72-Hf Evaluated Photon Data Library (EPDL97) by Red Cullen 6000 0 0 0 7.200000+4 1.769570+2 -1 0 0 37200 1451 1 0.0 0.0 0 0 0 67200 1451 2 0.0 0.0 0 0 3 67200 1451 3 0.0 0.0 0 0 154 347200 1451 4 72-HF LLNL Eval-Jul97 D.E.Cullen, et al. 7200 1451 5 UCRL50400,Vol.6,Rev.5 Dist-Jul97 Rev0-Oct89 7200 1451 6 ---- ENDF/B-VI MATERIAL 7200 7200 1451 7 ----- PHOTO-ATOMIC INTERACTION DATA 7200 1451 8 ------ ENDF/B-6 7200 1451 9 =================================================================7200 1451 10 The Livermore Evaluated Photon Data Library (EPDL97) in the 7200 1451 11 ENDF/B-VI format 7200 1451 12 =================================================================7200 1451 13 Contents 7200 1451 14 =================================================================7200 1451 15 MF/MT Description 7200 1451 16 =================================================================7200 1451 17 23/501 Total cross sections 7200 1451 18 23/502 Coherent scattering cross sections 7200 1451 19 23/504 Incoherent scattering cross sections 7200 1451 20 23/515 Pair production cross sections, Electron field 7200 1451 21 23/516 Pair production cross sections, Total 7200 1451 22 23/517 Pair production cross sections, Nuclear field 7200 1451 23 23/522 Total photoionization cross section 7200 1451 24 23/534 K (1S1/2) Photoionization subshell cross section 7200 1451 25 23/535 L1 (2S1/2) Photoionization subshell cross section 7200 1451 26 23/536 L2 (2P1/2) Photoionization subshell cross section 7200 1451 27 23/537 L3 (2P3/2) Photoionization subshell cross section 7200 1451 28 23/538 M1 (3S1/2) Photoionization subshell cross section 7200 1451 29 23/539 M2 (3P1/2) Photoionization subshell cross section 7200 1451 30 23/540 M3 (3P3/2) Photoionization subshell cross section 7200 1451 31 23/541 M4 (3D3/2) Photoionization subshell cross section 7200 1451 32 23/542 M5 (3D5/2) Photoionization subshell cross section 7200 1451 33 23/543 N1 (4S1/2) Photoionization subshell cross section 7200 1451 34 23/544 N2 (4P1/2) Photoionization subshell cross section 7200 1451 35 23/545 N3 (4P3/2) Photoionization subshell cross section 7200 1451 36 23/546 N4 (4D3/2) Photoionization subshell cross section 7200 1451 37 23/547 N5 (4D5/2) Photoionization subshell cross section 7200 1451 38 23/548 N6 (4F5/2) Photoionization subshell cross section 7200 1451 39 23/549 N7 (4F7/2) Photoionization subshell cross section 7200 1451 40 23/550 O1 (5S1/2) Photoionization subshell cross section 7200 1451 41 23/551 O2 (5P1/2) Photoionization subshell cross section 7200 1451 42 23/552 O3 (5P3/2) Photoionization subshell cross section 7200 1451 43 23/553 O4 (5D3/2) Photoionization subshell cross section 7200 1451 44 23/554 O5 (5D5/2) Photoionization subshell cross section 7200 1451 45 23/559 P1 (6S1/2) Photoionization subshell cross section 7200 1451 46 =================================================================7200 1451 47 27/502 Coherent scattering form factors 7200 1451 48 27/504 Incoherent scattering functions 7200 1451 49 27/505 Imaginary anomalous scattering factor 7200 1451 50 27/506 Real anomalous scattering factor 7200 1451 51 =================================================================7200 1451 52 Warning 7200 1451 53 =================================================================7200 1451 54 MF/MT combinations used to define photoionization subshell cross7200 1451 55 sections (MF=23, MT=534-572) and coherent anomalous scattering 7200 1451 56 factors (MF=27, MT=505 AND 506) are newly defined MF/MT numbers 7200 1451 57 for ENDF/B-VI that did not exist in earlier versions of ENDF/B. 7200 1451 58 If you are not prepared to use this data you need merely delete 7200 1451 59 it and all of the remaining data will still be consistent and 7200 1451 60 equivalent to the types of data in earlier versions of ENDF/B. 7200 1451 61 However, this will limit the range of problems to which this 7200 1451 62 data can be applied (see: ref. 1 for details). 7200 1451 63 =================================================================7200 1451 64 Definition of new types of data 7200 1451 65 =================================================================7200 1451 66 1) The total photoionization cross section is equal to the sum 7200 1451 67 of the photoionization subshell cross sections. 7200 1451 68 7200 1451 69 For each subshell on the second line of a section the C1 and 7200 1451 70 C2 fields are defined as, 7200 1451 71 7200 1451 72 EPE = The photoionization edge energy (similar to Q-value) 7200 1451 73 EFL = The fluorescence yield (eV/photoionization) 7200 1451 74 7200 1451 75 2) The angular distribution of coherently scattered photons is, 7200 1451 76 7200 1451 77 S(E,MU) = 3*T/8*(1 + MU**2)*((FF(M)+F1(E))**2+(F2(E))**2) 7200 1451 78 7200 1451 79 S(E,MU) = Angular distributions (barns per unit cosine) 7200 1451 80 T = The Thomson cross section 7200 1451 81 MU = The cosine of the scattering angle 7200 1451 82 FF(M) = The atomic form factor 7200 1451 83 M = Momentum transfer = SIN(THETA/2)/LAMBDA/4*PI 7200 1451 84 F1(E) = The real anomalous scattering factor 7200 1451 85 F2(E) = The imaginary anomalous scattering factor 7200 1451 86 7200 1451 87 F1(E) and F2(E) are isotropic. 7200 1451 88 7200 1451 89 When F1(E) = F2(E) = 0 this reduces to the result obtained 7200 1451 90 using only form factors (the older ENDF/B convention). 7200 1451 91 =================================================================7200 1451 92 Differences between EPDL97 and the data base presented here 7200 1451 93 =================================================================7200 1451 94 1) Energy range - EPDL97 - 1 eV to 100 GeV 7200 1451 95 Here - 1 eV TO 100 GeV (previously 100 MeV) 7200 1451 96 2) Type of Data - EPDL97 - Photon interaction including 7200 1451 97 photoexcitation 7200 1451 98 Here - Photon interaction - ENDF/B-VI has 7200 1451 99 no provision for photoexcitation 7200 1451 100 3) Secondary E - EPDL97 - Average energy of each secondary 7200 1451 101 (photons, electrons, positrons) 7200 1451 102 HERE - No secondary energy data 7200 1451 103 4) Interpolation- EPDL97 - Cross sections are Log X vs. Log Y 7200 1451 104 interpolable - the total cross 7200 1451 105 section is not included 7200 1451 106 - Form factors and scattering functions 7200 1451 107 are Log X vs. Log y, except first 7200 1451 108 interval. 7200 1451 109 - Anomalous scattering factors linearly 7200 1451 110 interpolable (they can be negative) 7200 1451 111 Here - Up through ENDF/B-V photon interaction7200 1451 112 cross sections were Log X vs. Log Y. 7200 1451 113 - For the first two Mods. of ENDF/B-VI 7200 1451 114 in order to consistently define the 7200 1451 115 total cross sections at ALL energies 7200 1451 116 all cross sections were linearized. 7200 1451 117 This was NOT a good idea. 7200 1451 118 - Starting with Mod. 3, cross sections 7200 1451 119 are left in Log X vs. Log. Y form so 7200 1451 120 that they are IDENTICAL to what's in 7200 1451 121 EPDL97. 7200 1451 122 The total is defined ONLY at the 7200 1451 123 energies tabulated in any other cross 7200 1451 124 section. 7200 1451 125 WARNING - As a result the total cross section 7200 1451 126 MUST NOT be interpolated to define the7200 1451 127 total between tabulated energies. The 7200 1451 128 ONLY consist way to define the total 7200 1451 129 between tabulated energies is to 7200 1451 130 interpolate all of the partials and 7200 1451 131 add them up. 7200 1451 132 =================================================================7200 1451 133 References 7200 1451 134 =================================================================7200 1451 135 1) D.E. Cullen, M.H. Chen, J.H. Hubbell, S.T. Perkins, 7200 1451 136 E.F. Plechaty, J.A. Rathkopf and J.H. Scofield, Tables and 7200 1451 137 graphs of photon interaction cross sections from 10 eV to 100 7200 1451 138 GeV derived from the LLNL Evaluated Photon data library (EPDL), 7200 1451 139 UCRL-50400, Vol. 6, Rev. 4, Part A: Z = 1 to 50 and Part B: 7200 1451 140 Z = 51 to 100, Lawrence Livermore National Laboratory (1989) 7200 1451 141 7200 1451 142 2) D.E. Cullen, J.H. Hubbell and L.D. Kissel, EPDL97: the 7200 1451 143 Evaluated Photon Data Library, '97 Version, UCRL-50400, Vol. 6, 7200 1451 144 Rev. 5, Lawrence Livermore National Laboratory (1997) 7200 1451 145 7200 1451 146 These are the primary references to the contents of this library7200 1451 147 and they contain a complete list of references to the sources 7200 1451 148 of data used in this library, methods of evaluation, accuracy 7200 1451 149 of the data, etc. 7200 1451 150 =================================================================7200 1451 151 History 7200 1451 152 =================================================================7200 1451 153 Mod. 1 - October, 1989 - Initial release. 7200 1451 154 Mod. 2 - August, 1990 - Updated photoionization total and 7200 1451 155 subshell cross sections. 7200 1451 156 Mod. 3 - July, 1997 - Complete re-evaluation. 7200 1451 157 =================================================================7200 1451 158 1 451 192 37200 1451 159 23 501 951 37200 1451 160 23 502 445 37200 1451 161 23 504 40 37200 1451 162 23 515 33 37200 1451 163 23 516 53 37200 1451 164 23 517 40 37200 1451 165 23 522 438 37200 1451 166 23 534 20 37200 1451 167 23 535 23 37200 1451 168 23 536 22 37200 1451 169 23 537 23 37200 1451 170 23 538 25 37200 1451 171 23 539 28 37200 1451 172 23 540 28 37200 1451 173 23 541 32 37200 1451 174 23 542 30 37200 1451 175 23 543 29 37200 1451 176 23 544 33 37200 1451 177 23 545 33 37200 1451 178 23 546 50 37200 1451 179 23 547 51 37200 1451 180 23 548 54 37200 1451 181 23 549 54 37200 1451 182 23 550 38 37200 1451 183 23 551 42 37200 1451 184 23 552 42 37200 1451 185 23 553 65 37200 1451 186 23 554 65 37200 1451 187 23 559 43 37200 1451 188 27 502 52 37200 1451 189 27 504 53 37200 1451 190 27 505 184 37200 1451 191 27 506 125 37200 1451 192 7200 1 0 193 7200 0 0 194 7.200000+4 1.769570+2 0 0 0 0720023501 195 0.0 0.0 0 0 1 2844720023501 196 2844 5 720023501 197 1.000000+0 3.318942-2 1.122441+0 5.636883-2 1.186812+0 7.349547-2720023501 198 1.244678+0 9.258829-2 1.258900+0 9.799740-2 1.270928+0 1.027667-1720023501 199 1.320146+0 1.246402-1 1.363213+0 1.472603-1 1.400896+0 1.703487-1720023501 200 1.462719+0 2.159978-1 1.487964+0 2.383179-1 1.536000+0 2.873847-1720023501 201 1.565275+0 3.221135-1 1.584900+0 3.484870-1 1.590126+0 3.558086-1720023501 202 1.627401+0 4.140059-1 1.646038+0 4.471311-1 1.678069+0 5.125156-1720023501 203 1.706770+0 5.821958-1 1.731370+0 6.525365-1 1.747771+0 7.062938-1720023501 204 1.762348+0 7.595781-1 1.776013+0 8.150117-1 1.788825+0 8.726917-1720023501 205 1.800836+0 9.327123-1 1.812096+0 9.951615-1 1.822653+0 1.060146+0720023501 206 1.832550+0 1.127796+0 1.841828+0 1.198261+0 1.850526+0 1.271708+0720023501 207 1.858681+0 1.348259+0 1.866326+0 1.427967+0 1.880660+0 1.603046+0720023501 208 1.893202+0 1.792526+0 1.904177+0 1.997743+0 1.913780+0 2.220217+0720023501 209 1.922183+0 2.461827+0 1.929535+0 2.725237+0 1.935968+0 3.014038+0720023501 210 1.941597+0 3.332060+0 1.946522+0 3.681898+0 1.950832+0 4.063430+0720023501 211 1.954603+0 4.473142+0 1.957903+0 4.904477+0 1.960790+0 5.348913+0720023501 212 1.963316+0 5.797240+0 1.965527+0 6.240668+0 1.967461+0 6.671578+0720023501 213 1.970846+0 7.531093+0 1.975288+0 8.882459+0 1.984162+0 1.240065+1720023501 214 1.988314+0 1.440533+1 1.990752+0 1.566919+1 1.995300+0 1.813448+1720023501 215 1.995628+0 1.832636+1 1.996238+0 1.866531+1 2.000504+0 2.103067+1720023501 216 2.002180+0 2.193816+1 2.005380+0 2.359358+1 2.007056+0 2.440342+1720023501 217 2.008656+0 2.512892+1 2.010256+0 2.580020+1 2.012389+0 2.659811+1720023501 218 2.014446+0 2.724839+1 2.016351+0 2.773457+1 2.017951+0 2.804999+1720023501 219 2.020008+0 2.832332+1 2.022751+0 2.844560+1 2.025036+0 2.833028+1720023501 220 2.025885+0 2.823692+1 2.028307+0 2.782195+1 2.030549+0 2.724708+1720023501 221 2.032436+0 2.662879+1 2.034768+0 2.570720+1 2.036451+0 2.494394+1720023501 222 2.039960+0 2.312699+1 2.041845+0 2.204720+1 2.043434+0 2.109387+1720023501 223 2.045531+0 1.979072+1 2.047164+0 1.875055+1 2.049264+0 1.739642+1720023501 224 2.051397+0 1.601833+1 2.053626+0 1.459469+1 2.056578+0 1.276329+1720023501 225 2.058711+0 1.149666+1 2.059321+0 1.114533+1 2.062178+0 9.569669+0720023501 226 2.063892+0 8.685549+0 2.068768+0 6.446175+0 2.070644+0 5.696939+0720023501 227 2.072144+0 5.142914+0 2.073644+0 4.628254+0 2.075777+0 3.962327+0720023501 228 2.078134+0 3.312941+0 2.080430+0 2.762452+0 2.082748+0 2.282392+0720023501 229 2.084465+0 1.972085+0 2.086725+0 1.617292+0 2.088950+0 1.321822+0720023501 230 2.091141+0 1.077299+0 2.093297+0 8.762053-1 2.096468+0 6.416718-1720023501 231 2.101834+0 3.762316-1 2.103941+0 3.069008-1 2.105409+0 2.678318-1720023501 232 2.106380+0 2.456756-1 2.107343+0 2.263392-1 2.108299+0 2.095622-1720023501 233 2.109247+0 1.951076-1 2.110188+0 1.827599-1 2.111121+0 1.723231-1720023501 234 2.112974+0 1.564375-1 2.114797+0 1.463097-1 2.116592+0 1.409184-1720023501 235 2.118359+0 1.394287-1 2.120099+0 1.411587-1 2.121811+0 1.455525-1720023501 236 2.125182+0 1.607477-1 2.128447+0 1.822233-1 2.131611+0 2.081045-1720023501 237 2.134675+0 2.371069-1 2.140613+0 3.022145-1 2.185146+0 1.077270+0720023501 238 2.190713+0 1.241032+0 2.195584+0 1.413965+0 2.199846+0 1.595047+0720023501 239 2.203575+0 1.781914+0 2.206838+0 1.971416+0 2.209693+0 2.160152+0720023501 240 2.212191+0 2.344911+0 2.216563+0 2.717374+0 2.230365+0 4.369439+0720023501 241 2.235167+0 5.118800+0 2.237911+0 5.581472+0 2.240655+0 6.064072+0720023501 242 2.246143+0 7.065413+0 2.246830+0 7.191769+0 2.251632+0 8.063578+0720023501 243 2.253518+0 8.392745+0 2.257120+0 8.983433+0 2.259006+0 9.266565+0720023501 244 2.260807+0 9.515871+0 2.262608+0 9.741792+0 2.265009+0 1.000194+1720023501 245 2.267324+0 1.020330+1 2.269468+0 1.034232+1 2.271269+0 1.042156+1720023501 246 2.273584+0 1.047076+1 2.276671+0 1.044115+1 2.279243+0 1.033241+1720023501 247 2.279908+0 1.029199+1 2.282816+0 1.005710+1 2.285142+0 9.803799+0720023501 248 2.287407+0 9.505224+0 2.289989+0 9.108139+0 2.292327+0 8.702905+0720023501 249 2.294615+0 8.270842+0 2.296999+0 7.790253+0 2.299291+0 7.306568+0720023501 250 2.301367+0 6.855744+0 2.303558+0 6.373055+0 2.305681+0 5.903700+0720023501 251 2.307884+0 5.420674+0 2.310264+0 4.909243+0 2.312000+0 4.546068+0720023501 252 2.314744+0 3.994696+0 2.317231+0 3.523559+0 2.319118+0 3.186685+0720023501 253 2.321047+0 2.861916+0 2.323320+0 2.506270+0 2.325088+0 2.250120+0720023501 254 2.327620+0 1.915139+0 2.329591+0 1.680145+0 2.330682+0 1.559652+0720023501 255 2.332317+0 1.391318+0 2.333953+0 1.237462+0 2.336354+0 1.036672+0720023501 256 2.339441+0 8.194712-1 2.344426+0 5.547100-1 2.347554+0 4.348689-1720023501 257 2.349870+0 3.654599-1 2.351399+0 3.275834-1 2.352917+0 2.956306-1720023501 258 2.354425+0 2.689332-1 2.355922+0 2.469870-1 2.357407+0 2.292693-1720023501 259 2.358880+0 2.153057-1 2.360342+0 2.046673-1 2.361793+0 1.969676-1720023501 260 2.363232+0 1.918601-1 2.366088+0 1.882173-1 2.368899+0 1.916959-1720023501 261 2.371666+0 2.006369-1 2.374390+0 2.137520-1 2.377072+0 2.300485-1720023501 262 2.379711+0 2.487666-1 2.384908+0 2.916476-1 2.389942+0 3.389108-1720023501 263 2.394819+0 3.886471-1 2.511900+0 1.625714+0 2.546003+0 2.435732+0720023501 264 2.552270+0 2.567976+0 2.558537+0 2.699280+0 2.564803+0 2.820083+0720023501 265 2.571070+0 2.918872+0 2.574203+0 2.956296+0 2.577337+0 2.983920+0720023501 266 2.580470+0 3.000608+0 2.583603+0 3.005493+0 2.586737+0 2.998034+0720023501 267 2.589870+0 2.978068+0 2.593003+0 2.945836+0 2.596137+0 2.902002+0720023501 268 2.600837+0 2.816950+0 2.602403+0 2.784200+0 2.608670+0 2.637493+0720023501 269 2.622770+0 2.291568+0 2.627470+0 2.197749+0 2.631387+0 2.135215+0720023501 270 2.633737+0 2.105564+0 2.636870+0 2.075900+0 2.640003+0 2.057904+0720023501 271 2.644703+0 2.052910+0 2.646270+0 2.056984+0 2.652537+0 2.100021+0720023501 272 2.658803+0 2.180610+0 2.661937+0 2.232405+0 2.668203+0 2.353481+0720023501 273 2.685182+0 2.744139+0 2.692787+0 2.927165+0 2.707520+0 3.274548+0720023501 274 2.735145+0 3.905258+0 2.783488+0 5.068346+0 2.867334+0 7.672349+0720023501 275 2.897926+0 8.920127+0 2.935726+0 1.076353+1 2.964559+0 1.246709+1720023501 276 2.993392+0 1.450717+1 3.022225+0 1.697342+1 3.043849+0 1.917851+1720023501 277 3.065474+0 2.176867+1 3.088793+0 2.510261+1 3.103896+0 2.763333+1720023501 278 3.118056+0 3.033141+1 3.131331+0 3.320345+1 3.143777+0 3.625595+1720023501 279 3.155444+0 3.949529+1 3.162300+0 4.161465+1 3.166382+0 4.292782+1720023501 280 3.176637+0 4.656008+1 3.186250+0 5.039887+1 3.195263+0 5.445136+1720023501 281 3.203713+0 5.872503+1 3.211634+0 6.322781+1 3.219060+0 6.796846+1720023501 282 3.226023+0 7.295723+1 3.232550+0 7.820660+1 3.238669+0 8.373190+1720023501 283 3.250142+0 9.612176+1 3.260181+0 1.099610+2 3.268965+0 1.254186+2720023501 284 3.276652+0 1.425660+2 3.283377+0 1.613186+2 3.289262+0 1.814270+2720023501 285 3.294411+0 2.025134+2 3.298916+0 2.241314+2 3.302859+0 2.458257+2720023501 286 3.309327+0 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6.899303+6 2.000000+2 6.866859+6720023522 1852 2.018366+2 6.837486+6 2.041738+2 6.800613+6 2.065380+2 6.760377+6720023522 1853 2.089296+2 6.720409+6 2.113489+2 6.680749+6 2.137962+2 6.636394+6720023522 1854 2.147100+2 6.620045+6 2.147100+2 6.916830+6 2.162719+2 6.896987+6720023522 1855 2.187762+2 6.862538+6 2.213095+2 6.828928+6 2.238721+2 6.796297+6720023522 1856 2.251400+2 6.778483+6 2.255900+2 6.771717+6 2.255900+2 6.968828+6720023522 1857 2.267000+2 6.956410+6 2.280000+2 6.940249+6 2.290868+2 6.925186+6720023522 1858 2.295000+2 6.919520+6 2.301000+2 6.910301+6 2.310000+2 6.895434+6720023522 1859 2.325000+2 6.868713+6 2.344229+2 6.832456+6 2.350000+2 6.821059+6720023522 1860 2.363000+2 6.794943+6 2.371374+2 6.777597+6 2.385000+2 6.746173+6720023522 1861 2.398833+2 6.712405+6 2.400000+2 6.709581+6 2.410000+2 6.684385+6720023522 1862 2.415000+2 6.671592+6 2.426610+2 6.641008+6 2.428000+2 6.637195+6720023522 1863 2.442000+2 6.597940+6 2.454709+2 6.561841+6 2.458000+2 6.552449+6720023522 1864 2.480000+2 6.488933+6 2.483133+2 6.479827+6 2.500000+2 6.431371+6720023522 1865 2.511886+2 6.397226+6 2.530000+2 6.343409+6 2.540973+2 6.310879+6720023522 1866 2.570396+2 6.225689+6 2.580000+2 6.198191+6 2.615000+2 6.097910+6720023522 1867 2.630268+2 6.055864+6 2.650000+2 6.002324+6 2.660725+2 5.974107+6720023522 1868 2.685300+2 5.910567+6 2.691535+2 5.894939+6 2.705700+2 5.858046+6720023522 1869 2.715000+2 5.834262+6 2.730000+2 5.796840+6 2.740000+2 5.772186+6720023522 1870 2.754229+2 5.737931+6 2.765000+2 5.711549+6 2.790000+2 5.652003+6720023522 1871 2.818383+2 5.587483+6 2.830000+2 5.561888+6 2.851018+2 5.516736+6720023522 1872 2.865000+2 5.486098+6 2.884032+2 5.445411+6 2.890000+2 5.432767+6720023522 1873 2.900000+2 5.412064+6 2.917427+2 5.376763+6 2.930000+2 5.350592+6720023522 1874 2.965000+2 5.280834+6 3.000000+2 5.214532+6 3.019952+2 5.178385+6720023522 1875 3.040000+2 5.142630+6 3.054921+2 5.116684+6 3.080000+2 5.071855+6720023522 1876 3.126079+2 4.992664+6 3.180000+2 4.901508+6 3.198895+2 4.870856+6720023522 1877 3.200000+2 4.869079+6 3.235937+2 4.812440+6 3.240000+2 4.805772+6720023522 1878 3.311311+2 4.693565+6 3.388442+2 4.576101+6 3.430000+2 4.516177+6720023522 1879 3.442200+2 4.499059+6 3.467369+2 4.464029+6 3.548134+2 4.351132+6720023522 1880 3.550000+2 4.348515+6 3.589219+2 4.293948+6 3.630781+2 4.238201+6720023522 1881 3.672823+2 4.183854+6 3.680000+2 4.174325+6 3.758200+2 4.072942+6720023522 1882 3.758200+2 4.324598+6 3.758374+2 4.324376+6 3.780000+2 4.297025+6720023522 1883 3.801894+2 4.269011+6 3.930000+2 4.111603+6 3.935501+2 4.105110+6720023522 1884 3.981072+2 4.049638+6 4.027170+2 3.995570+6 4.050000+2 3.968696+6720023522 1885 4.073803+2 3.940765+6 4.168694+2 3.833350+6 4.200000+2 3.798349+6720023522 1886 4.216965+2 3.779418+6 4.265795+2 3.725728+6 4.350000+2 3.635424+6720023522 1887 4.352700+2 3.632572+6 4.352700+2 3.689819+6 4.365158+2 3.676721+6720023522 1888 4.466836+2 3.572008+6 4.500000+2 3.538120+6 4.518559+2 3.519187+6720023522 1889 4.677351+2 3.360931+6 4.731513+2 3.309418+6 4.786301+2 3.259118+6720023522 1890 4.841724+2 3.208736+6 4.850000+2 3.201216+6 4.897788+2 3.157606+6720023522 1891 5.011872+2 3.058702+6 5.069907+2 3.009861+6 5.128614+2 2.960575+6720023522 1892 5.150000+2 2.943054+6 5.230000+2 2.878143+6 5.248075+2 2.863538+6720023522 1893 5.256900+2 2.856460+6 5.256900+2 2.927961+6 5.308844+2 2.886686+6720023522 1894 5.432503+2 2.793270+6 5.495409+2 2.747010+6 5.500000+2 2.743697+6720023522 1895 5.559043+2 2.700446+6 5.650000+2 2.635243+6 5.688529+2 2.608234+6720023522 1896 5.754399+2 2.562649+6 5.821032+2 2.518148+6 5.888437+2 2.474566+6720023522 1897 5.900000+2 2.467243+6 5.956621+2 2.431648+6 6.025596+2 2.387562+6720023522 1898 6.165950+2 2.302339+6 6.200000+2 2.282562+6 6.237348+2 2.261016+6720023522 1899 6.382635+2 2.179559+6 6.456542+2 2.139094+6 6.531306+2 2.099600+6720023522 1900 6.600000+2 2.064200+6 6.606934+2 2.060638+6 6.683439+2 2.021912+6720023522 1901 6.700000+2 2.013709+6 6.839116+2 1.947133+6 6.850000+2 1.942099+6720023522 1902 6.918310+2 1.910237+6 7.000000+2 1.872380+6 7.161434+2 1.801428+6720023522 1903 7.244360+2 1.766654+6 7.328245+2 1.732376+6 7.413102+2 1.698429+6720023522 1904 7.500000+2 1.664382+6 7.673615+2 1.599060+6 7.762471+2 1.567075+6720023522 1905 7.800000+2 1.553909+6 7.852356+2 1.535536+6 7.943282+2 1.504525+6720023522 1906 8.000000+2 1.485738+6 8.035261+2 1.474254+6 8.128305+2 1.444692+6720023522 1907 8.222426+2 1.415209+6 8.317638+2 1.386113+6 8.413951+2 1.357367+6720023522 1908 8.609938+2 1.301968+6 8.700000+2 1.277602+6 8.810489+2 1.248644+6720023522 1909 8.912509+2 1.222264+6 9.120108+2 1.171062+6 9.332543+2 1.121963+6720023522 1910 9.440609+2 1.098284+6 9.500000+2 1.085465+6 9.549926+2 1.074834+6720023522 1911 9.660509+2 1.051657+6 9.772372+2 1.028894+6 9.885531+2 1.006517+6720023522 1912 1.011579+3 9.634447+5 1.023293+3 9.424176+5 1.035142+3 9.219190+5720023522 1913 1.047129+3 9.018855+5 1.050000+3 8.971376+5 1.059254+3 8.819765+5720023522 1914 1.071519+3 8.624089+5 1.083927+3 8.433384+5 1.109175+3 8.062172+5720023522 1915 1.110000+3 8.050500+5 1.122018+3 7.883159+5 1.148154+3 7.535627+5720023522 1916 1.150000+3 7.511872+5 1.161449+3 7.367091+5 1.174898+3 7.199064+5720023522 1917 1.202264+3 6.875842+5 1.216186+3 6.720412+5 1.258925+3 6.273024+5720023522 1918 1.273503+3 6.128866+5 1.288250+3 5.987710+5 1.303167+3 5.849393+5720023522 1919 1.318257+3 5.713541+5 1.333521+3 5.581208+5 1.350000+3 5.443438+5720023522 1920 1.364583+3 5.326002+5 1.380384+3 5.201812+5 1.396368+3 5.080238+5720023522 1921 1.412538+3 4.961346+5 1.428894+3 4.844677+5 1.445440+3 4.730509+5720023522 1922 1.450000+3 4.699794+5 1.462177+3 4.619031+5 1.479108+3 4.510291+5720023522 1923 1.513561+3 4.298911+5 1.531087+3 4.196894+5 1.548817+3 4.096698+5720023522 1924 1.566751+3 3.999140+5 1.584893+3 3.903847+5 1.603245+3 3.810632+5720023522 1925 1.610000+3 3.777129+5 1.621810+3 3.718983+5 1.650000+3 3.585706+5720023522 1926 1.659587+3 3.542002+5 1.668700+3 3.500915+5 1.668700+3 1.016868+6720023522 1927 1.678804+3 1.009185+6 1.717908+3 9.805198+5 1.725500+3 9.751463+5720023522 1928 1.725500+3 1.259619+6 1.737801+3 1.262002+6 1.748000+3 1.264355+6720023522 1929 1.757924+3 1.267520+6 1.778279+3 1.275049+6 1.785000+3 1.277861+6720023522 1930 1.794000+3 1.279777+6 1.800000+3 1.280327+6 1.805000+3 1.280473+6720023522 1931 1.813000+3 1.280039+6 1.819701+3 1.278508+6 1.820000+3 1.278441+6720023522 1932 1.840772+3 1.264007+6 1.850000+3 1.257271+6 1.862087+3 1.247700+6720023522 1933 1.875000+3 1.236215+6 1.883649+3 1.227138+6 1.890000+3 1.220564+6720023522 1934 1.900000+3 1.208220+6 1.905461+3 1.201566+6 1.927525+3 1.167648+6720023522 1935 1.950000+3 1.134479+6 1.972423+3 1.102690+6 2.000000+3 1.065251+6720023522 1936 2.018366+3 1.041288+6 2.041738+3 1.011885+6 2.065380+3 9.833278+5720023522 1937 2.089296+3 9.555755+5 2.099000+3 9.446071+5 2.099000+3 1.089654+6720023522 1938 2.137962+3 1.043892+6 2.150000+3 1.030325+6 2.162719+3 1.016248+6720023522 1939 2.200000+3 9.765637+5 2.213095+3 9.630947+5 2.220000+3 9.561021+5720023522 1940 2.238721+3 9.372973+5 2.264644+3 9.119258+5 2.290868+3 8.872265+5720023522 1941 2.317395+3 8.632161+5 2.358100+3 8.281730+5 2.358100+3 8.780375+5720023522 1942 2.371374+3 8.667854+5 2.426610+3 8.218756+5 2.454709+3 8.003404+5720023522 1943 2.483133+3 7.791350+5 2.511886+3 7.583689+5 2.540973+3 7.380072+5720023522 1944 2.570396+3 7.181722+5 2.576000+3 7.144828+5 2.576000+3 7.452746+5720023522 1945 2.600160+3 7.293961+5 2.660725+3 6.917120+5 2.691535+3 6.736576+5720023522 1946 2.700000+3 6.687451+5 2.722701+3 6.557913+5 2.754229+3 6.382856+5720023522 1947 2.786121+3 6.212539+5 2.818383+3 6.046392+5 2.851018+3 5.884470+5720023522 1948 2.884032+3 5.726779+5 2.917427+3 5.573547+5 2.951209+3 5.424666+5720023522 1949 2.985383+3 5.279960+5 3.000000+3 5.219136+5 3.019952+3 5.137671+5720023522 1950 3.054921+3 4.998396+5 3.090295+3 4.863150+5 3.126079+3 4.731190+5720023522 1951 3.162278+3 4.602332+5 3.198895+3 4.477035+5 3.235937+3 4.355214+5720023522 1952 3.273407+3 4.236903+5 3.311311+3 4.121863+5 3.349654+3 4.009501+5720023522 1953 3.388442+3 3.900386+5 3.400000+3 3.868721+5 3.427678+3 3.793792+5720023522 1954 3.507519+3 3.589189+5 3.548134+3 3.490078+5 3.589219+3 3.393861+5720023522 1955 3.630781+3 3.300442+5 3.672823+3 3.209661+5 3.715352+3 3.119884+5720023522 1956 3.758374+3 3.032638+5 3.801894+3 2.947973+5 3.845918+3 2.865275+5720023522 1957 3.850000+3 2.857774+5 3.935501+3 2.706919+5 3.981072+3 2.631236+5720023522 1958 4.000000+3 2.600603+5 4.027170+3 2.557537+5 4.120975+3 2.416541+5720023522 1959 4.168694+3 2.349080+5 4.216965+3 2.283306+5 4.265795+3 2.219430+5720023522 1960 4.300000+3 2.176107+5 4.400000+3 2.056258+5 4.415704+3 2.038218+5720023522 1961 4.518559+3 1.924356+5 4.570882+3 1.869962+5 4.623810+3 1.817186+5720023522 1962 4.677351+3 1.765690+5 4.731513+3 1.715642+5 4.800000+3 1.654763+5720023522 1963 4.841724+3 1.619152+5 4.897788+3 1.573003+5 4.954502+3 1.528034+5720023522 1964 5.011872+3 1.484275+5 5.069907+3 1.441832+5 5.128614+3 1.400666+5720023522 1965 5.188000+3 1.360741+5 5.308844+3 1.284307+5 5.370318+3 1.247537+5720023522 1966 5.432503+3 1.211718+5 5.559043+3 1.143169+5 5.623413+3 1.110235+5720023522 1967 5.688529+3 1.078287+5 5.800000+3 1.026611+5 5.821032+3 1.017259+5720023522 1968 5.888437+3 9.879974+4 5.956621+3 9.594988+4 6.025596+3 9.316647+4720023522 1969 6.095369+3 9.046077+4 6.165950+3 8.783745+4 6.237348+3 8.529246+4720023522 1970 6.309573+3 8.282206+4 6.382635+3 8.042666+4 6.456542+3 7.809359+4720023522 1971 6.531306+3 7.582833+4 6.606934+3 7.362931+4 6.683439+3 7.148836+4720023522 1972 6.760830+3 6.941167+4 6.839116+3 6.738808+4 6.918310+3 6.541985+4720023522 1973 7.000000+3 6.347503+4 7.079458+3 6.166104+4 7.161434+3 5.985711+4720023522 1974 7.244360+3 5.810748+4 7.328245+3 5.641010+4 7.413102+3 5.476486+4720023522 1975 7.500000+3 5.314610+4 7.585776+3 5.160477+4 7.852356+3 4.718110+4720023522 1976 7.943282+3 4.579640+4 8.000000+3 4.496144+4 8.035261+3 4.445331+4720023522 1977 8.128305+3 4.315010+4 8.222426+3 4.187892+4 8.300000+3 4.087125+4720023522 1978 8.511380+3 3.828506+4 8.609938+3 3.715898+4 8.709636+3 3.605774+4720023522 1979 8.912509+3 3.395625+4 9.000000+3 3.310388+4 9.015711+3 3.295395+4720023522 1980 9.120108+3 3.198141+4 9.225714+3 3.103576+4 9.332543+3 3.011822+4720023522 1981 9.549926+3 2.835633+4 9.558300+3 2.829108+4 9.558300+3 7.483190+4720023522 1982 9.642000+3 7.336263+4 9.660509+3 7.300990+4 9.850000+3 6.953246+4720023522 1983 9.885531+3 6.886579+4 1.000000+4 6.677558+4 1.011579+4 6.474995+4720023522 1984 1.023293+4 6.278579+4 1.035142+4 6.088178+4 1.040000+4 6.012434+4720023522 1985 1.047129+4 5.903469+4 1.071519+4 5.550002+4 1.076300+4 5.484178+4720023522 1986 1.076300+4 7.566784+4 1.083927+4 7.432125+4 1.096478+4 7.215797+4720023522 1987 1.107000+4 7.041226+4 1.122018+4 6.794003+4 1.124500+4 6.754289+4720023522 1988 1.124500+4 7.813199+4 1.135011+4 7.627583+4 1.141500+4 7.516060+4720023522 1989 1.148154+4 7.407178+4 1.161449+4 7.196216+4 1.174898+4 6.991420+4720023522 1990 1.175000+4 6.989889+4 1.188502+4 6.789552+4 1.190000+4 6.767824+4720023522 1991 1.200000+4 6.625051+4 1.202264+4 6.593524+4 1.230269+4 6.220408+4720023522 1992 1.244515+4 6.039938+4 1.258925+4 5.862983+4 1.273503+4 5.691341+4720023522 1993 1.288250+4 5.524853+4 1.303167+4 5.363271+4 1.318257+4 5.206543+4720023522 1994 1.333521+4 5.054496+4 1.348963+4 4.906878+4 1.350000+4 4.897181+4720023522 1995 1.364583+4 4.764174+4 1.380384+4 4.624533+4 1.400000+4 4.457836+4720023522 1996 1.412538+4 4.355576+4 1.428894+4 4.227107+4 1.445440+4 4.102450+4720023522 1997 1.450000+4 4.069011+4 1.462177+4 3.980996+4 1.479108+4 3.863001+4720023522 1998 1.496236+4 3.748556+4 1.500000+4 3.724049+4 1.513561+4 3.637590+4720023522 1999 1.531087+4 3.529893+4 1.548817+4 3.424885+4 1.580000+4 3.249701+4720023522 2000 1.584893+4 3.223326+4 1.603245+4 3.126994+4 1.640590+4 2.942726+4720023522 2001 1.659587+4 2.854812+4 1.698244+4 2.687604+4 1.717908+4 2.607755+4720023522 2002 1.737801+4 2.530304+4 1.770000+4 2.411524+4 1.798871+4 2.310704+4720023522 2003 1.819701+4 2.241468+4 1.840772+4 2.174264+4 1.850000+4 2.145711+4720023522 2004 1.862087+4 2.108682+4 1.883649+4 2.044817+4 1.905461+4 1.982926+4720023522 2005 1.972423+4 1.808559+4 1.995262+4 1.753996+4 2.000000+4 1.742953+4720023522 2006 2.018366+4 1.701043+4 2.041738+4 1.649682+4 2.065380+4 1.599915+4720023522 2007 2.080000+4 1.570189+4 2.089296+4 1.551550+4 2.113489+4 1.504416+4720023522 2008 2.137962+4 1.458742+4 2.162719+4 1.414489+4 2.213095+4 1.330077+4720023522 2009 2.264644+4 1.250839+4 2.290868+4 1.212754+4 2.344229+4 1.140034+4720023522 2010 2.371374+4 1.105082+4 2.400000+4 1.069816+4 2.426610+4 1.038362+4720023522 2011 2.454709+4 1.006525+4 2.483133+4 9.756882+3 2.570396+4 8.888667+3720023522 2012 2.576800+4 8.829268+3 2.600160+4 8.616637+3 2.630268+4 8.352944+3720023522 2013 2.660725+4 8.095936+3 2.691535+4 7.847038+3 2.722701+4 7.605989+3720023522 2014 2.754229+4 7.372528+3 2.818383+4 6.926886+3 2.851018+4 6.714237+3720023522 2015 2.884032+4 6.508275+3 2.917427+4 6.308797+3 3.019952+4 5.739937+3720023522 2016 3.054921+4 5.562029+3 3.090295+4 5.389771+3 3.126079+4 5.222972+3720023522 2017 3.162278+4 5.061459+3 3.235937+4 4.753313+3 3.273407+4 4.606525+3720023522 2018 3.311311+4 4.463770+3 3.349654+4 4.325388+3 3.388442+4 4.191368+3720023522 2019 3.507519+4 3.814287+3 3.548134+4 3.695537+3 3.630781+4 3.468232+3720023522 2020 3.672823+4 3.360003+3 3.758374+4 3.153599+3 3.801894+4 3.055316+3720023522 2021 3.845918+4 2.960165+3 3.890451+4 2.868048+3 3.981072+4 2.692328+3720023522 2022 4.000000+4 2.657513+3 4.027170+4 2.608614+3 4.073803+4 2.527148+3720023522 2023 4.120975+4 2.448015+3 4.315191+4 2.155766+3 4.365158+4 2.088137+3720023522 2024 4.415704+4 2.022680+3 4.570882+4 1.838631+3 4.677351+4 1.724711+3720023522 2025 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