----------------------------------------------------------------
u= [0.60000000000000009, 0.80000000000000004]
basis= [[0.70710678118654746, -0.70710678118654746], [0.70710678118654746, 0.70710678118654746]]
coeffs= [-0.1414213562373095, 0.9899494936611668]

c0bar=-0.1414 c0=-0.1414 <b0|b0>= 1.0000 prod= 0.0200
c0bar=-0.1414 c1= 0.9899 <b0|b1>= 0.0000 prod=-0.0000

c1bar= 0.9899 c0=-0.1414 <b1|b0>= 0.0000 prod=-0.0000
c1bar= 0.9899 c1= 0.9899 <b1|b1>= 1.0000 prod= 0.9800

sumij= 1.0000
sumi = 1.0000

----------------------------------------------------------------
u= [0.60000000000000009, 0.80000000000000004]
basis= [[1.0, 0.0], [0.70710678118654746, 0.70710678118654746]]
coeffs= [-0.19999999999999996, 1.1313708498984762]

c0bar=-0.2000 c0=-0.2000 <b0|b0>= 1.0000 prod= 0.0400
c0bar=-0.2000 c1= 1.1314 <b0|b1>= 0.7071 prod=-0.1600

c1bar= 1.1314 c0=-0.2000 <b1|b0>= 0.7071 prod=-0.1600
c1bar= 1.1314 c1= 1.1314 <b1|b1>= 1.0000 prod= 1.2800

sumij= 1.0000
sumi = 1.3200