68-Er Evaluated Photon Data Library (EPDL97) by Red Cullen 6000 0 0 0 6.800000+4 1.658230+2 -1 0 0 36800 1451 1 0.0 0.0 0 0 0 66800 1451 2 0.0 0.0 0 0 3 66800 1451 3 0.0 0.0 0 0 152 326800 1451 4 68-ER LLNL Eval-Jul97 D.E.Cullen, et al. 6800 1451 5 UCRL50400,Vol.6,Rev.5 Dist-Jul97 Rev0-Oct89 6800 1451 6 ---- ENDF/B-VI MATERIAL 6800 6800 1451 7 ----- PHOTO-ATOMIC INTERACTION DATA 6800 1451 8 ------ ENDF/B-6 6800 1451 9 =================================================================6800 1451 10 The Livermore Evaluated Photon Data Library (EPDL97) in the 6800 1451 11 ENDF/B-VI format 6800 1451 12 =================================================================6800 1451 13 Contents 6800 1451 14 =================================================================6800 1451 15 MF/MT Description 6800 1451 16 =================================================================6800 1451 17 23/501 Total cross sections 6800 1451 18 23/502 Coherent scattering cross sections 6800 1451 19 23/504 Incoherent scattering cross sections 6800 1451 20 23/515 Pair production cross sections, Electron field 6800 1451 21 23/516 Pair production cross sections, Total 6800 1451 22 23/517 Pair production cross sections, Nuclear field 6800 1451 23 23/522 Total photoionization cross section 6800 1451 24 23/534 K (1S1/2) Photoionization subshell cross section 6800 1451 25 23/535 L1 (2S1/2) Photoionization subshell cross section 6800 1451 26 23/536 L2 (2P1/2) Photoionization subshell cross section 6800 1451 27 23/537 L3 (2P3/2) Photoionization subshell cross section 6800 1451 28 23/538 M1 (3S1/2) Photoionization subshell cross section 6800 1451 29 23/539 M2 (3P1/2) Photoionization subshell cross section 6800 1451 30 23/540 M3 (3P3/2) Photoionization subshell cross section 6800 1451 31 23/541 M4 (3D3/2) Photoionization subshell cross section 6800 1451 32 23/542 M5 (3D5/2) Photoionization subshell cross section 6800 1451 33 23/543 N1 (4S1/2) Photoionization subshell cross section 6800 1451 34 23/544 N2 (4P1/2) Photoionization subshell cross section 6800 1451 35 23/545 N3 (4P3/2) Photoionization subshell cross section 6800 1451 36 23/546 N4 (4D3/2) Photoionization subshell cross section 6800 1451 37 23/547 N5 (4D5/2) Photoionization subshell cross section 6800 1451 38 23/548 N6 (4F5/2) Photoionization subshell cross section 6800 1451 39 23/549 N7 (4F7/2) Photoionization subshell cross section 6800 1451 40 23/550 O1 (5S1/2) Photoionization subshell cross section 6800 1451 41 23/551 O2 (5P1/2) Photoionization subshell cross section 6800 1451 42 23/552 O3 (5P3/2) Photoionization subshell cross section 6800 1451 43 23/559 P1 (6S1/2) Photoionization subshell cross section 6800 1451 44 =================================================================6800 1451 45 27/502 Coherent scattering form factors 6800 1451 46 27/504 Incoherent scattering functions 6800 1451 47 27/505 Imaginary anomalous scattering factor 6800 1451 48 27/506 Real anomalous scattering factor 6800 1451 49 =================================================================6800 1451 50 Warning 6800 1451 51 =================================================================6800 1451 52 MF/MT combinations used to define photoionization subshell cross6800 1451 53 sections (MF=23, MT=534-572) and coherent anomalous scattering 6800 1451 54 factors (MF=27, MT=505 AND 506) are newly defined MF/MT numbers 6800 1451 55 for ENDF/B-VI that did not exist in earlier versions of ENDF/B. 6800 1451 56 If you are not prepared to use this data you need merely delete 6800 1451 57 it and all of the remaining data will still be consistent and 6800 1451 58 equivalent to the types of data in earlier versions of ENDF/B. 6800 1451 59 However, this will limit the range of problems to which this 6800 1451 60 data can be applied (see: ref. 1 for details). 6800 1451 61 =================================================================6800 1451 62 Definition of new types of data 6800 1451 63 =================================================================6800 1451 64 1) The total photoionization cross section is equal to the sum 6800 1451 65 of the photoionization subshell cross sections. 6800 1451 66 6800 1451 67 For each subshell on the second line of a section the C1 and 6800 1451 68 C2 fields are defined as, 6800 1451 69 6800 1451 70 EPE = The photoionization edge energy (similar to Q-value) 6800 1451 71 EFL = The fluorescence yield (eV/photoionization) 6800 1451 72 6800 1451 73 2) The angular distribution of coherently scattered photons is, 6800 1451 74 6800 1451 75 S(E,MU) = 3*T/8*(1 + MU**2)*((FF(M)+F1(E))**2+(F2(E))**2) 6800 1451 76 6800 1451 77 S(E,MU) = Angular distributions (barns per unit cosine) 6800 1451 78 T = The Thomson cross section 6800 1451 79 MU = The cosine of the scattering angle 6800 1451 80 FF(M) = The atomic form factor 6800 1451 81 M = Momentum transfer = SIN(THETA/2)/LAMBDA/4*PI 6800 1451 82 F1(E) = The real anomalous scattering factor 6800 1451 83 F2(E) = The imaginary anomalous scattering factor 6800 1451 84 6800 1451 85 F1(E) and F2(E) are isotropic. 6800 1451 86 6800 1451 87 When F1(E) = F2(E) = 0 this reduces to the result obtained 6800 1451 88 using only form factors (the older ENDF/B convention). 6800 1451 89 =================================================================6800 1451 90 Differences between EPDL97 and the data base presented here 6800 1451 91 =================================================================6800 1451 92 1) Energy range - EPDL97 - 1 eV to 100 GeV 6800 1451 93 Here - 1 eV TO 100 GeV (previously 100 MeV) 6800 1451 94 2) Type of Data - EPDL97 - Photon interaction including 6800 1451 95 photoexcitation 6800 1451 96 Here - Photon interaction - ENDF/B-VI has 6800 1451 97 no provision for photoexcitation 6800 1451 98 3) Secondary E - EPDL97 - Average energy of each secondary 6800 1451 99 (photons, electrons, positrons) 6800 1451 100 HERE - No secondary energy data 6800 1451 101 4) Interpolation- EPDL97 - Cross sections are Log X vs. Log Y 6800 1451 102 interpolable - the total cross 6800 1451 103 section is not included 6800 1451 104 - Form factors and scattering functions 6800 1451 105 are Log X vs. Log y, except first 6800 1451 106 interval. 6800 1451 107 - Anomalous scattering factors linearly 6800 1451 108 interpolable (they can be negative) 6800 1451 109 Here - Up through ENDF/B-V photon interaction6800 1451 110 cross sections were Log X vs. Log Y. 6800 1451 111 - For the first two Mods. of ENDF/B-VI 6800 1451 112 in order to consistently define the 6800 1451 113 total cross sections at ALL energies 6800 1451 114 all cross sections were linearized. 6800 1451 115 This was NOT a good idea. 6800 1451 116 - Starting with Mod. 3, cross sections 6800 1451 117 are left in Log X vs. Log. Y form so 6800 1451 118 that they are IDENTICAL to what's in 6800 1451 119 EPDL97. 6800 1451 120 The total is defined ONLY at the 6800 1451 121 energies tabulated in any other cross 6800 1451 122 section. 6800 1451 123 WARNING - As a result the total cross section 6800 1451 124 MUST NOT be interpolated to define the6800 1451 125 total between tabulated energies. The 6800 1451 126 ONLY consist way to define the total 6800 1451 127 between tabulated energies is to 6800 1451 128 interpolate all of the partials and 6800 1451 129 add them up. 6800 1451 130 =================================================================6800 1451 131 References 6800 1451 132 =================================================================6800 1451 133 1) D.E. Cullen, M.H. Chen, J.H. Hubbell, S.T. Perkins, 6800 1451 134 E.F. Plechaty, J.A. Rathkopf and J.H. Scofield, Tables and 6800 1451 135 graphs of photon interaction cross sections from 10 eV to 100 6800 1451 136 GeV derived from the LLNL Evaluated Photon data library (EPDL), 6800 1451 137 UCRL-50400, Vol. 6, Rev. 4, Part A: Z = 1 to 50 and Part B: 6800 1451 138 Z = 51 to 100, Lawrence Livermore National Laboratory (1989) 6800 1451 139 6800 1451 140 2) D.E. Cullen, J.H. Hubbell and L.D. Kissel, EPDL97: the 6800 1451 141 Evaluated Photon Data Library, '97 Version, UCRL-50400, Vol. 6, 6800 1451 142 Rev. 5, Lawrence Livermore National Laboratory (1997) 6800 1451 143 6800 1451 144 These are the primary references to the contents of this library6800 1451 145 and they contain a complete list of references to the sources 6800 1451 146 of data used in this library, methods of evaluation, accuracy 6800 1451 147 of the data, etc. 6800 1451 148 =================================================================6800 1451 149 History 6800 1451 150 =================================================================6800 1451 151 Mod. 1 - October, 1989 - Initial release. 6800 1451 152 Mod. 2 - August, 1990 - Updated photoionization total and 6800 1451 153 subshell cross sections. 6800 1451 154 Mod. 3 - July, 1997 - Complete re-evaluation. 6800 1451 155 =================================================================6800 1451 156 1 451 188 36800 1451 157 23 501 878 36800 1451 158 23 502 420 36800 1451 159 23 504 40 36800 1451 160 23 515 33 36800 1451 161 23 516 53 36800 1451 162 23 517 40 36800 1451 163 23 522 388 36800 1451 164 23 534 20 36800 1451 165 23 535 23 36800 1451 166 23 536 23 36800 1451 167 23 537 23 36800 1451 168 23 538 26 36800 1451 169 23 539 28 36800 1451 170 23 540 29 36800 1451 171 23 541 33 36800 1451 172 23 542 30 36800 1451 173 23 543 29 36800 1451 174 23 544 34 36800 1451 175 23 545 34 36800 1451 176 23 546 55 36800 1451 177 23 547 56 36800 1451 178 23 548 57 36800 1451 179 23 549 57 36800 1451 180 23 550 38 36800 1451 181 23 551 43 36800 1451 182 23 552 45 36800 1451 183 23 559 44 36800 1451 184 27 502 51 36800 1451 185 27 504 52 36800 1451 186 27 505 183 36800 1451 187 27 506 128 36800 1451 188 6800 1 0 189 6800 0 0 190 6.800000+4 1.658230+2 0 0 0 0680023501 191 0.0 0.0 0 0 1 2623680023501 192 2623 5 680023501 193 1.000000+0 1.101686-1 1.080511+0 1.588642-1 1.139633+0 2.058982-1680023501 194 1.201138+0 2.672346-1 1.232954+0 3.054973-1 1.258900+0 3.405715-1680023501 195 1.289117+0 3.854501-1 1.341824+0 4.777387-1 1.391289+0 5.832237-1680023501 196 1.414868+0 6.416553-1 1.460553+0 7.708791-1 1.503382+0 9.145931-1680023501 197 1.543535+0 1.073700+0 1.581178+0 1.248466+0 1.584900+0 1.267501+0680023501 198 1.616468+0 1.439037+0 1.649553+0 1.645437+0 1.680570+0 1.867561+0680023501 199 1.709648+0 2.105180+0 1.736909+0 2.357933+0 1.762466+0 2.625337+0680023501 200 1.786426+0 2.906785+0 1.808888+0 3.201557+0 1.829947+0 3.508827+0680023501 201 1.849689+0 3.827726+0 1.868197+0 4.157977+0 1.885549+0 4.499953+0680023501 202 1.918083+0 5.230018+0 1.946551+0 5.981058+0 1.971460+0 6.746058+0680023501 203 1.993255+0 7.514596+0 1.995300+0 7.593271+0 2.012326+0 8.277698+0680023501 204 2.029013+0 9.027676+0 2.048000+0 9.986411+0 2.069167+0 1.120390+1680023501 205 2.088331+0 1.247233+1 2.102704+0 1.355027+1 2.124264+0 1.540334+1680023501 206 2.151105+0 1.818575+1 2.166950+0 2.014912+1 2.182795+0 2.241496+1680023501 207 2.198640+0 2.504439+1 2.214485+0 2.811768+1 2.230330+0 3.174318+1680023501 208 2.246175+0 3.606592+1 2.261599+0 4.112783+1 2.271107+0 4.477346+1680023501 209 2.280021+0 4.863647+1 2.288378+0 5.272361+1 2.296212+0 5.704196+1680023501 210 2.303557+0 6.159857+1 2.310443+0 6.640031+1 2.316898+0 7.145358+1680023501 211 2.322950+0 7.676454+1 2.328624+0 8.233963+1 2.333943+0 8.818646+1680023501 212 2.343604+0 1.007374+2 2.352370+0 1.150340+2 2.360040+0 1.308451+2680023501 213 2.366751+0 1.483594+2 2.372623+0 1.676878+2 2.377762+0 1.887872+2680023501 214 2.382257+0 2.114312+2 2.386191+0 2.352352+2 2.389634+0 2.597179+2680023501 215 2.392646+0 2.843699+2 2.395281+0 3.087114+2 2.399605+0 3.549041+2680023501 216 2.405784+0 4.361118+2 2.415101+0 5.961510+2 2.421363+0 7.291279+2680023501 217 2.425611+0 8.292669+2 2.431552+0 9.784352+2 2.432295+0 9.975019+2680023501 218 2.437493+0 1.130809+3 2.439536+0 1.182077+3 2.443435+0 1.275798+3680023501 219 2.446066+0 1.334507+3 2.449205+0 1.398022+3 2.452360+0 1.452977+3680023501 220 2.455419+0 1.496183+3 2.457973+0 1.523688+3 2.460950+0 1.544981+3680023501 221 2.464414+0 1.554266+3 2.467199+0 1.549222+3 2.468419+0 1.543473+3680023501 222 2.471370+0 1.520752+3 2.474102+0 1.488902+3 2.476401+0 1.454467+3680023501 223 2.479242+0 1.402972+3 2.481759+0 1.349926+3 2.484869+0 1.276043+3680023501 224 2.487071+0 1.219094+3 2.489470+0 1.153544+3 2.491492+0 1.096113+3680023501 225 2.493339+0 1.042406+3 2.495567+0 9.766350+2 2.497273+0 9.259572+2680023501 226 2.499711+0 8.536945+2 2.502552+0 7.707256+2 2.503588+0 7.410019+2680023501 227 2.506187+0 6.682389+2 2.508787+0 5.985948+2 2.511900+0 5.195640+2680023501 228 2.512639+0 5.024029+2 2.514728+0 4.542368+2 2.520910+0 3.298920+2680023501 229 2.523783+0 2.817782+2 2.531560+0 1.822504+2 2.533926+0 1.605056+2680023501 230 2.535787+0 1.460489+2 2.537217+0 1.364633+2 2.538843+0 1.271337+2680023501 231 2.540366+0 1.198689+2 2.541689+0 1.146867+2 2.542986+0 1.106082+2680023501 232 2.543834+0 1.084636+2 2.544669+0 1.067528+2 2.570975+0 2.618745+2680023501 233 2.579658+0 4.318572+2 2.583789+0 5.447353+2 2.588242+0 6.946629+2680023501 234 2.592197+0 8.556062+2 2.595136+0 9.938820+2 2.598430+0 1.169043+3680023501 235 2.601708+0 1.365559+3 2.603674+0 1.494387+3 2.606871+0 1.721403+3680023501 236 2.610067+0 1.969982+3 2.616859+0 2.564989+3 2.618358+0 2.707097+3680023501 237 2.622291+0 3.095062+3 2.625312+0 3.404423+3 2.629246+0 3.815058+3680023501 238 2.632492+0 4.154498+3 2.635638+0 4.477860+3 2.638885+0 4.799441+3680023501 239 2.642031+0 5.093315+3 2.644828+0 5.334972+3 2.647919+0 5.575574+3680023501 240 2.648824+0 5.640102+3 2.652570+0 5.874970+3 2.655495+0 6.019076+3680023501 241 2.658902+0 6.139586+3 2.661672+0 6.198043+3 2.667803+0 6.198146+3680023501 242 2.669551+0 6.165827+3 2.674395+0 6.005016+3 2.677439+0 5.854220+3680023501 243 2.680389+0 5.675420+3 2.683635+0 5.446178+3 2.686782+0 5.196743+3680023501 244 2.689578+0 4.956989+3 2.692275+0 4.713554+3 2.696371+0 4.328794+3680023501 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2.995332+0 5.585400+1680023501 258 3.009279+0 5.229137+1 3.022790+0 4.919587+1 3.048967+0 4.400993+1680023501 259 3.073509+0 3.992358+1 3.096516+0 3.663719+1 3.118086+0 3.395125+1680023501 260 3.138307+0 3.172571+1 3.157265+0 2.985783+1 3.162300+0 2.940411+1680023501 261 3.192810+0 2.681240+1 3.223913+0 2.454274+1 3.251127+0 2.281226+1680023501 262 3.298753+0 2.022181+1 3.334472+0 1.857205+1 3.388050+0 1.646734+1680023501 263 3.467042+0 1.393358+1 3.611051+0 1.050085+1 3.712486+0 8.562601+0680023501 264 3.788563+0 7.197191+0 3.817091+0 6.684090+0 3.842054+0 6.224601+0680023501 265 3.863896+0 5.808741+0 3.883008+0 5.429420+0 3.899731+0 5.081532+0680023501 266 3.914364+0 4.761314+0 3.927167+0 4.465988+0 3.938370+0 4.193553+0680023501 267 3.948173+0 3.942655+0 3.956750+0 3.712448+0 3.971761+0 3.284309+0680023501 268 3.981100+0 2.999386+0 3.983018+0 2.944080+0 3.991462+0 2.682400+0680023501 269 3.997794+0 2.486226+0 4.006106+0 2.235872+0 4.016792+0 1.944941+0680023501 270 4.019263+0 1.886018+0 4.026679+0 1.737565+0 4.031622+0 1.669072+0680023501 271 4.034094+0 1.646287+0 4.036565+0 1.632288+0 4.043981+0 1.652434+0680023501 272 4.046452+0 1.683241+0 4.047688+0 1.703765+0 4.052014+0 1.804914+0680023501 273 4.054176+0 1.873993+0 4.056339+0 1.956487+0 4.057575+0 2.009967+0680023501 274 4.061900+0 2.236039+0 4.065145+0 2.448332+0 4.066226+0 2.527808+0680023501 275 4.070385+0 2.876729+0 4.075043+0 3.354465+0 4.084147+0 4.583378+0680023501 276 4.092340+0 6.058545+0 4.097764+0 7.241750+0 4.105433+0 9.203720+0680023501 277 4.110239+0 1.060413+1 4.115447+0 1.226368+1 4.120219+0 1.390478+1680023501 278 4.124813+0 1.558161+1 4.129455+0 1.735806+1 4.134276+0 1.927067+1680023501 279 4.138605+0 2.102861+1 4.143307+0 2.295708+1 4.146995+0 2.446753+1680023501 280 4.152128+0 2.653787+1 4.155791+0 2.797396+1 4.160165+0 2.962201+1680023501 281 4.165165+0 3.138775+1 4.166338+0 3.178015+1 4.172493+0 3.368238+1680023501 282 4.176399+0 3.473550+1 4.184868+0 3.654622+1 4.188266+0 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2.050066+5 4.073803+3 1.992165+5 4.168694+3 1.881412+5680023522 1837 4.216965+3 1.828218+5 4.265795+3 1.776125+5 4.300000+3 1.740844+5680023522 1838 4.315191+3 1.725425+5 4.365158+3 1.676082+5 4.570882+3 1.493102+5680023522 1839 4.623810+3 1.450713+5 4.650000+3 1.430370+5 4.731513+3 1.369421+5680023522 1840 4.800000+3 1.321043+5 4.841724+3 1.292433+5 4.897788+3 1.255349+5680023522 1841 4.900000+3 1.253914+5 4.954502+3 1.219071+5 5.011872+3 1.183885+5680023522 1842 5.188000+3 1.084599+5 5.248075+3 1.053453+5 5.308844+3 1.023229+5680023522 1843 5.370318+3 9.938007+4 5.432503+3 9.650855+4 5.500000+3 9.351545+4680023522 1844 5.623413+3 8.834348+4 5.688529+3 8.577943+4 5.821032+3 8.088332+4680023522 1845 5.888437+3 7.853485+4 6.000000+3 7.485823+4 6.095369+3 7.190507+4680023522 1846 6.165950+3 6.981007+4 6.309573+3 6.578515+4 6.382635+3 6.386262+4680023522 1847 6.456542+3 6.199386+4 6.531306+3 6.018083+4 6.606934+3 5.842342+4680023522 1848 6.683439+3 5.671370+4 6.839116+3 5.344743+4 7.000000+3 5.032894+4680023522 1849 7.161434+3 4.743491+4 7.244360+3 4.603880+4 7.300000+3 4.513416+4680023522 1850 7.413102+3 4.336493+4 7.498942+3 4.208778+4 7.585776+3 4.084936+4680023522 1851 7.673615+3 3.964891+4 7.762471+3 3.848247+4 7.852356+3 3.734336+4680023522 1852 8.000000+3 3.557015+4 8.128305+3 3.412005+4 8.222426+3 3.310880+4680023522 1853 8.317638+3 3.212750+4 8.347400+3 3.182929+4 8.347400+3 8.620782+4680023522 1854 8.413951+3 8.453126+4 8.609938+3 7.984773+4 8.810489+3 7.514249+4680023522 1855 8.912509+3 7.288921+4 9.120108+3 6.857865+4 9.274800+3 6.553319+4680023522 1856 9.274800+3 9.006655+4 9.332543+3 8.865204+4 9.340000+3 8.847149+4680023522 1857 9.440609+3 8.608550+4 9.549926+3 8.359362+4 9.550000+3 8.359197+4680023522 1858 9.660509+3 8.108474+4 9.716200+3 7.986056+4 9.716200+3 9.236360+4680023522 1859 9.772372+3 9.100356+4 9.885531+3 8.834788+4 1.000000+4 8.582608+4680023522 1860 1.011579+4 8.337800+4 1.023293+4 8.097656+4 1.040000+4 7.771460+4680023522 1861 1.059254+4 7.419558+4 1.060000+4 7.406371+4 1.071519+4 7.204353+4680023522 1862 1.096478+4 6.788730+4 1.109175+4 6.590241+4 1.122018+4 6.397724+4680023522 1863 1.135011+4 6.210694+4 1.148154+4 6.029257+4 1.161449+4 5.853251+4680023522 1864 1.174898+4 5.683024+4 1.188502+4 5.516487+4 1.190000+4 5.498572+4680023522 1865 1.202264+4 5.353598+4 1.216186+4 5.195260+4 1.230269+4 5.041715+4680023522 1866 1.258925+4 4.748536+4 1.273503+4 4.607556+4 1.288250+4 4.470684+4680023522 1867 1.303167+4 4.337961+4 1.348963+4 3.961438+4 1.350000+4 3.953451+4680023522 1868 1.364583+4 3.843173+4 1.380384+4 3.728457+4 1.396368+4 3.617229+4680023522 1869 1.428894+4 3.404852+4 1.450000+4 3.276228+4 1.462177+4 3.205020+4680023522 1870 1.479108+4 3.109562+4 1.531087+4 2.840354+4 1.540000+4 2.797482+4680023522 1871 1.548817+4 2.755669+4 1.566751+4 2.673265+4 1.579600+4 2.615804+4680023522 1872 1.584893+4 2.592584+4 1.621810+4 2.438337+4 1.650000+4 2.329087+4680023522 1873 1.659587+4 2.293453+4 1.678804+4 2.224288+4 1.698244+4 2.157239+4680023522 1874 1.717908+4 2.091867+4 1.737801+4 2.028527+4 1.757924+4 1.967154+4680023522 1875 1.778279+4 1.907642+4 1.800000+4 1.846857+4 1.840772+4 1.739122+4680023522 1876 1.862087+4 1.686269+4 1.883649+4 1.635008+4 1.927525+4 1.537239+4680023522 1877 1.950000+4 1.490306+4 1.995262+4 1.401081+4 2.000000+4 1.392176+4680023522 1878 2.018366+4 1.358359+4 2.041738+4 1.316928+4 2.065380+4 1.276776+4680023522 1879 2.113489+4 1.199616+4 2.137962+4 1.162800+4 2.162719+4 1.127142+4680023522 1880 2.213095+4 1.058951+4 2.264644+4 9.949805+3 2.290868+4 9.643370+3680023522 1881 2.317395+4 9.346632+3 2.344229+4 9.059037+3 2.371374+4 8.780198+3680023522 1882 2.398833+4 8.510071+3 2.400000+4 8.498849+3 2.426610+4 8.248200+3680023522 1883 2.454709+4 7.994543+3 2.483133+4 7.748886+3 2.511886+4 7.510973+3680023522 1884 2.540973+4 7.278845+3 2.691535+4 6.217608+3 2.722701+4 6.024976+3680023522 1885 2.754229+4 5.838459+3 2.800000+4 5.581170+3 2.818383+4 5.482258+3680023522 1886 2.851018+4 5.311791+3 2.884032+4 5.146757+3 2.917427+4 4.986985+3680023522 1887 2.951209+4 4.832294+3 2.985383+4 4.682498+3 3.090295+4 4.258646+3680023522 1888 3.126079+4 4.125571+3 3.162278+4 3.996664+3 3.235937+4 3.750869+3680023522 1889 3.273407+4 3.633711+3 3.311311+4 3.520301+3 3.349654+4 3.410509+3680023522 1890 3.388442+4 3.303642+3 3.427678+4 3.200186+3 3.507519+4 3.003079+3680023522 1891 3.589219+4 2.817786+3 3.672823+4 2.644149+3 3.715352+4 2.561356+3680023522 1892 3.758374+4 2.481214+3 3.801894+4 2.403321+3 3.845918+4 2.327846+3680023522 1893 3.890451+4 2.254800+3 3.935501+4 2.183607+3 3.981072+4 2.114710+3680023522 1894 4.027170+4 2.048015+3 4.073803+4 1.983459+3 4.168694+4 1.860504+3680023522 1895 4.265795+4 1.745314+3 4.315191+4 1.690435+3 4.365158+4 1.637157+3680023522 1896 4.466836+4 1.535694+3 4.500000+4 1.504484+3 4.570882+4 1.440576+3680023522 1897 4.731513+4 1.307684+3 4.786301+4 1.266212+3 4.897788+4 1.187240+3680023522 1898 5.011872+4 1.113282+3 5.069907+4 1.078060+3 5.128614+4 1.043974+3680023522 1899 5.188000+4 1.010970+3 5.308844+4 9.481222+2 5.370318+4 9.181708+2680023522 1900 5.559043+4 8.332261+2 5.623413+4 8.067201+2 5.688529+4 7.810061+2680023522 1901 5.757400+4 7.550174+2 5.757400+4 4.027127+3 5.821032+4 3.920577+3680023522 1902 5.850000+4 3.873393+3 5.895000+4 3.794363+3 5.956621+4 3.701205+3680023522 1903 5.970000+4 3.681408+3 6.095369+4 3.479458+3 6.100000+4 3.472292+3680023522 1904 6.237348+4 3.282662+3 6.309573+4 3.188732+3 6.350000+4 3.137782+3680023522 1905 6.382635+4 3.095430+3 6.531306+4 2.911912+3 6.683439+4 2.739321+3680023522 1906 6.760830+4 2.656911+3 7.000000+4 2.422870+3 7.079458+4 2.352210+3680023522 1907 7.161434+4 2.282266+3 7.328245+4 2.148541+3 7.413102+4 2.084653+3680023522 1908 7.498942+4 2.022674+3 7.585776+4 1.962531+3 7.852356+4 1.792448+3680023522 1909 7.943282+4 1.737964+3 8.035261+4 1.685140+3 8.128305+4 1.633924+3680023522 1910 8.317638+4 1.536129+3 8.709636+4 1.357808+3 8.810489+4 1.316168+3680023522 1911 9.015711+4 1.236693+3 9.332543+4 1.126259+3 9.440609+4 1.091691+3680023522 1912 9.549926+4 1.058187+3 9.660509+4 1.025715+3 9.772372+4 9.942419+2680023522 1913 9.885531+4 9.637356+2 1.023293+5 8.777299+2 1.035142+5 8.508074+2680023522 1914 1.071519+5 7.749066+2 1.096478+5 7.275548+2 1.135011+5 6.618236+2680023522 1915 1.161449+5 6.213438+2 1.174898+5 6.020443+2 1.188502+5 5.833467+2680023522 1916 1.230269+5 5.306710+2 1.258925+5 4.982292+2 1.288250+5 4.677732+2680023522 1917 1.303167+5 4.532556+2 1.348963+5 4.123556+2 1.364583+5 3.995614+2680023522 1918 1.396368+5 3.750092+2 1.445440+5 3.409851+2 1.479108+5 3.200409+2680023522 1919 1.500000+5 3.079196+2 1.513561+5 3.003849+2 1.548817+5 2.819390+2680023522 1920 1.566751+5 2.731468+2 1.584893+5 2.646289+2 1.621810+5 2.483828+2680023522 1921 1.650000+5 2.368815+2 1.659587+5 2.331369+2 1.698244+5 2.188311+2680023522 1922 1.757924+5 1.990038+2 1.778279+5 1.928046+2 1.840772+5 1.753429+2680023522 1923 1.862087+5 1.698816+2 1.883649+5 1.645910+2 1.927525+5 1.544996+2680023522 1924 1.972423+5 1.450284+2 2.018366+5 1.361413+2 2.065380+5 1.277993+2680023522 1925 2.089296+5 1.238235+2 2.162719+5 1.126236+2 2.213095+5 1.057263+2680023522 1926 2.264644+5 9.931424+1 2.290868+5 9.625560+1 2.317395+5 9.329134+1680023522 1927 2.344229+5 9.041967+1 2.371374+5 8.763646+1 2.398833+5 8.493989+1680023522 1928 2.426610+5 8.232652+1 2.454709+5 7.979414+1 2.511886+5 7.496098+1680023522 1929 2.540973+5 7.265534+1 2.570396+5 7.042091+1 2.600160+5 6.825792+1680023522 1930 2.660725+5 6.412946+1 2.691535+5 6.215994+1 2.722701+5 6.027359+1680023522 1931 2.754229+5 5.844451+1 2.818383+5 5.495140+1 2.884032+5 5.166719+1680023522 1932 2.917427+5 5.009966+1 2.951209+5 4.857971+1 3.000060+5 4.649190+1680023522 1933 3.019952+5 4.567727+1 3.054921+5 4.431057+1 3.090295+5 4.298528+1680023522 1934 3.126079+5 4.170019+1 3.162278+5 4.045536+1 3.198895+5 3.924776+1680023522 1935 3.235937+5 3.807620+1 3.273407+5 3.693975+1 3.311311+5 3.583725+1680023522 1936 3.388442+5 3.373001+1 3.427678+5 3.272340+1 3.467369+5 3.174717+1680023522 1937 3.507519+5 3.080010+1 3.548134+5 2.989747+1 3.630781+5 2.817148+1680023522 1938 3.672823+5 2.734632+1 3.758374+5 2.577056+1 3.801894+5 2.501708+1680023522 1939 3.981072+5 2.221826+1 4.000000+5 2.194854+1 4.027170+5 2.157671+1680023522 1940 4.073803+5 2.095884+1 4.120975+5 2.035901+1 4.168694+5 1.977634+1680023522 1941 4.216965+5 1.921037+1 4.415705+5 1.710878+1 4.466836+5 1.662036+1680023522 1942 4.518559+5 1.614616+1 4.623810+5 1.525521+1 4.677351+5 1.482836+1680023522 1943 4.786301+5 1.401096+1 4.841724+5 1.362019+1 4.897788+5 1.324033+1680023522 1944 4.954502+5 1.287107+1 5.011872+5 1.251214+1 5.069907+5 1.216340+1680023522 1945 5.128614+5 1.183160+1 5.188000+5 1.150899+1 5.308844+5 1.088993+1680023522 1946 5.370318+5 1.059320+1 5.432503+5 1.030455+1 5.495409+5 1.002443+1680023522 1947 5.559043+5 9.751956+0 5.623413+5 9.487022+0 5.688529+5 9.229378+0680023522 1948 5.754399+5 8.984688+0 5.821032+5 8.746487+0 5.956621+5 8.288873+0680023522 1949 6.000000+5 8.149689+0 6.025596+5 8.069126+0 6.095369+5 7.855383+0680023522 1950 6.165950+5 7.647806+0 6.237348+5 7.445893+0 6.309573+5 7.249317+0680023522 1951 6.382635+5 7.057932+0 6.456542+5 6.876118+0 6.531306+5 6.698987+0680023522 1952 6.606935+5 6.526423+0 6.683439+5 6.358322+0 6.760830+5 6.194980+0680023522 1953 6.839117+5 6.036007+0 6.998420+5 5.730328+0 7.079458+5 5.583346+0680023522 1954 7.161434+5 5.440139+0 7.244360+5 5.304101+0 7.328245+5 5.171482+0680023522 1955 7.413102+5 5.042178+0 7.498942+5 4.916156+0 7.585776+5 4.793617+0680023522 1956 7.673615+5 4.674232+0 7.762471+5 4.557823+0 7.852356+5 4.444369+0680023522 1957 8.035261+5 4.225868+0 8.128305+5 4.123331+0 8.413951+5 3.830525+0680023522 1958 8.511380+5 3.737672+0 8.609938+5 3.647303+0 8.709636+5 3.559207+0680023522 1959 8.912509+5 3.389375+0 9.015711+5 3.309882+0 9.120108+5 3.232255+0680023522 1960 9.225714+5 3.156530+0 9.332543+5 3.082591+0 9.440609+5 3.010395+0680023522 1961 9.549926+5 2.939892+0 9.660509+5 2.871107+0 9.772372+5 2.804236+0680023522 1962 9.885531+5 2.738966+0 1.000000+6 2.677122+0 1.011579+6 2.616679+0680023522 1963 1.023293+6 2.557597+0 1.035142+6 2.499879+0 1.047129+6 2.443461+0680023522 1964 1.059254+6 2.388321+0 1.071519+6 2.334454+0 1.083927+6 2.281980+0680023522 1965 1.096478+6 2.230689+0 1.109175+6 2.180550+0 1.122018+6 2.131563+0680023522 1966 1.135011+6 2.083672+0 1.148154+6 2.036859+0 1.161449+6 1.992163+0680023522 1967 1.174898+6 1.948470+0 1.202264+6 1.863961+0 1.216186+6 1.823089+0680023522 1968 1.244515+6 1.744366+0 1.250000+6 1.729722+0 1.258925+6 1.706291+0680023522 1969 1.273503+6 1.669045+0 1.288250+6 1.632631+0 1.318257+6 1.564119+0680023522 1970 1.333521+6 1.530951+0 1.348963+6 1.498497+0 1.364583+6 1.466733+0680023522 1971 1.396368+6 1.405451+0 1.412538+6 1.375775+0 1.428894+6 1.346740+0680023522 1972 1.462177+6 1.290504+0 1.479108+6 1.264062+0 1.513561+6 1.212794+0680023522 1973 1.531087+6 1.187950+0 1.640590+6 1.049761+0 1.678804+6 1.008562+0680023522 1974 1.698244+6 9.885811-1 1.717908+6 9.690008-1 1.737801+6 9.498076-1680023522 1975 1.798871+6 8.947299-1 1.819701+6 8.770897-1 1.840772+6 8.597976-1680023522 1976 1.862087+6 8.428464-1 1.883649+6 8.266996-1 1.905461+6 8.108620-1680023522 1977 1.927525+6 7.953359-1 1.949845+6 7.801099-1 1.972423+6 7.651761-1680023522 1978 2.018366+6 7.362920-1 2.044000+6 7.209258-1 2.089296+6 6.949968-1680023522 1979 2.113489+6 6.817530-1 2.162719+6 6.567321-1 2.187762+6 6.445740-1680023522 1980 2.213095+6 6.326435-1 2.238721+6 6.209343-1 2.290868+6 5.982655-1680023522 1981 2.317395+6 5.872435-1 2.371374+6 5.658050-1 2.398833+6 5.553812-1680023522 1982 2.454709+6 5.356816-1 2.511886+6 5.166900-1 2.540973+6 5.074500-1680023522 1983 2.570396+6 4.983755-1 2.630268+6 4.807923-1 2.660725+6 4.722347-1680023522 1984 2.722701+6 4.555739-1 2.754229+6 4.474650-1 2.818383+6 4.321307-1680023522 1985 2.884032+6 4.173287-1 2.917427+6 4.101207-1 2.951209+6 4.030372-1680023522 1986 3.019952+6 3.892999-1 3.054921+6 3.826080-1 3.126079+6 3.695673-1680023522 1987 3.162278+6 3.632144-1 3.235937+6 3.511851-1 3.311311+6 3.395597-1680023522 1988 3.349654+6 3.338933-1 3.427678+6 3.228426-1 3.507519+6 3.122067-1680023522 1989 3.548134+6 3.070209-1 3.630781+6 2.969063-1 3.672823+6 2.919747-1680023522 1990 3.758374+6 2.826231-1 3.845918+6 2.735752-1 3.890451+6 2.691615-1680023522 1991 4.000000+6 2.588063-1 4.120975+6 2.481829-1 4.168694+6 2.441958-1680023522 1992 4.265795+6 2.364128-1 4.315191+6 2.326148-1 4.415704+6 2.254037-1680023522 1993 4.518559+6 2.184193-1 4.570882+6 2.150094-1 4.677351+6 2.083486-1680023522 1994 4.841724+6 1.987832-1 4.897788+6 1.956935-1 5.011872+6 1.896572-1680023522 1995 5.069907+6 1.867092-1 5.188000+6 1.811123-1 5.308844+6 1.756855-1680023522 1996 5.370318+6 1.730340-1 5.495409+6 1.678505-1 5.688529+6 1.603975-1680023522 1997 5.754399+6 1.579874-1 5.888437+6 1.532754-1 6.025596+6 1.487039-1680023522 1998 6.095369+6 1.465359-1 6.237348+6 1.422964-1 6.309573+6 1.402232-1680023522 1999 6.456542+6 1.361672-1 6.760830+6 1.284348-1 6.839116+6 1.265714-1680023522 2000 7.079458+6 1.211416-1 7.413102+6 1.142625-1 7.498942+6 1.126454-1680023522 2001 7.762471+6 1.079319-1 7.852356+6 1.064053-1 8.000000+6 1.039809-1680023522 2002 8.035261+6 1.034188-1 8.222427+6 1.005265-1 8.317638+6 9.911085-2680023522 2003 8.511380+6 9.633905-2 8.912509+6 9.102581-2 9.015711+6 8.977641-2680023522 2004 9.440609+6 8.494995-2 9.549926+6 8.378467-2 9.772372+6 8.150187-2680023522 2005 9.885531+6 8.038810-2 1.011579+7 7.820680-2 1.023293+7 7.713838-2680023522 2006 1.047129+7 7.504518-2 1.096478+7 7.102777-2 1.109175+7 7.008010-2680023522 2007 1.174898+7 6.552988-2 1.202264+7 6.379400-2 1.230269+7 6.210402-2680023522 2008 1.244515+7 6.127878-2 1.273503+7 5.966158-2 1.288250+7 5.886902-2680023522 2009 1.318257+7 5.731540-2 1.380384+7 5.433011-2 1.400000+7 5.346715-2680023522 2010 1.500000+7 4.944259-2 1.531087+7 4.830571-2 1.566751+7 4.706066-2680023522 2011 1.584893+7 4.645221-2 1.621810+7 4.525914-2 1.640590+7 4.467414-2680023522 2012 1.678804+7 4.352675-2 1.778279+7 4.078554-2 1.819701+7 3.976033-2680023522 2013 1.949845+7 3.683779-2 2.000000+7 3.581830-2 2.041738+7 3.501006-2680023522 2014 2.065380+7 3.456877-2 2.113489+7 3.370304-2 2.137962+7 3.327834-2680023522 2015 2.162719+7 3.285898-2 2.238721+7 3.163238-2 2.371374+7 2.968894-2680023522 2016 2.400000+7 2.930645-2 2.426610+7 2.895932-2 2.600160+7 2.687687-2680023522 2017 2.691535+7 2.589264-2 2.786121+7 2.494445-2 2.800000+7 2.481093-2680023522 2018 2.851018+7 2.433306-2 2.917427+7 2.373716-2 2.951209+7 2.344470-2680023522 2019 3.019952+7 2.287055-2 3.054921+7 2.258878-2 3.235937+7 2.123112-2680023522 2020 3.311311+7 2.071981-2 3.672823+7 1.856761-2 3.845918+7 1.768439-2680023522 2021 4.027170+7 1.684319-2 4.073803+7 1.663923-2 4.168694+7 1.623961-2680023522 2022 4.265795+7 1.584966-2 4.315191+7 1.565821-2 4.365158+7 1.546908-2680023522 2023 4.415704+7 1.528223-2 4.677351+7 1.438129-2 4.786301+7 1.404089-2680023522 2024 4.841724+7 1.387377-2 5.559043+7 1.201685-2 5.888437+7 1.131858-2680023522 2025 6.165950+7 1.078930-2 6.237348+7 1.066089-2 6.309573+7 1.053402-2680023522 2026 6.456542+7 1.028528-2 6.606934+7 1.004246-2 6.683439+7 9.923205-3680023522 2027 6.760830+7 9.805367-3 6.839116+7 9.688930-3 7.161434+7 9.236840-3680023522 2028 7.413102+7 8.915628-3 7.498942+7 8.811079-3 9.120108+7 7.210094-3680023522 2029 1.011579+8 6.483948-3 1.083927+8 6.040946-3 1.096478+8 5.970115-3680023522 2030 1.109175+8 5.900116-3 1.122018+8 5.831023-3 1.135011+8 5.762749-3680023522 2031 1.174898+8 5.562719-3 1.202264+8 5.433244-3 1.230269+8 5.306775-3680023522 2032 1.273503+8 5.122576-3 1.288250+8 5.063152-3 1.333521+8 4.888993-3680023522 2033 1.348963+8 4.832286-3 1.778279+8 3.652205-3 2.018366+8 3.212374-3680023522 2034 2.162719+8 2.995217-3 2.187762+8 2.960480-3 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