h | q | a | theta (attained at l) | negative piece(s) | min Phi# | argmin p* | p* in (q^2,q) or mirror | Phi#(q^2) (Phi#(1-q^2) for mirror) | AND2 exact there | max Gamma, k<=3
('-9/16', '9/64', '9/64', '-3/32') | 101/232 | 3705/13231 | 4356299668/14559183431 (l=[3]) | [0] | -2.5727e-03 | 0.3520 | True | +1.7948e-02 | None | -2.645e-04
('-3/32', '9/64', '9/64', '-9/16') | 101/232 | 3705/13231 | 4356299668/14559183431 (l=[3]) | [2] | -2.5727e-03 | 0.6480 | True | +1.7948e-02 | None | -2.645e-04
('-1/2', '9/64', '9/64', '-3/32') | 105/236 | 3473/13755 | 5500869728/16705686375 (l=[3]) | [0] | -2.3405e-03 | 0.3549 | True | +1.6453e-02 | None | -3.335e-04
('-3/32', '9/64', '9/64', '-1/2') | 105/236 | 3473/13755 | 5500869728/16705686375 (l=[3]) | [2] | -2.3405e-03 | 0.6451 | True | +1.6453e-02 | None | -3.335e-04
('-17/32', '9/64', '9/64', '-3/32') | 103/234 | 3589/13493 | 1635075030/5200287793 (l=[3]) | [0] | -2.2932e-03 | 0.3527 | True | +1.7220e-02 | None | -4.699e-04
('-3/32', '9/64', '9/64', '-17/32') | 103/234 | 3589/13493 | 1635075030/5200287793 (l=[3]) | [2] | -2.2932e-03 | 0.6473 | True | +1.7220e-02 | None | -4.699e-04
('-43/64', '1/8', '1/8', '-5/64') | 93/224 | 1315/4061 | 96824413/405961957 (l=[3]) | [0] | -1.9390e-03 | 0.3312 | True | +1.6473e-02 | None | -7.863e-04
('-5/64', '1/8', '1/8', '-43/64') | 93/224 | 1315/4061 | 96824413/405961957 (l=[3]) | [2] | -1.9390e-03 | 0.6688 | True | +1.6473e-02 | None | -7.863e-04
('-23/64', '9/64', '9/64', '-7/64') | 57/122 | 748/3705 | 555376037/1395984834 (l=[3]) | [0] | -1.7264e-03 | 0.3966 | True | +2.0735e-02 | None | -6.544e-04
('-7/64', '9/64', '9/64', '-23/64') | 57/122 | 748/3705 | 555376037/1395984834 (l=[3]) | [2] | -1.7264e-03 | 0.6034 | True | +2.0735e-02 | None | -6.544e-04
('-23/32', '7/64', '7/64', '-1/16') | 89/220 | 3961/11659 | 1976523174/9462798887 (l=[3]) | [0] | -1.1657e-03 | 0.3070 | True | +1.2718e-02 | None | -1.162e-03
('-1/16', '7/64', '7/64', '-23/32') | 89/220 | 3961/11659 | 1976523174/9462798887 (l=[3]) | [2] | -1.1657e-03 | 0.6930 | True | +1.2718e-02 | None | -1.162e-03
('-25/64', '1/8', '1/8', '-5/64') | 111/242 | 961/4847 | 282591361/756806473 (l=[3]) | [0] | -1.0496e-03 | 0.3446 | True | +1.0965e-02 | None | -9.159e-04
('-5/64', '1/8', '1/8', '-25/64') | 111/242 | 961/4847 | 282591361/756806473 (l=[3]) | [2] | -1.0496e-03 | 0.6554 | True | +1.0965e-02 | None | -9.159e-04
('-5/16', '9/64', '9/64', '-1/8') | 39/82 | 955/5031 | 1147988996/2711530809 (l=[3]) | [0] | -7.4317e-04 | 0.4270 | True | +2.7057e-02 | None | -8.277e-04
('-1/8', '9/64', '9/64', '-5/16') | 39/82 | 955/5031 | 1147988996/2711530809 (l=[3]) | [2] | -7.4317e-04 | 0.5730 | True | +2.7057e-02 | None | -8.277e-04
('-27/64', '5/32', '5/32', '-9/64') | 37/80 | 31/129 | 16723/43929 (l=[3]) | [0] | -5.9666e-04 | 0.4192 | True | +3.3270e-02 | None | -9.115e-04
('-9/64', '5/32', '5/32', '-27/64') | 37/80 | 31/129 | 16723/43929 (l=[3]) | [2] | -5.9666e-04 | 0.5808 | True | +3.3270e-02 | None | -9.115e-04
('-41/64', '1/8', '1/8', '-5/64') | 95/226 | 3827/12445 | 3004610267/11781189875 (l=[3]) | [0] | -5.7469e-04 | 0.3264 | True | +1.5981e-02 | None | -2.130e-03
('-5/64', '1/8', '1/8', '-41/64') | 95/226 | 3827/12445 | 3004610267/11781189875 (l=[3]) | [2] | -5.7469e-04 | 0.6736 | True | +1.5981e-02 | None | -2.130e-03
('-11/32', '7/64', '7/64', '-1/16') | 113/244 | 2521/14803 | 1209560706/3118100417 (l=[3]) | [0] | -2.3912e-04 | 0.3259 | True | +7.0934e-03 | None | -1.208e-03
('-1/16', '7/64', '7/64', '-11/32') | 113/244 | 2521/14803 | 1209560706/3118100417 (l=[3]) | [2] | -2.3912e-04 | 0.6741 | True | +7.0934e-03 | None | -1.208e-03
('-41/64', '9/64', '9/64', '-7/64') | 48/113 | 2009/6240 | 794125991/3016065024 (l=[3]) | [0] | -1.7607e-04 | 0.3730 | True | +2.9020e-02 | None | -1.936e-03
('-7/64', '9/64', '9/64', '-41/64') | 48/113 | 2009/6240 | 794125991/3016065024 (l=[3]) | [2] | -1.7607e-04 | 0.6270 | True | +2.9020e-02 | None | -1.936e-03
('-25/64', '9/64', '9/64', '-7/64') | 56/121 | 1553/7280 | 2008118151/5227737088 (l=[3]) | [0] | -1.4952e-04 | 0.3884 | True | +2.1880e-02 | None | -2.414e-03
('-7/64', '9/64', '9/64', '-25/64') | 56/121 | 1553/7280 | 2008118151/5227737088 (l=[3]) | [2] | -1.4952e-04 | 0.6116 | True | +2.1880e-02 | None | -2.414e-03
('-47/64', '3/32', '3/32', '-3/64') | 87/218 | 3863/11397 | 1724676809/8779820499 (l=[3]) | [0] | -1.1911e-04 | 0.2718 | True | +7.9398e-03 | None | -5.655e-04
('-3/64', '3/32', '3/32', '-47/64') | 87/218 | 3863/11397 | 1724676809/8779820499 (l=[3]) | [2] | -1.1911e-04 | 0.7282 | True | +7.9398e-03 | None | -5.655e-04
('-53/64', '3/64', '3/64', '-1/64') | 3/8 | 73/195 | 11/78 (l=[1]) | [0] | -8.4617e-05 | 0.1801 | True | +6.6886e-04 | True | -6.689e-04
('-1/64', '3/64', '3/64', '-53/64') | 3/8 | 73/195 | 11/78 (l=[1]) | [2] | -8.4617e-05 | 0.8199 | True | +6.6886e-04 | True | -6.689e-04
('-23/32', '5/64', '5/64', '-1/32') | 87/218 | 1215/3799 | 6/29 (l=[1]) | [0] | -6.9270e-05 | 0.2247 | True | +2.5888e-03 | True | -7.167e-05
('-1/32', '5/64', '5/64', '-23/32') | 87/218 | 1215/3799 | 6/29 (l=[1]) | [2] | -6.9270e-05 | 0.7753 | True | +2.5888e-03 | True | -7.167e-05
('-27/64', '1/8', '1/8', '-5/64') | 109/240 | 3001/14279 | 61939681/172238857 (l=[3]) | [0] | -4.7675e-05 | 0.3377 | True | +1.1797e-02 | None | -2.039e-03
('-5/64', '1/8', '1/8', '-27/64') | 109/240 | 3001/14279 | 61939681/172238857 (l=[3]) | [2] | -4.7675e-05 | 0.6623 | True | +1.1797e-02 | None | -2.039e-03
all 34: Phi# is negative only on one piece, convex there, and positive at q^2 and q (at 1-q and 1-q^2 for the mirror images), so {Phi# < 0} is a subinterval of (q^2, q) or of (1-q, 1-q^2)
all 34: min Phi# in [-2.5727e-03, -4.7675e-05]; theta attained at l = 1 for 4; whenever l = 1: AND2 equals Phi#(q^2), 1[z1 = cbar, z2 = c] equals Phi#(q(1-q)) > 0, and the minimiser lies in (q^2, q(1-q)) (mirrored for the mirror images): True
