# Identifications: Projective Plane 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, 1.1102230246251565e-16
# 1, 0.0
# 2, 0.0
# 3, 2.220446049250313e-16
# 4, 0.0006505301638103367
# 5, 0.0006505301638105587
# 6, 0.0
# 7, 2
# 8, 0.0
# 9, 2.220446049250313e-16
# 10, 0.0
# 11, 2
# 12, 2
# 13, 0.0017108198585334966
# 14, 0.0017108198585333856
# 15, 2
# 16, 0.0
# 17, 2
# 18, 0.0
# 19, 2.220446049250313e-16
# 20, 0.008815596088503574
# 21, 0.008815596088504685
# 22, 0.2602622797711024
# 23, 0.2602622797711087
# 24, 2.220446049250313e-16
# 25, 2
# 26, 0.19617600407097058
# 27, 0.19617600407096936
# 28, 2.220446049250313e-16
# 29, 0.021663047229856125
# 30, 0.02166304722985457
# 31, 0.11467013435710471
# 32, 0.11467013435710582
# 33, 2
# 34, 2.220446049250313e-16
# 35, 0.0
# 36, 0.0
# 37, 2
# 38, 2
# 39, 0.0
# 40, 0.009074624468260684
# 41, 0.009074624468259684
# 42, 2
# 43, 0.0
# 44, 1.1102230246251565e-16
# 45, 0.09516721095526648
# 46, 0.09516721095526404
# 47, 0.0
# 48, 0.14072504399994779
# 49, 0.14072504399994723
# 50, 0.0
# 51, 0.185101900669998
# 52, 0.1851019006699972
# 53, 2
# 54, 0.0
# 55, 0.0
# 56, 0.0015552241298295577
# 57, 0.0015552241298287806
# 58, 0.27530814226942557
# 59, 0.2753081422694551
# 60, 0.025723692139818732
# 61, 0.02572369213986747
# 62, 2
# 63, 2

dots = [1.1102230246251565e-16, 0.0, 0.0, 2.220446049250313e-16, 0.0006505301638103367, 0.0006505301638105587, 0.0, 2, 0.0, 2.220446049250313e-16, 0.0, 2, 2, 0.0017108198585334966, 0.0017108198585333856, 2, 0.0, 2, 0.0, 2.220446049250313e-16, 0.008815596088503574, 0.008815596088504685, 0.2602622797711024, 0.2602622797711087, 2.220446049250313e-16, 2, 0.19617600407097058, 0.19617600407096936, 2.220446049250313e-16, 0.021663047229856125, 0.02166304722985457, 0.11467013435710471, 0.11467013435710582, 2, 2.220446049250313e-16, 0.0, 0.0, 2, 2, 0.0, 0.009074624468260684, 0.009074624468259684, 2, 0.0, 1.1102230246251565e-16, 0.09516721095526648, 0.09516721095526404, 0.0, 0.14072504399994779, 0.14072504399994723, 0.0, 0.185101900669998, 0.1851019006699972, 2, 0.0, 0.0, 0.0015552241298295577, 0.0015552241298287806, 0.27530814226942557, 0.2753081422694551, 0.025723692139818732, 0.02572369213986747, 2, 2]