# Identifications: Klein Bottle Horizontal Glued
# Comparison of Eigenfunctions on Level 2 to Eigenfunctions on Level 1
# Looking at K = 20 eigenvalues to either side of the closest level-1 eigenvalue.

# Dot value closer to zero means closer comparison.

# Eigenvalue Index, Dot Value
# 0, 2.220446049250313e-16
# 1, 0.0
# 2, 0.007208422818863691
# 3, 2.220446049250313e-16
# 4, 2.220446049250313e-16
# 5, 0.0006505301638103367
# 6, 0.08916117818499358
# 7, 2.220446049250313e-16
# 8, 0.0
# 9, 1.1102230246251565e-16
# 10, 0.0
# 11, 0.11312368070720147
# 12, 0.0
# 13, 2
# 14, 0.0017108198585333856
# 15, 0.0
# 16, 0.011440672902887083
# 17, 2.220446049250313e-16
# 18, 0.0
# 19, 0.008815596088504352
# 20, 0.007550097877229822
# 21, 2.220446049250313e-16
# 22, 0.2602622797711073
# 23, 0.0
# 24, 2
# 25, 0.0
# 26, 0.021125970899166124
# 27, 0.19617600407097247
# 28, 0.0
# 29, 0.02873650859488841
# 30, 0.021663047229855348
# 31, 0.08754815732229282
# 32, 0.11467013435711004
# 33, 2
# 34, 2
# 35, 2.220446049250313e-16
# 36, 0.0
# 37, 2
# 38, 0.26332463973073117
# 39, 2.220446049250313e-16
# 40, 0.0
# 41, 0.009074624468260462
# 42, 0.11919793065129702
# 43, 2.220446049250313e-16
# 44, 0.09516721095526859
# 45, 1.1102230246251565e-16
# 46, 0.0
# 47, 2.220446049250313e-16
# 48, 0.008885431644714115
# 49, 0.1407250439999469
# 50, 2.220446049250313e-16
# 51, 0.25778074451684296
# 52, 0.0
# 53, 0.18510190067000099
# 54, 0.0
# 55, 2
# 56, 0.0
# 57, 0.0015552241298304459
# 58, 0.0006700670542103548
# 59, 0.27530814227198264
# 60, 0.025723692140125265
# 61, 2.220446049250313e-16
# 62, 0.008519342893785309
# 63, 2

dots = [2.220446049250313e-16, 0.0, 0.007208422818863691, 2.220446049250313e-16, 2.220446049250313e-16, 0.0006505301638103367, 0.08916117818499358, 2.220446049250313e-16, 0.0, 1.1102230246251565e-16, 0.0, 0.11312368070720147, 0.0, 2, 0.0017108198585333856, 0.0, 0.011440672902887083, 2.220446049250313e-16, 0.0, 0.008815596088504352, 0.007550097877229822, 2.220446049250313e-16, 0.2602622797711073, 0.0, 2, 0.0, 0.021125970899166124, 0.19617600407097247, 0.0, 0.02873650859488841, 0.021663047229855348, 0.08754815732229282, 0.11467013435711004, 2, 2, 2.220446049250313e-16, 0.0, 2, 0.26332463973073117, 2.220446049250313e-16, 0.0, 0.009074624468260462, 0.11919793065129702, 2.220446049250313e-16, 0.09516721095526859, 1.1102230246251565e-16, 0.0, 2.220446049250313e-16, 0.008885431644714115, 0.1407250439999469, 2.220446049250313e-16, 0.25778074451684296, 0.0, 0.18510190067000099, 0.0, 2, 0.0, 0.0015552241298304459, 0.0006700670542103548, 0.27530814227198264, 0.025723692140125265, 2.220446049250313e-16, 0.008519342893785309, 2]