SL_2 standard  q=5 n=120 d=4 diam=6  lambda_2=0.809017 lambda_min=-0.809017 rho=0.809017 kappa=0.1529 tau(0)=5.2361
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 5.1190 at p = 0.11213 (mean time 8.9);  ratio to tau(0): 0.9776 ; ratio to d: 1.2797 ; (log_d n)^2 = 11.93
    tau(p) at p=0.11213 : 11.3172  >= 2 Var_p(dist) = 5.1190 : True ;  tau(p)/tau(0) = 2.1614
    (0.0s)
SL_2 random pair (4, 0, 1, 4) (4, 4, 4, 3)  q=5 n=120 d=4 diam=6  lambda_2=0.809017 lambda_min=-0.809017 rho=0.809017 kappa=0.1529 tau(0)=5.2361
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 4.8115 at p = 0.11557 (mean time 8.7);  ratio to tau(0): 0.9189 ; ratio to d: 1.2029 ; (log_d n)^2 = 11.93
    tau(p) at p=0.11557 : 11.0881  >= 2 Var_p(dist) = 4.8115 : True ;  tau(p)/tau(0) = 2.1176
    (0.0s)
SL_2 standard  q=7 n=336 d=4 diam=7  lambda_2=0.853553 lambda_min=-0.890388 rho=0.890388 kappa=0.0837 tau(0)=6.8284
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 7.6959 at p = 0.09076 (mean time 11.0);  ratio to tau(0): 1.1270 ; ratio to d: 1.9240 ; (log_d n)^2 = 17.61
    tau(p) at p=0.09076 : 17.6155  >= 2 Var_p(dist) = 7.6959 : True ;  tau(p)/tau(0) = 2.5797
    (0.0s)
SL_2 random pair (3, 6, 4, 6) (4, 6, 5, 6)  q=7 n=336 d=4 diam=6  lambda_2=0.804884 lambda_min=-0.822061 rho=0.822061 kappa=0.1413 tau(0)=5.1251
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 6.6702 at p = 0.11213 (mean time 8.9);  ratio to tau(0): 1.3015 ; ratio to d: 1.6675 ; (log_d n)^2 = 17.61
    tau(p) at p=0.11213 : 17.0087  >= 2 Var_p(dist) = 6.6702 : True ;  tau(p)/tau(0) = 3.3187
    (0.0s)
SL_2 standard  q=11 n=1320 d=4 diam=10  lambda_2=0.904508 lambda_min=-0.933013 rho=0.933013 kappa=0.0500 tau(0)=10.4721
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 12.7404 at p = 0.06128 (mean time 16.3);  ratio to tau(0): 1.2166 ; ratio to d: 3.1851 ; (log_d n)^2 = 26.87
    tau(p) at p=0.06128 : 30.4415  >= 2 Var_p(dist) = 12.7404 : True ;  tau(p)/tau(0) = 2.9069
    (0.1s)
SL_2 random pair (7, 9, 7, 6) (3, 0, 9, 4)  q=11 n=1320 d=4 diam=9  lambda_2=0.905900 lambda_min=-0.834261 rho=0.905900 kappa=0.0713 tau(0)=10.6270
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 11.5834 at p = 0.06316 (mean time 15.8);  ratio to tau(0): 1.0900 ; ratio to d: 2.8958 ; (log_d n)^2 = 26.87
    tau(p) at p=0.06316 : 28.9796  >= 2 Var_p(dist) = 11.5834 : True ;  tau(p)/tau(0) = 2.7270
    (0.1s)
SL_2 standard  q=13 n=2184 d=4 diam=10  lambda_2=0.918783 lambda_min=-0.956393 rho=0.956393 kappa=0.0322 tau(0)=12.3127
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 15.4193 at p = 0.05269 (mean time 19.0);  ratio to tau(0): 1.2523 ; ratio to d: 3.8548 ; (log_d n)^2 = 30.76
    tau(p) at p=0.05269 : 36.7373  >= 2 Var_p(dist) = 15.4193 : True ;  tau(p)/tau(0) = 2.9837
    (0.1s)
SL_2 random pair (1, 1, 4, 5) (1, 7, 0, 1)  q=13 n=2184 d=4 diam=10  lambda_2=0.853442 lambda_min=-0.851486 rho=0.853442 kappa=0.1143 tau(0)=6.8232
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 11.9879 at p = 0.08289 (mean time 12.1);  ratio to tau(0): 1.7569 ; ratio to d: 2.9970 ; (log_d n)^2 = 30.76
    tau(p) at p=0.08289 : 31.1037  >= 2 Var_p(dist) = 11.9879 : True ;  tau(p)/tau(0) = 4.5585
    (0.1s)
SL_2 standard  q=17 n=4896 d=4 diam=12  lambda_2=0.927319 lambda_min=-0.936327 rho=0.936327 kappa=0.0475 tau(0)=13.7587
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 19.2489 at p = 0.04530 (mean time 22.1);  ratio to tau(0): 1.3990 ; ratio to d: 4.8122 ; (log_d n)^2 = 37.56
    tau(p) at p=0.04530 : 48.4463  >= 2 Var_p(dist) = 19.2489 : True ;  tau(p)/tau(0) = 3.5211
    (0.2s)
SL_2 random pair (15, 10, 6, 12) (12, 8, 11, 6)  q=17 n=4896 d=4 diam=12  lambda_2=0.945048 lambda_min=-0.862212 rho=0.945048 kappa=0.0408 tau(0)=18.1977
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 18.9595 at p = 0.03779 (mean time 26.5);  ratio to tau(0): 1.0419 ; ratio to d: 4.7399 ; (log_d n)^2 = 37.56
    tau(p) at p=0.03779 : 45.9359  >= 2 Var_p(dist) = 18.9595 : True ;  tau(p)/tau(0) = 2.5243
    (0.2s)
SL_2 standard  q=23 n=12144 d=4 diam=14  lambda_2=0.948330 lambda_min=-0.955355 rho=0.955355 kappa=0.0329 tau(0)=19.3535
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 26.1657 at p = 0.03249 (mean time 30.8);  ratio to tau(0): 1.3520 ; ratio to d: 6.5414 ; (log_d n)^2 = 46.02
    tau(p) at p=0.03249 : 65.3828  >= 2 Var_p(dist) = 26.1657 : True ;  tau(p)/tau(0) = 3.3784
    (0.4s)
SL_2 random pair (11, 12, 16, 5) (20, 2, 10, 16)  q=23 n=12144 d=4 diam=11  lambda_2=0.882485 lambda_min=-0.880764 rho=0.882485 kappa=0.0902 tau(0)=8.5095
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 18.2964 at p = 0.06509 (mean time 15.4);  ratio to tau(0): 2.1501 ; ratio to d: 4.5741 ; (log_d n)^2 = 46.02
    tau(p) at p=0.06509 : 49.0146  >= 2 Var_p(dist) = 18.2964 : True ;  tau(p)/tau(0) = 5.7600
    (0.4s)
SL_2 standard  q=31 n=29760 d=4 diam=15  lambda_2=0.943187 lambda_min=-0.954930 rho=0.954930 kappa=0.0333 tau(0)=17.6017
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 32.0397 at p = 0.03058 (mean time 32.7);  ratio to tau(0): 1.8203 ; ratio to d: 8.0099 ; (log_d n)^2 = 55.21
    tau(p) at p=0.03058 : 83.6498  >= 2 Var_p(dist) = 32.0397 : True ;  tau(p)/tau(0) = 4.7524
    (1.0s)
SL_2 random pair (2, 17, 17, 21) (9, 9, 14, 21)  q=31 n=29760 d=4 diam=16  lambda_2=0.943936 lambda_min=-0.748528 rho=0.943936 kappa=0.0416 tau(0)=17.8368
    Step 1 (K^j(e,x) <= 2/n + rho^(j-1), j=1..4000): True  (max ratio lhs/rhs = 0.5000)
    2 max_p Var_p(dist) = 31.8019 at p = 0.03152 (mean time 31.7);  ratio to tau(0): 1.7829 ; ratio to d: 7.9505 ; (log_d n)^2 = 55.21
    tau(p) at p=0.03152 : 83.2498  >= 2 Var_p(dist) = 31.8019 : True ;  tau(p)/tau(0) = 4.6673
    (1.1s)
done
