]> Continued Fraction Expansions of Square Roots for n = 4001..5000

# Continued Fraction Expansions of Square Roots for n = 4001..5000

Note: This page uses MathML. To view it properly, you need a MathML-enabled browser. You may also have to install some fonts.

The square root of any natural number n can be expressed in the form of a continued fraction. When n is a perfect square, its continued fraction expansion is trivial. But when it is not a perfect square, its continued fraction expansion is both infinite and periodic. We are interested in the latter here.

 $\sqrt{4001}=\left[63;\stackrel{_}{3,1,17,3,9,2,2,9,3,17,1,3,126}\right]$ $\sqrt{4002}=\left[63;\stackrel{_}{3,1,4,1,3,126}\right]$ $\sqrt{4003}=\left[63;\stackrel{_}{3,1,2,2,41,1,3,9,2,13,1,1,2,2,2,1,4,1,3,1,6,4,4,1,1,1,2,20,1,2,2,7,63,7,2,2,1,20,2,1,1,1,4,4,6,1,3,1,4,1,2,2,2,1,1,13,2,9,3,1,41,2,2,1,3,126}\right]$ $\sqrt{4004}=\left[63;\stackrel{_}{3,1,1,1,1,4,2,4,1,1,1,1,3,126}\right]$ $\sqrt{4005}=\left[63;\stackrel{_}{3,1,1,31,14,31,1,1,3,126}\right]$ $\sqrt{4006}=\left[63;\stackrel{_}{3,2,2,2,1,1,1,1,17,2,7,1,20,4,1,1,1,3,1,1,2,1,3,2,1,2,1,11,1,13,6,1,24,2,5,1,1,6,8,3,2,41,1,3,4,8,1,4,5,1,4,1,1,1,62,1,1,1,4,1,5,4,1,8,4,3,1,41,2,3,8,6,1,1,5,2,24,1,6,13,1,11,1,2,1,2,3,1,2,1,1,3,1,1,1,4,20,1,7,2,17,1,1,1,1,2,2,2,3,126}\right]$ $\sqrt{4007}=\left[63;\stackrel{_}{3,3,11,4,1,3,1,1,3,1,1,9,5,1,1,1,6,63,6,1,1,1,5,9,1,1,3,1,1,3,1,4,11,3,3,126}\right]$ $\sqrt{4008}=\left[63;\stackrel{_}{3,4,5,3,1,1,1,4,1,1,1,3,5,4,3,126}\right]$ $\sqrt{4009}=\left[63;\stackrel{_}{3,6,3,126}\right]$ $\sqrt{4010}=\left[63;\stackrel{_}{3,12,3,126}\right]$ $\sqrt{4011}=\left[63;\stackrel{_}{3,126}\right]$ $\sqrt{4012}=\left[63;\stackrel{_}{2,1,15,5,1,30,1,5,15,1,2,126}\right]$ $\sqrt{4013}=\left[63;\stackrel{_}{2,1,6,1,3,1,1,1,9,9,1,1,1,3,1,6,1,2,126}\right]$ $\sqrt{4014}=\left[63;\stackrel{_}{2,1,4,4,1,5,1,6,5,2,1,3,25,14,25,3,1,2,5,6,1,5,1,4,4,1,2,126}\right]$ $\sqrt{4015}=\left[63;\stackrel{_}{2,1,2,1,20,2,1,1,6,13,1,13,6,1,1,2,20,1,2,1,2,126}\right]$ $\sqrt{4016}=\left[63;\stackrel{_}{2,1,2,4,1,2,3,1,1,1,1,6,1,5,2,7,2,5,1,6,1,1,1,1,3,2,1,4,2,1,2,126}\right]$ $\sqrt{4017}=\left[63;\stackrel{_}{2,1,1,1,2,1,1,1,2,126}\right]$ $\sqrt{4018}=\left[63;\stackrel{_}{2,1,1,2,1,1,1,6,2,2,3,2,3,2,2,6,1,1,1,2,1,1,2,126}\right]$ $\sqrt{4019}=\left[63;\stackrel{_}{2,1,1,8,2,5,3,2,3,1,1,1,12,25,3,1,1,2,1,1,10,1,17,5,63,5,17,1,10,1,1,2,1,1,3,25,12,1,1,1,3,2,3,5,2,8,1,1,2,126}\right]$ $\sqrt{4020}=\left[63;\stackrel{_}{2,2,11,7,1,5,6,5,1,7,11,2,2,126}\right]$ $\sqrt{4021}=\left[63;\stackrel{_}{2,2,3,8,6,4,1,1,6,1,9,1,2,2,1,9,1,6,1,1,4,6,8,3,2,2,126}\right]$ $\sqrt{4022}=\left[63;\stackrel{_}{2,2,1,1,2,8,1,2,17,1,3,2,2,1,62,1,2,2,3,1,17,2,1,8,2,1,1,2,2,126}\right]$ $\sqrt{4023}=\left[63;\stackrel{_}{2,2,1,13,2,1,1,1,2,13,1,2,2,126}\right]$ $\sqrt{4024}=\left[63;\stackrel{_}{2,3,2,1,7,1,3,4,1,4,2,10,8,2,1,3,6,13,1,14,1,13,6,3,1,2,8,10,2,4,1,4,3,1,7,1,2,3,2,126}\right]$ $\sqrt{4025}=\left[63;\stackrel{_}{2,3,1,7,6,1,1,4,1,1,6,7,1,3,2,126}\right]$ $\sqrt{4026}=\left[63;\stackrel{_}{2,4,1,1,2,1,2,2,1,1,1,7,1,4,1,7,1,1,1,2,2,1,2,1,1,4,2,126}\right]$ $\sqrt{4027}=\left[63;\stackrel{_}{2,5,1,1,4,1,41,2,17,1,1,1,3,13,1,4,1,5,4,1,2,2,4,3,1,1,1,1,1,2,2,9,2,1,10,1,6,7,3,8,1,2,1,20,2,2,3,1,2,4,63,4,2,1,3,2,2,20,1,2,1,8,3,7,6,1,10,1,2,9,2,2,1,1,1,1,1,3,4,2,2,1,4,5,1,4,1,13,3,1,1,1,17,2,41,1,4,1,1,5,2,126}\right]$ $\sqrt{4028}=\left[63;\stackrel{_}{2,6,1,30,1,6,2,126}\right]$ $\sqrt{4029}=\left[63;\stackrel{_}{2,9,3,1,2,1,6,1,2,1,3,9,2,126}\right]$ $\sqrt{4030}=\left[63;\stackrel{_}{2,13,1,1,1,1,3,1,3,2,4,2,3,1,3,1,1,1,1,13,2,126}\right]$ $\sqrt{4031}=\left[63;\stackrel{_}{2,24,1,8,1,4,5,1,1,3,5,4,5,3,1,1,5,4,1,8,1,24,2,126}\right]$ $\sqrt{4032}=\left[63;\stackrel{_}{2,126}\right]$ $\sqrt{4033}=\left[63;\stackrel{_}{1,1,41,1,5,13,1,17,4,1,1,1,5,2,2,7,1,1,7,2,2,5,1,1,1,4,17,1,13,5,1,41,1,1,126}\right]$ $\sqrt{4034}=\left[63;\stackrel{_}{1,1,17,1,1,1,4,2,2,1,1,1,4,1,8,3,1,62,1,3,8,1,4,1,1,1,2,2,4,1,1,1,17,1,1,126}\right]$ $\sqrt{4035}=\left[63;\stackrel{_}{1,1,11,21,11,1,1,126}\right]$ $\sqrt{4036}=\left[63;\stackrel{_}{1,1,7,1,30,1,7,1,1,126}\right]$ $\sqrt{4037}=\left[63;\stackrel{_}{1,1,6,5,2,1,2,3,1,2,1,1,1,31,7,2,3,1,10,1,3,2,7,31,1,1,1,2,1,3,2,1,2,5,6,1,1,126}\right]$ $\sqrt{4038}=\left[63;\stackrel{_}{1,1,5,42,5,1,1,126}\right]$ $\sqrt{4039}=\left[63;\stackrel{_}{1,1,4,4,1,6,3,1,20,2,2,1,5,1,41,1,1,13,1,1,1,1,1,1,3,63,3,1,1,1,1,1,1,13,1,1,41,1,5,1,2,2,20,1,3,6,1,4,4,1,1,126}\right]$ $\sqrt{4040}=\left[63;\stackrel{_}{1,1,3,1,1,2,31,2,1,1,3,1,1,126}\right]$ $\sqrt{4041}=\left[63;\stackrel{_}{1,1,3,7,1,1,1,17,1,1,24,1,10,1,1,2,13,1,2,1,2,2,1,4,2,1,1,1,1,2,1,1,3,2,1,1,4,1,15,14,15,1,4,1,1,2,3,1,1,2,1,1,1,1,2,4,1,2,2,1,2,1,13,2,1,1,10,1,24,1,1,17,1,1,1,7,3,1,1,126}\right]$ $\sqrt{4042}=\left[63;\stackrel{_}{1,1,2,1,3,7,4,1,3,20,1,13,5,1,2,2,2,1,5,13,1,20,3,1,4,7,3,1,2,1,1,126}\right]$ $\sqrt{4043}=\left[63;\stackrel{_}{1,1,2,2,5,8,1,8,1,8,5,2,2,1,1,126}\right]$ $\sqrt{4044}=\left[63;\stackrel{_}{1,1,2,4,1,8,1,30,1,8,1,4,2,1,1,126}\right]$ $\sqrt{4045}=\left[63;\stackrel{_}{1,1,1,1,126}\right]$ $\sqrt{4046}=\left[63;\stackrel{_}{1,1,1,1,4,3,2,2,1,1,9,4,1,62,1,4,9,1,1,2,2,3,4,1,1,1,1,126}\right]$ $\sqrt{4047}=\left[63;\stackrel{_}{1,1,1,1,1,1,8,2,8,1,1,1,1,1,1,126}\right]$ $\sqrt{4048}=\left[63;\stackrel{_}{1,1,1,1,1,13,1,1,17,1,1,1,17,1,1,13,1,1,1,1,1,126}\right]$ $\sqrt{4049}=\left[63;\stackrel{_}{1,1,1,2,1,1,15,3,25,7,1,10,1,2,3,1,3,4,1,4,1,2,1,1,1,1,2,1,4,1,4,3,1,3,2,1,10,1,7,25,3,15,1,1,2,1,1,1,126}\right]$ $\sqrt{4050}=\left[63;\stackrel{_}{1,1,1,3,2,3,1,1,1,126}\right]$ $\sqrt{4051}=\left[63;\stackrel{_}{1,1,1,5,8,3,4,2,1,1,6,2,12,3,1,3,2,20,1,3,2,3,2,2,2,1,1,4,1,1,41,1,7,1,1,24,1,13,5,2,6,4,11,3,63,3,11,4,6,2,5,13,1,24,1,1,7,1,41,1,1,4,1,1,2,2,2,3,2,3,1,20,2,3,1,3,12,2,6,1,1,2,4,3,8,5,1,1,1,126}\right]$ $\sqrt{4052}=\left[63;\stackrel{_}{1,1,1,9,7,1,5,1,4,1,2,7,1,1,1,1,10,1,30,1,10,1,1,1,1,7,2,1,4,1,5,1,7,9,1,1,1,126}\right]$ $\sqrt{4053}=\left[63;\stackrel{_}{1,1,1,31,6,31,1,1,1,126}\right]$ $\sqrt{4054}=\left[63;\stackrel{_}{1,2,25,7,2,4,1,1,1,2,8,8,1,41,1,1,3,1,7,1,2,2,6,1,1,1,5,2,2,2,1,2,3,13,1,5,1,3,2,1,1,3,20,1,17,4,5,3,2,4,3,1,1,12,5,1,62,1,5,12,1,1,3,4,2,3,5,4,17,1,20,3,1,1,2,3,1,5,1,13,3,2,1,2,2,2,5,1,1,1,6,2,2,1,7,1,3,1,1,41,1,8,8,2,1,1,1,4,2,7,25,2,1,126}\right]$ $\sqrt{4055}=\left[63;\stackrel{_}{1,2,8,1,3,4,1,1,1,3,1,2,1,24,1,2,1,3,1,1,1,4,3,1,8,2,1,126}\right]$ $\sqrt{4056}=\left[63;\stackrel{_}{1,2,5,4,1,9,1,4,5,2,1,126}\right]$ $\sqrt{4057}=\left[63;\stackrel{_}{1,2,3,1,1,1,4,1,8,1,41,1,1,3,2,1,4,1,1,1,1,2,1,1,1,13,1,1,11,15,1,5,7,1,3,1,5,3,1,2,4,1,17,2,1,1,2,17,1,4,2,1,3,5,1,3,1,7,5,1,15,11,1,1,13,1,1,1,2,1,1,1,1,4,1,2,3,1,1,41,1,8,1,4,1,1,1,3,2,1,126}\right]$ $\sqrt{4058}=\left[63;\stackrel{_}{1,2,2,1,3,2,2,3,1,2,2,1,126}\right]$ $\sqrt{4059}=\left[63;\stackrel{_}{1,2,2,4,1,2,63,2,1,4,2,2,1,126}\right]$ $\sqrt{4060}=\left[63;\stackrel{_}{1,2,1,1,4,1,2,1,4,1,1,2,1,126}\right]$ $\sqrt{4061}=\left[63;\stackrel{_}{1,2,1,1,1,5,1,2,1,3,1,4,3,4,4,6,7,2,1,31,5,1,1,24,1,17,4,17,1,24,1,1,5,31,1,2,7,6,4,4,3,4,1,3,1,2,1,5,1,1,1,2,1,126}\right]$ $\sqrt{4062}=\left[63;\stackrel{_}{1,2,1,3,8,1,5,5,1,1,1,1,1,20,1,1,1,1,1,5,5,1,8,3,1,2,1,126}\right]$ $\sqrt{4063}=\left[63;\stackrel{_}{1,2,1,6,1,2,1,126}\right]$ $\sqrt{4064}=\left[63;\stackrel{_}{1,2,1,126}\right]$ $\sqrt{4065}=\left[63;\stackrel{_}{1,3,8,3,1,126}\right]$ $\sqrt{4066}=\left[63;\stackrel{_}{1,3,3,1,6,3,8,5,2,2,1,4,2,1,1,3,1,1,1,13,1,1,7,1,62,1,7,1,1,13,1,1,1,3,1,1,2,4,1,2,2,5,8,3,6,1,3,3,1,126}\right]$ $\sqrt{4067}=\left[63;\stackrel{_}{1,3,2,2,6,3,3,2,3,3,6,2,2,3,1,126}\right]$ $\sqrt{4068}=\left[63;\stackrel{_}{1,3,1,1,3,2,3,9,1,1,11,14,11,1,1,9,3,2,3,1,1,3,1,126}\right]$ $\sqrt{4069}=\left[63;\stackrel{_}{1,3,1,2,1,2,1,9,1,8,1,9,1,2,1,2,1,3,1,126}\right]$ $\sqrt{4070}=\left[63;\stackrel{_}{1,3,1,10,1,3,1,126}\right]$ $\sqrt{4071}=\left[63;\stackrel{_}{1,4,8,1,10,1,2,2,3,1,4,1,3,2,2,1,10,1,8,4,1,126}\right]$ $\sqrt{4072}=\left[63;\stackrel{_}{1,4,3,13,1,6,1,1,2,1,2,1,4,1,4,2,31,2,4,1,4,1,2,1,2,1,1,6,1,13,3,4,1,126}\right]$ $\sqrt{4073}=\left[63;\stackrel{_}{1,4,1,1,3,1,5,1,15,9,1,3,11,2,1,7,3,3,7,1,2,11,3,1,9,15,1,5,1,3,1,1,4,1,126}\right]$ $\sqrt{4074}=\left[63;\stackrel{_}{1,4,1,4,3,1,1,1,20,1,1,1,3,4,1,4,1,126}\right]$ $\sqrt{4075}=\left[63;\stackrel{_}{1,5,11,2,3,1,1,1,3,2,11,5,1,126}\right]$ $\sqrt{4076}=\left[63;\stackrel{_}{1,5,2,1,1,4,1,1,17,1,2,4,15,1,2,1,2,2,4,7,3,1,1,24,1,30,1,24,1,1,3,7,4,2,2,1,2,1,15,4,2,1,17,1,1,4,1,1,2,5,1,126}\right]$ $\sqrt{4077}=\left[63;\stackrel{_}{1,5,1,2,1,2,4,2,1,2,1,5,1,126}\right]$ $\sqrt{4078}=\left[63;\stackrel{_}{1,6,9,1,2,7,5,1,17,2,2,4,3,20,1,41,1,1,1,1,1,2,2,1,8,2,2,1,1,3,5,1,4,13,1,62,1,13,4,1,5,3,1,1,2,2,8,1,2,2,1,1,1,1,1,41,1,20,3,4,2,2,17,1,5,7,2,1,9,6,1,126}\right]$ $\sqrt{4079}=\left[63;\stackrel{_}{1,6,1,1,11,12,1,2,5,4,1,2,1,1,1,4,2,9,2,1,2,25,5,1,3,3,2,63,2,3,3,1,5,25,2,1,2,9,2,4,1,1,1,2,1,4,5,2,1,12,11,1,1,6,1,126}\right]$ $\sqrt{4080}=\left[63;\stackrel{_}{1,6,1,126}\right]$ $\sqrt{4081}=\left[63;\stackrel{_}{1,7,1,1,9,3,2,1,6,1,4,2,4,1,6,1,2,3,9,1,1,7,1,126}\right]$ $\sqrt{4082}=\left[63;\stackrel{_}{1,8,7,2,2,7,8,1,126}\right]$ $\sqrt{4083}=\left[63;\stackrel{_}{1,8,1,5,5,2,1,1,2,2,4,2,63,2,4,2,2,1,1,2,5,5,1,8,1,126}\right]$ $\sqrt{4084}=\left[63;\stackrel{_}{1,9,1,1,1,13,1,1,5,25,2,1,1,1,1,1,7,2,1,2,2,3,2,4,1,2,11,3,1,3,1,1,1,6,1,7,8,2,1,1,5,1,3,1,7,1,2,1,1,1,41,1,30,1,41,1,1,1,2,1,7,1,3,1,5,1,1,2,8,7,1,6,1,1,1,3,1,3,11,2,1,4,2,3,2,2,1,2,7,1,1,1,1,1,2,25,5,1,1,13,1,1,1,9,1,126}\right]$ $\sqrt{4085}=\left[63;\stackrel{_}{1,10,1,1,1,2,4,31,1,2,1,2,6,2,1,2,1,31,4,2,1,1,1,10,1,126}\right]$ $\sqrt{4086}=\left[63;\stackrel{_}{1,11,1,3,1,4,3,6,2,2,1,1,24,1,62,1,24,1,1,2,2,6,3,4,1,3,1,11,1,126}\right]$ $\sqrt{4087}=\left[63;\stackrel{_}{1,13,4,1,1,1,41,1,41,1,1,1,4,13,1,126}\right]$ $\sqrt{4088}=\left[63;\stackrel{_}{1,14,1,126}\right]$ $\sqrt{4089}=\left[63;\stackrel{_}{1,17,3,1,1,2,25,5,3,2,5,7,1,4,4,4,1,7,5,2,3,5,25,2,1,1,3,17,1,126}\right]$ $\sqrt{4090}=\left[63;\stackrel{_}{1,20,3,13,1,7,1,1,2,12,2,1,1,7,1,13,3,20,1,126}\right]$ $\sqrt{4091}=\left[63;\stackrel{_}{1,24,1,1,2,4,1,2,1,1,4,2,1,9,6,1,1,1,2,3,12,2,63,2,12,3,2,1,1,1,6,9,1,2,4,1,1,2,1,4,2,1,1,24,1,126}\right]$ $\sqrt{4092}=\left[63;\stackrel{_}{1,30,1,126}\right]$ $\sqrt{4093}=\left[63;\stackrel{_}{1,41,1,1,1,13,1,1,4,4,1,1,13,1,1,1,41,1,126}\right]$ $\sqrt{4094}=\left[63;\stackrel{_}{1,62,1,126}\right]$ $\sqrt{4095}=\left[63;\stackrel{_}{1,126}\right]$ $\sqrt{4097}=\left[64;\stackrel{_}{128}\right]$ $\sqrt{4098}=\left[64;\stackrel{_}{64,128}\right]$ $\sqrt{4099}=\left[64;\stackrel{_}{42,1,2,13,1,8,4,1,1,1,2,2,2,7,8,2,2,25,4,1,7,1,2,1,3,2,1,1,2,1,2,3,1,9,12,1,2,2,1,3,1,1,3,4,1,5,3,2,17,1,6,5,1,20,1,1,63,1,1,20,1,5,6,1,17,2,3,5,1,4,3,1,1,3,1,2,2,1,12,9,1,3,2,1,2,1,1,2,3,1,2,1,7,1,4,25,2,2,8,7,2,2,2,1,1,1,4,8,1,13,2,1,42,128}\right]$ $\sqrt{4100}=\left[64;\stackrel{_}{32,128}\right]$ $\sqrt{4101}=\left[64;\stackrel{_}{25,1,1,1,1,4,1,1,11,10,1,1,2,2,1,1,2,1,1,6,6,3,1,31,3,1,5,1,1,1,6,1,7,1,2,42,2,1,7,1,6,1,1,1,5,1,3,31,1,3,6,6,1,1,2,1,1,2,2,1,1,10,11,1,1,4,1,1,1,1,25,128}\right]$ $\sqrt{4102}=\left[64;\stackrel{_}{21,2,1,13,1,1,3,1,1,1,1,2,5,1,2,1,1,8,1,1,2,1,5,2,1,1,1,1,3,1,1,13,1,2,21,128}\right]$ $\sqrt{4103}=\left[64;\stackrel{_}{18,3,2,2,5,2,2,3,18,128}\right]$ $\sqrt{4104}=\left[64;\stackrel{_}{16,128}\right]$ $\sqrt{4105}=\left[64;\stackrel{_}{14,4,2,1,7,3,6,2,2,1,4,1,1,1,2,4,1,24,1,4,2,1,1,1,4,1,2,2,6,3,7,1,2,4,14,128}\right]$ $\sqrt{4106}=\left[64;\stackrel{_}{12,1,4,4,1,12,128}\right]$ $\sqrt{4107}=\left[64;\stackrel{_}{11,1,1,1,4,3,1,2,42,2,1,3,4,1,1,1,11,128}\right]$ $\sqrt{4108}=\left[64;\stackrel{_}{10,1,2,13,1,8,1,13,2,1,10,128}\right]$ $\sqrt{4109}=\left[64;\stackrel{_}{9,1,5,1,5,1,1,4,25,2,2,1,1,1,3,31,1,3,2,4,1,2,6,18,6,2,1,4,2,3,1,31,3,1,1,1,2,2,25,4,1,1,5,1,5,1,9,128}\right]$ $\sqrt{4110}=\left[64;\stackrel{_}{9,6,1,1,1,3,8,3,1,1,1,6,9,128}\right]$ $\sqrt{4111}=\left[64;\stackrel{_}{8,1,1,5,1,1,2,1,2,1,17,1,1,2,2,1,42,25,1,1,1,1,1,9,4,5,1,6,3,1,1,13,1,2,8,4,1,4,3,12,1,1,20,1,5,1,3,1,8,2,1,2,1,3,1,2,3,1,3,1,1,63,1,1,3,1,3,2,1,3,1,2,1,2,8,1,3,1,5,1,20,1,1,12,3,4,1,4,8,2,1,13,1,1,3,6,1,5,4,9,1,1,1,1,1,25,42,1,2,2,1,1,17,1,2,1,2,1,1,5,1,1,8,128}\right]$ $\sqrt{4112}=\left[64;\stackrel{_}{8,128}\right]$ $\sqrt{4113}=\left[64;\stackrel{_}{7,1,1,6,4,1,1,2,15,1,1,1,3,1,3,4,2,17,1,7,14,7,1,17,2,4,3,1,3,1,1,1,15,2,1,1,4,6,1,1,7,128}\right]$ $\sqrt{4114}=\left[64;\stackrel{_}{7,8,2,2,3,1,6,1,3,2,2,8,7,128}\right]$ $\sqrt{4115}=\left[64;\stackrel{_}{6,1,2,1,10,1,11,1,10,1,2,1,6,128}\right]$ $\sqrt{4116}=\left[64;\stackrel{_}{6,2,2,4,1,2,1,1,1,7,2,1,1,2,42,2,1,1,2,7,1,1,1,2,1,4,2,2,6,128}\right]$ $\sqrt{4117}=\left[64;\stackrel{_}{6,9,1,2,2,1,1,2,1,42,18,3,4,3,1,9,1,13,2,1,5,2,3,2,3,31,1,3,1,3,1,1,1,2,11,3,2,10,3,1,3,1,4,1,3,1,3,10,2,3,11,2,1,1,1,3,1,3,1,31,3,2,3,2,5,1,2,13,1,9,1,3,4,3,18,42,1,2,1,1,2,2,1,9,6,128}\right]$ $\sqrt{4118}=\left[64;\stackrel{_}{5,1,4,1,2,1,17,1,1,2,9,2,9,2,1,1,17,1,2,1,4,1,5,128}\right]$ $\sqrt{4119}=\left[64;\stackrel{_}{5,1,1,2,1,12,8,2,11,5,21,5,11,2,8,12,1,2,1,1,5,128}\right]$ $\sqrt{4120}=\left[64;\stackrel{_}{5,2,1,13,1,1,2,1,3,2,2,1,5,1,2,2,3,1,2,1,1,13,1,2,5,128}\right]$ $\sqrt{4121}=\left[64;\stackrel{_}{5,7,1,4,1,2,2,1,1,1,2,1,1,2,1,1,1,2,2,1,4,1,7,5,128}\right]$ $\sqrt{4122}=\left[64;\stackrel{_}{4,1,13,2,7,14,7,2,13,1,4,128}\right]$ $\sqrt{4123}=\left[64;\stackrel{_}{4,1,2,1,42,14,4,14,42,1,2,1,4,128}\right]$ $\sqrt{4124}=\left[64;\stackrel{_}{4,1,1,2,1,1,1,9,4,25,2,3,1,15,3,1,1,1,1,5,1,4,3,2,6,3,18,32,18,3,6,2,3,4,1,5,1,1,1,1,3,15,1,3,2,25,4,9,1,1,1,2,1,1,4,128}\right]$ $\sqrt{4125}=\left[64;\stackrel{_}{4,2,2,1,2,4,1,3,3,31,1,4,5,1,10,1,5,4,1,31,3,3,1,4,2,1,2,2,4,128}\right]$ $\sqrt{4126}=\left[64;\stackrel{_}{4,3,1,1,1,4,8,2,1,6,2,5,2,1,2,21,25,1,1,1,4,1,12,42,1,2,1,10,1,13,2,1,3,1,1,1,1,4,1,1,8,64,8,1,1,4,1,1,1,1,3,1,2,13,1,10,1,2,1,42,12,1,4,1,1,1,25,21,2,1,2,5,2,6,1,2,8,4,1,1,1,3,4,128}\right]$ $\sqrt{4127}=\left[64;\stackrel{_}{4,7,3,4,8,1,17,2,6,3,1,1,1,1,1,63,1,1,1,1,1,3,6,2,17,1,8,4,3,7,4,128}\right]$ $\sqrt{4128}=\left[64;\stackrel{_}{4,128}\right]$ $\sqrt{4129}=\left[64;\stackrel{_}{3,1,7,1,4,2,7,1,1,2,1,2,7,5,4,1,1,3,2,1,13,1,1,2,2,8,6,1,1,1,4,2,25,3,1,42,11,1,1,1,15,2,2,5,5,2,2,15,1,1,1,11,42,1,3,25,2,4,1,1,1,6,8,2,2,1,1,13,1,2,3,1,1,4,5,7,2,1,2,1,1,7,2,4,1,7,1,3,128}\right]$ $\sqrt{4130}=\left[64;\stackrel{_}{3,1,3,2,1,1,8,1,1,2,3,1,3,128}\right]$ $\sqrt{4131}=\left[64;\stackrel{_}{3,1,1,1,63,1,1,1,3,128}\right]$ $\sqrt{4132}=\left[64;\stackrel{_}{3,1,1,3,2,4,6,1,1,5,1,1,2,2,4,2,1,10,42,1,3,5,1,6,1,2,1,1,1,1,17,1,3,14,32,14,3,1,17,1,1,1,1,2,1,6,1,5,3,1,42,10,1,2,4,2,2,1,1,5,1,1,6,4,2,3,1,1,3,128}\right]$ $\sqrt{4133}=\left[64;\stackrel{_}{3,2,7,7,2,3,128}\right]$ $\sqrt{4134}=\left[64;\stackrel{_}{3,2,1,1,1,12,4,2,1,4,2,4,1,2,4,12,1,1,1,2,3,128}\right]$ $\sqrt{4135}=\left[64;\stackrel{_}{3,3,2,4,1,1,20,1,7,1,1,1,1,1,2,1,2,13,1,11,1,13,2,1,2,1,1,1,1,1,7,1,20,1,1,4,2,3,3,128}\right]$ $\sqrt{4136}=\left[64;\stackrel{_}{3,4,1,4,3,128}\right]$ $\sqrt{4137}=\left[64;\stackrel{_}{3,7,1,2,2,2,1,1,3,3,5,18,5,3,3,1,1,2,2,2,1,7,3,128}\right]$ $\sqrt{4138}=\left[64;\stackrel{_}{3,18,21,2,1,1,2,1,2,2,1,13,1,1,2,4,1,1,4,2,1,1,13,1,2,2,1,2,1,1,2,21,18,3,128}\right]$ $\sqrt{4139}=\left[64;\stackrel{_}{2,1,63,1,2,128}\right]$ $\sqrt{4140}=\left[64;\stackrel{_}{2,1,11,32,11,1,2,128}\right]$ $\sqrt{4141}=\left[64;\stackrel{_}{2,1,5,1,3,3,3,5,1,4,1,3,14,25,1,2,31,1,5,6,3,1,2,1,4,2,2,2,2,4,1,2,1,3,6,5,1,31,2,1,25,14,3,1,4,1,5,3,3,3,1,5,1,2,128}\right]$ $\sqrt{4142}=\left[64;\stackrel{_}{2,1,3,1,3,2,1,2,1,2,3,1,3,1,2,128}\right]$ $\sqrt{4143}=\left[64;\stackrel{_}{2,1,2,1,2,1,1,2,1,9,5,2,42,2,5,9,1,2,1,1,2,1,2,1,2,128}\right]$ $\sqrt{4144}=\left[64;\stackrel{_}{2,1,2,13,1,13,2,1,2,128}\right]$ $\sqrt{4145}=\left[64;\stackrel{_}{2,1,1,1,1,1,2,1,1,11,7,1,24,1,7,11,1,1,2,1,1,1,1,1,2,128}\right]$ $\sqrt{4146}=\left[64;\stackrel{_}{2,1,1,3,5,3,8,1,7,1,2,3,1,17,1,1,1,2,7,5,64,5,7,2,1,1,1,17,1,3,2,1,7,1,8,3,5,3,1,1,2,128}\right]$ $\sqrt{4147}=\left[64;\stackrel{_}{2,1,1,13,1,2,2,5,2,2,1,13,1,1,2,128}\right]$ $\sqrt{4148}=\left[64;\stackrel{_}{2,2,7,1,1,1,6,7,1,9,32,9,1,7,6,1,1,1,7,2,2,128}\right]$ $\sqrt{4149}=\left[64;\stackrel{_}{2,2,2,1,2,1,6,1,5,1,1,3,25,2,13,1,4,1,2,31,1,5,1,4,3,2,1,2,6,14,6,2,1,2,3,4,1,5,1,31,2,1,4,1,13,2,25,3,1,1,5,1,6,1,2,1,2,2,2,128}\right]$ $\sqrt{4150}=\left[64;\stackrel{_}{2,2,1,1,1,4,3,11,2,2,21,14,3,1,2,1,1,4,1,1,2,1,3,14,21,2,2,11,3,4,1,1,1,2,2,128}\right]$ $\sqrt{4151}=\left[64;\stackrel{_}{2,2,1,63,1,2,2,128}\right]$ $\sqrt{4152}=\left[64;\stackrel{_}{2,3,2,2,5,5,5,2,2,3,2,128}\right]$ $\sqrt{4153}=\left[64;\stackrel{_}{2,3,1,17,1,1,1,2,1,4,1,1,1,4,7,1,5,3,1,6,42,1,4,2,1,1,5,1,1,5,15,1,13,2,1,1,1,1,2,2,1,1,1,1,2,13,1,15,5,1,1,5,1,1,2,4,1,42,6,1,3,5,1,7,4,1,1,1,4,1,2,1,1,1,17,1,3,2,128}\right]$ $\sqrt{4154}=\left[64;\stackrel{_}{2,4,1,1,1,12,4,12,1,1,1,4,2,128}\right]$ $\sqrt{4155}=\left[64;\stackrel{_}{2,5,1,1,1,3,1,1,1,5,2,128}\right]$ $\sqrt{4156}=\left[64;\stackrel{_}{2,7,11,1,1,2,2,1,10,25,1,2,3,1,4,1,1,1,1,13,1,2,1,1,4,4,1,15,3,4,8,2,1,2,1,9,5,3,1,2,2,6,42,1,4,1,1,1,2,3,1,1,8,32,8,1,1,3,2,1,1,1,4,1,42,6,2,2,1,3,5,9,1,2,1,2,8,4,3,15,1,4,4,1,1,2,1,13,1,1,1,1,4,1,3,2,1,25,10,1,2,2,1,1,11,7,2,128}\right]$ $\sqrt{4157}=\left[64;\stackrel{_}{2,9,2,2,1,2,31,1,6,1,1,1,1,1,1,6,1,31,2,1,2,2,9,2,128}\right]$ $\sqrt{4158}=\left[64;\stackrel{_}{2,13,1,4,1,13,2,128}\right]$ $\sqrt{4159}=\left[64;\stackrel{_}{2,25,3,2,1,4,2,5,1,2,4,2,2,1,6,12,1,2,1,63,1,2,1,12,6,1,2,2,4,2,1,5,2,4,1,2,3,25,2,128}\right]$ $\sqrt{4160}=\left[64;\stackrel{_}{2,128}\right]$ $\sqrt{4161}=\left[64;\stackrel{_}{1,1,42,1,1,128}\right]$ $\sqrt{4162}=\left[64;\stackrel{_}{1,1,17,1,13,2,1,1,3,1,1,3,2,1,6,2,8,1,3,64,3,1,8,2,6,1,2,3,1,1,3,1,1,2,13,1,17,1,1,128}\right]$ $\sqrt{4163}=\left[64;\stackrel{_}{1,1,11,4,2,1,3,9,1,1,1,9,3,1,2,4,11,1,1,128}\right]$ $\sqrt{4164}=\left[64;\stackrel{_}{1,1,8,9,1,4,3,1,4,1,5,1,1,1,2,10,2,1,1,1,5,1,4,1,3,4,1,9,8,1,1,128}\right]$ $\sqrt{4165}=\left[64;\stackrel{_}{1,1,6,3,2,3,6,1,1,128}\right]$ $\sqrt{4166}=\left[64;\stackrel{_}{1,1,5,9,25,1,2,2,3,2,1,2,2,4,1,2,1,6,1,5,1,12,18,2,1,3,64,3,1,2,18,12,1,5,1,6,1,2,1,4,2,2,1,2,3,2,2,1,25,9,5,1,1,128}\right]$ $\sqrt{4167}=\left[64;\stackrel{_}{1,1,4,3,1,1,2,1,4,1,8,2,1,1,11,7,11,1,1,2,8,1,4,1,2,1,1,3,4,1,1,128}\right]$ $\sqrt{4168}=\left[64;\stackrel{_}{1,1,3,1,1,1,31,1,1,1,3,1,1,128}\right]$ $\sqrt{4169}=\left[64;\stackrel{_}{1,1,3,5,3,25,1,1,17,1,15,5,9,1,2,1,3,1,2,2,3,1,1,1,1,2,1,7,2,1,6,1,10,1,6,1,2,7,1,2,1,1,1,1,3,2,2,1,3,1,2,1,9,5,15,1,17,1,1,25,3,5,3,1,1,128}\right]$ $\sqrt{4170}=\left[64;\stackrel{_}{1,1,2,1,4,3,1,20,1,3,4,1,2,1,1,128}\right]$ $\sqrt{4171}=\left[64;\stackrel{_}{1,1,2,1,1,128}\right]$ $\sqrt{4172}=\left[64;\stackrel{_}{1,1,2,4,18,4,2,1,1,128}\right]$ $\sqrt{4173}=\left[64;\stackrel{_}{1,1,2,31,1,8,1,31,2,1,1,128}\right]$ $\sqrt{4174}=\left[64;\stackrel{_}{1,1,1,1,5,1,1,4,4,11,1,1,25,3,8,1,9,21,2,3,3,4,1,6,2,1,2,1,1,1,2,2,3,1,7,1,5,3,1,2,1,13,1,1,1,1,1,6,1,42,4,1,17,1,1,1,12,3,1,5,8,2,3,1,2,3,3,64,3,3,2,1,3,2,8,5,1,3,12,1,1,1,17,1,4,42,1,6,1,1,1,1,1,13,1,2,1,3,5,1,7,1,3,2,2,1,1,1,2,1,2,6,1,4,3,3,2,21,9,1,8,3,25,1,1,11,4,4,1,1,5,1,1,1,1,128}\right]$ $\sqrt{4175}=\left[64;\stackrel{_}{1,1,1,1,2,4,1,3,1,1,1,3,1,4,2,1,1,1,1,128}\right]$ $\sqrt{4176}=\left[64;\stackrel{_}{1,1,1,1,1,4,1,1,5,14,5,1,1,4,1,1,1,1,1,128}\right]$ $\sqrt{4177}=\left[64;\stackrel{_}{1,1,1,2,2,1,15,2,4,1,9,7,1,42,4,1,3,4,5,6,1,1,1,1,2,1,2,2,3,14,14,3,2,2,1,2,1,1,1,1,6,5,4,3,1,4,42,1,7,9,1,4,2,15,1,2,2,1,1,1,128}\right]$ $\sqrt{4178}=\left[64;\stackrel{_}{1,1,1,3,7,3,64,3,7,3,1,1,1,128}\right]$ $\sqrt{4179}=\left[64;\stackrel{_}{1,1,1,4,1,1,42,1,1,4,1,1,1,128}\right]$ $\sqrt{4180}=\left[64;\stackrel{_}{1,1,1,7,2,2,2,7,1,1,1,128}\right]$ $\sqrt{4181}=\left[64;\stackrel{_}{1,1,1,17,1,4,4,2,2,2,31,1,10,1,3,1,2,2,1,3,1,10,1,31,2,2,2,4,4,1,17,1,1,1,128}\right]$ $\sqrt{4182}=\left[64;\stackrel{_}{1,2,64,2,1,128}\right]$ $\sqrt{4183}=\left[64;\stackrel{_}{1,2,11,2,2,1,5,5,1,63,1,5,5,1,2,2,11,2,1,128}\right]$ $\sqrt{4184}=\left[64;\stackrel{_}{1,2,6,7,2,4,1,2,2,2,1,1,15,1,1,2,2,2,1,4,2,7,6,2,1,128}\right]$ $\sqrt{4185}=\left[64;\stackrel{_}{1,2,4,7,1,5,1,13,1,1,11,4,11,1,1,13,1,5,1,7,4,2,1,128}\right]$ $\sqrt{4186}=\left[64;\stackrel{_}{1,2,3,14,12,1,6,1,2,4,1,4,1,4,2,1,6,1,12,14,3,2,1,128}\right]$ $\sqrt{4187}=\left[64;\stackrel{_}{1,2,2,2,2,1,1,2,18,9,1,9,18,2,1,1,2,2,2,2,1,128}\right]$ $\sqrt{4188}=\left[64;\stackrel{_}{1,2,1,1,42,1,1,2,1,128}\right]$ $\sqrt{4189}=\left[64;\stackrel{_}{1,2,1,1,1,1,11,6,2,1,1,2,3,1,1,6,4,42,1,9,1,4,3,1,2,1,1,3,1,7,1,5,1,1,2,2,2,13,1,31,2,3,9,1,2,25,1,1,5,8,2,4,3,10,2,10,3,4,2,8,5,1,1,25,2,1,9,3,2,31,1,13,2,2,2,1,1,5,1,7,1,3,1,1,2,1,3,4,1,9,1,42,4,6,1,1,3,2,1,1,2,6,11,1,1,1,1,2,1,128}\right]$ $\sqrt{4190}=\left[64;\stackrel{_}{1,2,1,2,2,2,4,1,1,3,3,1,8,2,12,2,8,1,3,3,1,1,4,2,2,2,1,2,1,128}\right]$ $\sqrt{4191}=\left[64;\stackrel{_}{1,2,1,4,2,3,21,3,2,4,1,2,1,128}\right]$ $\sqrt{4192}=\left[64;\stackrel{_}{1,2,1,13,1,1,1,3,3,1,3,2,2,3,5,2,1,31,1,2,5,3,2,2,3,1,3,3,1,1,1,13,1,2,1,128}\right]$ $\sqrt{4193}=\left[64;\stackrel{_}{1,3,18,3,1,128}\right]$ $\sqrt{4194}=\left[64;\stackrel{_}{1,3,5,2,1,1,1,2,64,2,1,1,1,2,5,3,1,128}\right]$ $\sqrt{4195}=\left[64;\stackrel{_}{1,3,3,14,11,1,2,2,2,8,1,5,3,1,1,1,3,1,1,5,1,1,1,1,4,2,1,1,1,20,1,24,1,20,1,1,1,2,4,1,1,1,1,5,1,1,3,1,1,1,3,5,1,8,2,2,2,1,11,14,3,3,1,128}\right]$ $\sqrt{4196}=\left[64;\stackrel{_}{1,3,2,9,1,1,11,3,1,25,6,2,3,1,1,2,2,1,1,1,1,1,6,5,32,5,6,1,1,1,1,1,2,2,1,1,3,2,6,25,1,3,11,1,1,9,2,3,1,128}\right]$ $\sqrt{4197}=\left[64;\stackrel{_}{1,3,1,1,1,2,1,6,10,1,1,1,5,1,1,17,1,31,2,4,7,2,1,1,42,1,1,2,7,4,2,31,1,17,1,1,5,1,1,1,10,6,1,2,1,1,1,3,1,128}\right]$ $\sqrt{4198}=\left[64;\stackrel{_}{1,3,1,4,5,2,2,1,6,2,21,7,1,1,2,1,3,1,3,42,1,13,2,2,1,2,9,1,1,2,64,2,1,1,9,2,1,2,2,13,1,42,3,1,3,1,2,1,1,7,21,2,6,1,2,2,5,4,1,3,1,128}\right]$ $\sqrt{4199}=\left[64;\stackrel{_}{1,3,1,128}\right]$ $\sqrt{4200}=\left[64;\stackrel{_}{1,4,5,4,1,128}\right]$ $\sqrt{4201}=\left[64;\stackrel{_}{1,4,2,2,4,15,1,42,3,1,2,7,1,2,1,4,1,1,1,13,1,3,8,2,1,1,2,1,1,1,4,1,1,4,3,1,25,6,7,2,5,1,2,2,1,1,8,18,2,2,18,8,1,1,2,2,1,5,2,7,6,25,1,3,4,1,1,4,1,1,1,2,1,1,2,8,3,1,13,1,1,1,4,1,2,1,7,2,1,3,42,1,15,4,2,2,4,1,128}\right]$ $\sqrt{4202}=\left[64;\stackrel{_}{1,4,1,1,1,4,2,1,17,1,4,1,17,1,2,4,1,1,1,4,1,128}\right]$ $\sqrt{4203}=\left[64;\stackrel{_}{1,4,1,9,7,9,1,4,1,128}\right]$ $\sqrt{4204}=\left[64;\stackrel{_}{1,5,5,2,8,5,3,1,1,25,2,1,2,1,1,3,42,1,17,1,1,4,1,2,15,1,5,1,7,1,3,1,2,1,10,14,3,5,1,5,1,1,1,3,1,4,1,1,1,1,1,1,1,2,3,1,4,32,4,1,3,2,1,1,1,1,1,1,1,4,1,3,1,1,1,5,1,5,3,14,10,1,2,1,3,1,7,1,5,1,15,2,1,4,1,1,17,1,42,3,1,1,2,1,2,25,1,1,3,5,8,2,5,5,1,128}\right]$ $\sqrt{4205}=\left[64;\stackrel{_}{1,5,2,31,1,24,1,31,2,5,1,128}\right]$ $\sqrt{4206}=\left[64;\stackrel{_}{1,5,1,5,25,1,3,2,1,3,4,4,1,20,1,4,4,3,1,2,3,1,25,5,1,5,1,128}\right]$ $\sqrt{4207}=\left[64;\stackrel{_}{1,6,4,1,1,1,20,1,42,3,2,13,1,63,1,13,2,3,42,1,20,1,1,1,4,6,1,128}\right]$ $\sqrt{4208}=\left[64;\stackrel{_}{1,6,1,1,1,3,2,2,18,8,18,2,2,3,1,1,1,6,1,128}\right]$ $\sqrt{4209}=\left[64;\stackrel{_}{1,7,8,1,1,9,2,4,1,2,1,1,25,2,1,1,1,42,1,1,1,2,25,1,1,2,1,4,2,9,1,1,8,7,1,128}\right]$ $\sqrt{4210}=\left[64;\stackrel{_}{1,7,1,1,1,13,1,3,3,1,13,1,1,1,7,1,128}\right]$ $\sqrt{4211}=\left[64;\stackrel{_}{1,8,3,1,1,2,12,1,1,2,3,3,4,1,2,4,1,5,11,1,1,1,2,9,1,1,1,1,5,25,1,3,1,1,17,1,63,1,17,1,1,3,1,25,5,1,1,1,1,9,2,1,1,1,11,5,1,4,2,1,4,3,3,2,1,1,12,2,1,1,3,8,1,128}\right]$ $\sqrt{4212}=\left[64;\stackrel{_}{1,8,1,128}\right]$ $\sqrt{4213}=\left[64;\stackrel{_}{1,9,1,4,1,2,1,3,2,4,2,1,2,1,1,1,3,3,3,42,1,31,2,10,3,14,9,1,10,1,9,14,3,10,2,31,1,42,3,3,3,1,1,1,2,1,2,4,2,3,1,2,1,4,1,9,1,128}\right]$ $\sqrt{4214}=\left[64;\stackrel{_}{1,10,1,4,3,1,1,1,1,2,25,1,1,2,1,1,25,2,1,1,1,1,3,4,1,10,1,128}\right]$ $\sqrt{4215}=\left[64;\stackrel{_}{1,11,1,128}\right]$ $\sqrt{4216}=\left[64;\stackrel{_}{1,13,2,3,2,4,1,3,8,2,1,1,8,16,8,1,1,2,8,3,1,4,2,3,2,13,1,128}\right]$ $\sqrt{4217}=\left[64;\stackrel{_}{1,15,4,7,1,6,1,3,5,2,1,1,2,1,11,11,1,2,1,1,2,5,3,1,6,1,7,4,15,1,128}\right]$ $\sqrt{4218}=\left[64;\stackrel{_}{1,17,1,1,3,2,2,1,2,1,2,2,3,1,1,17,1,128}\right]$ $\sqrt{4219}=\left[64;\stackrel{_}{1,20,1,1,1,13,1,3,2,1,1,25,2,1,1,3,1,2,1,2,1,2,6,2,8,5,12,1,3,1,7,1,6,3,42,1,63,1,42,3,6,1,7,1,3,1,12,5,8,2,6,2,1,2,1,2,1,3,1,1,2,25,1,1,2,3,1,13,1,1,1,20,1,128}\right]$ $\sqrt{4220}=\left[64;\stackrel{_}{1,24,1,128}\right]$ $\sqrt{4221}=\left[64;\stackrel{_}{1,31,2,31,1,128}\right]$ $\sqrt{4222}=\left[64;\stackrel{_}{1,42,3,14,9,4,1,2,2,1,2,1,4,3,1,2,1,1,1,11,5,1,1,3,2,1,1,5,3,6,1,1,9,2,5,1,2,2,18,7,6,21,2,64,2,21,6,7,18,2,2,1,5,2,9,1,1,6,3,5,1,1,2,3,1,1,5,11,1,1,1,2,1,3,4,1,2,1,2,2,1,4,9,14,3,42,1,128}\right]$ $\sqrt{4223}=\left[64;\stackrel{_}{1,63,1,128}\right]$ $\sqrt{4224}=\left[64;\stackrel{_}{1,128}\right]$ $\sqrt{4226}=\left[65;\stackrel{_}{130}\right]$ $\sqrt{4227}=\left[65;\stackrel{_}{65,130}\right]$ $\sqrt{4228}=\left[65;\stackrel{_}{43,2,1,13,1,3,1,1,4,3,1,5,2,3,18,3,2,5,1,3,4,1,1,3,1,13,1,2,43,130}\right]$ $\sqrt{4229}=\left[65;\stackrel{_}{32,1,1,32,130}\right]$ $\sqrt{4230}=\left[65;\stackrel{_}{26,130}\right]$ $\sqrt{4231}=\left[65;\stackrel{_}{21,1,2,14,8,1,1,1,1,12,2,2,8,3,1,2,2,2,2,7,4,4,1,25,4,1,3,1,1,6,1,2,43,65,43,2,1,6,1,1,3,1,4,25,1,4,4,7,2,2,2,2,1,3,8,2,2,12,1,1,1,1,8,14,2,1,21,130}\right]$ $\sqrt{4232}=\left[65;\stackrel{_}{18,1,1,2,1,1,1,15,1,1,1,2,1,1,18,130}\right]$ $\sqrt{4233}=\left[65;\stackrel{_}{16,3,1,7,2,1,1,1,3,2,3,1,1,1,2,7,1,3,16,130}\right]$ $\sqrt{4234}=\left[65;\stackrel{_}{14,2,4,1,2,1,1,1,1,5,21,1,1,21,5,1,1,1,1,2,1,4,2,14,130}\right]$ $\sqrt{4235}=\left[65;\stackrel{_}{13,130}\right]$ $\sqrt{4236}=\left[65;\stackrel{_}{11,1,4,1,2,1,7,1,15,2,1,1,2,5,1,4,2,1,3,32,3,1,2,4,1,5,2,1,1,2,15,1,7,1,2,1,4,1,11,130}\right]$ $\sqrt{4237}=\left[65;\stackrel{_}{10,1,5,3,2,4,4,1,1,2,9,1,1,1,1,1,5,1,1,2,1,3,1,13,1,2,10,1,1,32,43,2,1,2,1,17,1,6,1,2,2,6,2,2,1,6,1,17,1,2,1,2,43,32,1,1,10,2,1,13,1,3,1,2,1,1,5,1,1,1,1,1,9,2,1,1,4,4,2,3,5,1,10,130}\right]$ $\sqrt{4238}=\left[65;\stackrel{_}{10,130}\right]$ $\sqrt{4239}=\left[65;\stackrel{_}{9,3,2,2,4,2,2,3,9,130}\right]$ $\sqrt{4240}=\left[65;\stackrel{_}{8,1,2,14,8,14,2,1,8,130}\right]$ $\sqrt{4241}=\left[65;\stackrel{_}{8,7,1,1,6,3,9,1,2,2,1,4,1,25,4,2,4,1,3,3,1,15,1,1,15,1,3,3,1,4,2,4,25,1,4,1,2,2,1,9,3,6,1,1,7,8,130}\right]$ $\sqrt{4242}=\left[65;\stackrel{_}{7,1,1,1,8,1,1,1,7,130}\right]$ $\sqrt{4243}=\left[65;\stackrel{_}{7,4,2,1,6,6,18,2,4,2,1,21,43,2,1,1,1,2,1,8,1,1,2,1,1,2,1,5,2,14,65,14,2,5,1,2,1,1,2,1,1,8,1,2,1,1,1,2,43,21,1,2,4,2,18,6,6,1,2,4,7,130}\right]$ $\sqrt{4244}=\left[65;\stackrel{_}{6,1,5,1,1,1,11,5,7,1,17,1,2,1,3,2,5,4,2,7,1,2,3,2,1,1,1,25,2,3,32,3,2,25,1,1,1,2,3,2,1,7,2,4,5,2,3,1,2,1,17,1,7,5,11,1,1,1,5,1,6,130}\right]$ $\sqrt{4245}=\left[65;\stackrel{_}{6,1,1,32,26,32,1,1,6,130}\right]$ $\sqrt{4246}=\left[65;\stackrel{_}{6,5,21,1,1,8,1,3,1,13,1,2,5,1,6,2,1,1,18,43,2,1,1,2,1,1,64,1,1,2,1,1,2,43,18,1,1,2,6,1,5,2,1,13,1,3,1,8,1,1,21,5,6,130}\right]$ $\sqrt{4247}=\left[65;\stackrel{_}{5,1,11,65,11,1,5,130}\right]$ $\sqrt{4248}=\left[65;\stackrel{_}{5,1,1,1,15,1,1,1,5,130}\right]$ $\sqrt{4249}=\left[65;\stackrel{_}{5,2,2,1,4,8,2,11,2,1,1,1,2,3,1,2,3,1,5,2,3,2,25,1,1,1,3,16,43,2,1,1,7,14,2,1,4,1,3,7,1,7,1,4,3,18,3,4,1,7,1,7,3,1,4,1,2,14,7,1,1,2,43,16,3,1,1,1,25,2,3,2,5,1,3,2,1,3,2,1,1,1,2,11,2,8,4,1,2,2,5,130}\right]$ $\sqrt{4250}=\left[65;\stackrel{_}{5,4,1,4,2,2,4,1,4,5,130}\right]$ $\sqrt{4251}=\left[65;\stackrel{_}{5,130}\right]$ $\sqrt{4252}=\left[65;\stackrel{_}{4,1,4,1,1,1,2,1,2,3,3,1,10,9,1,15,2,2,43,14,2,7,5,3,3,32,3,3,5,7,2,14,43,2,2,15,1,9,10,1,3,3,2,1,2,1,1,1,4,1,4,130}\right]$ $\sqrt{4253}=\left[65;\stackrel{_}{4,1,1,1,6,4,1,1,32,18,1,1,1,1,18,32,1,1,4,6,1,1,1,4,130}\right]$ $\sqrt{4254}=\left[65;\stackrel{_}{4,2,25,1,1,1,4,2,1,4,1,1,8,6,1,2,1,42,1,2,1,6,8,1,1,4,1,2,4,1,1,1,25,2,4,130}\right]$ $\sqrt{4255}=\left[65;\stackrel{_}{4,2,1,13,1,4,11,1,1,1,11,4,1,13,1,2,4,130}\right]$ $\sqrt{4256}=\left[65;\stackrel{_}{4,4,1,31,1,4,4,130}\right]$ $\sqrt{4257}=\left[65;\stackrel{_}{4,14,4,130}\right]$ $\sqrt{4258}=\left[65;\stackrel{_}{3,1,17,1,8,2,1,1,1,64,1,1,1,2,8,1,17,1,3,130}\right]$ $\sqrt{4259}=\left[65;\stackrel{_}{3,1,4,1,12,4,2,2,1,2,1,4,2,25,1,1,1,7,65,7,1,1,1,25,2,4,1,2,1,2,2,4,12,1,4,1,3,130}\right]$ $\sqrt{4260}=\left[65;\stackrel{_}{3,1,2,1,1,2,11,2,11,2,1,1,2,1,3,130}\right]$ $\sqrt{4261}=\left[65;\stackrel{_}{3,1,1,1,1,1,1,1,8,11,1,3,25,1,5,1,10,43,2,2,1,5,1,4,2,1,2,3,1,1,2,2,8,3,1,1,32,14,2,9,1,1,3,1,2,5,3,6,4,1,2,10,1,1,10,2,1,4,6,3,5,2,1,3,1,1,9,2,14,32,1,1,3,8,2,2,1,1,3,2,1,2,4,1,5,1,2,2,43,10,1,5,1,25,3,1,11,8,1,1,1,1,1,1,1,3,130}\right]$ $\sqrt{4262}=\left[65;\stackrel{_}{3,1,1,11,3,2,1,6,5,1,3,1,1,1,64,1,1,1,3,1,5,6,1,2,3,11,1,1,3,130}\right]$ $\sqrt{4263}=\left[65;\stackrel{_}{3,2,3,130}\right]$ $\sqrt{4264}=\left[65;\stackrel{_}{3,2,1,13,1,4,3,2,2,1,4,1,31,1,4,1,2,2,3,4,1,13,1,2,3,130}\right]$ $\sqrt{4265}=\left[65;\stackrel{_}{3,3,1,7,2,1,1,6,3,1,1,2,1,1,1,1,1,1,2,1,1,3,6,1,1,2,7,1,3,3,130}\right]$ $\sqrt{4266}=\left[65;\stackrel{_}{3,5,1,1,1,1,7,12,1,13,1,1,2,3,1,4,2,4,1,3,2,1,1,13,1,12,7,1,1,1,1,5,3,130}\right]$ $\sqrt{4267}=\left[65;\stackrel{_}{3,9,1,2,1,1,6,1,2,5,1,6,1,5,2,1,6,1,1,2,1,9,3,130}\right]$ $\sqrt{4268}=\left[65;\stackrel{_}{3,32,3,130}\right]$ $\sqrt{4269}=\left[65;\stackrel{_}{2,1,25,2,7,5,10,1,2,3,1,1,1,1,1,1,5,1,11,32,1,1,2,2,6,8,1,1,3,1,42,1,3,1,1,8,6,2,2,1,1,32,11,1,5,1,1,1,1,1,1,3,2,1,10,5,7,2,25,1,2,130}\right]$ $\sqrt{4270}=\left[65;\stackrel{_}{2,1,8,1,2,130}\right]$ $\sqrt{4271}=\left[65;\stackrel{_}{2,1,5,65,5,1,2,130}\right]$ $\sqrt{4272}=\left[65;\stackrel{_}{2,1,3,2,2,1,1,7,1,1,2,2,3,1,2,130}\right]$ $\sqrt{4273}=\left[65;\stackrel{_}{2,1,2,1,1,11,3,3,1,3,5,5,2,43,8,6,1,3,9,1,3,1,15,1,1,4,1,13,1,2,2,2,1,1,1,1,2,2,2,1,13,1,4,1,1,15,1,3,1,9,3,1,6,8,43,2,5,5,3,1,3,3,11,1,1,2,1,2,130}\right]$ $\sqrt{4274}=\left[65;\stackrel{_}{2,1,1,1,18,18,1,1,1,2,130}\right]$ $\sqrt{4275}=\left[65;\stackrel{_}{2,1,1,1,1,4,1,1,1,1,2,130}\right]$ $\sqrt{4276}=\left[65;\stackrel{_}{2,1,1,3,1,10,8,1,1,1,2,14,6,2,7,1,2,2,8,3,2,2,2,9,1,1,1,4,1,1,2,1,4,7,1,25,3,1,1,2,6,2,43,7,1,2,32,2,1,7,43,2,6,2,1,1,3,25,1,7,4,1,2,1,1,4,1,1,1,9,2,2,2,3,8,2,2,1,7,2,6,14,2,1,1,1,8,10,1,3,1,1,2,130}\right]$ $\sqrt{4277}=\left[65;\stackrel{_}{2,1,1,32,10,32,1,1,2,130}\right]$ $\sqrt{4278}=\left[65;\stackrel{_}{2,2,5,1,4,1,5,2,2,130}\right]$ $\sqrt{4279}=\left[65;\stackrel{_}{2,2,2,2,3,1,17,1,10,1,17,1,3,2,2,2,2,130}\right]$ $\sqrt{4280}=\left[65;\stackrel{_}{2,2,1,2,3,1,5,1,3,2,1,2,2,130}\right]$ $\sqrt{4281}=\left[65;\stackrel{_}{2,3,25,1,7,1,3,4,1,42,1,4,3,1,7,1,25,3,2,130}\right]$ $\sqrt{4282}=\left[65;\stackrel{_}{2,3,2,7,3,1,4,1,13,1,2,1,1,21,4,5,1,2,2,1,5,4,21,1,1,2,1,13,1,4,1,3,7,2,3,2,130}\right]$ $\sqrt{4283}=\left[65;\stackrel{_}{2,4,65,4,2,130}\right]$ $\sqrt{4284}=\left[65;\stackrel{_}{2,4,1,2,1,4,2,130}\right]$ $\sqrt{4285}=\left[65;\stackrel{_}{2,5,1,2,1,3,1,3,2,3,3,2,1,8,32,1,1,1,1,2,14,6,6,14,2,1,1,1,1,32,8,1,2,3,3,2,3,1,3,1,2,1,5,2,130}\right]$ $\sqrt{4286}=\left[65;\stackrel{_}{2,7,4,1,9,3,1,2,1,64,1,2,1,3,9,1,4,7,2,130}\right]$ $\sqrt{4287}=\left[65;\stackrel{_}{2,9,1,1,2,1,4,1,42,1,4,1,2,1,1,9,2,130}\right]$ $\sqrt{4288}=\left[65;\stackrel{_}{2,14,18,1,1,1,3,1,1,3,2,2,4,3,1,2,1,6,1,31,1,6,1,2,1,3,4,2,2,3,1,1,3,1,1,1,18,14,2,130}\right]$ $\sqrt{4289}=\left[65;\stackrel{_}{2,25,1,2,3,4,1,15,1,1,3,1,1,2,1,2,2,9,1,1,1,7,1,1,7,1,1,1,9,2,2,1,2,1,1,3,1,1,15,1,4,3,2,1,25,2,130}\right]$ $\sqrt{4290}=\left[65;\stackrel{_}{2,130}\right]$ $\sqrt{4291}=\left[65;\stackrel{_}{1,1,43,5,1,13,1,2,1,1,1,1,4,4,6,1,1,1,12,2,4,1,1,3,1,4,2,5,1,3,1,2,18,2,1,3,1,5,2,4,1,3,1,1,4,2,12,1,1,1,6,4,4,1,1,1,1,2,1,13,1,5,43,1,1,130}\right]$ $\sqrt{4292}=\left[65;\stackrel{_}{1,1,18,4,1,1,1,2,32,2,1,1,1,4,18,1,1,130}\right]$ $\sqrt{4293}=\left[65;\stackrel{_}{1,1,11,2,2,3,4,4,2,4,4,3,2,2,11,1,1,130}\right]$ $\sqrt{4294}=\left[65;\stackrel{_}{1,1,8,4,3,1,64,1,3,4,8,1,1,130}\right]$ $\sqrt{4295}=\left[65;\stackrel{_}{1,1,6,2,1,1,11,3,9,26,9,3,11,1,1,2,6,1,1,130}\right]$ $\sqrt{4296}=\left[65;\stackrel{_}{1,1,5,5,16,5,5,1,1,130}\right]$ $\sqrt{4297}=\left[65;\stackrel{_}{1,1,4,2,1,4,1,3,2,2,7,1,3,1,1,1,3,2,5,43,1,1,14,16,3,7,2,1,1,2,7,3,16,14,1,1,43,5,2,3,1,1,1,3,1,7,2,2,3,1,4,1,2,4,1,1,130}\right]$ $\sqrt{4298}=\left[65;\stackrel{_}{1,1,3,1,2,1,2,18,2,1,2,1,3,1,1,130}\right]$ $\sqrt{4299}=\left[65;\stackrel{_}{1,1,3,4,11,1,2,4,1,9,3,1,1,1,4,2,2,5,1,5,8,1,1,3,65,3,1,1,8,5,1,5,2,2,4,1,1,1,3,9,1,4,2,1,11,4,3,1,1,130}\right]$ $\sqrt{4300}=\left[65;\stackrel{_}{1,1,2,1,6,5,3,5,1,13,1,2,1,2,2,4,1,4,1,1,1,5,1,1,2,32,2,1,1,5,1,1,1,4,1,4,2,2,1,2,1,13,1,5,3,5,6,1,2,1,1,130}\right]$ $\sqrt{4301}=\left[65;\stackrel{_}{1,1,2,1,1,4,1,1,1,32,6,1,6,1,6,32,1,1,1,4,1,1,2,1,1,130}\right]$ $\sqrt{4302}=\left[65;\stackrel{_}{1,1,2,3,2,5,1,1,8,1,4,1,4,4,1,1,1,6,1,1,1,4,4,1,4,1,8,1,1,5,2,3,2,1,1,130}\right]$ $\sqrt{4303}=\left[65;\stackrel{_}{1,1,2,14,5,1,1,1,2,1,4,7,1,1,43,5,43,1,1,7,4,1,2,1,1,1,5,14,2,1,1,130}\right]$ $\sqrt{4304}=\left[65;\stackrel{_}{1,1,1,1,7,1,1,1,1,130}\right]$ $\sqrt{4305}=\left[65;\stackrel{_}{1,1,1,1,2,1,1,1,1,130}\right]$ $\sqrt{4306}=\left[65;\stackrel{_}{1,1,1,1,1,2,1,1,2,1,3,1,1,1,8,9,3,1,6,1,1,6,1,3,9,8,1,1,1,3,1,2,1,1,2,1,1,1,1,1,130}\right]$ $\sqrt{4307}=\left[65;\stackrel{_}{1,1,1,2,5,3,65,3,5,2,1,1,1,130}\right]$ $\sqrt{4308}=\left[65;\stackrel{_}{1,1,1,2,1,7,2,10,2,7,1,2,1,1,1,130}\right]$ $\sqrt{4309}=\left[65;\stackrel{_}{1,1,1,4,43,1,1,4,1,2,1,13,1,5,1,1,1,2,1,1,4,3,1,1,7,6,2,3,5,2,2,1,1,2,10,1,1,4,6,32,1,1,1,18,10,1,7,1,5,2,1,2,1,25,1,1,8,4,8,1,1,25,1,2,1,2,5,1,7,1,10,18,1,1,1,32,6,4,1,1,10,2,1,1,2,2,5,3,2,6,7,1,1,3,4,1,1,2,1,1,1,5,1,13,1,2,1,4,1,1,43,4,1,1,1,130}\right]$ $\sqrt{4310}=\left[65;\stackrel{_}{1,1,1,6,4,11,1,2,3,1,1,12,1,1,3,2,1,11,4,6,1,1,1,130}\right]$ $\sqrt{4311}=\left[65;\stackrel{_}{1,1,1,12,2,6,1,4,2,1,1,2,3,14,3,2,1,1,2,4,1,6,2,12,1,1,1,130}\right]$ $\sqrt{4312}=\left[65;\stackrel{_}{1,1,1,130}\right]$ $\sqrt{4313}=\left[65;\stackrel{_}{1,2,16,11,1,7,3,2,2,1,3,2,1,1,9,1,1,18,4,5,2,6,2,5,4,18,1,1,9,1,1,2,3,1,2,2,3,7,1,11,16,2,1,130}\right]$ $\sqrt{4314}=\left[65;\stackrel{_}{1,2,7,2,1,1,5,8,1,1,2,1,2,12,1,3,3,4,1,17,1,20,1,17,1,4,3,3,1,12,2,1,2,1,1,8,5,1,1,2,7,2,1,130}\right]$ $\sqrt{4315}=\left[65;\stackrel{_}{1,2,4,1,2,1,1,3,1,21,8,1,2,2,11,1,1,14,13,14,1,1,11,2,2,1,8,21,1,3,1,1,2,1,4,2,1,130}\right]$ $\sqrt{4316}=\left[65;\stackrel{_}{1,2,3,2,2,1,1,1,1,1,3,7,2,4,1,3,1,2,2,32,2,2,1,3,1,4,2,7,3,1,1,1,1,1,2,2,3,2,1,130}\right]$ $\sqrt{4317}=\left[65;\stackrel{_}{1,2,2,1,1,1,7,9,1,42,1,9,7,1,1,1,2,2,1,130}\right]$ $\sqrt{4318}=\left[65;\stackrel{_}{1,2,2,6,1,6,1,6,2,2,1,130}\right]$ $\sqrt{4319}=\left[65;\stackrel{_}{1,2,1,1,3,1,2,65,2,1,3,1,1,2,1,130}\right]$ $\sqrt{4320}=\left[65;\stackrel{_}{1,2,1,1,1,13,1,31,1,13,1,1,1,2,1,130}\right]$ $\sqrt{4321}=\left[65;\stackrel{_}{1,2,1,3,4,3,1,2,1,130}\right]$ $\sqrt{4322}=\left[65;\stackrel{_}{1,2,1,6,1,64,1,6,1,2,1,130}\right]$ $\sqrt{4323}=\left[65;\stackrel{_}{1,2,1,130}\right]$ $\sqrt{4324}=\left[65;\stackrel{_}{1,3,8,1,1,14,11,1,7,1,5,1,2,4,1,10,6,1,4,1,6,10,1,4,2,1,5,1,7,1,11,14,1,1,8,3,1,130}\right]$ $\sqrt{4325}=\left[65;\stackrel{_}{1,3,3,1,130}\right]$ $\sqrt{4326}=\left[65;\stackrel{_}{1,3,2,1,1,4,1,2,25,1,20,1,25,2,1,4,1,1,2,3,1,130}\right]$ $\sqrt{4327}=\left[65;\stackrel{_}{1,3,1,1,5,6,11,1,3,1,21,7,1,2,3,1,8,1,1,1,2,6,1,13,1,3,18,1,1,5,1,3,43,1,1,2,5,1,1,2,1,1,2,3,1,1,2,65,2,1,1,3,2,1,1,2,1,1,5,2,1,1,43,3,1,5,1,1,18,3,1,13,1,6,2,1,1,1,8,1,3,2,1,7,21,1,3,1,11,6,5,1,1,3,1,130}\right]$ $\sqrt{4328}=\left[65;\stackrel{_}{1,3,1,2,2,2,3,1,4,1,17,1,31,1,17,1,4,1,3,2,2,2,1,3,1,130}\right]$