50-Sn Evaluated Photon Data Library (EPDL97) by Red Cullen 6000 0 0 0 5.000000+4 1.176700+2 -1 0 0 35000 1451 1 0.0 0.0 0 0 0 65000 1451 2 0.0 0.0 0 0 3 65000 1451 3 0.0 0.0 0 0 149 295000 1451 4 50-SN LLNL Eval-Jul97 D.E.Cullen, et al. 5000 1451 5 UCRL50400,Vol.6,Rev.5 Dist-Jul97 Rev0-Oct89 5000 1451 6 ---- ENDF/B-VI MATERIAL 5000 5000 1451 7 ----- PHOTO-ATOMIC INTERACTION DATA 5000 1451 8 ------ ENDF/B-6 5000 1451 9 =================================================================5000 1451 10 The Livermore Evaluated Photon Data Library (EPDL97) in the 5000 1451 11 ENDF/B-VI format 5000 1451 12 =================================================================5000 1451 13 Contents 5000 1451 14 =================================================================5000 1451 15 MF/MT Description 5000 1451 16 =================================================================5000 1451 17 23/501 Total cross sections 5000 1451 18 23/502 Coherent scattering cross sections 5000 1451 19 23/504 Incoherent scattering cross sections 5000 1451 20 23/515 Pair production cross sections, Electron field 5000 1451 21 23/516 Pair production cross sections, Total 5000 1451 22 23/517 Pair production cross sections, Nuclear field 5000 1451 23 23/522 Total photoionization cross section 5000 1451 24 23/534 K (1S1/2) Photoionization subshell cross section 5000 1451 25 23/535 L1 (2S1/2) Photoionization subshell cross section 5000 1451 26 23/536 L2 (2P1/2) Photoionization subshell cross section 5000 1451 27 23/537 L3 (2P3/2) Photoionization subshell cross section 5000 1451 28 23/538 M1 (3S1/2) Photoionization subshell cross section 5000 1451 29 23/539 M2 (3P1/2) Photoionization subshell cross section 5000 1451 30 23/540 M3 (3P3/2) Photoionization subshell cross section 5000 1451 31 23/541 M4 (3D3/2) Photoionization subshell cross section 5000 1451 32 23/542 M5 (3D5/2) Photoionization subshell cross section 5000 1451 33 23/543 N1 (4S1/2) Photoionization subshell cross section 5000 1451 34 23/544 N2 (4P1/2) Photoionization subshell cross section 5000 1451 35 23/545 N3 (4P3/2) Photoionization subshell cross section 5000 1451 36 23/546 N4 (4D3/2) Photoionization subshell cross section 5000 1451 37 23/547 N5 (4D5/2) Photoionization subshell cross section 5000 1451 38 23/550 O1 (5S1/2) Photoionization subshell cross section 5000 1451 39 23/551 O2 (5P1/2) Photoionization subshell cross section 5000 1451 40 23/552 O3 (5P3/2) Photoionization subshell cross section 5000 1451 41 =================================================================5000 1451 42 27/502 Coherent scattering form factors 5000 1451 43 27/504 Incoherent scattering functions 5000 1451 44 27/505 Imaginary anomalous scattering factor 5000 1451 45 27/506 Real anomalous scattering factor 5000 1451 46 =================================================================5000 1451 47 Warning 5000 1451 48 =================================================================5000 1451 49 MF/MT combinations used to define photoionization subshell cross5000 1451 50 sections (MF=23, MT=534-572) and coherent anomalous scattering 5000 1451 51 factors (MF=27, MT=505 AND 506) are newly defined MF/MT numbers 5000 1451 52 for ENDF/B-VI that did not exist in earlier versions of ENDF/B. 5000 1451 53 If you are not prepared to use this data you need merely delete 5000 1451 54 it and all of the remaining data will still be consistent and 5000 1451 55 equivalent to the types of data in earlier versions of ENDF/B. 5000 1451 56 However, this will limit the range of problems to which this 5000 1451 57 data can be applied (see: ref. 1 for details). 5000 1451 58 =================================================================5000 1451 59 Definition of new types of data 5000 1451 60 =================================================================5000 1451 61 1) The total photoionization cross section is equal to the sum 5000 1451 62 of the photoionization subshell cross sections. 5000 1451 63 5000 1451 64 For each subshell on the second line of a section the C1 and 5000 1451 65 C2 fields are defined as, 5000 1451 66 5000 1451 67 EPE = The photoionization edge energy (similar to Q-value) 5000 1451 68 EFL = The fluorescence yield (eV/photoionization) 5000 1451 69 5000 1451 70 2) The angular distribution of coherently scattered photons is, 5000 1451 71 5000 1451 72 S(E,MU) = 3*T/8*(1 + MU**2)*((FF(M)+F1(E))**2+(F2(E))**2) 5000 1451 73 5000 1451 74 S(E,MU) = Angular distributions (barns per unit cosine) 5000 1451 75 T = The Thomson cross section 5000 1451 76 MU = The cosine of the scattering angle 5000 1451 77 FF(M) = The atomic form factor 5000 1451 78 M = Momentum transfer = SIN(THETA/2)/LAMBDA/4*PI 5000 1451 79 F1(E) = The real anomalous scattering factor 5000 1451 80 F2(E) = The imaginary anomalous scattering factor 5000 1451 81 5000 1451 82 F1(E) and F2(E) are isotropic. 5000 1451 83 5000 1451 84 When F1(E) = F2(E) = 0 this reduces to the result obtained 5000 1451 85 using only form factors (the older ENDF/B convention). 5000 1451 86 =================================================================5000 1451 87 Differences between EPDL97 and the data base presented here 5000 1451 88 =================================================================5000 1451 89 1) Energy range - EPDL97 - 1 eV to 100 GeV 5000 1451 90 Here - 1 eV TO 100 GeV (previously 100 MeV) 5000 1451 91 2) Type of Data - EPDL97 - Photon interaction including 5000 1451 92 photoexcitation 5000 1451 93 Here - Photon interaction - ENDF/B-VI has 5000 1451 94 no provision for photoexcitation 5000 1451 95 3) Secondary E - EPDL97 - Average energy of each secondary 5000 1451 96 (photons, electrons, positrons) 5000 1451 97 HERE - No secondary energy data 5000 1451 98 4) Interpolation- EPDL97 - Cross sections are Log X vs. Log Y 5000 1451 99 interpolable - the total cross 5000 1451 100 section is not included 5000 1451 101 - Form factors and scattering functions 5000 1451 102 are Log X vs. Log y, except first 5000 1451 103 interval. 5000 1451 104 - Anomalous scattering factors linearly 5000 1451 105 interpolable (they can be negative) 5000 1451 106 Here - Up through ENDF/B-V photon interaction5000 1451 107 cross sections were Log X vs. Log Y. 5000 1451 108 - For the first two Mods. of ENDF/B-VI 5000 1451 109 in order to consistently define the 5000 1451 110 total cross sections at ALL energies 5000 1451 111 all cross sections were linearized. 5000 1451 112 This was NOT a good idea. 5000 1451 113 - Starting with Mod. 3, cross sections 5000 1451 114 are left in Log X vs. Log. Y form so 5000 1451 115 that they are IDENTICAL to what's in 5000 1451 116 EPDL97. 5000 1451 117 The total is defined ONLY at the 5000 1451 118 energies tabulated in any other cross 5000 1451 119 section. 5000 1451 120 WARNING - As a result the total cross section 5000 1451 121 MUST NOT be interpolated to define the5000 1451 122 total between tabulated energies. The 5000 1451 123 ONLY consist way to define the total 5000 1451 124 between tabulated energies is to 5000 1451 125 interpolate all of the partials and 5000 1451 126 add them up. 5000 1451 127 =================================================================5000 1451 128 References 5000 1451 129 =================================================================5000 1451 130 1) D.E. Cullen, M.H. Chen, J.H. Hubbell, S.T. Perkins, 5000 1451 131 E.F. Plechaty, J.A. Rathkopf and J.H. Scofield, Tables and 5000 1451 132 graphs of photon interaction cross sections from 10 eV to 100 5000 1451 133 GeV derived from the LLNL Evaluated Photon data library (EPDL), 5000 1451 134 UCRL-50400, Vol. 6, Rev. 4, Part A: Z = 1 to 50 and Part B: 5000 1451 135 Z = 51 to 100, Lawrence Livermore National Laboratory (1989) 5000 1451 136 5000 1451 137 2) D.E. Cullen, J.H. Hubbell and L.D. Kissel, EPDL97: the 5000 1451 138 Evaluated Photon Data Library, '97 Version, UCRL-50400, Vol. 6, 5000 1451 139 Rev. 5, Lawrence Livermore National Laboratory (1997) 5000 1451 140 5000 1451 141 These are the primary references to the contents of this library5000 1451 142 and they contain a complete list of references to the sources 5000 1451 143 of data used in this library, methods of evaluation, accuracy 5000 1451 144 of the data, etc. 5000 1451 145 =================================================================5000 1451 146 History 5000 1451 147 =================================================================5000 1451 148 Mod. 1 - October, 1989 - Initial release. 5000 1451 149 Mod. 2 - August, 1990 - Updated photoionization total and 5000 1451 150 subshell cross sections. 5000 1451 151 Mod. 3 - July, 1997 - Complete re-evaluation. 5000 1451 152 =================================================================5000 1451 153 1 451 182 35000 1451 154 23 501 926 35000 1451 155 23 502 456 35000 1451 156 23 504 40 35000 1451 157 23 515 33 35000 1451 158 23 516 52 35000 1451 159 23 517 39 35000 1451 160 23 522 410 35000 1451 161 23 534 21 35000 1451 162 23 535 25 35000 1451 163 23 536 26 35000 1451 164 23 537 25 35000 1451 165 23 538 27 35000 1451 166 23 539 40 35000 1451 167 23 540 33 35000 1451 168 23 541 39 35000 1451 169 23 542 48 35000 1451 170 23 543 32 35000 1451 171 23 544 42 35000 1451 172 23 545 41 35000 1451 173 23 546 71 35000 1451 174 23 547 72 35000 1451 175 23 550 52 35000 1451 176 23 551 46 35000 1451 177 23 552 48 35000 1451 178 27 502 50 35000 1451 179 27 504 52 35000 1451 180 27 505 162 35000 1451 181 27 506 114 35000 1451 182 5000 1 0 183 5000 0 0 184 5.000000+4 1.176700+2 0 0 0 0500023501 185 0.0 0.0 0 0 1 2768500023501 186 2768 5 500023501 187 1.000000+0 5.187204-3 1.154397+0 9.590274-3 1.258900+0 1.405044-2500023501 188 1.266039+0 1.440498-2 1.350000+0 1.925362-2 1.388478+0 2.188190-2500023501 189 1.476613+0 2.912146-2 1.566081+0 3.854158-2 1.584900+0 4.085368-2500023501 190 1.650044+0 4.972250-2 1.728841+0 6.287128-2 1.815381+0 8.094041-2500023501 191 1.906339+0 1.051912-1 1.970369+0 1.262393-1 1.995300+0 1.355947-1500023501 192 2.030396+0 1.497265-1 2.086672+0 1.754857-1 2.139431+0 2.038144-1500023501 193 2.196088+0 2.397712-1 2.235262+0 2.684600-1 2.278734+0 3.052189-1500023501 194 2.319489+0 3.450442-1 2.357697+0 3.879614-1 2.393516+0 4.342062-1500023501 195 2.427097+0 4.839529-1 2.458579+0 5.372842-1 2.488094+0 5.942754-1500023501 196 2.511900+0 6.463514-1 2.515764+0 6.551751-1 2.541704+0 7.202323-1500023501 197 2.566024+0 7.896626-1 2.588823+0 8.636651-1 2.611809+0 9.486812-1500023501 198 2.630236+0 1.025880+0 2.649022+0 1.114637+0 2.666633+0 1.208905+0500023501 199 2.683145+0 1.308942+0 2.698624+0 1.415025+0 2.713136+0 1.527469+0500023501 200 2.726740+0 1.646640+0 2.739495+0 1.772937+0 2.751452+0 1.906715+0500023501 201 2.762662+0 2.048251+0 2.777597+0 2.266356+0 2.792261+0 2.521934+0500023501 202 2.806484+0 2.821819+0 2.816649+0 3.077545+0 2.823784+0 3.283286+0500023501 203 2.830474+0 3.500175+0 2.836745+0 3.728803+0 2.848503+0 4.242290+0500023501 204 2.858792+0 4.817479+0 2.867794+0 5.464995+0 2.875671+0 6.195141+0500023501 205 2.882564+0 7.013755+0 2.888595+0 7.918865+0 2.894871+0 9.109084+0500023501 206 2.898490+0 9.938463+0 2.902530+0 1.101275+1 2.906065+0 1.209920+1500023501 207 2.909158+0 1.317584+1 2.914233+0 1.522790+1 2.921486+0 1.886062+1500023501 208 2.933587+0 2.701817+1 2.938026+0 3.069822+1 2.941633+0 3.394795+1500023501 209 2.945239+0 3.740936+1 2.952453+0 4.484368+1 2.953355+0 4.580845+1500023501 210 2.959667+0 5.266008+1 2.962147+0 5.535187+1 2.966881+0 6.037670+1500023501 211 2.969361+0 6.290249+1 2.971728+0 6.521484+1 2.974996+0 6.820780+1500023501 212 2.977758+0 7.051674+1 2.981309+0 7.313317+1 2.984465+0 7.507751+1500023501 213 2.988142+0 7.683456+1 2.992355+0 7.811211+1 2.995962+0 7.854294+1500023501 214 2.997217+0 7.854543+1 3.000800+0 7.813079+1 3.004159+0 7.718052+1500023501 215 3.006087+0 7.639574+1 3.009519+0 7.458605+1 3.013072+0 7.219188+1500023501 216 3.016974+0 6.901643+1 3.019575+0 6.662272+1 3.023181+0 6.299940+1500023501 217 3.026282+0 5.965290+1 3.028699+0 5.693392+1 3.031805+0 5.333722+1500023501 218 3.034961+0 4.961585+1 3.038258+0 4.571053+1 3.042626+0 4.059846+1500023501 219 3.046233+0 3.650077+1 3.050291+0 3.209349+1 3.053447+0 2.884997+1500023501 220 3.061111+0 2.176891+1 3.063436+0 1.986261+1 3.065655+0 1.815128+1500023501 221 3.067874+0 1.654584+1 3.071030+0 1.444305+1 3.075088+0 1.204262+1500023501 222 3.078295+0 1.037613+1 3.082530+0 8.466956+0 3.086715+0 6.879310+0500023501 223 3.090856+0 5.570795+0 3.096307+0 4.195664+0 3.104324+0 2.759353+0500023501 224 3.106955+0 2.411652+0 3.109565+0 2.116691+0 3.112155+0 1.867878+0500023501 225 3.162300+0 2.165824+0 3.407305+0 4.322045+0 3.441063+0 6.677419+0500023501 226 3.449532+0 7.723601+0 3.458002+0 8.945284+0 3.467531+0 1.045994+1500023501 227 3.474942+0 1.166231+1 3.477853+0 1.212189+1 3.484470+0 1.310176+1500023501 228 3.489102+0 1.370724+1 3.491881+0 1.402828+1 3.495879+0 1.442400+1500023501 229 3.499160+0 1.468303+1 3.502468+0 1.487790+1 3.506438+0 1.501694+1500023501 230 3.509879+0 1.504912+1 3.513585+0 1.498892+1 3.517290+0 1.482926+1500023501 231 3.518812+0 1.473504+1 3.522286+0 1.445877+1 3.526025+0 1.406978+1500023501 232 3.528708+0 1.373531+1 3.533065+0 1.310264+1 3.536884+0 1.246733+1500023501 233 3.543092+0 1.130588+1 3.546850+0 1.054612+1 3.548740+0 1.015315+1500023501 234 3.551699+0 9.528276+0 3.554320+0 8.969543+0 3.556647+0 8.472938+0500023501 235 3.559639+0 7.838582+0 3.563344+0 7.067378+0 3.566769+0 6.376770+0500023501 236 3.568109+0 6.113849+0 3.572344+0 5.315134+0 3.576181+0 4.639451+0500023501 237 3.578100+0 4.320549+0 3.581574+0 3.777318+0 3.585048+0 3.279552+0500023501 238 3.588470+0 2.834550+0 3.592256+0 2.394390+0 3.596098+0 2.002475+0500023501 239 3.600331+0 1.631775+0 3.604783+0 1.306365+0 3.614658+0 7.902657-1500023501 240 3.617730+0 6.789241-1 3.620731+0 5.891298-1 3.622700+0 5.394488-1500023501 241 3.624638+0 4.971076-1 3.626547+0 4.613243-1 3.628425+0 4.313904-1500023501 242 3.630274+0 4.066665-1 3.633915+0 3.703789-1 3.637441+0 3.489591-1500023501 243 3.640858+0 3.391842-1 3.644168+0 3.384906-1 3.647374+0 3.448480-1500023501 244 3.653586+0 3.732220-1 3.659410+0 4.148697-1 3.664870+0 4.638757-1500023501 245 3.669988+0 5.165865-1 3.680111+0 6.351588-1 3.687984+0 7.371559-1500023501 246 3.702680+0 9.441782-1 3.713702+0 1.111031+0 3.737531+0 1.502969+0500023501 247 3.746768+0 1.667046+0 3.755990+0 1.838397+0 3.765212+0 2.017956+0500023501 248 3.774435+0 2.206474+0 3.783657+0 2.404776+0 3.797207+0 2.715804+0500023501 249 3.820546+0 3.315721+0 3.857434+0 4.481226+0 3.890670+0 5.858151+0500023501 250 3.912429+0 7.002353+0 3.931212+0 8.203967+0 3.946748+0 9.394777+0500023501 251 3.956094+0 1.021909+1 3.965441+0 1.114169+1 3.974787+0 1.218073+1500023501 252 3.981100+0 1.296512+1 3.984133+0 1.335927+1 3.992627+0 1.457631+1500023501 253 4.000590+0 1.587048+1 4.011744+0 1.799670+1 4.021614+0 2.027551+1500023501 254 4.033916+0 2.384604+1 4.044681+0 2.792136+1 4.054099+0 3.253439+1500023501 255 4.062341+0 3.767239+1 4.069552+0 4.327231+1 4.075862+0 4.922970+1500023501 256 4.081383+0 5.541531+1 4.086214+0 6.169277+1 4.090441+0 6.793328+1500023501 257 4.097376+0 7.987883+1 4.121051+0 1.403852+2 4.129095+0 1.689689+2500023501 258 4.132216+0 1.812006+2 4.137289+0 2.024012+2 4.142362+0 2.251431+2500023501 259 4.152508+0 2.745498+2 4.153777+0 2.810196+2 4.162654+0 3.273858+2500023501 260 4.166142+0 3.458219+2 4.173686+0 3.851813+2 4.177013+0 4.019812+2500023501 261 4.180031+0 4.167526+2 4.184983+0 4.397146+2 4.188774+0 4.559629+2500023501 262 4.191870+0 4.682090+2 4.195934+0 4.826862+2 4.201158+0 4.982925+2500023501 263 4.206937+0 5.111356+2 4.211344+0 5.175360+2 4.215467+0 5.207225+2500023501 264 4.220506+0 5.208448+2 4.225515+0 5.168391+2 4.228329+0 5.128123+2500023501 265 4.233300+0 5.026822+2 4.237311+0 4.918420+2 4.242601+0 4.742074+2500023501 266 4.247491+0 4.549019+2 4.252281+0 4.336023+2 4.256535+0 4.130614+2500023501 267 4.259269+0 3.992011+2 4.262004+0 3.849281+2 4.265068+0 3.685492+2500023501 268 4.269089+0 3.466218+2 4.274260+0 3.180900+2 4.279333+0 2.901750+2500023501 269 4.284406+0 2.627686+2 4.290113+0 2.330019+2 4.294552+0 2.108963+2500023501 270 4.304698+0 1.646610+2 4.307429+0 1.533522+2 4.319897+0 1.082689+2500023501 271 4.325449+0 9.163801+1 4.329987+0 7.954803+1 4.334046+0 6.982967+1500023501 272 4.339264+0 5.876052+1 4.341915+0 5.371531+1 4.345891+0 4.682748+1500023501 273 4.349866+0 4.070145+1 4.352723+0 3.673617+1 4.357008+0 3.141720+1500023501 274 4.364041+0 2.414664+1 4.368165+0 2.062354+1 4.372288+0 1.757520+1500023501 275 4.377527+0 1.430357+1 4.385544+0 1.039188+1 4.396180+0 6.791483+0500023501 276 4.400206+0 5.794469+0 4.405573+0 4.711219+0 4.407921+0 4.313932+0500023501 277 4.411444+0 3.793972+0 4.414966+0 3.354886+0 4.417411+0 3.092071+0500023501 278 4.419629+0 2.880268+0 4.421570+0 2.713917+0 4.424755+0 2.475583+0500023501 279 4.426055+0 2.389516+0 4.428330+0 2.253087+0 4.431317+0 2.098798+0500023501 280 4.434197+0 1.973400+0 4.436659+0 1.882032+0 4.439122+0 1.803303+0500023501 281 4.441134+0 1.747298+0 4.444624+0 1.665280+0 4.447841+0 1.603794+0500023501 282 4.450357+0 1.563339+0 4.454721+0 1.505416+0 4.460109+0 1.448757+0500023501 283 4.476176+0 1.313066+0 4.481579+0 1.265093+0 4.488510+0 1.197767+0500023501 284 4.494901+0 1.130888+0 4.510577+0 9.705027-1 4.513328+0 9.474096-1500023501 285 4.517259+0 9.197051-1 4.520892+0 9.011688-1 4.522649+0 8.951457-1500023501 286 4.528270+0 8.915965-1 4.530124+0 8.965276-1 4.532123+0 9.057533-1500023501 287 4.533410+0 9.139977-1 4.534835+0 9.253800-1 4.540203+0 9.918514-1500023501 288 4.542441+0 1.031919+0 4.544119+0 1.067294+0 4.545419+0 1.098028+0500023501 289 4.549968+0 1.230577+0 4.552243+0 1.312790+0 4.554518+0 1.406711+0500023501 290 4.555860+0 1.467950+0 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3.349654+2 1.072780+6 3.350000+2 1.072683+6 3.467369+2 1.039502+6500023522 1858 3.507519+2 1.028065+6 3.550000+2 1.016033+6 3.630781+2 9.932548+5500023522 1859 3.672823+2 9.817181+5 3.758374+2 9.580819+5 3.801894+2 9.461750+5500023522 1860 3.850000+2 9.332610+5 3.890451+2 9.225213+5 3.935501+2 9.104368+5500023522 1861 4.000000+2 8.935475+5 4.073803+2 8.744878+5 4.120975+2 8.626908+5500023522 1862 4.216965+2 8.388062+5 4.265795+2 8.267054+5 4.315191+2 8.147134+5500023522 1863 4.365158+2 8.028464+5 4.415704+2 7.908120+5 4.518559+2 7.672860+5500023522 1864 4.623810+2 7.440181+5 4.700000+2 7.276608+5 4.786301+2 7.093957+5500023522 1865 4.841724+2 6.980280+5 4.946200+2 6.770995+5 4.946200+2 7.082175+5500023522 1866 4.954502+2 7.111666+5 4.964000+2 7.153632+5 4.977000+2 7.231227+5500023522 1867 4.988000+2 7.320314+5 4.998000+2 7.426228+5 5.007000+2 7.548106+5500023522 1868 5.011872+2 7.627993+5 5.015700+2 7.696695+5 5.025000+2 7.905165+5500023522 1869 5.035700+2 8.217190+5 5.035700+2 8.631756+5 5.037000+2 8.690603+5500023522 1870 5.037500+2 8.714139+5 5.065000+2 1.029432+6 5.069907+2 1.067902+6500023522 1871 5.074000+2 1.103133+6 5.075000+2 1.112139+6 5.082000+2 1.178516+6500023522 1872 5.090000+2 1.263630+6 5.098000+2 1.358510+6 5.105000+2 1.449071+6500023522 1873 5.112000+2 1.545656+6 5.118000+2 1.632123+6 5.123000+2 1.703325+6500023522 1874 5.129000+2 1.789436+6 5.135000+2 1.875009+6 5.136400+2 1.894079+6500023522 1875 5.139000+2 1.930289+6 5.145000+2 2.010320+6 5.150000+2 2.074722+6500023522 1876 5.157000+2 2.161222+6 5.159000+2 2.184113+6 5.165000+2 2.254436+6500023522 1877 5.173400+2 2.347188+6 5.182000+2 2.440460+6 5.188000+2 2.503207+6500023522 1878 5.190000+2 2.524715+6 5.197000+2 2.595966+6 5.200000+2 2.625431+6500023522 1879 5.210000+2 2.718871+6 5.220000+2 2.809750+6 5.222000+2 2.826907+6500023522 1880 5.224000+2 2.818999+6 5.234000+2 2.903268+6 5.249000+2 3.027176+6500023522 1881 5.265000+2 3.160462+6 5.270000+2 3.203049+6 5.290000+2 3.362287+6500023522 1882 5.305000+2 3.486348+6 5.308844+2 3.511031+6 5.315000+2 3.544425+6500023522 1883 5.343000+2 3.690360+6 5.361000+2 3.784712+6 5.370318+2 3.811396+6500023522 1884 5.380000+2 3.839429+6 5.400000+2 3.891437+6 5.415000+2 3.931239+6500023522 1885 5.445000+2 4.006954+6 5.480000+2 4.058452+6 5.495409+2 4.077930+6500023522 1886 5.520000+2 4.109405+6 5.540000+2 4.120400+6 5.559043+2 4.111161+6500023522 1887 5.600000+2 4.091451+6 5.623413+2 4.076446+6 5.690000+2 4.034444+6500023522 1888 5.754399+2 3.987811+6 5.754400+2 3.987810+6 5.760000+2 3.980366+6500023522 1889 5.821032+2 3.891819+6 5.956621+2 3.705002+6 6.000000+2 3.643079+6500023522 1890 6.050000+2 3.573451+6 6.095369+2 3.514881+6 6.165950+2 3.426478+6500023522 1891 6.200000+2 3.384976+6 6.237348+2 3.344021+6 6.382635+2 3.191285+6500023522 1892 6.456542+2 3.118782+6 6.531306+2 3.047934+6 6.700000+2 2.896490+6500023522 1893 6.760830+2 2.844625+6 6.839116+2 2.777796+6 6.918310+2 2.712544+6500023522 1894 7.000000+2 2.647537+6 7.079458+2 2.586489+6 7.103200+2 2.568631+6500023522 1895 7.103200+2 2.881058+6 7.250000+2 2.777398+6 7.413102+2 2.667061+6500023522 1896 7.498942+2 2.611782+6 7.500000+2 2.611105+6 7.533600+2 2.589262+6500023522 1897 7.533600+2 2.657399+6 7.535000+2 2.657985+6 7.538000+2 2.660242+6500023522 1898 7.541000+2 2.662313+6 7.544000+2 2.664211+6 7.547000+2 2.665936+6500023522 1899 7.551500+2 2.668121+6 7.555000+2 2.669548+6 7.560000+2 2.671081+6500023522 1900 7.565000+2 2.672131+6 7.570000+2 2.672701+6 7.576000+2 2.672764+6500023522 1901 7.583000+2 2.672091+6 7.585776+2 2.671564+6 7.589000+2 2.670935+6500023522 1902 7.597000+2 2.668688+6 7.600000+2 2.667443+6 7.620000+2 2.657352+6500023522 1903 7.630000+2 2.651849+6 7.640000+2 2.646173+6 7.673615+2 2.625935+6500023522 1904 7.685000+2 2.619141+6 7.700000+2 2.610054+6 7.762471+2 2.571844+6500023522 1905 7.820000+2 2.536779+6 7.852356+2 2.517054+6 7.943282+2 2.462960+6500023522 1906 8.035261+2 2.409382+6 8.050000+2 2.400969+6 8.128305+2 2.356468+6500023522 1907 8.200000+2 2.315507+6 8.222426+2 2.302901+6 8.317638+2 2.249779+6500023522 1908 8.430000+2 2.190764+6 8.493900+2 2.157916+6 8.511380+2 2.149085+6500023522 1909 8.609938+2 2.099092+6 8.690500+2 2.059520+6 8.690500+2 2.148538+6500023522 1910 8.810489+2 2.090405+6 9.015711+2 1.994854+6 9.120108+2 1.948714+6500023522 1911 9.332543+2 1.858328+6 9.440609+2 1.814547+6 9.500000+2 1.791157+6500023522 1912 9.700000+2 1.714885+6 9.772372+2 1.688498+6 9.850000+2 1.660795+6500023522 1913 9.885531+2 1.648188+6 1.000000+3 1.608406+6 1.011579+3 1.569561+6500023522 1914 1.047129+3 1.458193+6 1.071519+3 1.387640+6 1.083927+3 1.353228+6500023522 1915 1.096478+3 1.319705+6 1.109175+3 1.286804+6 1.122018+3 1.254742+6500023522 1916 1.148154+3 1.192326+6 1.150000+3 1.188095+6 1.202264+3 1.075755+6500023522 1917 1.216186+3 1.048404+6 1.230269+3 1.021611+6 1.244515+3 9.954599+5500023522 1918 1.258925+3 9.698651+5 1.288250+3 9.207510+5 1.300000+3 9.019373+5500023522 1919 1.318257+3 8.736041+5 1.330000+3 8.560569+5 1.364583+3 8.071283+5500023522 1920 1.380384+3 7.859515+5 1.412538+3 7.453482+5 1.428894+3 7.256723+5500023522 1921 1.450000+3 7.013350+5 1.462177+3 6.878387+5 1.496236+3 6.518726+5500023522 1922 1.513561+3 6.346447+5 1.548817+3 6.013411+5 1.566751+3 5.853769+5500023522 1923 1.584893+3 5.698622+5 1.610000+3 5.490836+5 1.621810+3 5.396636+5500023522 1924 1.640590+3 5.251565+5 1.650000+3 5.181006+5 1.678804+3 4.973203+5500023522 1925 1.698244+3 4.839777+5 1.717908+3 4.709353+5 1.737801+3 4.581857+5500023522 1926 1.757924+3 4.456545+5 1.778279+3 4.334750+5 1.798871+3 4.216463+5500023522 1927 1.840772+3 3.989826+5 1.862087+3 3.881328+5 1.883649+3 3.775881+5500023522 1928 1.905461+3 3.673013+5 1.927525+3 3.572830+5 1.950000+3 3.474204+5500023522 1929 1.972423+3 3.379116+5 2.000000+3 3.266967+5 2.018366+3 3.195226+5500023522 1930 2.065380+3 3.021796+5 2.070000+3 3.005496+5 2.089296+3 2.938760+5500023522 1931 2.113489+3 2.858126+5 2.162719+3 2.701282+5 2.187762+3 2.625822+5500023522 1932 2.213095+3 2.552465+5 2.290868+3 2.344751+5 2.317395+3 2.279506+5500023522 1933 2.344229+3 2.215958+5 2.371374+3 2.154240+5 2.426610+3 2.034951+5500023522 1934 2.454709+3 1.977599+5 2.483133+3 1.921912+5 2.540973+3 1.815345+5500023522 1935 2.570396+3 1.764394+5 2.600160+3 1.714824+5 2.650000+3 1.635426+5500023522 1936 2.660725+3 1.618972+5 2.691535+3 1.572991+5 2.722701+3 1.528165+5500023522 1937 2.786121+3 1.442449+5 2.818383+3 1.401462+5 2.851018+3 1.361681+5500023522 1938 2.917427+3 1.285357+5 2.951209+3 1.248633+5 3.000000+3 1.198217+5500023522 1939 3.019952+3 1.178380+5 3.126079+3 1.079658+5 3.140690+3 1.066993+5500023522 1940 3.235937+3 9.894684+4 3.311311+3 9.331574+4 3.349654+3 9.062716+4500023522 1941 3.427678+3 8.547307+4 3.467369+3 8.299449+4 3.507519+3 8.059037+4500023522 1942 3.548134+3 7.825831+4 3.589219+3 7.599442+4 3.650000+3 7.280348+4500023522 1943 3.715352+3 6.955936+4 3.758374+3 6.753490+4 3.801894+3 6.557203+4500023522 1944 3.845918+3 6.366350+4 3.926800+3 6.034553+4 3.926800+3 1.923884+5500023522 1945 3.935501+3 1.913486+5 4.000000+3 1.838845+5 4.027170+3 1.808630+5500023522 1946 4.070000+3 1.762314+5 4.073803+3 1.758015+5 4.160800+3 1.663363+5500023522 1947 4.160800+3 2.265010+5 4.168694+3 2.255280+5 4.216965+3 2.197134+5500023522 1948 4.265795+3 2.140593+5 4.280000+3 2.124560+5 4.295000+3 2.106280+5500023522 1949 4.315191+3 2.080494+5 4.355000+3 2.030851+5 4.415704+3 1.959694+5500023522 1950 4.440300+3 1.931855+5 4.440300+3 2.222575+5 4.472000+3 2.183999+5500023522 1951 4.518559+3 2.128515+5 4.570882+3 2.068475+5 4.623810+3 2.010082+5500023522 1952 4.650000+3 1.982368+5 4.677351+3 1.953538+5 4.786301+3 1.844470+5500023522 1953 4.800000+3 1.831241+5 4.841724+3 1.791748+5 4.897788+3 1.740556+5500023522 1954 4.954502+3 1.690814+5 5.011872+3 1.642115+5 5.069907+3 1.594261+5500023522 1955 5.128614+3 1.547837+5 5.188000+3 1.502794+5 5.248075+3 1.459123+5500023522 1956 5.308844+3 1.416757+5 5.432503+3 1.335277+5 5.495409+3 1.296366+5500023522 1957 5.500000+3 1.293589+5 5.623413+3 1.221445+5 5.688529+3 1.185639+5500023522 1958 5.821032+3 1.117130+5 5.888437+3 1.084406+5 5.956621+3 1.052502+5500023522 1959 6.025596+3 1.021389+5 6.095369+3 9.911453+4 6.165950+3 9.618162+4500023522 1960 6.237348+3 9.333690+4 6.456542+3 8.530932+4 6.606934+3 8.034907+4500023522 1961 6.683439+3 7.798400+4 6.760830+3 7.567747+4 6.839116+3 7.343965+4500023522 1962 6.918310+3 7.126988+4 6.998420+3 6.916613+4 7.000000+3 6.912553+4500023522 1963 7.079458+3 6.711607+4 7.161434+3 6.512821+4 7.244360+3 6.318479+4500023522 1964 7.328245+3 6.129963+4 7.413102+3 5.947123+4 7.498942+3 5.769644+4500023522 1965 7.673615+3 5.430752+4 7.762471+3 5.267093+4 7.943282+3 4.953981+4500023522 1966 8.000000+3 4.861150+4 8.035261+3 4.804652+4 8.128305+3 4.659793+4500023522 1967 8.222426+3 4.519322+4 8.317638+3 4.382215+4 8.413951+3 4.249339+4500023522 1968 8.511380+3 4.120440+4 8.709636+3 3.873647+4 8.810489+3 3.755996+4500023522 1969 9.015711+3 3.531608+4 9.120108+3 3.424641+4 9.225714+3 3.320978+4500023522 1970 9.332543+3 3.220476+4 9.440609+3 3.122355+4 9.549926+3 3.027195+4500023522 1971 9.660509+3 2.934897+4 9.800000+3 2.823969+4 9.885531+3 2.758636+4500023522 1972 1.000000+4 2.673680+4 1.023293+4 2.511749+4 1.035142+4 2.434605+4500023522 1973 1.047129+4 2.359861+4 1.059254+4 2.287432+4 1.071519+4 2.217064+4500023522 1974 1.083927+4 2.148897+4 1.096478+4 2.082547+4 1.109175+4 2.018287+4500023522 1975 1.122018+4 1.956015+4 1.135011+4 1.895712+4 1.161449+4 1.780780+4500023522 1976 1.174898+4 1.726028+4 1.202264+4 1.621643+4 1.216186+4 1.571144+4500023522 1977 1.230269+4 1.522251+4 1.244515+4 1.474913+4 1.288250+4 1.341605+4500023522 1978 1.303167+4 1.299976+4 1.318257+4 1.259463+4 1.333521+4 1.220249+4500023522 1979 1.348963+4 1.182286+4 1.350000+4 1.179796+4 1.364583+4 1.145531+4500023522 1980 1.380384+4 1.109929+4 1.396368+4 1.075464+4 1.412538+4 1.042092+4500023522 1981 1.445440+4 9.777380+3 1.479108+4 9.174519+3 1.500000+4 8.826144+3500023522 1982 1.531087+4 8.340962+3 1.548817+4 8.080462+3 1.566751+4 7.828282+3500023522 1983 1.584893+4 7.583196+3 1.603245+4 7.344576+3 1.621810+4 7.113389+3500023522 1984 1.640590+4 6.888655+3 1.698244+4 6.257168+3 1.717908+4 6.060119+3500023522 1985 1.778279+4 5.506352+3 1.800000+4 5.324270+3 1.819701+4 5.166008+3500023522 1986 1.840772+4 5.003868+3 1.850000+4 4.934825+3 1.883649+4 4.692155+3500023522 1987 1.905461+4 4.542925+3 1.972423+4 4.123774+3 2.000000+4 3.966663+3500023522 1988 2.065380+4 3.625777+3 2.089296+4 3.511199+3 2.113489+4 3.400279+3500023522 1989 2.137962+4 3.292710+3 2.162719+4 3.188390+3 2.213095+4 2.988348+3500023522 1990 2.238721+4 2.892802+3 2.264644+4 2.800379+3 2.317395+4 2.624510+3500023522 1991 2.344229+4 2.540867+3 2.398833+4 2.381649+3 2.426610+4 2.305909+3500023522 1992 2.454709+4 2.232601+3 2.483133+4 2.161531+3 2.511886+4 2.092780+3500023522 1993 2.540973+4 2.025634+3 2.630268+4 1.837130+3 2.660725+4 1.778157+3500023522 1994 2.754229+4 1.612603+3 2.818383+4 1.511062+3 2.851018+4 1.462770+3500023522 1995 2.884032+4 1.415997+3 2.900000+4 1.394082+3 2.917427+4 1.370525+3500023522 1996 2.918400+4 1.369226+3 2.918400+4 8.446668+3 2.937000+4 8.343231+3500023522 1997 3.000000+4 7.932631+3 3.019952+4 7.790363+3 3.054921+4 7.549332+3500023522 1998 3.070000+4 7.448546+3 3.090295+4 7.326438+3 3.126079+4 7.117899+3500023522 1999 3.162278+4 6.915227+3 3.198895+4 6.706618+3 3.235937+4 6.504328+3500023522 2000 3.273407+4 6.308166+3 3.311311+4 6.117948+3 3.349654+4 5.933468+3500023522 2001 3.388442+4 5.754352+3 3.427678+4 5.580620+3 3.548134+4 5.098411+3500023522 2002 3.630781+4 4.800431+3 3.672823+4 4.658073+3 3.758374+4 4.385882+3500023522 2003 3.801894+4 4.252757+3 3.845918+4 4.123684+3 3.890451+4 3.998549+3500023522 2004 3.935501+4 3.877056+3 4.000000+4 3.711797+3 4.027170+4 3.645066+3500023522 2005 4.073803+4 3.534331+3 4.120975+4 3.426970+3 4.168694+4 3.322882+3500023522 2006 4.216965+4 3.221971+3 4.265795+4 3.124136+3 4.315191+4 3.027406+3500023522 2007 4.518559+4 2.669624+3 4.570882+4 2.587008+3 4.623810+4 2.506856+3500023522 2008 4.731513+4 2.353855+3 4.786301+4 2.280889+3 5.011872+4 2.011019+3500023522 2009 5.188000+4 1.829843+3 5.308844+4 1.718249+3 5.432503+4 1.613477+3500023522 2010 5.495409+4 1.563455+3 5.623413+4 1.466289+3 5.821032+4 1.331734+3500023522 2011 5.888437+4 1.289681+3 5.956621+4 1.248960+3 6.165950+4 1.134367+3500023522 2012 6.382635+4 1.030305+3 6.456542+4 9.977879+2 6.683439+4 9.061729+2500023522 2013 6.839116+4 8.498177+2 6.998420+4 7.962390+2 7.079458+4 7.707326+2500023522 2014 7.161434+4 7.460441+2 7.413102+4 6.766321+2 7.762471+4 5.940417+2500023522 2015 7.943282+4 5.565714+2 8.035261+4 5.387337+2 8.128305+4 5.214652+2500023522 2016 8.413951+4 4.729163+2 8.609938+4 4.430923+2 8.810489+4 4.148451+2500023522 2017 9.332543+4 3.518674+2 9.440609+4 3.404704+2 9.549926+4 3.294322+2500023522 2018 9.660509+4 3.187524+2 9.772372+4 3.084172+2 1.047129+5 2.530832+2500023522 2019 1.096478+5 2.218338+2 1.109175+5 2.146447+2 1.122019+5 2.076423+2500023522 2020 1.135011+5 2.008697+2 1.148154+5 1.943180+2 1.161449+5 1.879804+2500023522 2021 1.174898+5 1.818497+2 1.202264+5 1.701727+2 1.258925+5 1.490211+2500023522 2022 1.273503+5 1.441574+2 1.288250+5 1.394533+2 1.333521+5 1.262438+2500023522 2023 1.348963+5 1.221249+2 1.364583+5 1.181407+2 1.380384+5 1.142866+2500023522 2024 1.412538+5 1.069516+2 1.428894+5 1.034634+2 1.500000+5 8.995937+1500023522 2025 1.548817+5 8.203421+1 1.584893+5 7.677272+1 1.603245+5 7.427002+1500023522 2026 1.659587+5 6.724131+1 1.698244+5 6.292938+1 1.717908+5 6.087870+1500023522 2027 1.737801+5 5.889483+1 1.757924+5 5.697569+1 1.819701+5 5.158574+1500023522 2028 1.840772+5 4.990497+1 1.883649+5 4.670658+1 1.949845+5 4.228941+1500023522 2029 1.972423+5 4.091197+1 2.000000+5 3.931037+1 2.018366+5 3.829055+1500023522 2030 2.065380+5 3.586047+1 2.113489+5 3.358470+1 2.162719+5 3.145382+1500023522 2031 2.187762+5 3.043967+1 2.213095+5 2.945824+1 2.238721+5 2.850932+1500023522 2032 2.264644+5 2.759098+1 2.290868+5 2.670226+1 2.317395+5 2.584220+1500023522 2033 2.398833+5 2.342510+1 2.426610+5 2.267113+1 2.483133+5 2.123530+1500023522 2034 2.517970+5 2.042176+1 2.540973+5 1.990761+1 2.570396+5 1.927526+1500023522 2035 2.600160+5 1.866303+1 2.630268+5 1.807027+1 2.660725+5 1.749634+1500023522 2036 2.691535+5 1.694072+1 2.722701+5 1.640290+1 2.818383+5 1.489186+1500023522 2037 2.851018+5 1.441979+1 2.884032+5 1.396268+1 2.917427+5 1.352025+1500023522 2038 2.951209+5 1.309863+1 3.000000+5 1.252066+1 3.019952+5 1.229432+1500023522 2039 3.162278+5 1.083145+1 3.198895+5 1.049380+1 3.273407+5 9.850773+0500023522 2040 3.349654+5 9.247167+0 3.388442+5 8.964351+0 3.467369+5 8.424728+0500023522 2041 3.507519+5 8.167228+0 3.548134+5 7.917602+0 3.672823+5 7.213587+0500023522 2042 3.715352+5 6.993510+0 3.758374+5 6.780201+0 3.801894+5 6.573408+0500023522 2043 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