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Python 2, 8787 85 bytes

f=lambda v,a=0,b=1,i=0i=1:v*v>=a*a and[i]*(v==a>0v==b)+[+[1-i]*(-(-1)**i*a==v)+f(v,b,a+b,i+1)or[] 

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Python 2, 87 bytes

f=lambda v,a=0,b=1,i=0:v*v>=a*a and[i]*(v==a>0)+[-i]*(-(-1)**i*a==v)+f(v,b,a+b,i+1)or[] 

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Python 2, 87 85 bytes

f=lambda v,a=0,b=1,i=1:v*v>=a*a and[i]*(v==b)+[1-i]*((-1)**i*a==v)+f(v,b,a+b,i+1)or[] 

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ovs
  • 61.2k
  • 3
  • 49
  • 164

Python 2, 87 bytes

f=lambda v,a=0,b=1,i=0:v*v>=a*a and[i]*(v==a>0)+[-i]*(-(-1)**i*a==v)+f(v,b,a+b,i+1)or[] 

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