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Periodensystem der Elemente (Quelle: größtenteils www.lenntech.de)
Zink    Zn    Kernladungszahl Z=30 (p=30)
 Zn(n+p)nSchwere IsotopSchwere KernHäufig-
keit
Spin/
Parität
StabilitätHalbwerts-
zeit [s]
Zerfalls-
arten
Zerfalls-
energie [eV]
Defekt-
energie [eV]
Bindungs-
energie [eV]
Wirkungsquer-
schnitt [barn]
 
1.Zn6434 63.92914286  63.91268547 48.6% 0+ radioakt. 28E15a 2ε 1.096E6 -66.003E6 559.097E6 0.78#σ(n.γ) 
2.Zn6636 65.92603345  65.90957605 27.9% 0+   stabil   -68.8994E6 578.136E6 0.85#σ(n.γ) 
3.Zn6838 67.92484418  67.90838678 18.8% 0+   stabil   -70.0072E6 595.387E6 1#σ(n.γ); 72E-3#σ(n.it) 
4.Zn6737 66.92712782  66.91067042 4.1% 5/2−   stabil   -67.88E6 585.188E6 6.9#σ(n.γ) 
5.Zn7040 69.92531922 69.90886182 0.6% 0+ radioakt. 13E15a 2ß- 0.998E6  -69.5647E6 611.087E6 83E-3#σ(n.γ); 8.7E-3#σ(n.it) 
6.Zn69+139 68.92655025  68.91009286  9/2+ radioakt. 13.76h IT=99.967; β−=0.033 0.439E6(IT); 1.345E6(β−) -68.418E6 601.869E6 68^±TSP 
7.Zn6939 68.92655025  68.91009286  1/2− radioakt. 56.4min β−=100 0.909E6 -68.418E6 601.869E6 91^±TSP 
8.Zn6535 64.92924098  64.91278359  5/2− radioakt. 243.625d K/β+=100 1.352E6 -65.9116E6 567.077E6 Nihil^±TSP 
9.Zn6333 62.9332116  62.9167542  3/2− radioakt. 38.4667 K/β+=100 3.367E6 -62.213E6 547.236E6 Nihil^±TSP 
10.Zn6232 61.93433023  61.91787283  0+ radioakt. 9.186h K/β+=100 1.626E6 -61.171E6 538.123E6 Nihil^±TSP 
11.Zn6131 60.93988153 60.92342413  3/2− radioakt. 89.1 K/β+=100 5.984E6 -56E6 524.88E6 Nihil^±TSP 
12.Zn6030 59.941827  59.9253696  0+ radioakt. 2.38min K/β+=100 4.156E6  -54.1878E6 514.997E6 Nihil^±TSP 
13.Zn5929 58.94926376  58.93280637  3/2− radioakt. 182.0E-3 ß-=99.9; β−n=0.10 9.097E6(β+); 5.678E6(Kp) -47.2605E6 499.998E6 Nihil^±TSP 
14.Zn58+128 57.95459155  57.93813415  0(+) radioakt. 85E-3 Kp=100 6.495E6  -42.2977E6 486.964E6 Nihil^±TSP 
15.Zn5828 57.95459155  57.93813415  0+ radioakt. 84E-3 K/β+<96.6; Kp>3.4 9.364E6(ε); 6.495E6(pε) -42.2977E6 486.964E6 Nihil^±TSP 
16.Zn5727 56.96478775  56.94833035  7/2− radioakt. 38E-3 K/β+<35; Kp>65 14.51E6(β+). 13.814E6(Kp) -32.8E6 469.395E6 Nihil^±TSP 
17.Zn5626 55.97237986  55.95592246  0+ radioakt. 500E-9 K/β+=<100; Kp=>0 12.873E6(β+); 12.318E6(Kp)  -25.728E6 454.252E6 Nihil^±TSP 
18.Zn5525 54.9839795 54.9675221  5/2− radioakt. 20E-3 K≈>0; K2p≈>0 ; Kp≈>0  16.701E6(β+); 16.999E6(2Kp); -0.518E6(Kp) -14.923E6 435.375E6 Nihil^±TSP 
19.Zn7141 70.9277216  70.9112642  1/2− radioakt. 2.45min ß-=100 2.813E6 -67.3269E6 616.92 E6 Nihil^±TSP 
20.Zn71+141 70.9277216 70.9112642  9/2+ radioakt. 3.96h β−≈100; IT<0.05 2.971E6(β−); 0.158E6(IT) -67.3269E6 616.92E6 Nihil^±TSP 
21.Zn7242 71.92685793  71.91040053  0+ radioakt. 46.5h β−=100 0.458E6 -68.1314E6 625.796E6 Nihil^±TSP 
22.Zn7343 72.92977915 72.91332176  1/2− radioakt. 23.5  β−=100 4.289E6 -65.4103E6 631.146E6 Nihil^±TSP 
23.Zn73+143 72.92977915  72.91332176  7/2+ radioakt. 5.8 β−=?; IT=? 4.486E6(β−); 0.196E6(IT) -65.4103E6 631.146E6 Nihil^±TSP 
24.Zn7444 73.92945859  73.91300119  0+ radioakt. 95.6 ß-=>0; β−n=>0 2.341E6(β−); -4.081E6(β−n) -65.7089E6 639.516E6 Nihil^±TSP 
25.Zn7545 74.93293677 74.91647937  7/2+ radioakt. 10.2 ß-=100 5.996E6 -62.469E6 644.348E6 Nihil^±TSP 
26.Zn7646 75.93329361  75.91683622  0+ radioakt. 5.7 ß-=100 4.16E6 -62.1366E6 652.087E6 Nihil^±TSP 
27.Zn7747 76.93695902  76.92050162  7/2+ radioakt. 2.08 ß-=100 7.27E6 -58.7223E6 656.744E6 Nihil^±TSP 
28.Zn77+147 76.93695902  76.92050162  1/2− radioakt. 1.05 IT>50; β−<50  0.772E6(IT); 8.042E6(β−) -58.7223E6 656.744E6 Nihil^±TSP 
29.Zn7848 77.93844019  77.92198279  0+ radioakt. 1.47 ß-=100 6.364E6 -57.3426E6 663.435E6 Nihil^±TSP 
30.Zn7949 78.94265127  78.92619387  (9/2+) radioakt. 995E-3 ß-=100; β−n=1.3 9.09E6(β−). 2.215E6(β−n) -53.42E6 667.584E6 Nihil^±TSP 
31.Zn8050 79.94434232  79.92788492  0+ radioakt. 540E-3 ß−=99.0; β−n=1.0 7.29E6(β−); 2.6593E6(β−n) -51.8448E6 674.08E6 Nihil^±TSP 
32.Zn8151 80.95047955  80.93402216   radioakt. 290E-3 ß-=92.5; β−n=7.5 11.855E6(β−); 4.936E6(β−n) -46.128E6 676.435E6 Nihil^±TSP 
33.Zn8252 81.95442053  81.93796314  0+ radioakt. <150E-9 ß-=?; β−n=? 10.647E6(β−); 7.455E6(β−n) -42.457E6 680.835E6 Nihil^±TSP 
34.Zn8353 82.96103035 82.94457295  5/2+ radioakt. <150E-9 ß-=>0; β−n=>0 13.088E6(β−); 8.733E&(β−n) -36.3E6 682.749E6 Nihil^±TSP 


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Please Select Elements
  all   nothing
Z=1WasserstoffH
Z=2HeliumHe
Z=3LithiumLi
Z=4BerylliumBe
Z=5BorB
Z=6KohlenstoffC
Z=7StickstoffN
Z=8SauerstoffO
Z=9FluorF
Z=10NeonNe
Z=11NatriumNa
Z=12MagnesiumMg
Z=13AluminiumAl
Z=14SiliziumSi
Z=15PhosphorP
Z=16SchwefelS
Z=17ChlorCl
Z=18ArgonAr
Z=19KaliumK
Z=20CalciumCa
Z=21ScandiumSc
Z=22TitanTi
Z=23VanadiumV
Z=24ChromCr
Z=25ManganMn
Z=26EisenFe
Z=27KobaltCo
Z=28NickelNi
Z=29KupferCu
Z=30ZinkZn
Z=31GalliumGa
Z=32GermaniumGe
Z=33ArsenAs
Z=34SelenSe
Z=35BromBr
Z=36KryptonKr
Z=37RubidiumRb
Z=38StrontiumSr
Z=39YttriumY
Z=40ZirkonZr
Z=41NiobNb
Z=42MolybdänMo
Z=43TechnetiumTc
Z=44RutheniumRu
Z=45RohdiumRh
Z=46PalladiumPd
Z=47SilberAg
Z=48CadmiumCd
Z=49IndiumIn
Z=50ZinnSn
Z=51AntimonSb
Z=52TellurTe
Z=53JodJ
Z=54XenonXe
Z=55CäsiumCs
Z=56BariumBa
Z=57LanthanLa
Z=58CerCe
Z=59PraseodymPr
Z=60NeodymNd
Z=61PromethiumPm
Z=62SamariumSm
Z=63EuropiumEu
Z=64GadoliniumGd
Z=65TerbiumTb
Z=66DysprosiumDy
Z=67HolmiumHo
Z=68ErbiumEr
Z=69ThuliumTm
Z=70YtterbiumYb
Z=71LutetiumLu
Z=72HafniumHf
Z=73TantalTa
Z=74WolframW
Z=75RheniumRe
Z=76OsmiumOs
Z=77IridiumIr
Z=78PlatinPt
Z=79GoldAu
Z=80QuecksilberHg
Z=81ThalliumTl
Z=82BleiPb
Z=83WismutBi
Z=84PoloniumPo
Z=85AstatinAt
Z=86RadonRn
Z=87FranciumFr
Z=88RadiumRa
Z=89ActiniumAc
Z=90ThoriumTh
Z=91ProtactiniumPa
Z=92UranU
Z=93NeptuniumNp
Z=94PlutoniumPu
Z=95AmericiumAm
Z=96CuriumCm
Z=97BerkeliumBk
Z=98CaliforniumCf
Z=99EinsteiniumEs
Z=100FermiumFm
Z=101MendeleviumMd
Z=102NobeliumNo
Z=103LawrenciumLr
Z=104RutherfordiumRf
Z=105DubniumDb
Z=106SeaborgiumSg
Z=107BohriumBh
Z=108HassiumHs
Z=109MeitneriumMt
Z=110DarmstadtiumDs
Z=111RoentgeniumRg
Z=112CoperniciumCn
Z=113UnuntriumUut
Z=114FleroviumFl
Z=115UnunpentiumUup
Z=116LivermoriumLv
Z=117UnunseptiumUus
Z=118UnunoctiumUuo


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Calculate for selected elements
with potenz N= to in            L = Z * Cx * Basis^N * Factor

and f=c/L and T=L/c with c= m/s and Comptonwavelength Cx [m]:   Ce= 2.4263102389E-12
Cp= 1.32140985623E-15  Cn= 1.3195909068E-15  Plk= 1.616199E-35  orb_Mercur= 57.91E9
Cx m    Basis   Factor
  Basis B with e= 2.7182818284590  phi= 1.618034  or 2 ,   Factor with pi= 3.141592   2pi= 6.283185  g= 0.61803398874989  or 18
show  digits                  Select Units
L Length   Lj   pc   AE   earthR   km   m   dm   cm   mm   µm   nm   A~   pm   fm
Frequency   THz   GHz   MHz   kHz   Hz   mHz   µHz
T Time   j   d   h   min   s   ms   µs   ns   ps
V Volume =L^3   km^3   m^3   hL=100L   dL=10L   dm^3=L   10ml=cL   cm^3=mL   mm^3=µL
m Mass =V*dens.   Mt   kt   t   kg   g   mg   µg   ng   pg   fg

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1 Listing - Modus     2 Searching - Modus     3 Factor-Search     4 Basis(+Factor)-Search     5 Basis(+Factor)-Harmonics-Search


Results      with Cp      Attention ! Factor 0.6180339887498948482 to L and to T, invers to f
BF ZN[1m=1m][1MHz=1.0E6Hz][1s=1s]
20.618HZ=1N=33L=0.00001 mf=42734728.034 MHzT=2.3400172318832E-14 s
20.618HeZ=2N=33L=0.00001 mf=21367364.017 MHzT=4.6800344637664E-14 s
20.618LiZ=3N=33L=0.00002 mf=14244909.345 MHzT=7.0200516956496E-14 s
20.618BeZ=4N=33L=0.00003 mf=10683682.009 MHzT=9.3600689275328E-14 s
20.618BZ=5N=33L=0.00004 mf=8546945.607 MHzT=1.1700086159416E-13 s
20.618CZ=6N=33L=0.00004 mf=7122454.672 MHzT=1.4040103391299E-13 s
20.618NZ=7N=33L=0.00005 mf=6104961.148 MHzT=1.6380120623182E-13 s
20.618OZ=8N=33L=0.00006 mf=5341841.004 MHzT=1.8720137855066E-13 s
20.618FZ=9N=33L=0.00006 mf=4748303.115 MHzT=2.1060155086949E-13 s
20.618NeZ=10N=33L=0.00007 mf=4273472.803 MHzT=2.3400172318832E-13 s
20.618NaZ=11N=33L=0.00008 mf=3884975.276 MHzT=2.5740189550715E-13 s
20.618MgZ=12N=33L=0.00008 mf=3561227.336 MHzT=2.8080206782598E-13 s
20.618AlZ=13N=33L=0.00009 mf=3287286.772 MHzT=3.0420224014482E-13 s
20.618SiZ=14N=33L=0.00010 mf=3052480.574 MHzT=3.2760241246365E-13 s
20.618PZ=15N=33L=0.00011 mf=2848981.869 MHzT=3.5100258478248E-13 s
20.618SZ=16N=33L=0.00011 mf=2670920.502 MHzT=3.7440275710131E-13 s
20.618ClZ=17N=33L=0.00012 mf=2513807.531 MHzT=3.9780292942014E-13 s
20.618ArZ=18N=33L=0.00013 mf=2374151.557 MHzT=4.2120310173898E-13 s
20.618KZ=19N=33L=0.00013 mf=2249196.212 MHzT=4.4460327405781E-13 s
20.618CaZ=20N=33L=0.00014 mf=2136736.402 MHzT=4.6800344637664E-13 s
20.618ScZ=21N=33L=0.00015 mf=2034987.049 MHzT=4.9140361869547E-13 s
20.618TiZ=22N=33L=0.00015 mf=1942487.638 MHzT=5.148037910143E-13 s
20.618VZ=23N=33L=0.00016 mf=1858031.654 MHzT=5.3820396333314E-13 s
20.618CrZ=24N=33L=0.00017 mf=1780613.668 MHzT=5.6160413565197E-13 s
20.618MnZ=25N=33L=0.00018 mf=1709389.121 MHzT=5.850043079708E-13 s
20.618FeZ=26N=33L=0.00018 mf=1643643.386 MHzT=6.0840448028963E-13 s
20.618CoZ=27N=33L=0.00019 mf=1582767.705 MHzT=6.3180465260846E-13 s
20.618NiZ=28N=33L=0.00020 mf=1526240.287 MHzT=6.552048249273E-13 s
20.618CuZ=29N=33L=0.00020 mf=1473611.312 MHzT=6.7860499724613E-13 s
20.618ZnZ=30N=33L=0.00021 mf=1424490.934 MHzT=7.0200516956496E-13 s
20.618GaZ=31N=33L=0.00022 mf=1378539.614 MHzT=7.2540534188379E-13 s
20.618GeZ=32N=33L=0.00022 mf=1335460.251 MHzT=7.4880551420262E-13 s
20.618AsZ=33N=33L=0.00023 mf=1294991.759 MHzT=7.7220568652146E-13 s
20.618SeZ=34N=33L=0.00024 mf=1256903.766 MHzT=7.9560585884029E-13 s
20.618BrZ=35N=33L=0.00025 mf=1220992.230 MHzT=8.1900603115912E-13 s
20.618KrZ=36N=33L=0.00025 mf=1187075.779 MHzT=8.4240620347795E-13 s
20.618RbZ=37N=33L=0.00026 mf=1154992.650 MHzT=8.6580637579678E-13 s
20.618SrZ=38N=33L=0.00027 mf=1124598.106 MHzT=8.8920654811562E-13 s
20.618YZ=39N=33L=0.00027 mf=1095762.257 MHzT=9.1260672043445E-13 s
20.618ZrZ=40N=33L=0.00028 mf=1068368.201 MHzT=9.3600689275328E-13 s
20.618NbZ=41N=33L=0.00029 mf=1042310.440 MHzT=9.5940706507211E-13 s
20.618MoZ=42N=33L=0.00029 mf=1017493.525 MHzT=9.8280723739094E-13 s
20.618TcZ=43N=33L=0.00030 mf=993830.885 MHzT=1.0062074097098E-12 s
20.618RuZ=44N=33L=0.00031 mf=971243.819 MHzT=1.0296075820286E-12 s
20.618RhZ=45N=33L=0.00032 mf=949660.623 MHzT=1.0530077543474E-12 s
20.618PdZ=46N=33L=0.00032 mf=929015.827 MHzT=1.0764079266663E-12 s
20.618AgZ=47N=33L=0.00033 mf=909249.533 MHzT=1.0998080989851E-12 s
20.618CdZ=48N=33L=0.00034 mf=890306.834 MHzT=1.1232082713039E-12 s
20.618InZ=49N=33L=0.00034 mf=872137.307 MHzT=1.1466084436228E-12 s
20.618SnZ=50N=33L=0.00035 mf=854694.561 MHzT=1.1700086159416E-12 s
20.618SbZ=51N=33L=0.00036 mf=837935.844 MHzT=1.1934087882604E-12 s
20.618TeZ=52N=33L=0.00036 mf=821821.693 MHzT=1.2168089605793E-12 s
20.618JZ=53N=33L=0.00037 mf=806315.623 MHzT=1.2402091328981E-12 s
20.618XeZ=54N=33L=0.00038 mf=791383.852 MHzT=1.2636093052169E-12 s
20.618CsZ=55N=33L=0.00039 mf=776995.055 MHzT=1.2870094775358E-12 s
20.618BaZ=56N=33L=0.00039 mf=763120.143 MHzT=1.3104096498546E-12 s
20.618LaZ=57N=33L=0.00040 mf=749732.071 MHzT=1.3338098221734E-12 s
20.618CeZ=58N=33L=0.00041 mf=736805.656 MHzT=1.3572099944923E-12 s
20.618PrZ=59N=33L=0.00041 mf=724317.424 MHzT=1.3806101668111E-12 s
20.618NdZ=60N=33L=0.00042 mf=712245.467 MHzT=1.4040103391299E-12 s
20.618PmZ=61N=33L=0.00043 mf=700569.312 MHzT=1.4274105114488E-12 s
20.618SmZ=62N=33L=0.00043 mf=689269.807 MHzT=1.4508106837676E-12 s
20.618EuZ=63N=33L=0.00044 mf=678329.016 MHzT=1.4742108560864E-12 s
20.618GdZ=64N=33L=0.00045 mf=667730.126 MHzT=1.4976110284052E-12 s
20.618TbZ=65N=33L=0.00046 mf=657457.354 MHzT=1.5210112007241E-12 s
20.618DyZ=66N=33L=0.00046 mf=647495.879 MHzT=1.5444113730429E-12 s
20.618HoZ=67N=33L=0.00047 mf=637831.762 MHzT=1.5678115453617E-12 s
20.618ErZ=68N=33L=0.00048 mf=628451.883 MHzT=1.5912117176806E-12 s
20.618TmZ=69N=33L=0.00048 mf=619343.885 MHzT=1.6146118899994E-12 s
20.618YbZ=70N=33L=0.00049 mf=610496.115 MHzT=1.6380120623182E-12 s
20.618LuZ=71N=33L=0.00050 mf=601897.578 MHzT=1.6614122346371E-12 s
20.618HfZ=72N=33L=0.00051 mf=593537.889 MHzT=1.6848124069559E-12 s
20.618TaZ=73N=33L=0.00051 mf=585407.233 MHzT=1.7082125792747E-12 s
20.618WZ=74N=33L=0.00052 mf=577496.325 MHzT=1.7316127515936E-12 s
20.618ReZ=75N=33L=0.00053 mf=569796.374 MHzT=1.7550129239124E-12 s
20.618OsZ=76N=33L=0.00053 mf=562299.053 MHzT=1.7784130962312E-12 s
20.618IrZ=77N=33L=0.00054 mf=554996.468 MHzT=1.8018132685501E-12 s
20.618PtZ=78N=33L=0.00055 mf=547881.129 MHzT=1.8252134408689E-12 s
20.618AuZ=79N=33L=0.00055 mf=540945.924 MHzT=1.8486136131877E-12 s
20.618HgZ=80N=33L=0.00056 mf=534184.100 MHzT=1.8720137855066E-12 s
20.618TlZ=81N=33L=0.00057 mf=527589.235 MHzT=1.8954139578254E-12 s
20.618PbZ=82N=33L=0.00058 mf=521155.220 MHzT=1.9188141301442E-12 s
20.618BiZ=83N=33L=0.00058 mf=514876.241 MHzT=1.9422143024631E-12 s
20.618PoZ=84N=33L=0.00059 mf=508746.762 MHzT=1.9656144747819E-12 s
20.618AtZ=85N=33L=0.00060 mf=502761.506 MHzT=1.9890146471007E-12 s
20.618RnZ=86N=33L=0.00060 mf=496915.442 MHzT=2.0124148194196E-12 s
20.618FrZ=87N=33L=0.00061 mf=491203.771 MHzT=2.0358149917384E-12 s
20.618RaZ=88N=33L=0.00062 mf=485621.909 MHzT=2.0592151640572E-12 s
20.618AcZ=89N=33L=0.00062 mf=480165.484 MHzT=2.082615336376E-12 s
20.618ThZ=90N=33L=0.00063 mf=474830.311 MHzT=2.1060155086949E-12 s
20.618PaZ=91N=33L=0.00064 mf=469612.396 MHzT=2.1294156810137E-12 s
20.618UZ=92N=33L=0.00065 mf=464507.913 MHzT=2.1528158533325E-12 s
20.618NpZ=93N=33L=0.00065 mf=459513.205 MHzT=2.1762160256514E-12 s
20.618PuZ=94N=33L=0.00066 mf=454624.766 MHzT=2.1996161979702E-12 s
20.618AmZ=95N=33L=0.00067 mf=449839.242 MHzT=2.223016370289E-12 s
20.618CmZ=96N=33L=0.00067 mf=445153.417 MHzT=2.2464165426079E-12 s
20.618BkZ=97N=33L=0.00068 mf=440564.207 MHzT=2.2698167149267E-12 s
20.618CfZ=98N=33L=0.00069 mf=436068.653 MHzT=2.2932168872455E-12 s
20.618EsZ=99N=33L=0.00069 mf=431663.920 MHzT=2.3166170595644E-12 s
20.618FmZ=100N=33L=0.00070 mf=427347.280 MHzT=2.3400172318832E-12 s
20.618MdZ=101N=33L=0.00071 mf=423116.119 MHzT=2.363417404202E-12 s
20.618NoZ=102N=33L=0.00072 mf=418967.922 MHzT=2.3868175765209E-12 s
20.618LrZ=103N=33L=0.00072 mf=414900.272 MHzT=2.4102177488397E-12 s
20.618RfZ=104N=33L=0.00073 mf=410910.846 MHzT=2.4336179211585E-12 s
20.618DbZ=105N=33L=0.00074 mf=406997.410 MHzT=2.4570180934774E-12 s
20.618SgZ=106N=33L=0.00074 mf=403157.812 MHzT=2.4804182657962E-12 s
20.618BhZ=107N=33L=0.00075 mf=399389.982 MHzT=2.503818438115E-12 s
20.618HsZ=108N=33L=0.00076 mf=395691.926 MHzT=2.5272186104339E-12 s
20.618MtZ=109N=33L=0.00076 mf=392061.725 MHzT=2.5506187827527E-12 s
20.618DsZ=110N=33L=0.00077 mf=388497.528 MHzT=2.5740189550715E-12 s
20.618RgZ=111N=33L=0.00078 mf=384997.550 MHzT=2.5974191273904E-12 s
20.618CnZ=112N=33L=0.00079 mf=381560.072 MHzT=2.6208192997092E-12 s
20.618UutZ=113N=33L=0.00079 mf=378183.434 MHzT=2.644219472028E-12 s
20.618FlZ=114N=33L=0.00080 mf=374866.035 MHzT=2.6676196443468E-12 s
20.618UupZ=115N=33L=0.00081 mf=371606.331 MHzT=2.6910198166657E-12 s
20.618LvZ=116N=33L=0.00081 mf=368402.828 MHzT=2.7144199889845E-12 s
20.618UusZ=117N=33L=0.00082 mf=365254.086 MHzT=2.7378201613033E-12 s
20.618UuoZ=118N=33L=0.00083 mf=362158.712 MHzT=2.7612203336222E-12 s
 
 
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