64-Gd Evaluated Photon Data Library (EPDL97) by Red Cullen 6000 0 0 0 6.400000+4 1.558990+2 -1 0 0 36400 1451 1 0.0 0.0 0 0 0 66400 1451 2 0.0 0.0 0 0 3 66400 1451 3 0.0 0.0 0 0 154 346400 1451 4 64-GD LLNL Eval-Jul97 D.E.Cullen, et al. 6400 1451 5 UCRL50400,Vol.6,Rev.5 Dist-Jul97 Rev0-Oct89 6400 1451 6 ---- ENDF/B-VI MATERIAL 6400 6400 1451 7 ----- PHOTO-ATOMIC INTERACTION DATA 6400 1451 8 ------ ENDF/B-6 6400 1451 9 =================================================================6400 1451 10 The Livermore Evaluated Photon Data Library (EPDL97) in the 6400 1451 11 ENDF/B-VI format 6400 1451 12 =================================================================6400 1451 13 Contents 6400 1451 14 =================================================================6400 1451 15 MF/MT Description 6400 1451 16 =================================================================6400 1451 17 23/501 Total cross sections 6400 1451 18 23/502 Coherent scattering cross sections 6400 1451 19 23/504 Incoherent scattering cross sections 6400 1451 20 23/515 Pair production cross sections, Electron field 6400 1451 21 23/516 Pair production cross sections, Total 6400 1451 22 23/517 Pair production cross sections, Nuclear field 6400 1451 23 23/522 Total photoionization cross section 6400 1451 24 23/534 K (1S1/2) Photoionization subshell cross section 6400 1451 25 23/535 L1 (2S1/2) Photoionization subshell cross section 6400 1451 26 23/536 L2 (2P1/2) Photoionization subshell cross section 6400 1451 27 23/537 L3 (2P3/2) Photoionization subshell cross section 6400 1451 28 23/538 M1 (3S1/2) Photoionization subshell cross section 6400 1451 29 23/539 M2 (3P1/2) Photoionization subshell cross section 6400 1451 30 23/540 M3 (3P3/2) Photoionization subshell cross section 6400 1451 31 23/541 M4 (3D3/2) Photoionization subshell cross section 6400 1451 32 23/542 M5 (3D5/2) Photoionization subshell cross section 6400 1451 33 23/543 N1 (4S1/2) Photoionization subshell cross section 6400 1451 34 23/544 N2 (4P1/2) Photoionization subshell cross section 6400 1451 35 23/545 N3 (4P3/2) Photoionization subshell cross section 6400 1451 36 23/546 N4 (4D3/2) Photoionization subshell cross section 6400 1451 37 23/547 N5 (4D5/2) Photoionization subshell cross section 6400 1451 38 23/548 N6 (4F5/2) Photoionization subshell cross section 6400 1451 39 23/549 N7 (4F7/2) Photoionization subshell cross section 6400 1451 40 23/550 O1 (5S1/2) Photoionization subshell cross section 6400 1451 41 23/551 O2 (5P1/2) Photoionization subshell cross section 6400 1451 42 23/552 O3 (5P3/2) Photoionization subshell cross section 6400 1451 43 23/553 O4 (5D3/2) Photoionization subshell cross section 6400 1451 44 23/554 O5 (5D5/2) Photoionization subshell cross section 6400 1451 45 23/559 P1 (6S1/2) Photoionization subshell cross section 6400 1451 46 =================================================================6400 1451 47 27/502 Coherent scattering form factors 6400 1451 48 27/504 Incoherent scattering functions 6400 1451 49 27/505 Imaginary anomalous scattering factor 6400 1451 50 27/506 Real anomalous scattering factor 6400 1451 51 =================================================================6400 1451 52 Warning 6400 1451 53 =================================================================6400 1451 54 MF/MT combinations used to define photoionization subshell cross6400 1451 55 sections (MF=23, MT=534-572) and coherent anomalous scattering 6400 1451 56 factors (MF=27, MT=505 AND 506) are newly defined MF/MT numbers 6400 1451 57 for ENDF/B-VI that did not exist in earlier versions of ENDF/B. 6400 1451 58 If you are not prepared to use this data you need merely delete 6400 1451 59 it and all of the remaining data will still be consistent and 6400 1451 60 equivalent to the types of data in earlier versions of ENDF/B. 6400 1451 61 However, this will limit the range of problems to which this 6400 1451 62 data can be applied (see: ref. 1 for details). 6400 1451 63 =================================================================6400 1451 64 Definition of new types of data 6400 1451 65 =================================================================6400 1451 66 1) The total photoionization cross section is equal to the sum 6400 1451 67 of the photoionization subshell cross sections. 6400 1451 68 6400 1451 69 For each subshell on the second line of a section the C1 and 6400 1451 70 C2 fields are defined as, 6400 1451 71 6400 1451 72 EPE = The photoionization edge energy (similar to Q-value) 6400 1451 73 EFL = The fluorescence yield (eV/photoionization) 6400 1451 74 6400 1451 75 2) The angular distribution of coherently scattered photons is, 6400 1451 76 6400 1451 77 S(E,MU) = 3*T/8*(1 + MU**2)*((FF(M)+F1(E))**2+(F2(E))**2) 6400 1451 78 6400 1451 79 S(E,MU) = Angular distributions (barns per unit cosine) 6400 1451 80 T = The Thomson cross section 6400 1451 81 MU = The cosine of the scattering angle 6400 1451 82 FF(M) = The atomic form factor 6400 1451 83 M = Momentum transfer = SIN(THETA/2)/LAMBDA/4*PI 6400 1451 84 F1(E) = The real anomalous scattering factor 6400 1451 85 F2(E) = The imaginary anomalous scattering factor 6400 1451 86 6400 1451 87 F1(E) and F2(E) are isotropic. 6400 1451 88 6400 1451 89 When F1(E) = F2(E) = 0 this reduces to the result obtained 6400 1451 90 using only form factors (the older ENDF/B convention). 6400 1451 91 =================================================================6400 1451 92 Differences between EPDL97 and the data base presented here 6400 1451 93 =================================================================6400 1451 94 1) Energy range - EPDL97 - 1 eV to 100 GeV 6400 1451 95 Here - 1 eV TO 100 GeV (previously 100 MeV) 6400 1451 96 2) Type of Data - EPDL97 - Photon interaction including 6400 1451 97 photoexcitation 6400 1451 98 Here - Photon interaction - ENDF/B-VI has 6400 1451 99 no provision for photoexcitation 6400 1451 100 3) Secondary E - EPDL97 - Average energy of each secondary 6400 1451 101 (photons, electrons, positrons) 6400 1451 102 HERE - No secondary energy data 6400 1451 103 4) Interpolation- EPDL97 - Cross sections are Log X vs. Log Y 6400 1451 104 interpolable - the total cross 6400 1451 105 section is not included 6400 1451 106 - Form factors and scattering functions 6400 1451 107 are Log X vs. Log y, except first 6400 1451 108 interval. 6400 1451 109 - Anomalous scattering factors linearly 6400 1451 110 interpolable (they can be negative) 6400 1451 111 Here - Up through ENDF/B-V photon interaction6400 1451 112 cross sections were Log X vs. Log Y. 6400 1451 113 - For the first two Mods. of ENDF/B-VI 6400 1451 114 in order to consistently define the 6400 1451 115 total cross sections at ALL energies 6400 1451 116 all cross sections were linearized. 6400 1451 117 This was NOT a good idea. 6400 1451 118 - Starting with Mod. 3, cross sections 6400 1451 119 are left in Log X vs. Log. Y form so 6400 1451 120 that they are IDENTICAL to what's in 6400 1451 121 EPDL97. 6400 1451 122 The total is defined ONLY at the 6400 1451 123 energies tabulated in any other cross 6400 1451 124 section. 6400 1451 125 WARNING - As a result the total cross section 6400 1451 126 MUST NOT be interpolated to define the6400 1451 127 total between tabulated energies. The 6400 1451 128 ONLY consist way to define the total 6400 1451 129 between tabulated energies is to 6400 1451 130 interpolate all of the partials and 6400 1451 131 add them up. 6400 1451 132 =================================================================6400 1451 133 References 6400 1451 134 =================================================================6400 1451 135 1) D.E. Cullen, M.H. Chen, J.H. Hubbell, S.T. Perkins, 6400 1451 136 E.F. Plechaty, J.A. Rathkopf and J.H. Scofield, Tables and 6400 1451 137 graphs of photon interaction cross sections from 10 eV to 100 6400 1451 138 GeV derived from the LLNL Evaluated Photon data library (EPDL), 6400 1451 139 UCRL-50400, Vol. 6, Rev. 4, Part A: Z = 1 to 50 and Part B: 6400 1451 140 Z = 51 to 100, Lawrence Livermore National Laboratory (1989) 6400 1451 141 6400 1451 142 2) D.E. Cullen, J.H. Hubbell and L.D. Kissel, EPDL97: the 6400 1451 143 Evaluated Photon Data Library, '97 Version, UCRL-50400, Vol. 6, 6400 1451 144 Rev. 5, Lawrence Livermore National Laboratory (1997) 6400 1451 145 6400 1451 146 These are the primary references to the contents of this library6400 1451 147 and they contain a complete list of references to the sources 6400 1451 148 of data used in this library, methods of evaluation, accuracy 6400 1451 149 of the data, etc. 6400 1451 150 =================================================================6400 1451 151 History 6400 1451 152 =================================================================6400 1451 153 Mod. 1 - October, 1989 - Initial release. 6400 1451 154 Mod. 2 - August, 1990 - Updated photoionization total and 6400 1451 155 subshell cross sections. 6400 1451 156 Mod. 3 - July, 1997 - Complete re-evaluation. 6400 1451 157 =================================================================6400 1451 158 1 451 192 36400 1451 159 23 501 964 36400 1451 160 23 502 460 36400 1451 161 23 504 40 36400 1451 162 23 515 33 36400 1451 163 23 516 53 36400 1451 164 23 517 40 36400 1451 165 23 522 435 36400 1451 166 23 534 20 36400 1451 167 23 535 24 36400 1451 168 23 536 24 36400 1451 169 23 537 24 36400 1451 170 23 538 26 36400 1451 171 23 539 29 36400 1451 172 23 540 30 36400 1451 173 23 541 33 36400 1451 174 23 542 31 36400 1451 175 23 543 29 36400 1451 176 23 544 33 36400 1451 177 23 545 35 36400 1451 178 23 546 55 36400 1451 179 23 547 55 36400 1451 180 23 548 55 36400 1451 181 23 549 56 36400 1451 182 23 550 37 36400 1451 183 23 551 42 36400 1451 184 23 552 43 36400 1451 185 23 553 64 36400 1451 186 23 554 64 36400 1451 187 23 559 47 36400 1451 188 27 502 53 36400 1451 189 27 504 54 36400 1451 190 27 505 196 36400 1451 191 27 506 172 36400 1451 192 6400 1 0 193 6400 0 0 194 6.400000+4 1.558990+2 0 0 0 0640023501 195 0.0 0.0 0 0 1 2882640023501 196 2882 5 640023501 197 1.000000+0 1.022416-1 1.053569+0 1.308517-1 1.092367+0 1.557316-1640023501 198 1.128740+0 1.827897-1 1.194809+0 2.427671-1 1.252877+0 3.098037-1640023501 199 1.258900+0 3.177762-1 1.303913+0 3.827854-1 1.327065+0 4.214185-1640023501 200 1.370474+0 5.038866-1 1.408457+0 5.885439-1 1.441692+0 6.742130-1640023501 201 1.470773+0 7.593997-1 1.496218+0 8.431737-1 1.518483+0 9.253330-1640023501 202 1.557447+0 1.089779+0 1.584900+0 1.224413+0 1.586670+0 1.233558+0640023501 203 1.608587+0 1.356901+0 1.641463+0 1.569360+0 1.657900+0 1.690071+0640023501 204 1.682581+0 1.895648+0 1.707308+0 2.137493+0 1.727914+0 2.374320+0640023501 205 1.744398+0 2.593988+0 1.756762+0 2.781307+0 1.770841+0 3.024056+0640023501 206 1.783161+0 3.269241+0 1.793940+0 3.517162+0 1.803372+0 3.768311+0640023501 207 1.811625+0 4.023377+0 1.818847+0 4.283390+0 1.825166+0 4.549751+0640023501 208 1.830695+0 4.823965+0 1.835532+0 5.106988+0 1.843469+0 5.696382+0640023501 209 1.849951+0 6.342151+0 1.854813+0 6.956414+0 1.858459+0 7.503128+0640023501 210 1.863244+0 8.341023+0 1.873998+0 1.067364+1 1.878600+0 1.177685+1640023501 211 1.883201+0 1.284746+1 1.884351+0 1.309937+1 1.887802+0 1.379204+1640023501 212 1.888953+0 1.399644+1 1.892404+0 1.450762+1 1.893554+0 1.463891+1640023501 213 1.895279+0 1.479434+1 1.897005+0 1.489627+1 1.898155+0 1.493273+1640023501 214 1.899881+0 1.493800+1 1.901606+0 1.488206+1 1.903907+0 1.471014+1640023501 215 1.906207+0 1.442681+1 1.908508+0 1.403491+1 1.910521+0 1.360760+1640023501 216 1.912175+0 1.320199+1 1.913792+0 1.276175+1 1.915698+0 1.219430+1640023501 217 1.920155+0 1.070643+1 1.922213+0 9.969218+0 1.924756+0 9.039164+0640023501 218 1.926917+0 8.248571+0 1.927922+0 7.884960+0 1.930142+0 7.098451+0640023501 219 1.932463+0 6.312447+0 1.934988+0 5.513333+0 1.938109+0 4.625170+0640023501 220 1.943505+0 3.390827+0 1.946269+0 2.915343+0 1.948041+0 2.665865+0640023501 221 1.949478+0 2.494426+0 1.950849+0 2.355588+0 1.952220+0 2.240018+0640023501 222 1.953047+0 2.181134+0 1.953991+0 2.123469+0 1.955406+0 2.055214+0640023501 223 1.956822+0 2.007622+0 1.957972+0 1.983186+0 1.959697+0 1.968676+0640023501 224 1.960560+0 1.970680+0 1.961646+0 1.981325+0 1.962973+0 2.005771+0640023501 225 1.963842+0 2.028079+0 1.965553+0 2.085253+0 1.967210+0 2.155665+0640023501 226 1.995300+0 4.105051+0 2.018575+0 6.952453+0 2.023544+0 7.587897+0640023501 227 2.026028+0 7.905462+0 2.028512+0 8.216832+0 2.033481+0 8.797900+0640023501 228 2.034723+0 8.929766+0 2.038449+0 9.279352+0 2.039691+0 9.377625+0640023501 229 2.043418+0 9.605963+0 2.044660+0 9.657379+0 2.046523+0 9.709058+0640023501 230 2.048386+0 9.728593+0 2.049628+0 9.723046+0 2.051491+0 9.686143+0640023501 231 2.053355+0 9.614514+0 2.055839+0 9.465160+0 2.058323+0 9.256011+0640023501 232 2.060807+0 8.990755+0 2.063292+0 8.674905+0 2.063913+0 8.588844+0640023501 233 2.067717+0 8.010190+0 2.068881+0 7.818579+0 2.073539+0 7.012778+0640023501 234 2.075140+0 6.729741+0 2.078818+0 6.089763+0 2.085688+0 5.021707+0640023501 235 2.088134+0 4.706472+0 2.090308+0 4.461877+0 2.092404+0 4.260012+0640023501 236 2.093102+0 4.200379+0 2.095587+0 4.019865+0 2.097450+0 3.916797+0640023501 237 2.098692+0 3.863296+0 2.101952+0 3.778905+0 2.103039+0 3.768071+0640023501 238 2.108008+0 3.818243+0 2.109250+0 3.853882+0 2.112976+0 4.007466+0640023501 239 2.115460+0 4.143125+0 2.118692+0 4.351169+0 2.131407+0 5.368657+0640023501 240 2.136547+0 5.815398+0 2.213634+0 1.253933+1 2.224531+0 1.364421+1640023501 241 2.229980+0 1.419468+1 2.235429+0 1.472575+1 2.240877+0 1.522359+1640023501 242 2.246326+0 1.567782+1 2.251774+0 1.608455+1 2.257223+0 1.644853+1640023501 243 2.273569+0 1.746090+1 2.279017+0 1.785848+1 2.284466+0 1.833061+1640023501 244 2.289914+0 1.889704+1 2.295363+0 1.956970+1 2.300811+0 2.035234+1640023501 245 2.306260+0 2.124181+1 2.317157+0 2.330671+1 2.359817+0 3.414272+1640023501 246 2.370434+0 3.760513+1 2.380388+0 4.125693+1 2.389720+0 4.511359+1640023501 247 2.398468+0 4.918598+1 2.406670+0 5.348312+1 2.414359+0 5.801340+1640023501 248 2.421568+0 6.278495+1 2.428325+0 6.780572+1 2.434661+0 7.308359+1640023501 249 2.440601+0 7.862659+1 2.446169+0 8.444362+1 2.451389+0 9.054525+1640023501 250 2.456283+0 9.694470+1 2.465460+0 1.112055+2 2.473489+0 1.269990+2640023501 251 2.480515+0 1.445165+2 2.486662+0 1.638723+2 2.492041+0 1.850256+2640023501 252 2.496748+0 2.077504+2 2.500866+0 2.316612+2 2.504470+0 2.562735+2640023501 253 2.507623+0 2.810739+2 2.510382+0 3.055780+2 2.511900+0 3.204673+2640023501 254 2.514908+0 3.521187+2 2.521377+0 4.340505+2 2.531543+0 6.037742+2640023501 255 2.535921+0 6.924856+2 2.539035+0 7.607535+2 2.542148+0 8.327420+2640023501 256 2.548374+0 9.847799+2 2.549153+0 1.004242+3 2.554601+0 1.140511+3640023501 257 2.556741+0 1.193019+3 2.560827+0 1.289187+3 2.562968+0 1.336449+3640023501 258 2.565011+0 1.378938+3 2.567054+0 1.418410+3 2.569778+0 1.465597+3640023501 259 2.572405+0 1.504382+3 2.574837+0 1.533723+3 2.576880+0 1.553080+3640023501 260 2.579507+0 1.570418+3 2.583009+0 1.579657+3 2.585928+0 1.574866+3640023501 261 2.587012+0 1.570172+3 2.590104+0 1.548192+3 2.592968+0 1.516796+3640023501 262 2.595377+0 1.482563+3 2.598355+0 1.431088+3 2.600504+0 1.388213+3640023501 263 2.604608+0 1.294859+3 2.606851+0 1.238492+3 2.608509+0 1.194916+3640023501 264 2.611418+0 1.115318+3 2.614185+0 1.037060+3 2.616866+0 9.599879+2640023501 265 2.619590+0 8.815548+2 2.622436+0 8.005818+2 2.626206+0 6.965970+2640023501 266 2.628930+0 6.248809+2 2.629708+0 6.050302+2 2.633357+0 5.163034+2640023501 267 2.635546+0 4.668039+2 2.642161+0 3.360737+2 2.644168+0 3.022732+2640023501 268 2.647999+0 2.453831+2 2.654980+0 1.667343+2 2.657399+0 1.466293+2640023501 269 2.659479+0 1.321073+2 2.660996+0 1.230701+2 2.662478+0 1.154802+2640023501 270 2.664043+0 1.087514+2 2.664987+0 1.053147+2 2.665921+0 1.023732+2640023501 271 2.666840+0 9.991373+1 2.667745+0 9.790981+1 2.668635+0 9.633696+1640023501 272 2.670389+0 9.438496+1 2.672087+0 9.392403+1 2.675378+0 9.699432+1640023501 273 2.687720+0 1.569134+2 2.692348+0 2.018928+2 2.703041+0 3.690932+2640023501 274 2.708128+0 4.885613+2 2.712022+0 6.019156+2 2.715004+0 7.032678+2640023501 275 2.719265+0 8.724590+2 2.722433+0 1.018392+3 2.725949+0 1.202041+3640023501 276 2.729387+0 1.404707+3 2.731451+0 1.537569+3 2.734804+0 1.771710+3640023501 277 2.738157+0 2.028130+3 2.745283+0 2.642105+3 2.746855+0 2.788788+3640023501 278 2.750391+0 3.130905+3 2.752775+0 3.369212+3 2.754151+0 3.508806+3640023501 279 2.758277+0 3.932986+3 2.761683+0 4.283718+3 2.764984+0 4.617914+3640023501 280 2.768389+0 4.950342+3 2.771690+0 5.254195+3 2.774624+0 5.504107+3640023501 281 2.777866+0 5.752982+3 2.778816+0 5.819740+3 2.782746+0 6.062780+3640023501 282 2.785814+0 6.211974+3 2.789389+0 6.336843+3 2.792295+0 6.397538+3640023501 283 2.798726+0 6.398338+3 2.800560+0 6.365156+3 2.805510+0 6.205239+3640023501 284 2.808023+0 6.087281+3 2.810819+0 5.929683+3 2.812617+0 5.814973+3640023501 285 2.815780+0 5.590492+3 2.819067+0 5.331145+3 2.821813+0 5.098165+3640023501 286 2.825343+0 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4.073803+1 9.403986+6640023522 1840 4.120975+1 9.168804+6 4.150000+1 9.030909+6 4.168694+1 8.945057+6640023522 1841 4.220000+1 8.719165+6 4.265795+1 8.529075+6 4.315191+1 8.333470+6640023522 1842 4.415704+1 7.972244+6 4.500000+1 7.703631+6 4.518559+1 7.647757+6640023522 1843 4.570882+1 7.496294+6 4.650000+1 7.288110+6 4.677351+1 7.220453+6640023522 1844 4.731513+1 7.094438+6 4.800000+1 6.947315+6 4.841724+1 6.863316+6640023522 1845 4.900000+1 6.754657+6 4.954502+1 6.660853+6 5.011872+1 6.568811+6640023522 1846 5.069907+1 6.483992+6 5.128614+1 6.406007+6 5.188000+1 6.334573+6640023522 1847 5.248075+1 6.265109+6 5.370318+1 6.147901+6 5.432503+1 6.097770+6640023522 1848 5.466000+1 6.073187+6 5.466000+1 6.134070+6 5.500000+1 6.111003+6640023522 1849 5.520000+1 6.096685+6 5.575000+1 6.060377+6 5.623413+1 6.032926+6640023522 1850 5.754399+1 5.973270+6 5.800000+1 5.957082+6 5.821032+1 5.950295+6640023522 1851 5.900000+1 5.922531+6 5.920000+1 5.916872+6 5.956621+1 5.907515+6640023522 1852 6.095369+1 5.883479+6 6.165950+1 5.876885+6 6.237348+1 5.867703+6640023522 1853 6.309573+1 5.862987+6 6.500000+1 5.864983+6 6.531306+1 5.867396+6640023522 1854 6.800000+1 5.885034+6 6.839116+1 5.889919+6 6.918310+1 5.895211+6640023522 1855 7.000000+1 5.902588+6 7.161434+1 5.923742+6 7.328245+1 5.938055+6640023522 1856 7.400000+1 5.945992+6 7.500000+1 5.958690+6 7.762471+1 5.978148+6640023522 1857 7.800000+1 5.981722+6 7.852356+1 5.986911+6 7.900000+1 5.990451+6640023522 1858 8.000000+1 5.993161+6 8.128305+1 5.998722+6 8.150000+1 5.999780+6640023522 1859 8.222426+1 6.004128+6 8.300000+1 6.006367+6 8.317638+1 6.006939+6640023522 1860 8.413951+1 6.005319+6 8.500000+1 6.004333+6 8.511380+1 6.004281+6640023522 1861 8.650000+1 6.005243+6 8.709636+1 6.004032+6 8.800000+1 6.002441+6640023522 1862 8.810489+1 6.001823+6 8.912509+1 5.996131+6 9.015711+1 5.991786+6640023522 1863 9.120108+1 5.987713+6 9.332543+1 5.975007+6 9.400000+1 5.969522+6640023522 1864 9.660509+1 5.949515+6 9.800000+1 5.936303+6 9.900000+1 5.927685+6640023522 1865 1.000000+2 5.915874+6 1.023293+2 5.889621+6 1.035142+2 5.874098+6640023522 1866 1.040000+2 5.868003+6 1.050000+2 5.855666+6 1.060000+2 5.843608+6640023522 1867 1.071519+2 5.826386+6 1.083927+2 5.808443+6 1.096478+2 5.790586+6640023522 1868 1.115000+2 5.761246+6 1.122018+2 5.750370+6 1.135011+2 5.730732+6640023522 1869 1.148154+2 5.707127+6 1.150000+2 5.703851+6 1.161449+2 5.683627+6640023522 1870 1.174898+2 5.657497+6 1.190000+2 5.628921+6 1.202264+2 5.606155+6640023522 1871 1.220000+2 5.568774+6 1.230269+2 5.547542+6 1.244515+2 5.515698+6640023522 1872 1.250000+2 5.503671+6 1.258925+2 5.484288+6 1.273503+2 5.453115+6640023522 1873 1.280000+2 5.437841+6 1.288250+2 5.418634+6 1.288400+2 5.418287+6640023522 1874 1.303167+2 5.384544+6 1.307000+2 5.375183+6 1.315000+2 5.355795+6640023522 1875 1.318257+2 5.347961+6 1.333521+2 5.311557+6 1.345000+2 5.284637+6640023522 1876 1.350000+2 5.273034+6 1.362400+2 5.241868+6 1.375000+2 5.210694+6640023522 1877 1.380384+2 5.197523+6 1.390000+2 5.172520+6 1.405000+2 5.134114+6640023522 1878 1.412538+2 5.115085+6 1.415000+2 5.108904+6 1.430000+2 5.071650+6640023522 1879 1.440000+2 5.045368+6 1.445440+2 5.031209+6 1.462177+2 4.988239+6640023522 1880 1.480000+2 4.943433+6 1.496236+2 4.901377+6 1.500000+2 4.891765+6640023522 1881 1.513561+2 4.857499+6 1.515000+2 4.853887+6 1.540000+2 4.792106+6640023522 1882 1.548817+2 4.769090+6 1.563000+2 4.732585+6 1.563000+2 5.191480+6640023522 1883 1.566751+2 5.184719+6 1.570000+2 5.178920+6 1.577000+2 5.170049+6640023522 1884 1.584893+2 5.163557+6 1.594000+2 5.159221+6 1.603245+2 5.158684+6640023522 1885 1.605000+2 5.158717+6 1.621600+2 5.163269+6 1.621600+2 5.481545+6640023522 1886 1.621810+2 5.481648+6 1.623000+2 5.482237+6 1.627000+2 5.483198+6640023522 1887 1.632000+2 5.486179+6 1.635000+2 5.489011+6 1.639000+2 5.491335+6640023522 1888 1.643000+2 5.495171+6 1.647000+2 5.497658+6 1.650000+2 5.500467+6640023522 1889 1.655000+2 5.502292+6 1.659587+2 5.505290+6 1.665000+2 5.506134+6640023522 1890 1.669000+2 5.507426+6 1.678804+2 5.505952+6 1.685000+2 5.502460+6640023522 1891 1.688000+2 5.500426+6 1.695000+2 5.492901+6 1.698244+2 5.488744+6640023522 1892 1.705000+2 5.476848+6 1.710000+2 5.466796+6 1.713000+2 5.459776+6640023522 1893 1.717908+2 5.446920+6 1.722000+2 5.436339+6 1.730000+2 5.410931+6640023522 1894 1.737801+2 5.383995+6 1.740000+2 5.375910+6 1.750000+2 5.336294+6640023522 1895 1.755000+2 5.315237+6 1.757924+2 5.302433+6 1.761000+2 5.289036+6640023522 1896 1.765600+2 5.267950+6 1.772000+2 5.237991+6 1.778279+2 5.207562+6640023522 1897 1.785000+2 5.174427+6 1.798871+2 5.104903+6 1.800000+2 5.099340+6640023522 1898 1.810000+2 5.047920+6 1.820000+2 4.996696+6 1.842000+2 4.885471+6640023522 1899 1.851100+2 4.840379+6 1.862087+2 4.786944+6 1.865000+2 4.772659+6640023522 1900 1.900000+2 4.606366+6 1.905461+2 4.581380+6 1.927525+2 4.481765+6640023522 1901 1.950000+2 4.386471+6 1.952700+2 4.375332+6 1.980000+2 4.267676+6640023522 1902 2.000000+2 4.193697+6 2.010000+2 4.157132+6 2.020000+2 4.121618+6640023522 1903 2.040000+2 4.053649+6 2.041738+2 4.047698+6 2.065380+2 3.970907+6640023522 1904 2.070000+2 3.956564+6 2.090000+2 3.896525+6 2.100000+2 3.867836+6640023522 1905 2.113489+2 3.830427+6 2.122300+2 3.806924+6 2.128000+2 3.791395+6640023522 1906 2.137962+2 3.764961+6 2.150000+2 3.734225+6 2.162719+2 3.702696+6640023522 1907 2.170000+2 3.685293+6 2.187762+2 3.644162+6 2.190000+2 3.638900+6640023522 1908 2.198000+2 3.620632+6 2.213095+2 3.587220+6 2.220000+2 3.572464+6640023522 1909 2.238721+2 3.533622+6 2.240000+2 3.530997+6 2.264644+2 3.483143+6640023522 1910 2.270000+2 3.472912+6 2.290868+2 3.435336+6 2.300000+2 3.418387+6640023522 1911 2.300300+2 3.417843+6 2.330000+2 3.366192+6 2.340000+2 3.349530+6640023522 1912 2.344229+2 3.342696+6 2.365000+2 3.308420+6 2.371374+2 3.298271+6640023522 1913 2.380400+2 3.284026+6 2.400000+2 3.254266+6 2.440000+2 3.196948+6640023522 1914 2.450000+2 3.183352+6 2.454709+2 3.177097+6 2.483133+2 3.138678+6640023522 1915 2.500000+2 3.116636+6 2.511886+2 3.101670+6 2.540973+2 3.064942+6640023522 1916 2.570396+2 3.029384+6 2.580000+2 3.018126+6 2.600160+2 2.995193+6640023522 1917 2.630268+2 2.960458+6 2.660725+2 2.926451+6 2.722701+2 2.859610+6640023522 1918 2.730000+2 2.852170+6 2.786121+2 2.796476+6 2.788600+2 2.794098+6640023522 1919 2.788600+2 3.092707+6 2.800000+2 3.081539+6 2.830000+2 3.051843+6640023522 1920 2.851018+2 3.031301+6 2.884032+2 2.999348+6 2.900000+2 2.984458+6640023522 1921 2.917427+2 2.968357+6 2.951209+2 2.937445+6 3.000000+2 2.893723+6640023522 1922 3.019952+2 2.875817+6 3.054921+2 2.844720+6 3.090295+2 2.814722+6640023522 1923 3.100000+2 2.806746+6 3.113000+2 2.795621+6 3.113000+2 2.878093+6640023522 1924 3.198895+2 2.808772+6 3.200000+2 2.807929+6 3.273407+2 2.747736+6640023522 1925 3.311311+2 2.717773+6 3.320000+2 2.710936+6 3.388442+2 2.657526+6640023522 1926 3.430000+2 2.626704+6 3.467369+2 2.598673+6 3.507519+2 2.568798+6640023522 1927 3.550000+2 2.537893+6 3.589219+2 2.509046+6 3.600000+2 2.501306+6640023522 1928 3.672823+2 2.450707+6 3.700000+2 2.431935+6 3.715352+2 2.421175+6640023522 1929 3.758374+2 2.391250+6 3.801894+2 2.362137+6 3.813900+2 2.354149+6640023522 1930 3.813900+2 2.456735+6 3.845918+2 2.435302+6 3.850000+2 2.432612+6640023522 1931 3.890451+2 2.405583+6 3.935501+2 2.376503+6 4.000000+2 2.334485+6640023522 1932 4.027170+2 2.316891+6 4.073803+2 2.287069+6 4.100000+2 2.270787+6640023522 1933 4.120975+2 2.257710+6 4.168694+2 2.228708+6 4.240000+2 2.185799+6640023522 1934 4.280000+2 2.162504+6 4.315191+2 2.142132+6 4.365158+2 2.113246+6640023522 1935 4.415704+2 2.083803+6 4.466836+2 2.055015+6 4.500000+2 2.036826+6640023522 1936 4.600000+2 1.983316+6 4.623810+2 1.970714+6 4.677351+2 1.942860+6640023522 1937 4.700000+2 1.931356+6 4.730000+2 1.916210+6 4.731513+2 1.915441+6640023522 1938 4.786301+2 1.887571+6 4.850000+2 1.856331+6 4.897788+2 1.833029+6640023522 1939 4.954502+2 1.806130+6 5.011872+2 1.779331+6 5.050000+2 1.761854+6640023522 1940 5.069907+2 1.752801+6 5.080000+2 1.748234+6 5.128614+2 1.726064+6640023522 1941 5.230000+2 1.681283+6 5.300000+2 1.651292+6 5.370318+2 1.622207+6640023522 1942 5.400000+2 1.609963+6 5.495409+2 1.571566+6 5.500000+2 1.569753+6640023522 1943 5.559043+2 1.546338+6 5.688529+2 1.496973+6 5.754399+2 1.472424+6640023522 1944 5.800000+2 1.455895+6 5.821032+2 1.448391+6 5.888437+2 1.424495+6640023522 1945 5.956621+2 1.400950+6 6.000000+2 1.386364+6 6.025596+2 1.377843+6640023522 1946 6.095369+2 1.354413+6 6.165950+2 1.331413+6 6.309573+2 1.286200+6640023522 1947 6.382635+2 1.264306+6 6.456542+2 1.242424+6 6.500000+2 1.229887+6640023522 1948 6.531306+2 1.220934+6 6.606934+2 1.199238+6 6.683439+2 1.177937+6640023522 1949 6.839116+2 1.136697+6 6.850000+2 1.133854+6 6.998420+2 1.096233+6640023522 1950 7.000000+2 1.095840+6 7.079458+2 1.076371+6 7.161434+2 1.056787+6640023522 1951 7.244360+2 1.037365+6 7.328245+2 1.018363+6 7.413102+2 9.993906+5640023522 1952 7.500000+2 9.805533+5 7.585776+2 9.623253+5 7.673615+2 9.442532+5640023522 1953 7.852356+2 9.091615+5 8.035261+2 8.745303+5 8.222426+2 8.409861+5640023522 1954 8.317638+2 8.247625+5 8.413951+2 8.088512+5 8.511380+2 7.930176+5640023522 1955 8.609938+2 7.774978+5 8.709636+2 7.619504+5 8.810489+2 7.467392+5640023522 1956 8.912509+2 7.318669+5 9.015711+2 7.173239+5 9.120108+2 7.028605+5640023522 1957 9.225714+2 6.886784+5 9.440609+2 6.609609+5 9.549926+2 6.474563+5640023522 1958 9.660509+2 6.341820+5 9.772372+2 6.212062+5 9.885531+2 6.083359+5640023522 1959 1.000000+3 5.955779+5 1.023293+3 5.709275+5 1.047129+3 5.473695+5640023522 1960 1.059254+3 5.357638+5 1.071519+3 5.243506+5 1.083927+3 5.130667+5640023522 1961 1.096478+3 5.020452+5 1.135011+3 4.704041+5 1.161449+3 4.502350+5640023522 1962 1.188502+3 4.307270+5 1.199800+3 4.229325+5 1.199800+3 1.363120+6640023522 1963 1.202264+3 1.359354+6 1.216186+3 1.338407+6 1.230269+3 1.317802+6640023522 1964 1.231600+3 1.315873+6 1.231600+3 1.733331+6 1.258925+3 1.721000+6640023522 1965 1.261500+3 1.719985+6 1.272000+3 1.712948+6 1.273503+3 1.713508+6640023522 1966 1.274000+3 1.713697+6 1.288250+3 1.708192+6 1.303167+3 1.703199+6640023522 1967 1.318257+3 1.694277+6 1.320000+3 1.693165+6 1.333521+3 1.676098+6640023522 1968 1.340000+3 1.666769+6 1.350000+3 1.648908+6 1.364583+3 1.623643+6640023522 1969 1.370000+3 1.613811+6 1.396368+3 1.559214+6 1.428894+3 1.480643+6640023522 1970 1.462177+3 1.401967+6 1.479108+3 1.364145+6 1.496236+3 1.327282+6640023522 1971 1.500000+3 1.319364+6 1.531087+3 1.256481+6 1.541800+3 1.235805+6640023522 1972 1.541800+3 1.422315+6 1.566751+3 1.372637+6 1.570000+3 1.366360+6640023522 1973 1.603245+3 1.303666+6 1.610000+3 1.291452+6 1.621810+3 1.270257+6640023522 1974 1.640590+3 1.237118+6 1.650000+3 1.221107+6 1.659587+3 1.205102+6640023522 1975 1.670000+3 1.188052+6 1.678804+3 1.173771+6 1.686900+3 1.160860+6640023522 1976 1.686900+3 1.230693+6 1.699000+3 1.211302+6 1.717908+3 1.181911+6640023522 1977 1.757924+3 1.122430+6 1.770000+3 1.105341+6 1.778279+3 1.093815+6640023522 1978 1.800000+3 1.064125+6 1.840772+3 1.011201+6 1.862087+3 9.850732+5640023522 1979 1.864600+3 9.820259+5 1.864600+3 1.025377+6 1.883649+3 1.002262+6640023522 1980 1.900000+3 9.830177+5 1.905461+3 9.766797+5 1.927525+3 9.516898+5640023522 1981 1.960000+3 9.161420+5 1.995262+3 8.795770+5 2.018366+3 8.567894+5640023522 1982 2.041738+3 8.345478+5 2.070000+3 8.084956+5 2.113489+3 7.707063+5640023522 1983 2.137962+3 7.504439+5 2.150000+3 7.407176+5 2.162719+3 7.306341+5640023522 1984 2.187762+3 7.113354+5 2.238721+3 6.742559+5 2.264644+3 6.564819+5640023522 1985 2.317395+3 6.220524+5 2.350000+3 6.020920+5 2.371374+3 5.893606+5640023522 1986 2.400000+3 5.728917+5 2.426610+3 5.581552+5 2.454709+3 5.431576+5640023522 1987 2.483133+3 5.285854+5 2.511886+3 5.144268+5 2.540973+3 5.006669+5640023522 1988 2.570396+3 4.871432+5 2.600160+3 4.739229+5 2.630268+3 4.610333+5640023522 1989 2.691535+3 4.361305+5 2.722701+3 4.241994+5 2.754229+3 4.126023+5640023522 1990 2.786121+3 4.012059+5 2.818383+3 3.901416+5 2.884032+3 3.688981+5640023522 1991 2.900000+3 3.639847+5 2.917427+3 3.587276+5 2.951209+3 3.488113+5640023522 1992 3.019952+3 3.298195+5 3.090295+3 3.118544+5 3.162278+3 2.949031+5640023522 1993 3.198895+3 2.867862+5 3.235937+3 2.788133+5 3.300000+3 2.656682+5640023522 1994 3.427678+3 2.418855+5 3.467369+3 2.351262+5 3.507519+3 2.285571+5640023522 1995 3.548134+3 2.221246+5 3.589219+3 2.158308+5 3.715352+3 1.980302+5640023522 1996 3.801894+3 1.869879+5 3.890451+3 1.765521+5 3.900000+3 1.754773+5640023522 1997 3.935501+3 1.715611+5 3.981072+3 1.667179+5 4.000000+3 1.647627+5640023522 1998 4.027170+3 1.619959+5 4.073803+3 1.573971+5 4.168694+3 1.485531+5640023522 1999 4.216965+3 1.443086+5 4.265795+3 1.401782+5 4.315191+3 1.361620+5640023522 2000 4.365158+3 1.322642+5 4.415704+3 1.284837+5 4.466836+3 1.248134+5640023522 2001 4.518559+3 1.212295+5 4.623810+3 1.143529+5 4.677351+3 1.110652+5640023522 2002 4.731513+3 1.078755+5 4.786301+3 1.047650+5 4.800000+3 1.040070+5640023522 2003 4.841724+3 1.017378+5 4.897788+3 9.879967+4 5.011872+3 9.318250+4640023522 2004 5.069907+3 9.048754+4 5.128614+3 8.787446+4 5.188000+3 8.532446+4640023522 2005 5.248075+3 8.285210+4 5.308844+3 8.044483+4 5.370318+3 7.810184+4640023522 2006 5.432503+3 7.583051+4 5.495409+3 7.362705+4 5.500000+3 7.346974+4640023522 2007 5.688529+3 6.739011+4 5.754399+3 6.542358+4 5.888437+3 6.165223+4640023522 2008 5.956621+3 5.984430+4 6.000000+3 5.873218+4 6.025596+3 5.808966+4640023522 2009 6.095369+3 5.638858+4 6.165950+3 5.473307+4 6.382635+3 5.006256+4640023522 2010 6.456542+3 4.860025+4 6.531306+3 4.716827+4 6.606934+3 4.577647+4640023522 2011 6.683439+3 4.442693+4 6.760830+3 4.311394+4 6.839116+3 4.184152+4640023522 2012 6.918310+3 4.060711+4 7.000000+3 3.938433+4 7.161434+3 3.711667+4640023522 2013 7.242700+3 3.604526+4 7.242700+3 9.950511+4 7.244360+3 9.945198+4640023522 2014 7.293000+3 9.791119+4 7.328245+3 9.681378+4 7.380000+3 9.523181+4640023522 2015 7.413102+3 9.416747+4 7.500000+3 9.145189+4 7.585776+3 8.874750+4640023522 2016 7.673615+3 8.609232+4 7.762471+3 8.351725+4 7.852356+3 8.101627+4640023522 2017 7.943282+3 7.859074+4 7.947000+3 7.849159+4 7.947000+3 1.076566+5640023522 2018 8.000000+3 1.057570+5 8.040000+3 1.043539+5 8.070000+3 1.034549+5640023522 2019 8.128305+3 1.015406+5 8.245900+3 9.782179+4 8.317638+3 9.560033+4640023522 2020 8.349800+3 9.462521+4 8.349800+3 1.093687+5 8.480000+3 1.050853+5640023522 2021 8.511380+3 1.041151+5 8.709636+3 9.826993+4 8.810489+3 9.542967+4640023522 2022 8.912509+3 9.267358+4 8.920000+3 9.247543+4 9.015711+3 9.001257+4640023522 2023 9.120108+3 8.743170+4 9.225714+3 8.492725+4 9.332543+3 8.246649+4640023522 2024 9.549926+3 7.769690+4 9.660509+3 7.541810+4 9.885531+3 7.106272+4640023522 2025 1.000000+4 6.898292+4 1.011579+4 6.697225+4 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