1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.6. Probability Distributions
1.3.6.7. Tables for Probability Distributions

1.3.6.7.3.

Upper Critical Values of the F Distribution

How to Use This Table

This table contains the upper critical values of the F distribution. This table is used for one-sided F tests at the α = 0.05, 0.10, and 0.01 levels.

More specifically, a test statistic is computed with ν₁ and ν₂ degrees of freedom, and the result is compared to this table. For a one-sided test, the null hypothesis is rejected when the test statistic is greater than the tabled value. This is demonstrated with the graph of an F distribution with ν₁ = 10 and ν₂ = 10. The shaded area of the graph indicates the rejection region at the α significance level. Since this is a one-sided test, we have α probability in the upper tail of exceeding the critical value and zero in the lower tail. Because the F distribution is asymmetric, a two-sided test requires a set of of tables (not included here) that contain the rejection regions for both the lower and upper tails.

Contents

The following tables for ν₂ from 1 to 100 are included:

1. One sided, 5% significance level, ν₁ = 1 - 10
2. One sided, 5% significance level, ν₁ = 11 - 20
3. One sided, 10% significance level, ν₁ = 1 - 10
4. One sided, 10% significance level, ν₁ = 11 - 20
5. One sided, 1% significance level, ν₁ = 1 - 10
6. One sided, 1% significance level, ν₁ = 11 - 20

Upper critical values of the F distribution for ν1 numerator degrees of freedom and ν2 denominator degrees of freedom 5% significance level $F_{.05}({\nu }_1,{\nu }_2)$ \ ν1 1 2 3 4 5 6 7 8 9 10 ν2 1 161.448 199.500 215.707 224.583 230.162 233.986 236.768 238.882 240.543 241.882 2 18.513 19.000 19.164 19.247 19.296 19.330 19.353 19.371 19.385 19.396 3 10.128 9.552 9.277 9.117 9.013 8.941 8.887 8.845 8.812 8.786 4 7.709 6.944 6.591 6.388 6.256 6.163 6.094 6.041 5.999 5.964 5 6.608 5.786 5.409 5.192 5.050 4.950 4.876 4.818 4.772 4.735 6 5.987 5.143 4.757 4.534 4.387 4.284 4.207 4.147 4.099 4.060 7 5.591 4.737 4.347 4.120 3.972 3.866 3.787 3.726 3.677 3.637 8 5.318 4.459 4.066 3.838 3.687 3.581 3.500 3.438 3.388 3.347 9 5.117 4.256 3.863 3.633 3.482 3.374 3.293 3.230 3.179 3.137 10 4.965 4.103 3.708 3.478 3.326 3.217 3.135 3.072 3.020 2.978 11 4.844 3.982 3.587 3.357 3.204 3.095 3.012 2.948 2.896 2.854 12 4.747 3.885 3.490 3.259 3.106 2.996 2.913 2.849 2.796 2.753 13 4.667 3.806 3.411 3.179 3.025 2.915 2.832 2.767 2.714 2.671 14 4.600 3.739 3.344 3.112 2.958 2.848 2.764 2.699 2.646 2.602 15 4.543 3.682 3.287 3.056 2.901 2.790 2.707 2.641 2.588 2.544 16 4.494 3.634 3.239 3.007 2.852 2.741 2.657 2.591 2.538 2.494 17 4.451 3.592 3.197 2.965 2.810 2.699 2.614 2.548 2.494 2.450 18 4.414 3.555 3.160 2.928 2.773 2.661 2.577 2.510 2.456 2.412 19 4.381 3.522 3.127 2.895 2.740 2.628 2.544 2.477 2.423 2.378 20 4.351 3.493 3.098 2.866 2.711 2.599 2.514 2.447 2.393 2.348 21 4.325 3.467 3.072 2.840 2.685 2.573 2.488 2.420 2.366 2.321 22 4.301 3.443 3.049 2.817 2.661 2.549 2.464 2.397 2.342 2.297 23 4.279 3.422 3.028 2.796 2.640 2.528 2.442 2.375 2.320 2.275 24 4.260 3.403 3.009 2.776 2.621 2.508 2.423 2.355 2.300 2.255 25 4.242 3.385 2.991 2.759 2.603 2.490 2.405 2.337 2.282 2.236 26 4.225 3.369 2.975 2.743 2.587 2.474 2.388 2.321 2.265 2.220 27 4.210 3.354 2.960 2.728 2.572 2.459 2.373 2.305 2.250 2.204 28 4.196 3.340 2.947 2.714 2.558 2.445 2.359 2.291 2.236 2.190 29 4.183 3.328 2.934 2.701 2.545 2.432 2.346 2.278 2.223 2.177 30 4.171 3.316 2.922 2.690 2.534 2.421 2.334 2.266 2.211 2.165 31 4.160 3.305 2.911 2.679 2.523 2.409 2.323 2.255 2.199 2.153 32 4.149 3.295 2.901 2.668 2.512 2.399 2.313 2.244 2.189 2.142 33 4.139 3.285 2.892 2.659 2.503 2.389 2.303 2.235 2.179 2.133 34 4.130 3.276 2.883 2.650 2.494 2.380 2.294 2.225 2.170 2.123 35 4.121 3.267 2.874 2.641 2.485 2.372 2.285 2.217 2.161 2.114 36 4.113 3.259 2.866 2.634 2.477 2.364 2.277 2.209 2.153 2.106 37 4.105 3.252 2.859 2.626 2.470 2.356 2.270 2.201 2.145 2.098 38 4.098 3.245 2.852 2.619 2.463 2.349 2.262 2.194 2.138 2.091 39 4.091 3.238 2.845 2.612 2.456 2.342 2.255 2.187 2.131 2.084 40 4.085 3.232 2.839 2.606 2.449 2.336 2.249 2.180 2.124 2.077 41 4.079 3.226 2.833 2.600 2.443 2.330 2.243 2.174 2.118 2.071 42 4.073 3.220 2.827 2.594 2.438 2.324 2.237 2.168 2.112 2.065 43 4.067 3.214 2.822 2.589 2.432 2.318 2.232 2.163 2.106 2.059 44 4.062 3.209 2.816 2.584 2.427 2.313 2.226 2.157 2.101 2.054 45 4.057 3.204 2.812 2.579 2.422 2.308 2.221 2.152 2.096 2.049 46 4.052 3.200 2.807 2.574 2.417 2.304 2.216 2.147 2.091 2.044 47 4.047 3.195 2.802 2.570 2.413 2.299 2.212 2.143 2.086 2.039 48 4.043 3.191 2.798 2.565 2.409 2.295 2.207 2.138 2.082 2.035 49 4.038 3.187 2.794 2.561 2.404 2.290 2.203 2.134 2.077 2.030 50 4.034 3.183 2.790 2.557 2.400 2.286 2.199 2.130 2.073 2.026 51 4.030 3.179 2.786 2.553 2.397 2.283 2.195 2.126 2.069 2.022 52 4.027 3.175 2.783 2.550 2.393 2.279 2.192 2.122 2.066 2.018 53 4.023 3.172 2.779 2.546 2.389 2.275 2.188 2.119 2.062 2.015 54 4.020 3.168 2.776 2.543 2.386 2.272 2.185 2.115 2.059 2.011 55 4.016 3.165 2.773 2.540 2.383 2.269 2.181 2.112 2.055 2.008 56 4.013 3.162 2.769 2.537 2.380 2.266 2.178 2.109 2.052 2.005 57 4.010 3.159 2.766 2.534 2.377 2.263 2.175 2.106 2.049 2.001 58 4.007 3.156 2.764 2.531 2.374 2.260 2.172 2.103 2.046 1.998 59 4.004 3.153 2.761 2.528 2.371 2.257 2.169 2.100 2.043 1.995 60 4.001 3.150 2.758 2.525 2.368 2.254 2.167 2.097 2.040 1.993 61 3.998 3.148 2.755 2.523 2.366 2.251 2.164 2.094 2.037 1.990 62 3.996 3.145 2.753 2.520 2.363 2.249 2.161 2.092 2.035 1.987 63 3.993 3.143 2.751 2.518 2.361 2.246 2.159 2.089 2.032 1.985 64 3.991 3.140 2.748 2.515 2.358 2.244 2.156 2.087 2.030 1.982 65 3.989 3.138 2.746 2.513 2.356 2.242 2.154 2.084 2.027 1.980 66 3.986 3.136 2.744 2.511 2.354 2.239 2.152 2.082 2.025 1.977 67 3.984 3.134 2.742 2.509 2.352 2.237 2.150 2.080 2.023 1.975 68 3.982 3.132 2.740 2.507 2.350 2.235 2.148 2.078 2.021 1.973 69 3.980 3.130 2.737 2.505 2.348 2.233 2.145 2.076 2.019 1.971 70 3.978 3.128 2.736 2.503 2.346 2.231 2.143 2.074 2.017 1.969 71 3.976 3.126 2.734 2.501 2.344 2.229 2.142 2.072 2.015 1.967 72 3.974 3.124 2.732 2.499 2.342 2.227 2.140 2.070 2.013 1.965 73 3.972 3.122 2.730 2.497 2.340 2.226 2.138 2.068 2.011 1.963 74 3.970 3.120 2.728 2.495 2.338 2.224 2.136 2.066 2.009 1.961 75 3.968 3.119 2.727 2.494 2.337 2.222 2.134 2.064 2.007 1.959 76 3.967 3.117 2.725 2.492 2.335 2.220 2.133 2.063 2.006 1.958 77 3.965 3.115 2.723 2.490 2.333 2.219 2.131 2.061 2.004 1.956 78 3.963 3.114 2.722 2.489 2.332 2.217 2.129 2.059 2.002 1.954 79 3.962 3.112 2.720 2.487 2.330 2.216 2.128 2.058 2.001 1.953 80 3.960 3.111 2.719 2.486 2.329 2.214 2.126 2.056 1.999 1.951 81 3.959 3.109 2.717 2.484 2.327 2.213 2.125 2.055 1.998 1.950 82 3.957 3.108 2.716 2.483 2.326 2.211 2.123 2.053 1.996 1.948 83 3.956 3.107 2.715 2.482 2.324 2.210 2.122 2.052 1.995 1.947 84 3.955 3.105 2.713 2.480 2.323 2.209 2.121 2.051 1.993 1.945 85 3.953 3.104 2.712 2.479 2.322 2.207 2.119 2.049 1.992 1.944 86 3.952 3.103 2.711 2.478 2.321 2.206 2.118 2.048 1.991 1.943 87 3.951 3.101 2.709 2.476 2.319 2.205 2.117 2.047 1.989 1.941 88 3.949 3.100 2.708 2.475 2.318 2.203 2.115 2.045 1.988 1.940 89 3.948 3.099 2.707 2.474 2.317 2.202 2.114 2.044 1.987 1.939 90 3.947 3.098 2.706 2.473 2.316 2.201 2.113 2.043 1.986 1.938 91 3.946 3.097 2.705 2.472 2.315 2.200 2.112 2.042 1.984 1.936 92 3.945 3.095 2.704 2.471 2.313 2.199 2.111 2.041 1.983 1.935 93 3.943 3.094 2.703 2.470 2.312 2.198 2.110 2.040 1.982 1.934 94 3.942 3.093 2.701 2.469 2.311 2.197 2.109 2.038 1.981 1.933 95 3.941 3.092 2.700 2.467 2.310 2.196 2.108 2.037 1.980 1.932 96 3.940 3.091 2.699 2.466 2.309 2.195 2.106 2.036 1.979 1.931 97 3.939 3.090 2.698 2.465 2.308 2.194 2.105 2.035 1.978 1.930 98 3.938 3.089 2.697 2.465 2.307 2.193 2.104 2.034 1.977 1.929 99 3.937 3.088 2.696 2.464 2.306 2.192 2.103 2.033 1.976 1.928 100 3.936 3.087 2.696 2.463 2.305 2.191 2.103 2.032 1.975 1.927 \ ν1 11 12 13 14 15 16 17 18 19 20 ν2 1 242.983 243.906 244.690 245.364 245.950 246.464 246.918 247.323 247.686 248.013 2 19.405 19.413 19.419 19.424 19.429 19.433 19.437 19.440 19.443 19.446 3 8.763 8.745 8.729 8.715 8.703 8.692 8.683 8.675 8.667 8.660 4 5.936 5.912 5.891 5.873 5.858 5.844 5.832 5.821 5.811 5.803 5 4.704 4.678 4.655 4.636 4.619 4.604 4.590 4.579 4.568 4.558 6 4.027 4.000 3.976 3.956 3.938 3.922 3.908 3.896 3.884 3.874 7 3.603 3.575 3.550 3.529 3.511 3.494 3.480 3.467 3.455 3.445 8 3.313 3.284 3.259 3.237 3.218 3.202 3.187 3.173 3.161 3.150 9 3.102 3.073 3.048 3.025 3.006 2.989 2.974 2.960 2.948 2.936 10 2.943 2.913 2.887 2.865 2.845 2.828 2.812 2.798 2.785 2.774 11 2.818 2.788 2.761 2.739 2.719 2.701 2.685 2.671 2.658 2.646 12 2.717 2.687 2.660 2.637 2.617 2.599 2.583 2.568 2.555 2.544 13 2.635 2.604 2.577 2.554 2.533 2.515 2.499 2.484 2.471 2.459 14 2.565 2.534 2.507 2.484 2.463 2.445 2.428 2.413 2.400 2.388 15 2.507 2.475 2.448 2.424 2.403 2.385 2.368 2.353 2.340 2.328 16 2.456 2.425 2.397 2.373 2.352 2.333 2.317 2.302 2.288 2.276 17 2.413 2.381 2.353 2.329 2.308 2.289 2.272 2.257 2.243 2.230 18 2.374 2.342 2.314 2.290 2.269 2.250 2.233 2.217 2.203 2.191 19 2.340 2.308 2.280 2.256 2.234 2.215 2.198 2.182 2.168 2.155 20 2.310 2.278 2.250 2.225 2.203 2.184 2.167 2.151 2.137 2.124 21 2.283 2.250 2.222 2.197 2.176 2.156 2.139 2.123 2.109 2.096 22 2.259 2.226 2.198 2.173 2.151 2.131 2.114 2.098 2.084 2.071 23 2.236 2.204 2.175 2.150 2.128 2.109 2.091 2.075 2.061 2.048 24 2.216 2.183 2.155 2.130 2.108 2.088 2.070 2.054 2.040 2.027 25 2.198 2.165 2.136 2.111 2.089 2.069 2.051 2.035 2.021 2.007 26 2.181 2.148 2.119 2.094 2.072 2.052 2.034 2.018 2.003 1.990 27 2.166 2.132 2.103 2.078 2.056 2.036 2.018 2.002 1.987 1.974 28 2.151 2.118 2.089 2.064 2.041 2.021 2.003 1.987 1.972 1.959 29 2.138 2.104 2.075 2.050 2.027 2.007 1.989 1.973 1.958 1.945 30 2.126 2.092 2.063 2.037 2.015 1.995 1.976 1.960 1.945 1.932 31 2.114 2.080 2.051 2.026 2.003 1.983 1.965 1.948 1.933 1.920 32 2.103 2.070 2.040 2.015 1.992 1.972 1.953 1.937 1.922 1.908 33 2.093 2.060 2.030 2.004 1.982 1.961 1.943 1.926 1.911 1.898 34 2.084 2.050 2.021 1.995 1.972 1.952 1.933 1.917 1.902 1.888 35 2.075 2.041 2.012 1.986 1.963 1.942 1.924 1.907 1.892 1.878 36 2.067 2.033 2.003 1.977 1.954 1.934 1.915 1.899 1.883 1.870 37 2.059 2.025 1.995 1.969 1.946 1.926 1.907 1.890 1.875 1.861 38 2.051 2.017 1.988 1.962 1.939 1.918 1.899 1.883 1.867 1.853 39 2.044 2.010 1.981 1.954 1.931 1.911 1.892 1.875 1.860 1.846 40 2.038 2.003 1.974 1.948 1.924 1.904 1.885 1.868 1.853 1.839 41 2.031 1.997 1.967 1.941 1.918 1.897 1.879 1.862 1.846 1.832 42 2.025 1.991 1.961 1.935 1.912 1.891 1.872 1.855 1.840 1.826 43 2.020 1.985 1.955 1.929 1.906 1.885 1.866 1.849 1.834 1.820 44 2.014 1.980 1.950 1.924 1.900 1.879 1.861 1.844 1.828 1.814 45 2.009 1.974 1.945 1.918 1.895 1.874 1.855 1.838 1.823 1.808 46 2.004 1.969 1.940 1.913 1.890 1.869 1.850 1.833 1.817 1.803 47 1.999 1.965 1.935 1.908 1.885 1.864 1.845 1.828 1.812 1.798 48 1.995 1.960 1.930 1.904 1.880 1.859 1.840 1.823 1.807 1.793 49 1.990 1.956 1.926 1.899 1.876 1.855 1.836 1.819 1.803 1.789 50 1.986 1.952 1.921 1.895 1.871 1.850 1.831 1.814 1.798 1.784 51 1.982 1.947 1.917 1.891 1.867 1.846 1.827 1.810 1.794 1.780 52 1.978 1.944 1.913 1.887 1.863 1.842 1.823 1.806 1.790 1.776 53 1.975 1.940 1.910 1.883 1.859 1.838 1.819 1.802 1.786 1.772 54 1.971 1.936 1.906 1.879 1.856 1.835 1.816 1.798 1.782 1.768 55 1.968 1.933 1.903 1.876 1.852 1.831 1.812 1.795 1.779 1.764 56 1.964 1.930 1.899 1.873 1.849 1.828 1.809 1.791 1.775 1.761 57 1.961 1.926 1.896 1.869 1.846 1.824 1.805 1.788 1.772 1.757 58 1.958 1.923 1.893 1.866 1.842 1.821 1.802 1.785 1.769 1.754 59 1.955 1.920 1.890 1.863 1.839 1.818 1.799 1.781 1.766 1.751 60 1.952 1.917 1.887 1.860 1.836 1.815 1.796 1.778 1.763 1.748 61 1.949 1.915 1.884 1.857 1.834 1.812 1.793 1.776 1.760 1.745 62 1.947 1.912 1.882 1.855 1.831 1.809 1.790 1.773 1.757 1.742 63 1.944 1.909 1.879 1.852 1.828 1.807 1.787 1.770 1.754 1.739 64 1.942 1.907 1.876 1.849 1.826 1.804 1.785 1.767 1.751 1.737 65 1.939 1.904 1.874 1.847 1.823 1.802 1.782 1.765 1.749 1.734 66 1.937 1.902 1.871 1.845 1.821 1.799 1.780 1.762 1.746 1.732 67 1.935 1.900 1.869 1.842 1.818 1.797 1.777 1.760 1.744 1.729 68 1.932 1.897 1.867 1.840 1.816 1.795 1.775 1.758 1.742 1.727 69 1.930 1.895 1.865 1.838 1.814 1.792 1.773 1.755 1.739 1.725 70 1.928 1.893 1.863 1.836 1.812 1.790 1.771 1.753 1.737 1.722 71 1.926 1.891 1.861 1.834 1.810 1.788 1.769 1.751 1.735 1.720 72 1.924 1.889 1.859 1.832 1.808 1.786 1.767 1.749 1.733 1.718 73 1.922 1.887 1.857 1.830 1.806 1.784 1.765 1.747 1.731 1.716 74 1.921 1.885 1.855 1.828 1.804 1.782 1.763 1.745 1.729 1.714 75 1.919 1.884 1.853 1.826 1.802 1.780 1.761 1.743 1.727 1.712 76 1.917 1.882 1.851 1.824 1.800 1.778 1.759 1.741 1.725 1.710 77 1.915 1.880 1.849 1.822 1.798 1.777 1.757 1.739 1.723 1.708 78 1.914 1.878 1.848 1.821 1.797 1.775 1.755 1.738 1.721 1.707 79 1.912 1.877 1.846 1.819 1.795 1.773 1.754 1.736 1.720 1.705 80 1.910 1.875 1.845 1.817 1.793 1.772 1.752 1.734 1.718 1.703 81 1.909 1.874 1.843 1.816 1.792 1.770 1.750 1.733 1.716 1.702 82 1.907 1.872 1.841 1.814 1.790 1.768 1.749 1.731 1.715 1.700 83 1.906 1.871 1.840 1.813 1.789 1.767 1.747 1.729 1.713 1.698 84 1.905 1.869 1.838 1.811 1.787 1.765 1.746 1.728 1.712 1.697 85 1.903 1.868 1.837 1.810 1.786 1.764 1.744 1.726 1.710 1.695 86 1.902 1.867 1.836 1.808 1.784 1.762 1.743 1.725 1.709 1.694 87 1.900 1.865 1.834 1.807 1.783 1.761 1.741 1.724 1.707 1.692 88 1.899 1.864 1.833 1.806 1.782 1.760 1.740 1.722 1.706 1.691 89 1.898 1.863 1.832 1.804 1.780 1.758 1.739 1.721 1.705 1.690 90 1.897 1.861 1.830 1.803 1.779 1.757 1.737 1.720 1.703 1.688 91 1.895 1.860 1.829 1.802 1.778 1.756 1.736 1.718 1.702 1.687 92 1.894 1.859 1.828 1.801 1.776 1.755 1.735 1.717 1.701 1.686 93 1.893 1.858 1.827 1.800 1.775 1.753 1.734 1.716 1.699 1.684 94 1.892 1.857 1.826 1.798 1.774 1.752 1.733 1.715 1.698 1.683 95 1.891 1.856 1.825 1.797 1.773 1.751 1.731 1.713 1.697 1.682 96 1.890 1.854 1.823 1.796 1.772 1.750 1.730 1.712 1.696 1.681 97 1.889 1.853 1.822 1.795 1.771 1.749 1.729 1.711 1.695 1.680 98 1.888 1.852 1.821 1.794 1.770 1.748 1.728 1.710 1.694 1.679 99 1.887 1.851 1.820 1.793 1.769 1.747 1.727 1.709 1.693 1.678 100 1.886 1.850 1.819 1.792 1.768 1.746 1.726 1.708 1.691 1.676

Upper critical values of the F distribution for ν1 numerator degrees of freedom and ν2 denominator degrees of freedom 10% significance level $F_{.10}({\nu }_1,{\nu }_2)$ \ ν1 1 2 3 4 5 6 7 8 9 10 ν2 1 39.863 49.500 53.593 55.833 57.240 58.204 58.906 59.439 59.858 60.195 2 8.526 9.000 9.162 9.243 9.293 9.326 9.349 9.367 9.381 9.392 3 5.538 5.462 5.391 5.343 5.309 5.285 5.266 5.252 5.240 5.230 4 4.545 4.325 4.191 4.107 4.051 4.010 3.979 3.955 3.936 3.920 5 4.060 3.780 3.619 3.520 3.453 3.405 3.368 3.339 3.316 3.297 6 3.776 3.463 3.289 3.181 3.108 3.055 3.014 2.983 2.958 2.937 7 3.589 3.257 3.074 2.961 2.883 2.827 2.785 2.752 2.725 2.703 8 3.458 3.113 2.924 2.806 2.726 2.668 2.624 2.589 2.561 2.538 9 3.360 3.006 2.813 2.693 2.611 2.551 2.505 2.469 2.440 2.416 10 3.285 2.924 2.728 2.605 2.522 2.461 2.414 2.377 2.347 2.323 11 3.225 2.860 2.660 2.536 2.451 2.389 2.342 2.304 2.274 2.248 12 3.177 2.807 2.606 2.480 2.394 2.331 2.283 2.245 2.214 2.188 13 3.136 2.763 2.560 2.434 2.347 2.283 2.234 2.195 2.164 2.138 14 3.102 2.726 2.522 2.395 2.307 2.243 2.193 2.154 2.122 2.095 15 3.073 2.695 2.490 2.361 2.273 2.208 2.158 2.119 2.086 2.059 16 3.048 2.668 2.462 2.333 2.244 2.178 2.128 2.088 2.055 2.028 17 3.026 2.645 2.437 2.308 2.218 2.152 2.102 2.061 2.028 2.001 18 3.007 2.624 2.416 2.286 2.196 2.130 2.079 2.038 2.005 1.977 19 2.990 2.606 2.397 2.266 2.176 2.109 2.058 2.017 1.984 1.956 20 2.975 2.589 2.380 2.249 2.158 2.091 2.040 1.999 1.965 1.937 21 2.961 2.575 2.365 2.233 2.142 2.075 2.023 1.982 1.948 1.920 22 2.949 2.561 2.351 2.219 2.128 2.060 2.008 1.967 1.933 1.904 23 2.937 2.549 2.339 2.207 2.115 2.047 1.995 1.953 1.919 1.890 24 2.927 2.538 2.327 2.195 2.103 2.035 1.983 1.941 1.906 1.877 25 2.918 2.528 2.317 2.184 2.092 2.024 1.971 1.929 1.895 1.866 26 2.909 2.519 2.307 2.174 2.082 2.014 1.961 1.919 1.884 1.855 27 2.901 2.511 2.299 2.165 2.073 2.005 1.952 1.909 1.874 1.845 28 2.894 2.503 2.291 2.157 2.064 1.996 1.943 1.900 1.865 1.836 29 2.887 2.495 2.283 2.149 2.057 1.988 1.935 1.892 1.857 1.827 30 2.881 2.489 2.276 2.142 2.049 1.980 1.927 1.884 1.849 1.819 31 2.875 2.482 2.270 2.136 2.042 1.973 1.920 1.877 1.842 1.812 32 2.869 2.477 2.263 2.129 2.036 1.967 1.913 1.870 1.835 1.805 33 2.864 2.471 2.258 2.123 2.030 1.961 1.907 1.864 1.828 1.799 34 2.859 2.466 2.252 2.118 2.024 1.955 1.901 1.858 1.822 1.793 35 2.855 2.461 2.247 2.113 2.019 1.950 1.896 1.852 1.817 1.787 36 2.850 2.456 2.243 2.108 2.014 1.945 1.891 1.847 1.811 1.781 37 2.846 2.452 2.238 2.103 2.009 1.940 1.886 1.842 1.806 1.776 38 2.842 2.448 2.234 2.099 2.005 1.935 1.881 1.838 1.802 1.772 39 2.839 2.444 2.230 2.095 2.001 1.931 1.877 1.833 1.797 1.767 40 2.835 2.440 2.226 2.091 1.997 1.927 1.873 1.829 1.793 1.763 41 2.832 2.437 2.222 2.087 1.993 1.923 1.869 1.825 1.789 1.759 42 2.829 2.434 2.219 2.084 1.989 1.919 1.865 1.821 1.785 1.755 43 2.826 2.430 2.216 2.080 1.986 1.916 1.861 1.817 1.781 1.751 44 2.823 2.427 2.213 2.077 1.983 1.913 1.858 1.814 1.778 1.747 45 2.820 2.425 2.210 2.074 1.980 1.909 1.855 1.811 1.774 1.744 46 2.818 2.422 2.207 2.071 1.977 1.906 1.852 1.808 1.771 1.741 47 2.815 2.419 2.204 2.068 1.974 1.903 1.849 1.805 1.768 1.738 48 2.813 2.417 2.202 2.066 1.971 1.901 1.846 1.802 1.765 1.735 49 2.811 2.414 2.199 2.063 1.968 1.898 1.843 1.799 1.763 1.732 50 2.809 2.412 2.197 2.061 1.966 1.895 1.840 1.796 1.760 1.729 51 2.807 2.410 2.194 2.058 1.964 1.893 1.838 1.794 1.757 1.727 52 2.805 2.408 2.192 2.056 1.961 1.891 1.836 1.791 1.755 1.724 53 2.803 2.406 2.190 2.054 1.959 1.888 1.833 1.789 1.752 1.722 54 2.801 2.404 2.188 2.052 1.957 1.886 1.831 1.787 1.750 1.719 55 2.799 2.402 2.186 2.050 1.955 1.884 1.829 1.785 1.748 1.717 56 2.797 2.400 2.184 2.048 1.953 1.882 1.827 1.782 1.746 1.715 57 2.796 2.398 2.182 2.046 1.951 1.880 1.825 1.780 1.744 1.713 58 2.794 2.396 2.181 2.044 1.949 1.878 1.823 1.779 1.742 1.711 59 2.793 2.395 2.179 2.043 1.947 1.876 1.821 1.777 1.740 1.709 60 2.791 2.393 2.177 2.041 1.946 1.875 1.819 1.775 1.738 1.707 61 2.790 2.392 2.176 2.039 1.944 1.873 1.818 1.773 1.736 1.705 62 2.788 2.390 2.174 2.038 1.942 1.871 1.816 1.771 1.735 1.703 63 2.787 2.389 2.173 2.036 1.941 1.870 1.814 1.770 1.733 1.702 64 2.786 2.387 2.171 2.035 1.939 1.868 1.813 1.768 1.731 1.700 65 2.784 2.386 2.170 2.033 1.938 1.867 1.811 1.767 1.730 1.699 66 2.783 2.385 2.169 2.032 1.937 1.865 1.810 1.765 1.728 1.697 67 2.782 2.384 2.167 2.031 1.935 1.864 1.808 1.764 1.727 1.696 68 2.781 2.382 2.166 2.029 1.934 1.863 1.807 1.762 1.725 1.694 69 2.780 2.381 2.165 2.028 1.933 1.861 1.806 1.761 1.724 1.693 70 2.779 2.380 2.164 2.027 1.931 1.860 1.804 1.760 1.723 1.691 71 2.778 2.379 2.163 2.026 1.930 1.859 1.803 1.758 1.721 1.690 72 2.777 2.378 2.161 2.025 1.929 1.858 1.802 1.757 1.720 1.689 73 2.776 2.377 2.160 2.024 1.928 1.856 1.801 1.756 1.719 1.687 74 2.775 2.376 2.159 2.022 1.927 1.855 1.800 1.755 1.718 1.686 75 2.774 2.375 2.158 2.021 1.926 1.854 1.798 1.754 1.716 1.685 76 2.773 2.374 2.157 2.020 1.925 1.853 1.797 1.752 1.715 1.684 77 2.772 2.373 2.156 2.019 1.924 1.852 1.796 1.751 1.714 1.683 78 2.771 2.372 2.155 2.018 1.923 1.851 1.795 1.750 1.713 1.682 79 2.770 2.371 2.154 2.017 1.922 1.850 1.794 1.749 1.712 1.681 80 2.769 2.370 2.154 2.016 1.921 1.849 1.793 1.748 1.711 1.680 81 2.769 2.369 2.153 2.016 1.920 1.848 1.792 1.747 1.710 1.679 82 2.768 2.368 2.152 2.015 1.919 1.847 1.791 1.746 1.709 1.678 83 2.767 2.368 2.151 2.014 1.918 1.846 1.790 1.745 1.708 1.677 84 2.766 2.367 2.150 2.013 1.917 1.845 1.790 1.744 1.707 1.676 85 2.765 2.366 2.149 2.012 1.916 1.845 1.789 1.744 1.706 1.675 86 2.765 2.365 2.149 2.011 1.915 1.844 1.788 1.743 1.705 1.674 87 2.764 2.365 2.148 2.011 1.915 1.843 1.787 1.742 1.705 1.673 88 2.763 2.364 2.147 2.010 1.914 1.842 1.786 1.741 1.704 1.672 89 2.763 2.363 2.146 2.009 1.913 1.841 1.785 1.740 1.703 1.671 90 2.762 2.363 2.146 2.008 1.912 1.841 1.785 1.739 1.702 1.670 91 2.761 2.362 2.145 2.008 1.912 1.840 1.784 1.739 1.701 1.670 92 2.761 2.361 2.144 2.007 1.911 1.839 1.783 1.738 1.701 1.669 93 2.760 2.361 2.144 2.006 1.910 1.838 1.782 1.737 1.700 1.668 94 2.760 2.360 2.143 2.006 1.910 1.838 1.782 1.736 1.699 1.667 95 2.759 2.359 2.142 2.005 1.909 1.837 1.781 1.736 1.698 1.667 96 2.759 2.359 2.142 2.004 1.908 1.836 1.780 1.735 1.698 1.666 97 2.758 2.358 2.141 2.004 1.908 1.836 1.780 1.734 1.697 1.665 98 2.757 2.358 2.141 2.003 1.907 1.835 1.779 1.734 1.696 1.665 99 2.757 2.357 2.140 2.003 1.906 1.835 1.778 1.733 1.696 1.664 100 2.756 2.356 2.139 2.002 1.906 1.834 1.778 1.732 1.695 1.663 \ ν1 11 12 13 14 15 16 17 18 19 20 ν2 1 60.473 60.705 60.903 61.073 61.220 61.350 61.464 61.566 61.658 61.740 2 9.401 9.408 9.415 9.420 9.425 9.429 9.433 9.436 9.439 9.441 3 5.222 5.216 5.210 5.205 5.200 5.196 5.193 5.190 5.187 5.184 4 3.907 3.896 3.886 3.878 3.870 3.864 3.858 3.853 3.849 3.844 5 3.282 3.268 3.257 3.247 3.238 3.230 3.223 3.217 3.212 3.207 6 2.920 2.905 2.892 2.881 2.871 2.863 2.855 2.848 2.842 2.836 7 2.684 2.668 2.654 2.643 2.632 2.623 2.615 2.607 2.601 2.595 8 2.519 2.502 2.488 2.475 2.464 2.455 2.446 2.438 2.431 2.425 9 2.396 2.379 2.364 2.351 2.340 2.329 2.320 2.312 2.305 2.298 10 2.302 2.284 2.269 2.255 2.244 2.233 2.224 2.215 2.208 2.201 11 2.227 2.209 2.193 2.179 2.167 2.156 2.147 2.138 2.130 2.123 12 2.166 2.147 2.131 2.117 2.105 2.094 2.084 2.075 2.067 2.060 13 2.116 2.097 2.080 2.066 2.053 2.042 2.032 2.023 2.014 2.007 14 2.073 2.054 2.037 2.022 2.010 1.998 1.988 1.978 1.970 1.962 15 2.037 2.017 2.000 1.985 1.972 1.961 1.950 1.941 1.932 1.924 16 2.005 1.985 1.968 1.953 1.940 1.928 1.917 1.908 1.899 1.891 17 1.978 1.958 1.940 1.925 1.912 1.900 1.889 1.879 1.870 1.862 18 1.954 1.933 1.916 1.900 1.887 1.875 1.864 1.854 1.845 1.837 19 1.932 1.912 1.894 1.878 1.865 1.852 1.841 1.831 1.822 1.814 20 1.913 1.892 1.875 1.859 1.845 1.833 1.821 1.811 1.802 1.794 21 1.896 1.875 1.857 1.841 1.827 1.815 1.803 1.793 1.784 1.776 22 1.880 1.859 1.841 1.825 1.811 1.798 1.787 1.777 1.768 1.759 23 1.866 1.845 1.827 1.811 1.796 1.784 1.772 1.762 1.753 1.744 24 1.853 1.832 1.814 1.797 1.783 1.770 1.759 1.748 1.739 1.730 25 1.841 1.820 1.802 1.785 1.771 1.758 1.746 1.736 1.726 1.718 26 1.830 1.809 1.790 1.774 1.760 1.747 1.735 1.724 1.715 1.706 27 1.820 1.799 1.780 1.764 1.749 1.736 1.724 1.714 1.704 1.695 28 1.811 1.790 1.771 1.754 1.740 1.726 1.715 1.704 1.694 1.685 29 1.802 1.781 1.762 1.745 1.731 1.717 1.705 1.695 1.685 1.676 30 1.794 1.773 1.754 1.737 1.722 1.709 1.697 1.686 1.676 1.667 31 1.787 1.765 1.746 1.729 1.714 1.701 1.689 1.678 1.668 1.659 32 1.780 1.758 1.739 1.722 1.707 1.694 1.682 1.671 1.661 1.652 33 1.773 1.751 1.732 1.715 1.700 1.687 1.675 1.664 1.654 1.645 34 1.767 1.745 1.726 1.709 1.694 1.680 1.668 1.657 1.647 1.638 35 1.761 1.739 1.720 1.703 1.688 1.674 1.662 1.651 1.641 1.632 36 1.756 1.734 1.715 1.697 1.682 1.669 1.656 1.645 1.635 1.626 37 1.751 1.729 1.709 1.692 1.677 1.663 1.651 1.640 1.630 1.620 38 1.746 1.724 1.704 1.687 1.672 1.658 1.646 1.635 1.624 1.615 39 1.741 1.719 1.700 1.682 1.667 1.653 1.641 1.630 1.619 1.610 40 1.737 1.715 1.695 1.678 1.662 1.649 1.636 1.625 1.615 1.605 41 1.733 1.710 1.691 1.673 1.658 1.644 1.632 1.620 1.610 1.601 42 1.729 1.706 1.687 1.669 1.654 1.640 1.628 1.616 1.606 1.596 43 1.725 1.703 1.683 1.665 1.650 1.636 1.624 1.612 1.602 1.592 44 1.721 1.699 1.679 1.662 1.646 1.632 1.620 1.608 1.598 1.588 45 1.718 1.695 1.676 1.658 1.643 1.629 1.616 1.605 1.594 1.585 46 1.715 1.692 1.672 1.655 1.639 1.625 1.613 1.601 1.591 1.581 47 1.712 1.689 1.669 1.652 1.636 1.622 1.609 1.598 1.587 1.578 48 1.709 1.686 1.666 1.648 1.633 1.619 1.606 1.594 1.584 1.574 49 1.706 1.683 1.663 1.645 1.630 1.616 1.603 1.591 1.581 1.571 50 1.703 1.680 1.660 1.643 1.627 1.613 1.600 1.588 1.578 1.568 51 1.700 1.677 1.658 1.640 1.624 1.610 1.597 1.586 1.575 1.565 52 1.698 1.675 1.655 1.637 1.621 1.607 1.594 1.583 1.572 1.562 53 1.695 1.672 1.652 1.635 1.619 1.605 1.592 1.580 1.570 1.560 54 1.693 1.670 1.650 1.632 1.616 1.602 1.589 1.578 1.567 1.557 55 1.691 1.668 1.648 1.630 1.614 1.600 1.587 1.575 1.564 1.555 56 1.688 1.666 1.645 1.628 1.612 1.597 1.585 1.573 1.562 1.552 57 1.686 1.663 1.643 1.625 1.610 1.595 1.582 1.571 1.560 1.550 58 1.684 1.661 1.641 1.623 1.607 1.593 1.580 1.568 1.558 1.548 59 1.682 1.659 1.639 1.621 1.605 1.591 1.578 1.566 1.555 1.546 60 1.680 1.657 1.637 1.619 1.603 1.589 1.576 1.564 1.553 1.543 61 1.679 1.656 1.635 1.617 1.601 1.587 1.574 1.562 1.551 1.541 62 1.677 1.654 1.634 1.616 1.600 1.585 1.572 1.560 1.549 1.540 63 1.675 1.652 1.632 1.614 1.598 1.583 1.570 1.558 1.548 1.538 64 1.673 1.650 1.630 1.612 1.596 1.582 1.569 1.557 1.546 1.536 65 1.672 1.649 1.628 1.610 1.594 1.580 1.567 1.555 1.544 1.534 66 1.670 1.647 1.627 1.609 1.593 1.578 1.565 1.553 1.542 1.532 67 1.669 1.646 1.625 1.607 1.591 1.577 1.564 1.552 1.541 1.531 68 1.667 1.644 1.624 1.606 1.590 1.575 1.562 1.550 1.539 1.529 69 1.666 1.643 1.622 1.604 1.588 1.574 1.560 1.548 1.538 1.527 70 1.665 1.641 1.621 1.603 1.587 1.572 1.559 1.547 1.536 1.526 71 1.663 1.640 1.619 1.601 1.585 1.571 1.557 1.545 1.535 1.524 72 1.662 1.639 1.618 1.600 1.584 1.569 1.556 1.544 1.533 1.523 73 1.661 1.637 1.617 1.599 1.583 1.568 1.555 1.543 1.532 1.522 74 1.659 1.636 1.616 1.597 1.581 1.567 1.553 1.541 1.530 1.520 75 1.658 1.635 1.614 1.596 1.580 1.565 1.552 1.540 1.529 1.519 76 1.657 1.634 1.613 1.595 1.579 1.564 1.551 1.539 1.528 1.518 77 1.656 1.632 1.612 1.594 1.578 1.563 1.550 1.538 1.527 1.516 78 1.655 1.631 1.611 1.593 1.576 1.562 1.548 1.536 1.525 1.515 79 1.654 1.630 1.610 1.592 1.575 1.561 1.547 1.535 1.524 1.514 80 1.653 1.629 1.609 1.590 1.574 1.559 1.546 1.534 1.523 1.513 81 1.652 1.628 1.608 1.589 1.573 1.558 1.545 1.533 1.522 1.512 82 1.651 1.627 1.607 1.588 1.572 1.557 1.544 1.532 1.521 1.511 83 1.650 1.626 1.606 1.587 1.571 1.556 1.543 1.531 1.520 1.509 84 1.649 1.625 1.605 1.586 1.570 1.555 1.542 1.530 1.519 1.508 85 1.648 1.624 1.604 1.585 1.569 1.554 1.541 1.529 1.518 1.507 86 1.647 1.623 1.603 1.584 1.568 1.553 1.540 1.528 1.517 1.506 87 1.646 1.622 1.602 1.583 1.567 1.552 1.539 1.527 1.516 1.505 88 1.645 1.622 1.601 1.583 1.566 1.551 1.538 1.526 1.515 1.504 89 1.644 1.621 1.600 1.582 1.565 1.550 1.537 1.525 1.514 1.503 90 1.643 1.620 1.599 1.581 1.564 1.550 1.536 1.524 1.513 1.503 91 1.643 1.619 1.598 1.580 1.564 1.549 1.535 1.523 1.512 1.502 92 1.642 1.618 1.598 1.579 1.563 1.548 1.534 1.522 1.511 1.501 93 1.641 1.617 1.597 1.578 1.562 1.547 1.534 1.521 1.510 1.500 94 1.640 1.617 1.596 1.578 1.561 1.546 1.533 1.521 1.509 1.499 95 1.640 1.616 1.595 1.577 1.560 1.545 1.532 1.520 1.509 1.498 96 1.639 1.615 1.594 1.576 1.560 1.545 1.531 1.519 1.508 1.497 97 1.638 1.614 1.594 1.575 1.559 1.544 1.530 1.518 1.507 1.497 98 1.637 1.614 1.593 1.575 1.558 1.543 1.530 1.517 1.506 1.496 99 1.637 1.613 1.592 1.574 1.557 1.542 1.529 1.517 1.505 1.495 100 1.636 1.612 1.592 1.573 1.557 1.542 1.528 1.516 1.505 1.494

Upper critical values of the F distribution for ν1 numerator degrees of freedom and ν2 denominator degrees of freedom 1% significance level $F_{.01}({\nu }_1,{\nu }_2)$ \ ν1 1 2 3 4 5 6 7 8 9 10 ν2 1 4052.19 4999.52 5403.34 5624.62 5763.65 5858.97 5928.33 5981.10 6022.50 6055.85 2 98.502 99.000 99.166 99.249 99.300 99.333 99.356 99.374 99.388 99.399 3 34.116 30.816 29.457 28.710 28.237 27.911 27.672 27.489 27.345 27.229 4 21.198 18.000 16.694 15.977 15.522 15.207 14.976 14.799 14.659 14.546 5 16.258 13.274 12.060 11.392 10.967 10.672 10.456 10.289 10.158 10.051 6 13.745 10.925 9.780 9.148 8.746 8.466 8.260 8.102 7.976 7.874 7 12.246 9.547 8.451 7.847 7.460 7.191 6.993 6.840 6.719 6.620 8 11.259 8.649 7.591 7.006 6.632 6.371 6.178 6.029 5.911 5.814 9 10.561 8.022 6.992 6.422 6.057 5.802 5.613 5.467 5.351 5.257 10 10.044 7.559 6.552 5.994 5.636 5.386 5.200 5.057 4.942 4.849 11 9.646 7.206 6.217 5.668 5.316 5.069 4.886 4.744 4.632 4.539 12 9.330 6.927 5.953 5.412 5.064 4.821 4.640 4.499 4.388 4.296 13 9.074 6.701 5.739 5.205 4.862 4.620 4.441 4.302 4.191 4.100 14 8.862 6.515 5.564 5.035 4.695 4.456 4.278 4.140 4.030 3.939 15 8.683 6.359 5.417 4.893 4.556 4.318 4.142 4.004 3.895 3.805 16 8.531 6.226 5.292 4.773 4.437 4.202 4.026 3.890 3.780 3.691 17 8.400 6.112 5.185 4.669 4.336 4.102 3.927 3.791 3.682 3.593 18 8.285 6.013 5.092 4.579 4.248 4.015 3.841 3.705 3.597 3.508 19 8.185 5.926 5.010 4.500 4.171 3.939 3.765 3.631 3.523 3.434 20 8.096 5.849 4.938 4.431 4.103 3.871 3.699 3.564 3.457 3.368 21 8.017 5.780 4.874 4.369 4.042 3.812 3.640 3.506 3.398 3.310 22 7.945 5.719 4.817 4.313 3.988 3.758 3.587 3.453 3.346 3.258 23 7.881 5.664 4.765 4.264 3.939 3.710 3.539 3.406 3.299 3.211 24 7.823 5.614 4.718 4.218 3.895 3.667 3.496 3.363 3.256 3.168 25 7.770 5.568 4.675 4.177 3.855 3.627 3.457 3.324 3.217 3.129 26 7.721 5.526 4.637 4.140 3.818 3.591 3.421 3.288 3.182 3.094 27 7.677 5.488 4.601 4.106 3.785 3.558 3.388 3.256 3.149 3.062 28 7.636 5.453 4.568 4.074 3.754 3.528 3.358 3.226 3.120 3.032 29 7.598 5.420 4.538 4.045 3.725 3.499 3.330 3.198 3.092 3.005 30 7.562 5.390 4.510 4.018 3.699 3.473 3.305 3.173 3.067 2.979 31 7.530 5.362 4.484 3.993 3.675 3.449 3.281 3.149 3.043 2.955 32 7.499 5.336 4.459 3.969 3.652 3.427 3.258 3.127 3.021 2.934 33 7.471 5.312 4.437 3.948 3.630 3.406 3.238 3.106 3.000 2.913 34 7.444 5.289 4.416 3.927 3.611 3.386 3.218 3.087 2.981 2.894 35 7.419 5.268 4.396 3.908 3.592 3.368 3.200 3.069 2.963 2.876 36 7.396 5.248 4.377 3.890 3.574 3.351 3.183 3.052 2.946 2.859 37 7.373 5.229 4.360 3.873 3.558 3.334 3.167 3.036 2.930 2.843 38 7.353 5.211 4.343 3.858 3.542 3.319 3.152 3.021 2.915 2.828 39 7.333 5.194 4.327 3.843 3.528 3.305 3.137 3.006 2.901 2.814 40 7.314 5.179 4.313 3.828 3.514 3.291 3.124 2.993 2.888 2.801 41 7.296 5.163 4.299 3.815 3.501 3.278 3.111 2.980 2.875 2.788 42 7.280 5.149 4.285 3.802 3.488 3.266 3.099 2.968 2.863 2.776 43 7.264 5.136 4.273 3.790 3.476 3.254 3.087 2.957 2.851 2.764 44 7.248 5.123 4.261 3.778 3.465 3.243 3.076 2.946 2.840 2.754 45 7.234 5.110 4.249 3.767 3.454 3.232 3.066 2.935 2.830 2.743 46 7.220 5.099 4.238 3.757 3.444 3.222 3.056 2.925 2.820 2.733 47 7.207 5.087 4.228 3.747 3.434 3.213 3.046 2.916 2.811 2.724 48 7.194 5.077 4.218 3.737 3.425 3.204 3.037 2.907 2.802 2.715 49 7.182 5.066 4.208 3.728 3.416 3.195 3.028 2.898 2.793 2.706 50 7.171 5.057 4.199 3.720 3.408 3.186 3.020 2.890 2.785 2.698 51 7.159 5.047 4.191 3.711 3.400 3.178 3.012 2.882 2.777 2.690 52 7.149 5.038 4.182 3.703 3.392 3.171 3.005 2.874 2.769 2.683 53 7.139 5.030 4.174 3.695 3.384 3.163 2.997 2.867 2.762 2.675 54 7.129 5.021 4.167 3.688 3.377 3.156 2.990 2.860 2.755 2.668 55 7.119 5.013 4.159 3.681 3.370 3.149 2.983 2.853 2.748 2.662 56 7.110 5.006 4.152 3.674 3.363 3.143 2.977 2.847 2.742 2.655 57 7.102 4.998 4.145 3.667 3.357 3.136 2.971 2.841 2.736 2.649 58 7.093 4.991 4.138 3.661 3.351 3.130 2.965 2.835 2.730 2.643 59 7.085 4.984 4.132 3.655 3.345 3.124 2.959 2.829 2.724 2.637 60 7.077 4.977 4.126 3.649 3.339 3.119 2.953 2.823 2.718 2.632 61 7.070 4.971 4.120 3.643 3.333 3.113 2.948 2.818 2.713 2.626 62 7.062 4.965 4.114 3.638 3.328 3.108 2.942 2.813 2.708 2.621 63 7.055 4.959 4.109 3.632 3.323 3.103 2.937 2.808 2.703 2.616 64 7.048 4.953 4.103 3.627 3.318 3.098 2.932 2.803 2.698 2.611 65 7.042 4.947 4.098 3.622 3.313 3.093 2.928 2.798 2.693 2.607 66 7.035 4.942 4.093 3.618 3.308 3.088 2.923 2.793 2.689 2.602 67 7.029 4.937 4.088 3.613 3.304 3.084 2.919 2.789 2.684 2.598 68 7.023 4.932 4.083 3.608 3.299 3.080 2.914 2.785 2.680 2.593 69 7.017 4.927 4.079 3.604 3.295 3.075 2.910 2.781 2.676 2.589 70 7.011 4.922 4.074 3.600 3.291 3.071 2.906 2.777 2.672 2.585 71 7.006 4.917 4.070 3.596 3.287 3.067 2.902 2.773 2.668 2.581 72 7.001 4.913 4.066 3.591 3.283 3.063 2.898 2.769 2.664 2.578 73 6.995 4.908 4.062 3.588 3.279 3.060 2.895 2.765 2.660 2.574 74 6.990 4.904 4.058 3.584 3.275 3.056 2.891 2.762 2.657 2.570 75 6.985 4.900 4.054 3.580 3.272 3.052 2.887 2.758 2.653 2.567 76 6.981 4.896 4.050 3.577 3.268 3.049 2.884 2.755 2.650 2.563 77 6.976 4.892 4.047 3.573 3.265 3.046 2.881 2.751 2.647 2.560 78 6.971 4.888 4.043 3.570 3.261 3.042 2.877 2.748 2.644 2.557 79 6.967 4.884 4.040 3.566 3.258 3.039 2.874 2.745 2.640 2.554 80 6.963 4.881 4.036 3.563 3.255 3.036 2.871 2.742 2.637 2.551 81 6.958 4.877 4.033 3.560 3.252 3.033 2.868 2.739 2.634 2.548 82 6.954 4.874 4.030 3.557 3.249 3.030 2.865 2.736 2.632 2.545 83 6.950 4.870 4.027 3.554 3.246 3.027 2.863 2.733 2.629 2.542 84 6.947 4.867 4.024 3.551 3.243 3.025 2.860 2.731 2.626 2.539 85 6.943 4.864 4.021 3.548 3.240 3.022 2.857 2.728 2.623 2.537 86 6.939 4.861 4.018 3.545 3.238 3.019 2.854 2.725 2.621 2.534 87 6.935 4.858 4.015 3.543 3.235 3.017 2.852 2.723 2.618 2.532 88 6.932 4.855 4.012 3.540 3.233 3.014 2.849 2.720 2.616 2.529 89 6.928 4.852 4.010 3.538 3.230 3.012 2.847 2.718 2.613 2.527 90 6.925 4.849 4.007 3.535 3.228 3.009 2.845 2.715 2.611 2.524 91 6.922 4.846 4.004 3.533 3.225 3.007 2.842 2.713 2.609 2.522 92 6.919 4.844 4.002 3.530 3.223 3.004 2.840 2.711 2.606 2.520 93 6.915 4.841 3.999 3.528 3.221 3.002 2.838 2.709 2.604 2.518 94 6.912 4.838 3.997 3.525 3.218 3.000 2.835 2.706 2.602 2.515 95 6.909 4.836 3.995 3.523 3.216 2.998 2.833 2.704 2.600 2.513 96 6.906 4.833 3.992 3.521 3.214 2.996 2.831 2.702 2.598 2.511 97 6.904 4.831 3.990 3.519 3.212 2.994 2.829 2.700 2.596 2.509 98 6.901 4.829 3.988 3.517 3.210 2.992 2.827 2.698 2.594 2.507 99 6.898 4.826 3.986 3.515 3.208 2.990 2.825 2.696 2.592 2.505 100 6.895 4.824 3.984 3.513 3.206 2.988 2.823 2.694 2.590 2.503 \ ν1 11 12 13 14 15 16 17 18 19 20 ν2 1. 6083.35 6106.35 6125.86 6142.70 6157.28 6170.12 6181.42 6191.52 6200.58 6208.74 2. 99.408 99.416 99.422 99.428 99.432 99.437 99.440 99.444 99.447 99.449 3. 27.133 27.052 26.983 26.924 26.872 26.827 26.787 26.751 26.719 26.690 4. 14.452 14.374 14.307 14.249 14.198 14.154 14.115 14.080 14.048 14.020 5. 9.963 9.888 9.825 9.770 9.722 9.680 9.643 9.610 9.580 9.553 6. 7.790 7.718 7.657 7.605 7.559 7.519 7.483 7.451 7.422 7.396 7. 6.538 6.469 6.410 6.359 6.314 6.275 6.240 6.209 6.181 6.155 8. 5.734 5.667 5.609 5.559 5.515 5.477 5.442 5.412 5.384 5.359 9. 5.178 5.111 5.055 5.005 4.962 4.924 4.890 4.860 4.833 4.808 10. 4.772 4.706 4.650 4.601 4.558 4.520 4.487 4.457 4.430 4.405 11. 4.462 4.397 4.342 4.293 4.251 4.213 4.180 4.150 4.123 4.099 12. 4.220 4.155 4.100 4.052 4.010 3.972 3.939 3.909 3.883 3.858 13. 4.025 3.960 3.905 3.857 3.815 3.778 3.745 3.716 3.689 3.665 14. 3.864 3.800 3.745 3.698 3.656 3.619 3.586 3.556 3.529 3.505 15. 3.730 3.666 3.612 3.564 3.522 3.485 3.452 3.423 3.396 3.372 16. 3.616 3.553 3.498 3.451 3.409 3.372 3.339 3.310 3.283 3.259 17. 3.519 3.455 3.401 3.353 3.312 3.275 3.242 3.212 3.186 3.162 18. 3.434 3.371 3.316 3.269 3.227 3.190 3.158 3.128 3.101 3.077 19. 3.360 3.297 3.242 3.195 3.153 3.116 3.084 3.054 3.027 3.003 20. 3.294 3.231 3.177 3.130 3.088 3.051 3.018 2.989 2.962 2.938 21. 3.236 3.173 3.119 3.072 3.030 2.993 2.960 2.931 2.904 2.880 22. 3.184 3.121 3.067 3.019 2.978 2.941 2.908 2.879 2.852 2.827 23. 3.137 3.074 3.020 2.973 2.931 2.894 2.861 2.832 2.805 2.781 24. 3.094 3.032 2.977 2.930 2.889 2.852 2.819 2.789 2.762 2.738 25. 3.056 2.993 2.939 2.892 2.850 2.813 2.780 2.751 2.724 2.699 26. 3.021 2.958 2.904 2.857 2.815 2.778 2.745 2.715 2.688 2.664 27. 2.988 2.926 2.871 2.824 2.783 2.746 2.713 2.683 2.656 2.632 28. 2.959 2.896 2.842 2.795 2.753 2.716 2.683 2.653 2.626 2.602 29. 2.931 2.868 2.814 2.767 2.726 2.689 2.656 2.626 2.599 2.574 30. 2.906 2.843 2.789 2.742 2.700 2.663 2.630 2.600 2.573 2.549 31. 2.882 2.820 2.765 2.718 2.677 2.640 2.606 2.577 2.550 2.525 32. 2.860 2.798 2.744 2.696 2.655 2.618 2.584 2.555 2.527 2.503 33. 2.840 2.777 2.723 2.676 2.634 2.597 2.564 2.534 2.507 2.482 34. 2.821 2.758 2.704 2.657 2.615 2.578 2.545 2.515 2.488 2.463 35. 2.803 2.740 2.686 2.639 2.597 2.560 2.527 2.497 2.470 2.445 36. 2.786 2.723 2.669 2.622 2.580 2.543 2.510 2.480 2.453 2.428 37. 2.770 2.707 2.653 2.606 2.564 2.527 2.494 2.464 2.437 2.412 38. 2.755 2.692 2.638 2.591 2.549 2.512 2.479 2.449 2.421 2.397 39. 2.741 2.678 2.624 2.577 2.535 2.498 2.465 2.434 2.407 2.382 40. 2.727 2.665 2.611 2.563 2.522 2.484 2.451 2.421 2.394 2.369 41. 2.715 2.652 2.598 2.551 2.509 2.472 2.438 2.408 2.381 2.356 42. 2.703 2.640 2.586 2.539 2.497 2.460 2.426 2.396 2.369 2.344 43. 2.691 2.629 2.575 2.527 2.485 2.448 2.415 2.385 2.357 2.332 44. 2.680 2.618 2.564 2.516 2.475 2.437 2.404 2.374 2.346 2.321 45. 2.670 2.608 2.553 2.506 2.464 2.427 2.393 2.363 2.336 2.311 46. 2.660 2.598 2.544 2.496 2.454 2.417 2.384 2.353 2.326 2.301 47. 2.651 2.588 2.534 2.487 2.445 2.408 2.374 2.344 2.316 2.291 48. 2.642 2.579 2.525 2.478 2.436 2.399 2.365 2.335 2.307 2.282 49. 2.633 2.571 2.517 2.469 2.427 2.390 2.356 2.326 2.299 2.274 50. 2.625 2.562 2.508 2.461 2.419 2.382 2.348 2.318 2.290 2.265 51. 2.617 2.555 2.500 2.453 2.411 2.374 2.340 2.310 2.282 2.257 52. 2.610 2.547 2.493 2.445 2.403 2.366 2.333 2.302 2.275 2.250 53. 2.602 2.540 2.486 2.438 2.396 2.359 2.325 2.295 2.267 2.242 54. 2.595 2.533 2.479 2.431 2.389 2.352 2.318 2.288 2.260 2.235 55. 2.589 2.526 2.472 2.424 2.382 2.345 2.311 2.281 2.253 2.228 56. 2.582 2.520 2.465 2.418 2.376 2.339 2.305 2.275 2.247 2.222 57. 2.576 2.513 2.459 2.412 2.370 2.332 2.299 2.268 2.241 2.215 58. 2.570 2.507 2.453 2.406 2.364 2.326 2.293 2.262 2.235 2.209 59. 2.564 2.502 2.447 2.400 2.358 2.320 2.287 2.256 2.229 2.203 60. 2.559 2.496 2.442 2.394 2.352 2.315 2.281 2.251 2.223 2.198 61. 2.553 2.491 2.436 2.389 2.347 2.309 2.276 2.245 2.218 2.192 62. 2.548 2.486 2.431 2.384 2.342 2.304 2.270 2.240 2.212 2.187 63. 2.543 2.481 2.426 2.379 2.337 2.299 2.265 2.235 2.207 2.182 64. 2.538 2.476 2.421 2.374 2.332 2.294 2.260 2.230 2.202 2.177 65. 2.534 2.471 2.417 2.369 2.327 2.289 2.256 2.225 2.198 2.172 66. 2.529 2.466 2.412 2.365 2.322 2.285 2.251 2.221 2.193 2.168 67. 2.525 2.462 2.408 2.360 2.318 2.280 2.247 2.216 2.188 2.163 68. 2.520 2.458 2.403 2.356 2.314 2.276 2.242 2.212 2.184 2.159 69. 2.516 2.454 2.399 2.352 2.310 2.272 2.238 2.208 2.180 2.155 70. 2.512 2.450 2.395 2.348 2.306 2.268 2.234 2.204 2.176 2.150 71. 2.508 2.446 2.391 2.344 2.302 2.264 2.230 2.200 2.172 2.146 72. 2.504 2.442 2.388 2.340 2.298 2.260 2.226 2.196 2.168 2.143 73. 2.501 2.438 2.384 2.336 2.294 2.256 2.223 2.192 2.164 2.139 74. 2.497 2.435 2.380 2.333 2.290 2.253 2.219 2.188 2.161 2.135 75. 2.494 2.431 2.377 2.329 2.287 2.249 2.215 2.185 2.157 2.132 76. 2.490 2.428 2.373 2.326 2.284 2.246 2.212 2.181 2.154 2.128 77. 2.487 2.424 2.370 2.322 2.280 2.243 2.209 2.178 2.150 2.125 78. 2.484 2.421 2.367 2.319 2.277 2.239 2.206 2.175 2.147 2.122 79. 2.481 2.418 2.364 2.316 2.274 2.236 2.202 2.172 2.144 2.118 80. 2.478 2.415 2.361 2.313 2.271 2.233 2.199 2.169 2.141 2.115 81. 2.475 2.412 2.358 2.310 2.268 2.230 2.196 2.166 2.138 2.112 82. 2.472 2.409 2.355 2.307 2.265 2.227 2.193 2.163 2.135 2.109 83. 2.469 2.406 2.352 2.304 2.262 2.224 2.191 2.160 2.132 2.106 84. 2.466 2.404 2.349 2.302 2.259 2.222 2.188 2.157 2.129 2.104 85. 2.464 2.401 2.347 2.299 2.257 2.219 2.185 2.154 2.126 2.101 86. 2.461 2.398 2.344 2.296 2.254 2.216 2.182 2.152 2.124 2.098 87. 2.459 2.396 2.342 2.294 2.252 2.214 2.180 2.149 2.121 2.096 88. 2.456 2.393 2.339 2.291 2.249 2.211 2.177 2.147 2.119 2.093 89. 2.454 2.391 2.337 2.289 2.247 2.209 2.175 2.144 2.116 2.091 90. 2.451 2.389 2.334 2.286 2.244 2.206 2.172 2.142 2.114 2.088 91. 2.449 2.386 2.332 2.284 2.242 2.204 2.170 2.139 2.111 2.086 92. 2.447 2.384 2.330 2.282 2.240 2.202 2.168 2.137 2.109 2.083 93. 2.444 2.382 2.327 2.280 2.237 2.200 2.166 2.135 2.107 2.081 94. 2.442 2.380 2.325 2.277 2.235 2.197 2.163 2.133 2.105 2.079 95. 2.440 2.378 2.323 2.275 2.233 2.195 2.161 2.130 2.102 2.077 96. 2.438 2.375 2.321 2.273 2.231 2.193 2.159 2.128 2.100 2.075 97. 2.436 2.373 2.319 2.271 2.229 2.191 2.157 2.126 2.098 2.073 98. 2.434 2.371 2.317 2.269 2.227 2.189 2.155 2.124 2.096 2.071 99. 2.432 2.369 2.315 2.267 2.225 2.187 2.153 2.122 2.094 2.069 100. 2.430 2.368 2.313 2.265 2.223 2.185 2.151 2.120 2.092 2.067