0.133519308974 0.132613471989 0.131762073419 0.130960032429 0.130202926646 (0, 1) -0.0672349884883 -0.0667538269417 -0.0663023300239 -0.0658776922919 -0.065477467957 -0.065099514659 (0, 2) -0.0672349884883 -0.0667538269417 -0.0663023300239 -0.0658776922919 -0.065477467957 -0.065099514659 (1, 0) -0.106842995533 -0.106270378076 -0.105720812241 -0.105193186942 -0.104686444654 -0.104199580662 (1, 1) 0.0894731443443 0.0897406288362 0.0900018780714 0.090256820563 0.0905054159804 0.0907476536552 (1, 2) 0.0173575392929 0.0165204643788 0.0157119041437 0.0149310232785 0.014176952863 0.0134488070154 (2, 0) 0.0396051707795 0.0395143418482 0.0394167579066 0.0393141461715 0.0392079200273 0.0390992363447 (2, 1) -0.0759220158719 -0.0769757949221 -0.0779768577009 -0.0789291207469 -0.079836087378 -0.080700904673 (2, 2) 0.0363214172369 0.03746491051 0.0385627239179 0.0396169732966 0.040629694926 0.0416028396681 (3, 0) 0.0396051707795 0.0395143418482 0.0394167579066 0.0393141461715 0.0392079200273 0.0390992363447 (3, 1) 0.0363214172369 0.03746491051 0.0385627239179 0.0396169732966 0.040629694926 0.0416028396681 (3, 2) -0.0759220158719 -0.0769757949221 -0.0779768577009 -0.0789291207469 -0.079836087378 -0.080700904673 (4, 0) -0.106842995533 -0.106270378076 -0.105720812241 -0.105193186942 -0.104686444654 -0.104199580662 (4, 1) 0.0173575392929 0.0165204643788 0.0157119041437 0.0149310232785 0.014176952863 0.0134488070154 (4, 2) 0.0894731443443 0.0897406288362 0.0900018780714 0.090256820563 0.0905054159804 0.0907476536552 Hodge numbers are 8, 0, and 40. Euler is 10 and Signature is -38. l1 is 2, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 768346379737650928958016 3623598452350100268286896 16694895743560450296043664 75225213558153133761710273 331831562037523452043721616 1434339480192508090287341565 (0, 1) -768336772760447526222720 -3623567175190622383790208 -16694795795011577056489024 -75224899776822454507638688 -331830593446490248600175712 -1434336538143899285573089200 (1, 0) -768336772760447526222720 -3623567175190622383790208 -16694795795011577056489024 -75224899776822454507638688 -331830593446490248600175712 -1434336538143899285573089200 (1, 1) 768327165783603742260080 3623535898031860908746840 16694695846464115076309384 75224585995494525811090388 331829624855462351862913788 1434333596095300620541319050 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.2500031259 0.250002157898 0.250001496702 0.250001042811 0.250000729733 0.250000512789 (0, 1) -0.25 -0.25 -0.25 -0.25 -0.25 -0.25 (1, 0) -0.25 -0.25 -0.25 -0.25 -0.25 -0.25 (1, 1) 0.2499968741 0.249997842102 0.249998503298 0.249998957189 0.249999270267 0.249999487211 l1 is 2, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 134365903706242185477292 598211224596490286054664 2604108281751709157780754 11095830135555972812321561 46321069959772154778692592 189629278733408025964481863 (0, 1) -67178148364519391370998 -299089973718506200778988 -1302004166601417959113057 -5547758177112646779124988 -23160050684369475667573344 -94813168342399610625114749 (0, 2) -67178148364519391370998 -299089973718506200778988 -1302004166601417959113057 -5547758177112646779124988 -23160050684369475667573344 -94813168342399610625114749 (1, 0) -134364549711021186213250 -598207047186302953398710 -2604095618585948419794340 -11095792387736891757515906 -46320959222035140690846690 -189628958794369490630500710 (1, 1) 67177471367088701125305 299087885013770739177671 1301997835019243219807350 5547739303204481530483803 23159995315503621976792383 94813008372885412799365280 (1, 2) 67177471367088701125305 299087885013770739177671 1301997835019243219807350 5547739303204481530483803 23159995315503621976792383 94813008372885412799365280 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250010197359 0.250007408675 0.2500054056 0.250003960212 0.250002912663 0.250002150258 (0, 1) -0.124996160987 -0.124997168584 -0.124997905059 -0.124998445149 -0.124998842504 -0.12499913577 (0, 2) -0.124996160987 -0.124997168584 -0.124997905059 -0.124998445149 -0.124998842504 -0.12499913577 (1, 0) -0.250007678025 -0.250005662831 -0.250004189883 -0.250003109703 -0.250002314992 -0.250001728459 (1, 1) 0.12499490132 0.124996295663 0.1249972972 0.124998019894 0.124998543668 0.124998924871 (1, 2) 0.12499490132 0.124996295663 0.1249972972 0.124998019894 0.124998543668 0.124998924871 l1 is 3, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 1353995220999264042 4177410187332655954 12663165760737986414 37747819081054805655 110737737014087845902 319939038535333981153 (1, 0) -676997430690245693 -2088704735461601317 -6331582174739305707 -18873908165248641185 -55368865853690780961 -159969514197825749469 (2, 0) -676997430690245693 -2088704735461601317 -6331582174739305707 -18873908165248641185 -55368865853690780961 -159969514197825749469 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.5000000664 0.500000042874 0.500000027862 0.500000018217 0.50000001198 0.500000007923 (1, 0) -0.2499999668 -0.249999978563 -0.249999986069 -0.249999990892 -0.24999999401 -0.249999996038 (2, 0) -0.2499999668 -0.249999978563 -0.249999986069 -0.249999990892 -0.24999999401 -0.249999996038 l1 is 3, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 134365903706242185477292 598211224596490286054664 2604108281751709157780754 11095830135555972812321561 46321069959772154778692592 189629278733408025964481863 (0, 1) -134364549711021186213250 -598207047186302953398710 -2604095618585948419794340 -11095792387736891757515906 -46320959222035140690846690 -189628958794369490630500710 (1, 0) -67178148364519391370998 -299089973718506200778988 -1302004166601417959113057 -5547758177112646779124988 -23160050684369475667573344 -94813168342399610625114749 (1, 1) 67177471367088701125305 299087885013770739177671 1301997835019243219807350 5547739303204481530483803 23159995315503621976792383 94813008372885412799365280 (2, 0) -67178148364519391370998 -299089973718506200778988 -1302004166601417959113057 -5547758177112646779124988 -23160050684369475667573344 -94813168342399610625114749 (2, 1) 67177471367088701125305 299087885013770739177671 1301997835019243219807350 5547739303204481530483803 23159995315503621976792383 94813008372885412799365280 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.250010197359 0.250007408675 0.2500054056 0.250003960212 0.250002912663 0.250002150258 (0, 1) -0.250007678025 -0.250005662831 -0.250004189883 -0.250003109703 -0.250002314992 -0.250001728459 (1, 0) -0.124996160987 -0.124997168584 -0.124997905059 -0.124998445149 -0.124998842504 -0.12499913577 (1, 1) 0.12499490132 0.124996295663 0.1249972972 0.124998019894 0.124998543668 0.124998924871 (2, 0) -0.124996160987 -0.124997168584 -0.124997905059 -0.124998445149 -0.124998842504 -0.12499913577 (2, 1) 0.12499490132 0.124996295663 0.1249972972 0.124998019894 0.124998543668 0.124998924871 l1 is 3, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 30773001304486223575202 131620924991437114039148 551017930778456230479134 2260092112018196597996651 9090889126142863428134784 35890250972546329287417511 (0, 1) -15385823654632612155580 -65808373790624890691597 -275502633806347746246360 -1130027182099557771595498 -4545389194202924670144441 -17944965516753896976718179 (0, 2) -15385823654632612155580 -65808373790624890691597 -275502633806347746246360 -1130027182099557771595498 -4545389194202924670144441 -17944965516753896976718179 (1, 0) -15385823654632612155580 -65808373790624890691597 -275502633806347746246360 -1130027182099557771595498 -4545389194202924670144441 -17944965516753896976718179 (1, 1) 18106255579525831312961 78657460023606749760964 334244679982816238932095 1390759502371307943056876 5671750170652361744712792 22690443159910200587948040 (1, 2) -2721108922323909403074 -12851174937717320670684 -58748377758643231991442 -260751194179915420102563 -1126416345315290765349312 -4745637612670501436979330 (2, 0) -15385823654632612155580 -65808373790624890691597 -275502633806347746246360 -1130027182099557771595498 -4545389194202924670144441 -17944965516753896976718179 (2, 1) -2721108922323909403074 -12851174937717320670684 -58748377758643231991442 -260751194179915420102563 -1126416345315290765349312 -4745637612670501436979330 (2, 2) 18106255579525831312961 78657460023606749760964 334244679982816238932095 1390759502371307943056876 5671750170652361744712792 22690443159910200587948040 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.2296989317 0.227768425503 0.22591826017 0.224143836135 0.222440928334 0.220805640036 (0, 1) -0.114844412537 -0.113880598272 -0.112956534126 -0.112070046254 -0.111219109371 -0.110401835846 (0, 2) -0.114844412537 -0.113880598272 -0.112956534126 -0.112070046254 -0.111219109371 -0.110401835846 (1, 0) -0.114844412537 -0.113880598272 -0.112956534126 -0.112070046254 -0.111219109371 -0.110401835846 (1, 1) 0.13515053415 0.136115787249 0.137040869915 0.137928081933 0.138779535833 0.139597179982 (1, 2) -0.0203111749262 -0.0222388034548 -0.0240869317488 -0.025859907492 -0.0275617812587 -0.0291963283078 (2, 0) -0.114844412537 -0.113880598272 -0.112956534126 -0.112070046254 -0.111219109371 -0.110401835846 (2, 1) -0.0203111749262 -0.0222388034548 -0.0240869317488 -0.025859907492 -0.0275617812587 -0.0291963283078 (2, 2) 0.13515053415 0.136115787249 0.137040869915 0.137928081933 0.138779535833 0.139597179982 l1 is 5, l2 is 1 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 3447608549280894764 11009504759787437038 34521985960611340580 106385822601400499593 322465566380914470026 962097726086774221775 (1, 0) -2784156642319388782 -8893263345667095679 -27892496824924379070 -85972136794240934035 -260631292765098296836 -777715615936070906070 (2, 0) 1060352547488327728 3388511323978103820 10631504550248396280 32779226868819445881 99398512227994203813 296666757962525036290 (3, 0) 1060352547488327728 3388511323978103820 10631504550248396280 32779226868819445881 99398512227994203813 296666757962525036290 (4, 0) -2784156642319388782 -8893263345667095679 -27892496824924379070 -85972136794240934035 -260631292765098296836 -777715615936070906070 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.309573856725 0.309490006934 0.309420000481 0.309361339957 0.309312018252 0.309270414287 (1, 0) -0.249999991927 -0.249999994965 -0.249999996838 -0.249999998 -0.249999998727 -0.249999999185 (2, 0) 0.0952130797106 0.0952550015678 0.0952900029218 0.0953193320212 0.0953439921464 0.0953647936716 (3, 0) 0.0952130797106 0.0952550015678 0.0952900029218 0.0953193320212 0.0953439921464 0.0953647936716 (4, 0) -0.249999991927 -0.249999994965 -0.249999996838 -0.249999998 -0.249999998727 -0.249999999185 l1 is 5, l2 is 2 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 292882391605037978059344 1351111144814891578655324 6091442672324407382601744 26868447380598012293049639 116060697813657486933053264 491409243816621989176569751 (0, 1) -292878943996488697164580 -1351100135310131791218286 -6091408150338446771261164 -26868340994775410892550046 -116060375348091106018583238 -491408281718895902402347976 (1, 0) -235509528975886809311887 -1087384369998468116617867 -4906030259953289551626546 -21653192086230765652920720 -93582192218750815133877600 -396411354442373069140920754 (1, 1) 235506744819244489923105 1087375476735122449522188 4906002367456464627247476 21653106114093971411986685 93581931587458050035580764 396410576726757133070014684 (2, 0) 89073136661969521649863 411844436170761269538549 1860358898065522480102994 8219125286597099133431693 35552327607438673389123920 150708203558366476909762061 (2, 1) -89072076309422033322135 -411841047659437291434729 -1860348266560972231706714 -8219092507370230313985812 -35552228208926445394920107 -150707906891608514384725771 (3, 0) 89073136661969521649863 411844436170761269538549 1860358898065522480102994 8219125286597099133431693 35552327607438673389123920 150708203558366476909762061 (3, 1) -89072076309422033322135 -411841047659437291434729 -1860348266560972231706714 -8219092507370230313985812 -35552228208926445394920107 -150707906891608514384725771 (4, 0) -235509528975886809311887 -1087384369998468116617867 -4906030259953289551626546 -21653192086230765652920720 -93582192218750815133877600 -396411354442373069140920754 (4, 1) 235506744819244489923105 1087375476735122449522188 4906002367456464627247476 21653106114093971411986685 93581931587458050035580764 396410576726757133070014684 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.155450788579 0.155316164121 0.155202593568 0.155106480801 0.155024898926 0.154955454915 (0, 1) -0.15544895872 -0.15531489853 -0.155201713989 -0.155105866656 -0.155024468201 -0.154955151538 (1, 0) -0.124999464108 -0.124999612298 -0.124999718692 -0.1249997953 -0.124999850623 -0.12499989069 (1, 1) 0.124997986384 0.124998589978 0.124999008024 0.124999298999 0.124999502492 0.124999645454 (2, 0) 0.0472766193265 0.047343327961 0.0473996951918 0.0474474605999 0.047488048045 0.0475226270886 (2, 1) -0.0472760565319 -0.0473429384367 -0.0473994243139 -0.0474472713716 -0.0474879152762 -0.0475225335411 (3, 0) 0.0472766193265 0.047343327961 0.0473996951918 0.0474474605999 0.047488048045 0.0475226270886 (3, 1) -0.0472760565319 -0.0473429384367 -0.0473994243139 -0.0474472713716 -0.0474879152762 -0.0475225335411 (4, 0) -0.124999464108 -0.124999612298 -0.124999718692 -0.1249997953 -0.124999850623 -0.12499989069 (4, 1) 0.124997986384 0.124998589978 0.124999008024 0.124999298999 0.124999502492 0.124999645454 l1 is 5, l2 is 3 Exact values (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 58221902352250189827314 255710444577937196196020 1098677085502782175103010 4622665788482989455730905 19064411943254391059843728 77133020238142832973034843 (0, 1) -29109227371850454466275 -127849717536588704379491 -549321281758410781881215 -2311279701330194027615656 -9532044738844005072686851 -38566029070208373099406534 (0, 2) -29109227371850454466275 -127849717536588704379491 -549321281758410781881215 -2311279701330194027615656 -9532044738844005072686851 -38566029070208373099406534 (1, 0) -46763460730099884470731 -205580701449043766553970 -884010088113617818243750 -3722050775360705752557161 -15359363341317540000202051 -62174758864976930913154896 (1, 1) 32919568029602715938788 145923207315898808981566 632587028907077266881437 2684684201434475319792610 11165016058843390038090497 45541109842280322717243677 (1, 2) 13841108543854849143161 59648600869799290476725 251395166709715626983243 1037280601789436191830516 4194086651181384863814718 16632871307080672125005149 (2, 0) 17653186551585289189095 77727567865168834783937 334677876945107099685452 1410736755028751552094536 5827212738558851514203138 23608408715424782093628051 (2, 1) -23989470175268941626701 -107600861361995572312921 -471678062236685869666850 -2022969971443107575805670 -8497421509210408867011449 -34990050394843659571539605 (2, 2) 6337343976231140765334 29876682008150715632804 137010816796129018377678 612265995641224843157015 2670308169163785347012124 11381938346176840002947844 (3, 0) 17653186551585289189095 77727567865168834783937 334677876945107099685452 1410736755028751552094536 5827212738558851514203138 23608408715424782093628051 (3, 1) 6337343976231140765334 29876682008150715632804 137010816796129018377678 612265995641224843157015 2670308169163785347012124 11381938346176840002947844 (3, 2) -23989470175268941626701 -107600861361995572312921 -471678062236685869666850 -2022969971443107575805670 -8497421509210408867011449 -34990050394843659571539605 (4, 0) -46763460730099884470731 -205580701449043766553970 -884010088113617818243750 -3722050775360705752557161 -15359363341317540000202051 -62174758864976930913154896 (4, 1) 13841108543854849143161 59648600869799290476725 251395166709715626983243 1037280601789436191830516 4194086651181384863814718 16632871307080672125005149 (4, 2) 32919568029602715938788 145923207315898808981566 632587028907077266881437 2684684201434475319792610 11165016058843390038090497 45541109842280322717243677 Proportions (r1,r2) n=25 n=26 n=27 n=28 n=29 n=30 (0, 0) 0.145755668004 0.144950288093 0.144182630672 0.143448777086 0.142745434459 0.142069814766 (0, 1) -0.072873518543 -0.07247202366 -0.0720890501248 -0.071722737881 -0.0713715099936 -0.0710340213483 (0, 2) -0.072873518543 -0.07247202366 -0.0720890501248 -0.071722737881 -0.0713715099936 -0.0710340213483 (1, 0) -0.117070023162 -0.11653408194 -0.116011248188 -0.115501240282 -0.115003756722 -0.114518483106 (1, 1) 0.0824125189098 0.0827170394812 0.083016259427 0.0833100819265 0.083598438431 0.0838812874115 (1, 2) 0.034650534253 0.0338120012841 0.0329913283463 0.0321884905009 0.0314033668053 0.030635763235 (2, 0) 0.04419388399 0.0440601218829 0.0439207637642 0.0437774374265 0.0436314540688 0.0434838703678 (2, 1) -0.0600564582949 -0.0609938943997 -0.0618997016874 -0.0627760218374 -0.0636247332844 -0.0644474955459 (2, 2) 0.0158652288453 0.0169356933054 0.0179803331268 0.0189996016032 0.0199940234654 0.0209641716028 (3, 0) 0.04419388399 0.0440601218829 0.0439207637642 0.0437774374265 0.0436314540688 0.0434838703678 (3, 1) 0.0158652288453 0.0169356933054 0.0179803331268 0.0189996016032 0.0199940234654 0.0209641716028 (3, 2) -0.0600564582949 -0.0609938943997 -0.0618997016874 -0.0627760218374 -0.0636247332844 -0.0644474955459 (4, 0) -0.117070023162 -0.11653408194 -0.116011248188 -0.115501240282 -0.115003756722 -0.114518483106 (4, 1) 0.034650534253 0.0338120012841 0.0329913283463 0.0321884905009 0.0314033668053 0.030635763235 (4, 2) 0.0824125189098 0.0827170394812 0.083016259427 0.0833100819265 0.083598438431 0.0838812874115

Output too long: 150676 -- MAX_OUTPUT (=150000) exceeded (type 'smc?' to learn how to raise this limit): attempting to terminate...

Cstatistic(2,4,2,4,3,7,0,8,2)

Hodge numbers are 0, 8, and 2. Euler is 20 and other is 9. l1 is 2, l2 is 2 Exact values (r1,r2) n=3 n=4 n=5 n=6 n=7 (0, 0) 676 8003 37494 232988 1057868 (0, 1) 0 0 0 0 0 (1, 0) 0 0 0 0 0 (1, 1) 1284 5682 45030 210882 1117932 Proportions (r1,r2) n=3 n=4 n=5 n=6 n=7 (0, 0) 0.344897959184 0.584800876872 0.454340555475 0.524901435105 0.486197260778 (0, 1) 0.0 0.0 0.0 0.0 0.0 (1, 0) 0.0 0.0 0.0 0.0 0.0 (1, 1) 0.655102040816 0.415199123128 0.545659444525 0.475098564895 0.513802739222 l1 is 2, l2 is 3 Exact values (r1,r2) n=3 n=4 n=5 n=6 n=7 (0, 0) 334 3017 13806 81410 362384 (0, 1) 171 2493 11844 75789 347742 (0, 2) 171 2493 11844 75789 347742 (1, 0) 330 1470 13800 66648 362364 (1, 1) 477 2106 15615 72117 377784 (1, 2) 477 2106 15615 72117 377784 Proportions (r1,r2) n=3 n=4 n=5 n=6 n=7 (0, 0) 0.170408163265 0.220460358056 0.167296786389 0.183409556852 0.166552072801 (0, 1) 0.0872448979592 0.182170259408 0.143521884543 0.170745939126 0.159822593988 (0, 2) 0.0872448979592 0.182170259408 0.143521884543 0.170745939126 0.159822593988 (1, 0) 0.168367346939 0.107416879795 0.167224080268 0.150152071552 0.166542880779 (1, 1) 0.243367346939 0.153891121666 0.189217682129 0.162473246671 0.173629929221 (1, 2) 0.243367346939 0.153891121666 0.189217682129 0.162473246671 0.173629929221 l1 is 3, l2 is 2 Exact values (r1,r2) n=3 n=4 n=5 n=6 n=7 (0, 0) 334 3017 13806 81410 362384 (0, 1) 330 1470 13800 66648 362364 (1, 0) 171 2493 11844 75789 347742 (1, 1) 477 2106 15615 72117 377784 (2, 0) 171 2493 11844 75789 347742 (2, 1) 477 2106 15615 72117 377784 Proportions (r1,r2) n=3 n=4 n=5 n=6 n=7 (0, 0) 0.170408163265 0.220460358056 0.167296786389 0.183409556852 0.166552072801 (0, 1) 0.168367346939 0.107416879795 0.167224080268 0.150152071552 0.166542880779 (1, 0) 0.0872448979592 0.182170259408 0.143521884543 0.170745939126 0.159822593988 (1, 1) 0.243367346939 0.153891121666 0.189217682129 0.162473246671 0.173629929221 (2, 0) 0.0872448979592 0.182170259408 0.143521884543 0.170745939126 0.159822593988 (2, 1) 0.243367346939 0.153891121666 0.189217682129 0.162473246671 0.173629929221 l1 is 3, l2 is 3 Exact values (r1,r2) n=3 n=4 n=5 n=6 n=7 (0, 0) 512 3223 18746 95490 445900 (0, 1) 76 632 4430 26284 139424 (0, 2) 76 632 4430 26284 139424 (1, 0) 76 632 4430 26284 139424 (1, 1) 76 657 4385 26266 139614 (1, 2) 496 3310 18644 95356 446488 (2, 0) 76 632 4430 26284 139424 (2, 1) 496 3310 18644 95356 446488 (2, 2) 76 657 4385 26266 139614 Proportions (r1,r2) n=3 n=4 n=5 n=6 n=7 (0, 0) 0.261224489796 0.235513335769 0.22715816005 0.215130556244 0.204936115452 (0, 1) 0.0387755102041 0.0461819510413 0.0536813533033 0.0592155360804 0.0640794190643 (0, 2) 0.0387755102041 0.0461819510413 0.0536813533033 0.0592155360804 0.0640794190643 (1, 0) 0.0387755102041 0.0461819510413 0.0536813533033 0.0592155360804 0.0640794190643 (1, 1) 0.0387755102041 0.0480087687249 0.0531360573894 0.0591749836664 0.0641667432668 (1, 2) 0.25306122449 0.241870661308 0.225922155979 0.214828666051 0.205206360879 (2, 0) 0.0387755102041 0.0461819510413 0.0536813533033 0.0592155360804 0.0640794190643 (2, 1) 0.25306122449 0.241870661308 0.225922155979 0.214828666051 0.205206360879 (2, 2) 0.0387755102041 0.0480087687249 0.0531360573894 0.0591749836664 0.0641667432668

(r1,r2) n=0 n=1 n=2 n=3 n=4 n=5 n=6 n=7 (0, 0) 0 2 24 104 456 1782 6402 21336 (0, 1) 0 -3 -12 -75 -342 -1362 -4977 -16839 (0, 2) 0 0 3 23 106 479 1781 6171 (0, 3) 0 0 3 23 106 479 1781 6171 (0, 4) 0 -3 -12 -75 -342 -1362 -4977 -16839 (1, 0) 0 -3 -12 -75 -342 -1362 -4977 -16839 (1, 1) 0 1 12 63 293 1243 4653 16101 (1, 2) 0 0 -3 -24 -141 -621 -2505 -9089 (1, 3) 0 0 0 -6 -31 -100 -289 -649 (1, 4) 0 0 9 42 205 852 3129 10476 (2, 0) 0 0 3 23 106 479 1781 6171 (2, 1) 0 0 -3 -24 -141 -621 -2505 -9089 (2, 2) 0 0 1 13 94 488 2131 8191 (2, 3) 0 0 0 -6 -39 -234 -1106 -4624 (2, 4) 0 0 0 -6 -31 -100 -289 -649 (3, 0) 0 0 3 23 106 479 1781 6171 (3, 1) 0 0 0 -6 -31 -100 -289 -649 (3, 2) 0 0 0 -6 -39 -234 -1106 -4624 (3, 3) 0 0 1 13 94 488 2131 8191 (3, 4) 0 0 -3 -24 -141 -621 -2505 -9089 (4, 0) 0 -3 -12 -75 -342 -1362 -4977 -16839 (4, 1) 0 0 9 42 205 852 3129 10476 (4, 2) 0 0 0 -6 -31 -100 -289 -649 (4, 3) 0 0 -3 -24 -141 -621 -2505 -9089 (4, 4) 0 1 12 63 293 1243 4653 16101

q^-1 + 24 + 324*q + 3200*q^2 + 25650*q^3 + 176256*q^4 + 1073720*q^5 + 5930496*q^6 + 30178575*q^7 + O(q^8)

#Produces tables that indicase distributions of gamma_S(r1,l1,r2,l2,n) for varying r1 and r2
#first prime ranges from l1start to l1stop, second prime ranges from l2start to l2stop
#lists n from N0 to N in table. probably limit range to 10 for the sake of visualization
#For N greater than 20, this will take more than a few minutes. for N around 30, this might take around 15 minutes. 
# seems that l_1 = l_2
def Cstatistic(l1start,l1stop,N0,N,h10,h20,h11):
    print "Hodge numbers are {}, {}, and {}. Euler is {} and other is {}.".format(h10,h20,h11,2-4*h10+2*h20+h11, 1-2*h10+h20)

    def generatingFunctionWithPrecision(M):

        def numerator(NN):
            return prod(((1-x*q^n)*(1-x^(-1)*q^n)*(1-y*q^n)*(1-y^(-1)*q^n))^h10 for n in range (1,NN))

        def Denominator1(NN):
            return prod((sum((x*y*q^n)^k for k in range(0,NN))) for n in range(1,NN))
    
        def Denominator2(NN):
            return prod((sum((x^(-1)*y^(-1)*q^n)^k for k in range(0,NN))) for n in range(1,NN))

        def Denominator3(NN):
            if h20 == 0:
                return 1
            else:
                return prod((sum(binomial(k,h20-1)*(x^(-1)*y*q^n)^(k-h20+1) for k in range(h20-1,NN+h20-1))) for n in range(1,NN))
    
        def Denominator4(NN):
            if h20 == 0:
                return 1
            else:
                return prod((sum(binomial(k,h20-1)*(x*y^(-1)*q^n)^(k-h20+1) for k in range(h20-1,NN+h20-1))) for n in range(1,NN))

        def Denominator5(NN):
            if h11 == 0:
                return 1
            else:
                return prod((sum(binomial(k,h11-1)*(q^n)^(k-h11+1) for k in range(h11-1,NN+h11-1))) for n in range(1,NN))

        def genFxnHelper(NN):
            return numerator(NN) * Denominator1(NN) * Denominator2(NN) * Denominator3(NN) * Denominator4(NN) * Denominator5(NN)
    
        def genFxnUpTo(NN):
            return taylor(genFxnHelper(NN),q,0,NN)
        
        


        theFxn = genFxnUpTo(M+1)

        lstOfDumbCoeffs = [(k,theFxn.coefficient(q^k)) for k in range(1,M+1)]
        return lstOfDumbCoeffs
    
    theFxn = generatingFunctionWithPrecision(2*N)
    
    def Cfunction(r1,l1,r2,l2):

        def ComputeMatrix(m,theFxn1):
            #print "m={}".format(m)
            #print len(theFxn1)

            scaledFxn = x^m*y^m*theFxn1[m-1][1]
            #print "scaledFxn is {}".format(scaledFxn)

            # creates 2m+1 x 2m+1 list of zeros
            matrix = []
            for i in range(0,2*m+1):
                matrix.append([])
                for j in range(0,2*m+1):
                    matrix[i].append(0)

            # top left quadrant
            for i in range(0,m+1):
                for j in range(0,m+1):
                    matrix[i][j] = scaledFxn.coefficient(x^(i+m)*y^(j+m)).coefficient(x,0).coefficient(y,0)

            # top right quadrant
            for i in range(0,m+1):
                for j in range(m+1,2*m+1):
                    matrix[i][j] = scaledFxn.coefficient(x^(i+m)*y^(j-(m+1))).coefficient(x,0).coefficient(y,0)

            # bottom left quadrant
            for i in range(m+1,2*m+1):
                for j in range(0,m+1):
                    matrix[i][j] = scaledFxn.coefficient(x^(i-m-1)*y^(j+m)).coefficient(x,0).coefficient(y,0)

            # bottom right quadrant
            for i in range(m+1,2*m+1):
                for j in range(m+1,2*m+1):
                    matrix[i][j] = scaledFxn.coefficient(x,(i-m-1)).coefficient(y,(j-m-1))
    
            return matrix

        def natefunction(m):

            matrix = ComputeMatrix(m,theFxn)

            sum = 0
        
        
            for n in range(-m,m+1):
                if (n % l1) == r1:
                    for t in range(-m,m+1):
                        if (t % l2) == r2:
                            #print "about to input ({},{})".format(n,t)
                            #print "matrix size is {}".format(len(matrix))
                            sum = sum + matrix[n][t]
                        
        

            return sum
    
        lst = []
        for n in range(0,N+1):
            lst.append(natefunction(n))
        return lst
    
    for l1 in range(l1start,l1stop):
        if l1 in [1,Primes()]:
            print "l1 is {}".format(l1)
            
    
            header= ["(r1,r2)"]
    
            for n in range(N0,N+1):
                header.append("n={}".format(n))
            
            rows = [header]
    

            for a in range(0,l1):
                for b in range(0,l1):
                    lst = [(a,b)]
                    for n in range(N0,N+1):
                        lst.append(Cfunction(a,l1,b,l1)[n])
                    rows.append(lst)
                
    
            #return table(rows)

            print
            
            print "Exact values"
            
            print table(rows)
            
            print
    
            #stats = rows
   
            total = []
    
            for a in range(0,N+1-N0):
                colsum = 0
                for t in range(1,l1*l1+1):
                    colsum = colsum + rows[t][a+1]
                total.append(colsum)
    
            for a in range(0,N+1-N0):
                #total = 0
                #for t in range(1,l1*l2+1):
                    #total = total + rows[t][a+1]
                #print total
                for b in range(0,l1*l1):
                    if total[a] == 0:
                        rows[b+1][a+1] = "N/A"
                    else:
                        rows[b+1][a+1] = float(rows[b+1][a+1] / total[a])
    
            print "Proportions"
        
            print table(rows)
   

Cstatistic(2,6,3,10,0,8,2)

Hodge numbers are 0, 8, and 2. Euler is 20 and other is 9. l1 is 2 Exact values (r1,r2) n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 (0, 0) 676 8003 37494 232988 1057868 5011454 20769234 84432304 (0, 1) 0 0 0 0 0 0 0 0 (1, 0) 0 0 0 0 0 0 0 0 (1, 1) 1284 5682 45030 210882 1117932 4858536 21138146 83580520 Proportions (r1,r2) n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 (0, 0) 0.344897959184 0.584800876872 0.454340555475 0.524901435105 0.486197260778 0.507746613725 0.495598484086 0.502534877933 (0, 1) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (1, 0) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 (1, 1) 0.655102040816 0.415199123128 0.545659444525 0.475098564895 0.513802739222 0.492253386275 0.504401515914 0.497465122067 l1 is 3 Exact values (r1,r2) n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 (0, 0) 512 3223 18746 95490 445900 1940758 7926104 30666624 (0, 1) 76 632 4430 26284 139424 674918 3021783 12667504 (0, 2) 76 632 4430 26284 139424 674918 3021783 12667504 (1, 0) 76 632 4430 26284 139424 674918 3021783 12667504 (1, 1) 76 657 4385 26266 139614 674641 3021666 12668522 (1, 2) 496 3310 18644 95356 446488 1940139 7925406 30669570 (2, 0) 76 632 4430 26284 139424 674918 3021783 12667504 (2, 1) 496 3310 18644 95356 446488 1940139 7925406 30669570 (2, 2) 76 657 4385 26266 139614 674641 3021666 12668522 Proportions (r1,r2) n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 (0, 0) 0.261224489796 0.235513335769 0.22715816005 0.215130556244 0.204936115452 0.196632215433 0.189133847069 0.182525495792 (0, 1) 0.0387755102041 0.0461819510413 0.0536813533033 0.0592155360804 0.0640794190643 0.0683808190282 0.0721062256815 0.0753960542917 (0, 2) 0.0387755102041 0.0461819510413 0.0536813533033 0.0592155360804 0.0640794190643 0.0683808190282 0.0721062256815 0.0753960542917 (1, 0) 0.0387755102041 0.0461819510413 0.0536813533033 0.0592155360804 0.0640794190643 0.0683808190282 0.0721062256815 0.0753960542917 (1, 1) 0.0387755102041 0.0480087687249 0.0531360573894 0.0591749836664 0.0641667432668 0.0683527541568 0.0721034338105 0.075402113353 (1, 2) 0.25306122449 0.241870661308 0.225922155979 0.214828666051 0.205206360879 0.19656950007 0.189117191292 0.182543030168 (2, 0) 0.0387755102041 0.0461819510413 0.0536813533033 0.0592155360804 0.0640794190643 0.0683808190282 0.0721062256815 0.0753960542917 (2, 1) 0.25306122449 0.241870661308 0.225922155979 0.214828666051 0.205206360879 0.19656950007 0.189117191292 0.182543030168 (2, 2) 0.0387755102041 0.0480087687249 0.0531360573894 0.0591749836664 0.0641667432668 0.0683527541568 0.0721034338105 0.075402113353 l1 is 5 Exact values (r1,r2) n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 (0, 0) 270 2161 11160 57178 264154 1139480 4619930 17741540 (0, 1) 0 36 328 2552 15652 84684 413672 1864059 (0, 2) 32 392 2282 13590 70126 333234 1468596 6068560 (0, 3) 32 392 2282 13590 70126 333234 1468596 6068560 (0, 4) 0 36 328 2552 15652 84684 413672 1864059 (1, 0) 0 36 328 2552 15652 84684 413672 1864059 (1, 1) 73 343 2503 13659 70760 334495 1471055 6074478 (1, 2) 36 292 2224 13136 69324 331284 1464143 6059625 (1, 3) 8 40 432 2706 16264 85982 416862 1871036 (1, 4) 360 1890 11316 56576 263540 1138068 4616236 17735160 (2, 0) 32 392 2282 13590 70126 333234 1468596 6068560 (2, 1) 36 292 2224 13136 69324 331284 1464143 6059625 (2, 2) 4 77 419 2919 16503 86913 418754 1875386 (2, 3) 256 1932 10912 56224 262288 1135411 4611134 17724058 (2, 4) 8 40 432 2706 16264 85982 416862 1871036 (3, 0) 32 392 2282 13590 70126 333234 1468596 6068560 (3, 1) 8 40 432 2706 16264 85982 416862 1871036 (3, 2) 256 1932 10912 56224 262288 1135411 4611134 17724058 (3, 3) 4 77 419 2919 16503 86913 418754 1875386 (3, 4) 36 292 2224 13136 69324 331284 1464143 6059625 (4, 0) 0 36 328 2552 15652 84684 413672 1864059 (4, 1) 360 1890 11316 56576 263540 1138068 4616236 17735160 (4, 2) 8 40 432 2706 16264 85982 416862 1871036 (4, 3) 36 292 2224 13136 69324 331284 1464143 6059625 (4, 4) 73 343 2503 13659 70760 334495 1471055 6074478 Proportions (r1,r2) n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 (0, 0) 0.137755102041 0.15791012057 0.135233386651 0.128816995967 0.121405460061 0.115448951823 0.110241441961 0.105596344241 (0, 1) 0.0 0.00263061746438 0.0039746013281 0.00574943113975 0.00719367588933 0.00857994790268 0.00987110146232 0.011094742387 (0, 2) 0.0163265306122 0.0286445012788 0.027652561679 0.0306170725663 0.0322299843736 0.0337623442374 0.0350438514648 0.0361196238211 (0, 3) 0.0163265306122 0.0286445012788 0.027652561679 0.0306170725663 0.0322299843736 0.0337623442374 0.0350438514648 0.0361196238211 (0, 4) 0.0 0.00263061746438 0.0039746013281 0.00574943113975 0.00719367588933 0.00857994790268 0.00987110146232 0.011094742387 (1, 0) 0.0 0.00263061746438 0.0039746013281 0.00574943113975 0.00719367588933 0.00857994790268 0.00987110146232 0.011094742387 (1, 1) 0.0372448979592 0.0250639386189 0.0303305705007 0.0307725234866 0.0325213714496 0.0338901052585 0.0351025284807 0.0361548473228 (1, 2) 0.0183673469388 0.0213372305444 0.0269497358344 0.0295942505689 0.0318613843184 0.0335647756482 0.0349375933308 0.0360664433567 (1, 3) 0.00408163265306 0.00292290829375 0.00523484077359 0.00609637957059 0.00747495174189 0.00871145766105 0.00994722170653 0.0111362689791 (1, 4) 0.183673469388 0.13810741688 0.137123745819 0.12746074301 0.121123265006 0.115305891901 0.110153295195 0.105558370949 (2, 0) 0.0163265306122 0.0286445012788 0.027652561679 0.0306170725663 0.0322299843736 0.0337623442374 0.0350438514648 0.0361196238211 (2, 1) 0.0183673469388 0.0213372305444 0.0269497358344 0.0295942505689 0.0318613843184 0.0335647756482 0.0349375933308 0.0360664433567 (2, 2) 0.00204081632653 0.00562659846547 0.00507731084291 0.00657624980287 0.00758479639673 0.00880578399775 0.00999236888586 0.0111621598599 (2, 3) 0.130612244898 0.141176470588 0.132228200281 0.126667718026 0.120547844471 0.115036692033 0.110031550529 0.10549229266 (2, 4) 0.00408163265306 0.00292290829375 0.00523484077359 0.00609637957059 0.00747495174189 0.00871145766105 0.00994722170653 0.0111362689791 (3, 0) 0.0163265306122 0.0286445012788 0.027652561679 0.0306170725663 0.0322299843736 0.0337623442374 0.0350438514648 0.0361196238211 (3, 1) 0.00408163265306 0.00292290829375 0.00523484077359 0.00609637957059 0.00747495174189 0.00871145766105 0.00994722170653 0.0111362689791 (3, 2) 0.130612244898 0.141176470588 0.132228200281 0.126667718026 0.120547844471 0.115036692033 0.110031550529 0.10549229266 (3, 3) 0.00204081632653 0.00562659846547 0.00507731084291 0.00657624980287 0.00758479639673 0.00880578399775 0.00999236888586 0.0111621598599 (3, 4) 0.0183673469388 0.0213372305444 0.0269497358344 0.0295942505689 0.0318613843184 0.0335647756482 0.0349375933308 0.0360664433567 (4, 0) 0.0 0.00263061746438 0.0039746013281 0.00574943113975 0.00719367588933 0.00857994790268 0.00987110146232 0.011094742387 (4, 1) 0.183673469388 0.13810741688 0.137123745819 0.12746074301 0.121123265006 0.115305891901 0.110153295195 0.105558370949 (4, 2) 0.00408163265306 0.00292290829375 0.00523484077359 0.00609637957059 0.00747495174189 0.00871145766105 0.00994722170653 0.0111362689791 (4, 3) 0.0183673469388 0.0213372305444 0.0269497358344 0.0295942505689 0.0318613843184 0.0335647756482 0.0349375933308 0.0360664433567 (4, 4) 0.0372448979592 0.0250639386189 0.0303305705007 0.0307725234866 0.0325213714496 0.0338901052585 0.0351025284807 0.0361548473228

 1 in [1,0]

True

[1,Primes(4)]    

[1, Set of all prime numbers: 2, 3, 5, 7, ...]

2 in Primes(4)

True

def OnePrimes(n):
    lst = [1]
    for i in range(2,n+1):
        if i in Primes():
            lst.append(i)
    return lst

OnePrimes(10)

[1, 2, 3, 5, 7]

  2 in OnePrimes(10)  

True

Cnormstatistic(2,5,2,5,28,30,0,0,1)

Hodge numbers are 0, 0, and 1. Euler is 3 and Signature is 1. l1 is 2, l2 is 2 Exact values (r1,r2) n=28 n=29 n=30 (0, 0) 4056034 5850570 8395576 (0, 1) 0 0 0 (1, 0) 0 0 0 (1, 1) 4055312 5851428 8394560 Proportions (r1,r2) n=28 n=29 n=30 (0, 0) 0.50004450556 0.499963339594 0.50003025586 (0, 1) 0.0 0.0 0.0 (1, 0) 0.0 0.0 0.0 (1, 1) 0.49995549444 0.500036660406 0.49996974414 l1 is 2, l2 is 3 Exact values (r1,r2) n=28 n=29 n=30 (0, 0) 1363554 1964922 2817274 (0, 1) 1346240 1942824 2789151 (0, 2) 1346240 1942824 2789151 (1, 0) 1340228 1935744 2779466 (1, 1) 1357542 1957842 2807547 (1, 2) 1357542 1957842 2807547 Proportions (r1,r2) n=28 n=29 n=30 (0, 0) 0.168104529137 0.167913376844 0.167793399648 (0, 1) 0.165969988212 0.166024981375 0.166118428106 (0, 2) 0.165969988212 0.166024981375 0.166118428106 (1, 0) 0.165228804196 0.165419956489 0.165541601331 (1, 1) 0.167363345122 0.167308351958 0.167214071405 (1, 2) 0.167363345122 0.167308351958 0.167214071405 l1 is 3, l2 is 2 Exact values (r1,r2) n=28 n=29 n=30 (0, 0) 1363554 1964922 2817274 (0, 1) 1340228 1935744 2779466 (1, 0) 1346240 1942824 2789151 (1, 1) 1357542 1957842 2807547 (2, 0) 1346240 1942824 2789151 (2, 1) 1357542 1957842 2807547 Proportions (r1,r2) n=28 n=29 n=30 (0, 0) 0.168104529137 0.167913376844 0.167793399648 (0, 1) 0.165228804196 0.165419956489 0.165541601331 (1, 0) 0.165969988212 0.166024981375 0.166118428106 (1, 1) 0.167363345122 0.167308351958 0.167214071405 (2, 0) 0.165969988212 0.166024981375 0.166118428106 (2, 1) 0.167363345122 0.167308351958 0.167214071405 l1 is 3, l2 is 3 Exact values (r1,r2) n=28 n=29 n=30 (0, 0) 2703782 3900666 5596740 (0, 1) 0 0 0 (0, 2) 0 0 0 (1, 0) 0 0 0 (1, 1) 2703782 3900666 5596698 (1, 2) 0 0 0 (2, 0) 0 0 0 (2, 1) 0 0 0 (2, 2) 2703782 3900666 5596698 Proportions (r1,r2) n=28 n=29 n=30 (0, 0) 0.333333333333 0.333333333333 0.333335000979 (0, 1) 0.0 0.0 0.0 (0, 2) 0.0 0.0 0.0 (1, 0) 0.0 0.0 0.0 (1, 1) 0.333333333333 0.333333333333 0.33333249951 (1, 2) 0.0 0.0 0.0 (2, 0) 0.0 0.0 0.0 (2, 1) 0.0 0.0 0.0 (2, 2) 0.333333333333 0.333333333333 0.33333249951