pcf_spectral_phase2_congruence.csv

label,group,d,tau,tau_sector,Delta_shape,delta_lead,delta_sign,lambda_rational,galois_prediction,galois_hit,is_degenerate_boundary,b0_mod4,abc_tuple,z0,z0_C,z0_digits,z0_region,admits_2f1,mean_zero_density,mean_entropy,mean_omega_p3,arithmetic_purity,retention_stability,dist_to_log,dist_to_pi,nearest_cluster,D_p2,C_p2,period_p2,omega_p2,D_p3,C_p3,period_p3,omega_p3,D_p5,C_p5,period_p5,omega_p5,D_p7,C_p7,period_p7,omega_p7,D_p11,C_p11,period_p11,omega_p11,D_p13,C_p13,period_p13,omega_p13,D_p17,C_p17,period_p17,omega_p17,D_p19,C_p19,period_p19,omega_p19,D_p23,C_p23,period_p23,omega_p23
log-k=2,Log ladder,1.0,log-type,log-type,1.0,-2,-,True,degenerate,,False,2,"(-1.0-1.0j, -1.0+1.0j, 1.0)",0.209794344408,1.0,60.0,"real[0,1]",True,0.958444,0.369477,0.381749,0.790628,0.381749,0.174347,0.454932,log,0.996000,2,2,0.983936,0.990000,3,3,0.939394,0.984000,5,5,0.838384,0.974000,6,7,0.628571,0.958000,10,11,0.045455,0.950000,11,13,0.000000,0.936000,14,17,0.000000,0.928000,18,19,0.000000,0.910000,19,23,0.000000
log-k=3,Log ladder,1.0,log-type,log-type,4.0,-3,-,True,degenerate,,False,3,"(-1.5-0.866025403784j, -1.5+0.866025403784j, 1.0)",0.438204433756,1.0,70.007201,"real[0,1]",True,0.960000,0.360088,0.387831,0.570847,0.387831,0.208667,0.495055,log,0.994000,2,2,0.975904,0.994000,3,3,0.957576,0.984000,5,5,0.868687,0.978000,7,7,0.642857,0.960000,10,11,0.045455,0.954000,12,13,0.000000,0.936000,14,17,0.000000,0.928000,18,19,0.000000,0.912000,19,23,0.000000
log-k=4,Log ladder,1.0,log-type,log-type,9.0,-4,-,True,degenerate,,False,0,"(-2.0, -2.0, 1.0)",0.54481030664,1.0,60.0,"real[0,1]",True,0.959333,0.358950,0.414013,1.106608,0.414013,0.301645,0.323013,log,0.996000,2,2,0.987952,0.992000,3,3,0.945455,0.984000,4,5,0.868687,0.974000,7,7,0.628571,0.964000,9,11,0.295455,0.952000,12,13,0.000000,0.934000,14,17,0.000000,0.928000,15,19,0.000000,0.910000,17,23,0.000000
log-k=5,Log ladder,1.0,log-type,log-type,16.0,-5,-,True,degenerate,,False,1,"(-3.61803398875, -1.38196601125, 1.0)",0.609464706369,1.0,60.0,"real[0,1]",True,0.960000,0.361596,0.390677,0.858834,0.390677,0.176879,0.378307,log,0.994000,2,2,0.975904,0.990000,3,3,0.939394,0.990000,4,5,0.858586,0.978000,6,7,0.628571,0.962000,9,11,0.113636,0.950000,12,13,0.000000,0.938000,15,17,0.000000,0.926000,18,19,0.000000,0.912000,21,23,0.000000
log-k=6,Log ladder,1.0,log-type,log-type,25.0,-6,-,True,degenerate,,False,2,"(-4.73205080757, -1.26794919243, 1.0)",0.654218339052,1.0,60.0,"real[0,1]",True,0.959778,0.360327,0.384974,1.078306,0.384974,0.168522,0.378043,log,0.996000,2,2,0.987952,0.994000,3,3,0.957576,0.984000,4,5,0.818182,0.976000,6,7,0.628571,0.958000,9,11,0.045455,0.954000,11,13,0.027027,0.936000,16,17,0.000000,0.928000,15,19,0.000000,0.912000,20,23,0.000000
log-k=7,Log ladder,1.0,log-type,log-type,36.0,-7,-,True,degenerate,,False,3,"(-5.79128784748, -1.20871215252, 1.0)",0.687683960634,1.0,60.0,"real[0,1]",True,0.960222,0.353941,0.391054,1.108599,0.391054,0.319519,0.487365,log,0.994000,2,2,0.975904,0.992000,3,3,0.945455,0.984000,5,5,0.838384,0.986000,5,7,0.714286,0.958000,10,11,0.045455,0.952000,9,13,0.000000,0.934000,15,17,0.000000,0.932000,14,19,0.000000,0.910000,22,23,0.000000
log-k=8,Log ladder,1.0,log-type,log-type,49.0,-8,-,True,degenerate,,False,0,"(-6.82842712475, -1.17157287525, 1.0)",0.71398393408,1.0,60.0,"real[0,1]",True,0.959111,0.363142,0.385562,1.054777,0.385562,0.155815,0.418692,log,0.996000,2,2,0.987952,0.990000,3,3,0.939394,0.984000,5,5,0.868687,0.976000,6,7,0.628571,0.958000,9,11,0.045455,0.952000,11,13,0.000000,0.936000,13,17,0.000000,0.930000,15,19,0.000000,0.910000,20,23,0.000000
log-k=10,Log ladder,1.0,log-type,log-type,81.0,-10,-,True,degenerate,,False,2,"(-8.87298334621, -1.12701665379, 1.0)",0.75322352736,1.0,60.0,"real[0,1]",True,0.960667,0.354091,0.386254,0.889216,0.386254,0.196095,0.435248,log,0.996000,2,2,0.983936,0.992000,3,3,0.945455,0.990000,4,5,0.858586,0.978000,7,7,0.642857,0.960000,9,11,0.045455,0.952000,12,13,0.000000,0.936000,14,17,0.000000,0.928000,15,19,0.000000,0.914000,22,23,0.000000
pi-m=0,Pi family,1.0,pi-type,pi-type,1.0,-2,-,True,degenerate,,False,1,"(-1.0-1.0j, -1.0+1.0j, 1.0)",0.132121997573,0.5,60.0,"real[0,1]",True,0.969333,0.280278,0.417650,1.894171,0.417650,0.494422,0.200705,pi,0.998000,2,2,0.991968,0.992000,2,3,0.951515,0.988000,4,5,0.848485,0.980000,6,7,0.671429,0.970000,7,11,0.295455,0.966000,11,13,0.000000,0.952000,14,17,0.000000,0.944000,14,19,0.000000,0.934000,17,23,0.000000
pi-m=1,Pi family,1.0,pi-type,pi-type,1.0,-2,-,True,degenerate,,False,1,"(-1.0-1.0j, -1.0+1.0j, 1.0)",0.132121997573,1.0,60.0,"real[0,1]",True,0.968667,0.289635,0.417891,1.308288,0.417891,0.299299,0.260260,pi,0.998000,2,2,0.991968,0.990000,3,3,0.939394,0.986000,4,5,0.848485,0.980000,6,7,0.685714,0.970000,9,11,0.295455,0.964000,12,13,0.000000,0.950000,13,17,0.000000,0.946000,15,19,0.000000,0.934000,17,23,0.000000
pi-m=2,Pi family,1.0,pi-type,pi-type,1.0,-2,-,True,degenerate,,False,1,"(-1.0-1.0j, -1.0+1.0j, 1.0)",0.32101373169,1.0,60.0,"real[0,1]",True,0.967111,0.303630,0.413369,1.544425,0.413369,0.429630,0.197402,pi,0.998000,2,2,0.991968,0.996000,2,3,0.957576,0.984000,4,5,0.818182,0.978000,6,7,0.657143,0.968000,9,11,0.295455,0.960000,10,13,0.000000,0.950000,14,17,0.000000,0.940000,17,19,0.000000,0.930000,19,23,0.000000
pi-m=3,Pi family,1.0,pi-type,pi-type,1.0,-2,-,True,degenerate,,False,1,"(-1.0-1.0j, -1.0+1.0j, 1.0)",0.45946797625,1.0,60.0,"real[0,1]",True,0.966444,0.305348,0.417462,1.616243,0.417462,0.425307,0.155587,pi,0.998000,2,2,0.991968,0.992000,2,3,0.945455,0.992000,4,5,0.868687,0.974000,6,7,0.628571,0.964000,9,11,0.295455,0.958000,11,13,0.027027,0.948000,14,17,0.000000,0.940000,15,19,0.000000,0.932000,18,23,0.000000
pi-m=4,Pi family,1.0,pi-type,pi-type,1.0,-2,-,True,degenerate,,False,1,"(-1.0-1.0j, -1.0+1.0j, 1.0)",0.570130151875,1.0,60.0,"real[0,1]",True,0.967111,0.302280,0.437424,1.230317,0.437424,0.375299,0.319331,pi,0.998000,2,2,0.991968,0.990000,3,3,0.939394,0.992000,4,5,0.868687,0.988000,5,7,0.814286,0.962000,9,11,0.295455,0.958000,11,13,0.027027,0.946000,16,17,0.000000,0.942000,14,19,0.000000,0.928000,21,23,0.000000
pi-m=5,Pi family,1.0,pi-type,pi-type,1.0,-2,-,True,degenerate,,False,1,"(-1.0-1.0j, -1.0+1.0j, 1.0)",0.662777690583,1.0,60.0,"real[0,1]",True,0.965556,0.309619,0.431487,1.893488,0.431487,0.509012,0.186670,pi,0.998000,2,2,0.991968,0.996000,2,3,0.957576,0.988000,4,5,0.838384,0.990000,5,7,0.800000,0.958000,8,11,0.295455,0.954000,11,13,0.000000,0.944000,14,17,0.000000,0.938000,15,19,0.000000,0.924000,17,23,0.000000
apery-zeta3,Apery-isolated,3.0,Apery-isolated,,1152.0,-1,-,False,log-type,,False,1,None,None,None,0.0,none,False,0.962667,0.334791,0.515002,1.179689,0.515002,0.659339,0.560612,pi,0.994000,2,2,0.991968,0.992000,3,3,0.975758,0.988000,4,5,0.919192,0.978000,7,7,0.828571,0.962000,9,11,0.568182,0.958000,10,13,0.351351,0.940000,13,17,0.000000,0.936000,16,19,0.000000,0.916000,19,23,0.000000
probe-d1-pos-4n2-6n1,M2-2 probe,1.0,V_quad-mystery,,52.0,4,+,False,pi-type,,False,1,None,None,None,0.0,none,False,0.356000,1.858743,0.133166,1.078517,0.133166,2.647429,2.712345,log-distant,0.000000,1,2,0.248996,0.990000,3,3,0.939394,0.002000,4,5,0.010101,0.004000,7,42,0.000000,0.180000,11,110,0.000000,0.076000,13,156,0.000000,0.936000,15,17,0.000000,0.102000,19,342,0.000000,0.914000,17,23,0.000000
probe-d1-neg-n2-8n4,M2-2 probe,1.0,V_quad-mystery,,60.0,-1,-,False,log-type,,False,0,None,None,None,0.0,none,False,0.962000,0.342857,0.334409,0.964344,0.334409,0.525464,0.653170,log,0.998000,2,2,0.497992,0.992000,3,3,0.945455,0.984000,5,5,0.818182,0.978000,7,7,0.657143,0.964000,9,11,0.090909,0.956000,10,13,0.000000,0.940000,14,17,0.000000,0.930000,16,19,0.000000,0.916000,18,23,0.000000
probe-d1-boundary-nn1-3n2,M2-2 probe,1.0,algebraic/rational,algebraic/rational,13.0,1,+,False,degenerate-boundary,,True,2,"(-2.41421356237, 0.414213562373, 1.0)",9.66649601573e-69,2.0,60.0,"real[0,1]",True,0.513778,1.888587,0.222540,0.657289,0.222540,2.156161,2.236245,log-distant,0.996000,2,2,0.987952,0.996000,3,3,0.957576,0.200000,5,10,0.030303,0.286000,7,21,0.000000,0.092000,11,55,0.000000,0.076000,13,156,0.027027,0.968000,11,17,0.000000,0.052000,19,171,0.000000,0.958000,16,23,0.000000
vquad-1-0-1,V_quad,2.0,V_quad-mystery,,-4.0,1,+,False,pi-type,,False,1,None,None,None,0.0,none,False,0.148222,2.979558,0.043395,0.142857,0.043395,3.245861,3.316782,log-distant,0.500000,2,2,0.248996,0.166000,3,6,0.127273,0.200000,5,20,0.000000,0.214000,6,14,0.014286,0.080000,11,110,0.000000,0.076000,13,52,0.000000,0.032000,17,-1,0.000000,0.026000,19,114,0.000000,0.040000,23,-1,0.000000
vquad-2-2-1,V_quad,2.0,V_quad-mystery,,-4.0,1,+,False,pi-type,,False,1,None,None,None,0.0,none,False,0.153333,2.939532,0.027331,0.400000,0.027331,3.480747,3.539746,log-distant,0.332000,2,6,0.080321,0.332000,3,6,0.145455,0.300000,3,10,0.020202,0.124000,7,112,0.000000,0.080000,11,264,0.000000,0.074000,13,364,0.000000,0.046000,17,-1,0.000000,0.050000,19,-1,0.000000,0.042000,23,-1,0.000000
vquad-1-1-1,V_quad,2.0,V_quad-mystery,,-3.0,1,+,False,pi-type,,False,1,None,None,None,0.0,none,False,0.133111,3.029317,0.022157,0.000000,0.022157,3.383075,3.455175,log-distant,0.332000,2,6,0.120482,0.250000,3,24,0.054545,0.160000,5,100,0.010101,0.166000,7,42,0.014286,0.112000,11,88,0.000000,0.062000,13,364,0.000000,0.044000,17,272,0.000000,0.044000,19,-1,0.000000,0.028000,23,368,0.000000
vquad-2-1-1,V_quad,2.0,V_quad-mystery,,-7.0,1,+,False,pi-type,,False,1,None,None,None,0.0,none,False,0.166000,2.946754,0.032239,0.385965,0.032239,3.201857,3.254102,log-distant,0.500000,2,2,0.124498,0.332000,2,3,0.145455,0.160000,5,100,0.020202,0.124000,7,112,0.000000,0.084000,11,264,0.000000,0.064000,13,364,0.000000,0.096000,17,204,0.000000,0.092000,18,114,0.000000,0.042000,23,-1,0.000000
vquad-3-1-1,V_quad,2.0,V_quad-mystery,,-11.0,1,+,False,pi-type,,False,1,None,None,None,0.0,none,False,0.164667,2.983420,0.015910,0.235294,0.015910,3.485813,3.554896,log-distant,0.332000,2,6,0.040161,0.332000,3,6,0.072727,0.266000,5,60,0.030303,0.124000,7,112,0.000000,0.082000,11,110,0.000000,0.076000,13,-1,0.000000,0.174000,13,68,0.000000,0.052000,19,-1,0.000000,0.044000,23,-1,0.000000
vquad-1-4-3,V_quad,2.0,V_quad-mystery,,4.0,1,+,True,degenerate,,False,3,None,None,None,0.0,none,False,0.166889,2.977666,0.067005,0.200000,0.067005,3.412748,3.477404,log-distant,0.500000,2,2,0.497992,0.248000,3,24,0.084848,0.300000,4,10,0.020202,0.164000,7,42,0.000000,0.078000,11,264,0.000000,0.072000,13,-1,0.000000,0.056000,17,-1,0.000000,0.048000,19,342,0.000000,0.036000,23,-1,0.000000
vquad-1--4-3,V_quad,2.0,V_quad-mystery,,4.0,1,+,True,degenerate,,False,3,None,None,None,0.0,none,False,0.169111,2.977489,0.065225,0.200000,0.065225,3.412845,3.477187,log-distant,0.500000,2,2,0.497992,0.250000,3,24,0.054545,0.300000,4,10,0.020202,0.166000,7,42,0.014286,0.082000,11,264,0.000000,0.074000,13,-1,0.000000,0.060000,17,-1,0.000000,0.050000,19,342,0.000000,0.040000,23,-1,0.000000