History of Pisot numbers less than the golden ratio

   number-header: $\theta_r$ Numbers:-  '1':-    number: '1.324717957244746025960908854478097340734404056901733364534015050302827851245547594054699347981787280'-    comment: A root of $P_{2}$, with minimal polynomial $x^{3} - x - 1$. This is the-      plastic ratio, the smallest Pisot number. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,3]}[$\Delta(2,3,\infty)$].-  '2':-    number: '1.380277569097614115673301691822731877816626701558763025411771331211249574118641526187864568249035509'-    comment: A root of $Q_{2}$, with minimal polynomial $x^{4} - x^{3} - 1$.-  '3':-    number: '1.443268791270373107628127607386911604676011966654571598409233793623784837874189050037590075664743962'-    comment: A root of $Q_{3}$, with minimal polynomial $x^{5} - x^{4} - x^{3} + x^{2}-      - 1$.-  '4':-    number: '1.465571231876768026656731225219939108025577568472285701643183111249262996685017840478125801194909270'-    comment: A root of $P_{3}$, with minimal polynomial $x^{3} - x^{2} - 1$. This-      is the supergolden ratio. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,4]}[$\Delta(2,4,\infty)$].-  '5':-    number: '1.501594803539087366377783127371046108486398336253585342248394186063343612597128898134114246029200202'-    comment: A root of $Q_{4}$, with minimal polynomial $x^{6} - x^{5} - x^{4} + x^{2}-      - 1$.-  '6':-    number: '1.534157744914266915435970076109375701882545038516595135368531863008063023214082281436789664835483494'-    comment: A root of $P_{4}$, with minimal polynomial $x^{5} - x^{3} - x^{2} - x-      - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,5]}[$\Delta(2,5,\infty)$].-  '7':-    number: '1.545215649732755243252550624105116119691470055364233123560610725498211588166533120504318279380159156'-    comment: A root of $Q_{5}$, with minimal polynomial $x^{7} - x^{6} - x^{5} + x^{2}-      - 1$.-  '8':-    number: '1.561752067720297294702995364060723780790847286947276642846284783946252241043942944496244054750817375'-    comment: The root in $(1,\varphi)$ of $E$, with minimal polynomial $x^{6} - 2x^{5}-      + x^{4} - x^{2} + x - 1$.-  '9':-    number: '1.570147312196054362910665435137126553873131607424527436931654877897330661544162320222760040702620119'-    comment: A root of $P_{5}$, with minimal polynomial $x^{5} - x^{4} - x^{2} - 1$.-      It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,6]}[$\Delta(2,6,\infty)$].-  '10':-    number: '1.573678968393516988774251418629321467812704061507913408937274370051211297448790471881548837806219190'-    comment: A root of $Q_{6}$, with minimal polynomial $x^{8} - x^{7} - x^{6} + x^{2}-      - 1$.-  '11':-    number: '1.590005373901363925162015541663808196898573270019121975693623393697501137164006258637372010170673034'-    comment: A root of $P_{6}$, with minimal polynomial $x^{7} - x^{5} - x^{4} - x^{3}-      - x^{2} - x - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,7]}[$\Delta(2,7,\infty)$].-  '12':-    number: '1.591184305667102506280378163106102721323455556070427118636105671632990046340380662184687387274732566'-    comment: A root of $Q_{7}$, with minimal polynomial $x^{9} - x^{8} - x^{7} + x^{2}-      - 1$.-  '13':-    number: '1.601347333787636724232618164313101117665668726676556628193381197227260290102478499805029985176068445'-    comment: A root of $P_{7}$, with minimal polynomial $x^{7} - x^{6} - x^{4} - x^{2}-      - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,8]}[$\Delta(2,8,\infty)$].-  '14':-    number: '1.601755861696983255736192654219002170232459847383645956556081860539331501794067175848485666834280654'-    comment: A root of $Q_{8}$, with minimal polynomial $x^{10} - x^{9} - x^{8} +-      x^{2} - 1$.-  '15':-    number: '1.607982727928201149922420457795797515362209291893843383821724387553882342235678008938055023076222152'-    comment: A root of $P_{8}$, with minimal polynomial $x^{9} - x^{7} - x^{6} - x^{5}-      - x^{4} - x^{3} - x^{2} - x - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,9]}[$\Delta(2,9,\infty)$].-  '16':-    number: '1.608128385187386959402200323538480539244506229939808475627654880454135115549049193244125291977586775'-    comment: A root of $Q_{9}$, with minimal polynomial $x^{11} - x^{10} - x^{9} +-      x^{2} - 1$.-  '17':-    number: '1.611930396564119819833599200722692620452821331844328319226299635293730595602174524805609485749220372'-    comment: A root of $P_{9}$, with minimal polynomial $x^{9} - x^{8} - x^{6} - x^{4}-      - x^{2} - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,10]}[$\Delta(2,10,\infty)$].-  '18':-    number: '1.611983421246492155859040049756323314852853437636639613720385059950750148002686762196644934656348672'-    comment: A root of $Q_{10}$, with minimal polynomial $x^{12} - x^{11} - x^{10}-      + x^{2} - 1$.-  '19':-    number: '1.614306823257148514569632339911304106948171748039112819042361616990015585866967144509566552856428042'-    comment: A root of $P_{10}$, with minimal polynomial $x^{11} - x^{9} - x^{8} --      x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$. It is the growth rate-      of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,11]}[$\Delta(2,11,\infty)$].-  '20':-    number: '1.614326414939127104073078356579636391949011342705773229044712283319374524946453994526083157310377742'-    comment: A root of $Q_{11}$, with minimal polynomial $x^{13} - x^{12} - x^{11}-      + x^{2} - 1$.-  '21':-    number: '1.615749202755210610743641798789103362281243911263783155770251095174096083205827141199474172669686514'-    comment: A root of $P_{11}$, with minimal polynomial $x^{11} - x^{10} - x^{8}-      - x^{6} - x^{4} - x^{2} - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,12]}[$\Delta(2,12,\infty)$].-  '22':-    number: '1.615756517540843375529686781971131464046866598458441577197107007695607669818877612432159677719427740'-    comment: A root of $Q_{12}$, with minimal polynomial $x^{14} - x^{13} - x^{12}-      + x^{2} - 1$.-  '23':-    number: '1.616629684394572703598804670579966020060105074535041910104107096102528067389296930735657559212555402'-    comment: A root of $P_{12}$, with minimal polynomial $x^{13} - x^{11} - x^{10}-      - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.-  '24':-    number: '1.616632435387905008141467676752220700831348754409358539038135095071601155042700459931124659244537941'-    comment: A root of $Q_{13}$, with minimal polynomial $x^{15} - x^{14} - x^{13}-      + x^{2} - 1$.-  '25':-    number: '1.617169296355092563480671132600765362456967191135302102729539392961745062210998433921295220014506215'-    comment: A root of $P_{13}$, with minimal polynomial $x^{13} - x^{12} - x^{10}-      - x^{8} - x^{6} - x^{4} - x^{2} - 1$.-  '26':-    number: '1.617170336172016847605481712611059501452437635469882386057255508606235491186675769348455132093009414'-    comment: A root of $Q_{14}$, with minimal polynomial $x^{16} - x^{15} - x^{14}-      + x^{2} - 1$.-  '27':-    number: '1.617500905431324014411963007650991447867821260857169838924218729322581246942327161872141255472644582'-    comment: A root of $P_{14}$, with minimal polynomial $x^{15} - x^{13} - x^{12}-      - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} --      x^{2} - x - 1$.-  '28':-    number: '1.617501299812909557233137493529053056922071157913856951616026650849537504285172555316810694539178691'-    comment: A root of $Q_{15}$, with minimal polynomial $x^{17} - x^{16} - x^{15}-      + x^{2} - 1$.-  '29':-    number: '1.617705069957556644470177554481987140361426228819198259427878209593425193281904169829510686690774651'-    comment: A root of $P_{15}$, with minimal polynomial $x^{15} - x^{14} - x^{12}-      - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.-  '30':-    number: '1.617705219888455097146323069204504687107702709103938695316495370965365042281749410718148250134450673'-    comment: A root of $Q_{16}$, with minimal polynomial $x^{18} - x^{17} - x^{16}-      + x^{2} - 1$.-  '31':-    number: '1.617830928788973863699424746173140971640051423343242480743578861627018039776784999830916329455401512'-    comment: A root of $P_{16}$, with minimal polynomial $x^{17} - x^{15} - x^{14}-      - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5}-      - x^{4} - x^{3} - x^{2} - x - 1$.-  '32':-    number: '1.617830985877812298846657162479186429296004329244380834320484689516026034285121093064090212646902933'-    comment: A root of $Q_{17}$, with minimal polynomial $x^{19} - x^{18} - x^{17}-      + x^{2} - 1$.-  '33':-    number: '1.617908581767165011975654251943379527724351187695218752887992225503193582039747807291459082094368585'-    comment: A root of $P_{17}$, with minimal polynomial $x^{17} - x^{16} - x^{14}-      - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.-  '34':-    number: '1.617908603527805385791372655209449553767018177375841206557773359477283053340186177065247280643988320'-    comment: A root of $Q_{18}$, with minimal polynomial $x^{20} - x^{19} - x^{18}-      + x^{2} - 1$.-  '35':-    number: '1.617956519953564239208622399882582744059606376335285602101209468687677811493689474942744891506041932'-    comment: A root of $P_{18}$, with minimal polynomial $x^{19} - x^{17} - x^{16}-      - x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7}-      - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.-  '36':-    number: '1.617956528253976570213724233669342650311982524814136763277345754456220908746937624048581615827138001'-    comment: A root of $Q_{19}$, with minimal polynomial $x^{21} - x^{20} - x^{19}-      + x^{2} - 1$.-  '37':-    number: '1.617986125385249151581179065219836276338293750679622676312918048191078288185448939191521385866321094'-    comment: A root of $P_{19}$, with minimal polynomial $x^{19} - x^{18} - x^{16}-      - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.-  '38':-    number: '1.617986128552861828746775573560971560626559554179903857177524556107337154595403717855874656309277088'-    comment: A root of $Q_{20}$, with minimal polynomial $x^{22} - x^{21} - x^{20}-      + x^{2} - 1$.-  '39':-    number: '1.618004413617124503253339884205705740949886990727485864190374404055016480918880509307231034414017485'-    comment: A root of $P_{20}$, with minimal polynomial $x^{21} - x^{19} - x^{18}-      - x^{17} - x^{16} - x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9}-      - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.-  '40':-    number: '1.618004414826328965224816813048886874741852358452825536420120516315769101498118708366546047544102188'-    comment: A root of $Q_{21}$, with minimal polynomial $x^{23} - x^{22} - x^{21}-      + x^{2} - 1$.-  '41':-    number: '1.618015712751258280635900473733667949090056927598243987323992158078160732484712147251547557149689392'-    comment: A root of $P_{21}$, with minimal polynomial $x^{21} - x^{20} - x^{18}-      - x^{16} - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.-  '42':-    number: '1.618015713212954752257255964375369229374123216484787415640736393798376918798139605181967819732712222'-    comment: A root of $Q_{22}$, with minimal polynomial $x^{24} - x^{23} - x^{22}-      + x^{2} - 1$.-  '43':-    number: '1.618022694541460339603743229827892343352486377764735927967607280632891128415448447893953664301512573'-    comment: A root of $P_{22}$, with minimal polynomial $x^{23} - x^{21} - x^{20}-      - x^{19} - x^{18} - x^{17} - x^{16} - x^{15} - x^{14} - x^{13} - x^{12} - x^{11}-      - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x-      - 1$.-  '44':-    number: '1.618022694717768294416502444185158998331096020868084111924521311236631268730313972376491207972498484'-    comment: A root of $Q_{23}$, with minimal polynomial $x^{25} - x^{24} - x^{23}-      + x^{2} - 1$.-  '45':-    number: '1.618027008938025718553681758942751295768660974229159521330823899915592183362260151838715294021339562'-    comment: A root of $P_{23}$, with minimal polynomial $x^{23} - x^{22} - x^{20}-      - x^{18} - x^{16} - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2}-      - 1$.-  '46':-    number: '1.618027009005358347427925536092720504146670868386797655664278670383537383085953832521182612767970098'-    comment: A root of $Q_{24}$, with minimal polynomial $x^{26} - x^{25} - x^{24}-      + x^{2} - 1$.-  '47':-    number: '1.618029675146055305698946786118197148936629694393732406286549986112999293588968023123008043461804993'-    comment: A root of $P_{24}$, with minimal polynomial $x^{25} - x^{23} - x^{22}-      - x^{21} - x^{20} - x^{19} - x^{18} - x^{17} - x^{16} - x^{15} - x^{14} - x^{13}-      - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} --      x^{3} - x^{2} - x - 1$.-  '48':-    number: '1.618029675171771354015094432833994648403067615748015040807374613270327489817157619418160494014043687'-    comment: A root of $Q_{25}$, with minimal polynomial $x^{27} - x^{26} - x^{25}-      + x^{2} - 1$.-  '49':-    number: '1.618031322858835939379993750912293610423937558487693101083392560992438305802819245773759782326311482'-    comment: A root of $P_{25}$, with minimal polynomial $x^{25} - x^{24} - x^{22}-      - x^{20} - x^{18} - x^{16} - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4}-      - x^{2} - 1$.-  '50':-    number: '1.618031322868657922029597723248317005726758817620183761258070106896742787251271592809502788045381653'-    comment: A root of $Q_{26}$, with minimal polynomial $x^{28} - x^{27} - x^{26}-      + x^{2} - 1$.+- comment: A root of $P_{2}$, with minimal polynomial $x^{3} - x - 1$. This is the+    plastic ratio, the smallest Pisot number. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,3]}[$\Delta(2,3,\infty)$].+  params:+    r: '1'+  number: '1.324717957244746025960908854478097340734404056901733364534015050302827851245547594054699347981787280'+- comment: A root of $Q_{2}$, with minimal polynomial $x^{4} - x^{3} - 1$.+  params:+    r: '2'+  number: '1.380277569097614115673301691822731877816626701558763025411771331211249574118641526187864568249035509'+- comment: A root of $Q_{3}$, with minimal polynomial $x^{5} - x^{4} - x^{3} + x^{2}+    - 1$.+  params:+    r: '3'+  number: '1.443268791270373107628127607386911604676011966654571598409233793623784837874189050037590075664743962'+- comment: A root of $P_{3}$, with minimal polynomial $x^{3} - x^{2} - 1$. This is+    the supergolden ratio. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,4]}[$\Delta(2,4,\infty)$].+  params:+    r: '4'+  number: '1.465571231876768026656731225219939108025577568472285701643183111249262996685017840478125801194909270'+- comment: A root of $Q_{4}$, with minimal polynomial $x^{6} - x^{5} - x^{4} + x^{2}+    - 1$.+  params:+    r: '5'+  number: '1.501594803539087366377783127371046108486398336253585342248394186063343612597128898134114246029200202'+- comment: A root of $P_{4}$, with minimal polynomial $x^{5} - x^{3} - x^{2} - x -+    1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,5]}[$\Delta(2,5,\infty)$].+  params:+    r: '6'+  number: '1.534157744914266915435970076109375701882545038516595135368531863008063023214082281436789664835483494'+- comment: A root of $Q_{5}$, with minimal polynomial $x^{7} - x^{6} - x^{5} + x^{2}+    - 1$.+  params:+    r: '7'+  number: '1.545215649732755243252550624105116119691470055364233123560610725498211588166533120504318279380159156'+- comment: The root in $(1,\varphi)$ of $E$, with minimal polynomial $x^{6} - 2x^{5}+    + x^{4} - x^{2} + x - 1$.+  params:+    r: '8'+  number: '1.561752067720297294702995364060723780790847286947276642846284783946252241043942944496244054750817375'+- comment: A root of $P_{5}$, with minimal polynomial $x^{5} - x^{4} - x^{2} - 1$.+    It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,6]}[$\Delta(2,6,\infty)$].+  params:+    r: '9'+  number: '1.570147312196054362910665435137126553873131607424527436931654877897330661544162320222760040702620119'+- comment: A root of $Q_{6}$, with minimal polynomial $x^{8} - x^{7} - x^{6} + x^{2}+    - 1$.+  params:+    r: '10'+  number: '1.573678968393516988774251418629321467812704061507913408937274370051211297448790471881548837806219190'+- comment: A root of $P_{6}$, with minimal polynomial $x^{7} - x^{5} - x^{4} - x^{3}+    - x^{2} - x - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,7]}[$\Delta(2,7,\infty)$].+  params:+    r: '11'+  number: '1.590005373901363925162015541663808196898573270019121975693623393697501137164006258637372010170673034'+- comment: A root of $Q_{7}$, with minimal polynomial $x^{9} - x^{8} - x^{7} + x^{2}+    - 1$.+  params:+    r: '12'+  number: '1.591184305667102506280378163106102721323455556070427118636105671632990046340380662184687387274732566'+- comment: A root of $P_{7}$, with minimal polynomial $x^{7} - x^{6} - x^{4} - x^{2}+    - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,8]}[$\Delta(2,8,\infty)$].+  params:+    r: '13'+  number: '1.601347333787636724232618164313101117665668726676556628193381197227260290102478499805029985176068445'+- comment: A root of $Q_{8}$, with minimal polynomial $x^{10} - x^{9} - x^{8} + x^{2}+    - 1$.+  params:+    r: '14'+  number: '1.601755861696983255736192654219002170232459847383645956556081860539331501794067175848485666834280654'+- comment: A root of $P_{8}$, with minimal polynomial $x^{9} - x^{7} - x^{6} - x^{5}+    - x^{4} - x^{3} - x^{2} - x - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,9]}[$\Delta(2,9,\infty)$].+  params:+    r: '15'+  number: '1.607982727928201149922420457795797515362209291893843383821724387553882342235678008938055023076222152'+- comment: A root of $Q_{9}$, with minimal polynomial $x^{11} - x^{10} - x^{9} + x^{2}+    - 1$.+  params:+    r: '16'+  number: '1.608128385187386959402200323538480539244506229939808475627654880454135115549049193244125291977586775'+- comment: A root of $P_{9}$, with minimal polynomial $x^{9} - x^{8} - x^{6} - x^{4}+    - x^{2} - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,10]}[$\Delta(2,10,\infty)$].+  params:+    r: '17'+  number: '1.611930396564119819833599200722692620452821331844328319226299635293730595602174524805609485749220372'+- comment: A root of $Q_{10}$, with minimal polynomial $x^{12} - x^{11} - x^{10} ++    x^{2} - 1$.+  params:+    r: '18'+  number: '1.611983421246492155859040049756323314852853437636639613720385059950750148002686762196644934656348672'+- comment: A root of $P_{10}$, with minimal polynomial $x^{11} - x^{9} - x^{8} - x^{7}+    - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,11]}[$\Delta(2,11,\infty)$].+  params:+    r: '19'+  number: '1.614306823257148514569632339911304106948171748039112819042361616990015585866967144509566552856428042'+- comment: A root of $Q_{11}$, with minimal polynomial $x^{13} - x^{12} - x^{11} ++    x^{2} - 1$.+  params:+    r: '20'+  number: '1.614326414939127104073078356579636391949011342705773229044712283319374524946453994526083157310377742'+- comment: A root of $P_{11}$, with minimal polynomial $x^{11} - x^{10} - x^{8} -+    x^{6} - x^{4} - x^{2} - 1$. It is the growth rate of HREF{Growth_rates_of_hyperbolic_Coxeter_triangle_groups#[inf,12]}[$\Delta(2,12,\infty)$].+  params:+    r: '21'+  number: '1.615749202755210610743641798789103362281243911263783155770251095174096083205827141199474172669686514'+- comment: A root of $Q_{12}$, with minimal polynomial $x^{14} - x^{13} - x^{12} ++    x^{2} - 1$.+  params:+    r: '22'+  number: '1.615756517540843375529686781971131464046866598458441577197107007695607669818877612432159677719427740'+- comment: A root of $P_{12}$, with minimal polynomial $x^{13} - x^{11} - x^{10} -+    x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.+  params:+    r: '23'+  number: '1.616629684394572703598804670579966020060105074535041910104107096102528067389296930735657559212555402'+- comment: A root of $Q_{13}$, with minimal polynomial $x^{15} - x^{14} - x^{13} ++    x^{2} - 1$.+  params:+    r: '24'+  number: '1.616632435387905008141467676752220700831348754409358539038135095071601155042700459931124659244537941'+- comment: A root of $P_{13}$, with minimal polynomial $x^{13} - x^{12} - x^{10} -+    x^{8} - x^{6} - x^{4} - x^{2} - 1$.+  params:+    r: '25'+  number: '1.617169296355092563480671132600765362456967191135302102729539392961745062210998433921295220014506215'+- comment: A root of $Q_{14}$, with minimal polynomial $x^{16} - x^{15} - x^{14} ++    x^{2} - 1$.+  params:+    r: '26'+  number: '1.617170336172016847605481712611059501452437635469882386057255508606235491186675769348455132093009414'+- comment: A root of $P_{14}$, with minimal polynomial $x^{15} - x^{13} - x^{12} -+    x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2}+    - x - 1$.+  params:+    r: '27'+  number: '1.617500905431324014411963007650991447867821260857169838924218729322581246942327161872141255472644582'+- comment: A root of $Q_{15}$, with minimal polynomial $x^{17} - x^{16} - x^{15} ++    x^{2} - 1$.+  params:+    r: '28'+  number: '1.617501299812909557233137493529053056922071157913856951616026650849537504285172555316810694539178691'+- comment: A root of $P_{15}$, with minimal polynomial $x^{15} - x^{14} - x^{12} -+    x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+  params:+    r: '29'+  number: '1.617705069957556644470177554481987140361426228819198259427878209593425193281904169829510686690774651'+- comment: A root of $Q_{16}$, with minimal polynomial $x^{18} - x^{17} - x^{16} ++    x^{2} - 1$.+  params:+    r: '30'+  number: '1.617705219888455097146323069204504687107702709103938695316495370965365042281749410718148250134450673'+- comment: A root of $P_{16}$, with minimal polynomial $x^{17} - x^{15} - x^{14} -+    x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4}+    - x^{3} - x^{2} - x - 1$.+  params:+    r: '31'+  number: '1.617830928788973863699424746173140971640051423343242480743578861627018039776784999830916329455401512'+- comment: A root of $Q_{17}$, with minimal polynomial $x^{19} - x^{18} - x^{17} ++    x^{2} - 1$.+  params:+    r: '32'+  number: '1.617830985877812298846657162479186429296004329244380834320484689516026034285121093064090212646902933'+- comment: A root of $P_{17}$, with minimal polynomial $x^{17} - x^{16} - x^{14} -+    x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+  params:+    r: '33'+  number: '1.617908581767165011975654251943379527724351187695218752887992225503193582039747807291459082094368585'+- comment: A root of $Q_{18}$, with minimal polynomial $x^{20} - x^{19} - x^{18} ++    x^{2} - 1$.+  params:+    r: '34'+  number: '1.617908603527805385791372655209449553767018177375841206557773359477283053340186177065247280643988320'+- comment: A root of $P_{18}$, with minimal polynomial $x^{19} - x^{17} - x^{16} -+    x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} -+    x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.+  params:+    r: '35'+  number: '1.617956519953564239208622399882582744059606376335285602101209468687677811493689474942744891506041932'+- comment: A root of $Q_{19}$, with minimal polynomial $x^{21} - x^{20} - x^{19} ++    x^{2} - 1$.+  params:+    r: '36'+  number: '1.617956528253976570213724233669342650311982524814136763277345754456220908746937624048581615827138001'+- comment: A root of $P_{19}$, with minimal polynomial $x^{19} - x^{18} - x^{16} -+    x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+  params:+    r: '37'+  number: '1.617986125385249151581179065219836276338293750679622676312918048191078288185448939191521385866321094'+- comment: A root of $Q_{20}$, with minimal polynomial $x^{22} - x^{21} - x^{20} ++    x^{2} - 1$.+  params:+    r: '38'+  number: '1.617986128552861828746775573560971560626559554179903857177524556107337154595403717855874656309277088'+- comment: A root of $P_{20}$, with minimal polynomial $x^{21} - x^{19} - x^{18} -+    x^{17} - x^{16} - x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9}+    - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.+  params:+    r: '39'+  number: '1.618004413617124503253339884205705740949886990727485864190374404055016480918880509307231034414017485'+- comment: A root of $Q_{21}$, with minimal polynomial $x^{23} - x^{22} - x^{21} ++    x^{2} - 1$.+  params:+    r: '40'+  number: '1.618004414826328965224816813048886874741852358452825536420120516315769101498118708366546047544102188'+- comment: A root of $P_{21}$, with minimal polynomial $x^{21} - x^{20} - x^{18} -+    x^{16} - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+  params:+    r: '41'+  number: '1.618015712751258280635900473733667949090056927598243987323992158078160732484712147251547557149689392'+- comment: A root of $Q_{22}$, with minimal polynomial $x^{24} - x^{23} - x^{22} ++    x^{2} - 1$.+  params:+    r: '42'+  number: '1.618015713212954752257255964375369229374123216484787415640736393798376918798139605181967819732712222'+- comment: A root of $P_{22}$, with minimal polynomial $x^{23} - x^{21} - x^{20} -+    x^{19} - x^{18} - x^{17} - x^{16} - x^{15} - x^{14} - x^{13} - x^{12} - x^{11}+    - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x -+    1$.+  params:+    r: '43'+  number: '1.618022694541460339603743229827892343352486377764735927967607280632891128415448447893953664301512573'+- comment: A root of $Q_{23}$, with minimal polynomial $x^{25} - x^{24} - x^{23} ++    x^{2} - 1$.+  params:+    r: '44'+  number: '1.618022694717768294416502444185158998331096020868084111924521311236631268730313972376491207972498484'+- comment: A root of $P_{23}$, with minimal polynomial $x^{23} - x^{22} - x^{20} -+    x^{18} - x^{16} - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+  params:+    r: '45'+  number: '1.618027008938025718553681758942751295768660974229159521330823899915592183362260151838715294021339562'+- comment: A root of $Q_{24}$, with minimal polynomial $x^{26} - x^{25} - x^{24} ++    x^{2} - 1$.+  params:+    r: '46'+  number: '1.618027009005358347427925536092720504146670868386797655664278670383537383085953832521182612767970098'+- comment: A root of $P_{24}$, with minimal polynomial $x^{25} - x^{23} - x^{22} -+    x^{21} - x^{20} - x^{19} - x^{18} - x^{17} - x^{16} - x^{15} - x^{14} - x^{13}+    - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3}+    - x^{2} - x - 1$.+  params:+    r: '47'+  number: '1.618029675146055305698946786118197148936629694393732406286549986112999293588968023123008043461804993'+- comment: A root of $Q_{25}$, with minimal polynomial $x^{27} - x^{26} - x^{25} ++    x^{2} - 1$.+  params:+    r: '48'+  number: '1.618029675171771354015094432833994648403067615748015040807374613270327489817157619418160494014043687'+- comment: A root of $P_{25}$, with minimal polynomial $x^{25} - x^{24} - x^{22} -+    x^{20} - x^{18} - x^{16} - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} -+    x^{2} - 1$.+  params:+    r: '49'+  number: '1.618031322858835939379993750912293610423937558487693101083392560992438305802819245773759782326311482'+- comment: A root of $Q_{26}$, with minimal polynomial $x^{28} - x^{27} - x^{26} ++    x^{2} - 1$.+  params:+    r: '50'+  number: '1.618031322868657922029597723248317005726758817620183761258070106896742787251271592809502788045381653'+- params:+    r: '51'+  number: '1.618032341163605579648903926964992013213279130267502064682574041562690271509451899678934653848486982'+  comment: A root of $P_{26}$, with minimal polynomial $x^{27} - x^{25} - x^{24} -+    x^{23} - x^{22} - x^{21} - x^{20} - x^{19} - x^{18} - x^{17} - x^{16} - x^{15}+    - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} -+    x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.+- params:+    r: '52'+  number: '1.618032341167357077065889192222780195487817567190728533925877968326127861216819008444098812251153325'+  comment: A root of $Q_{27}$, with minimal polynomial $x^{29} - x^{28} - x^{27} ++    x^{2} - 1$.+- params:+    r: '53'+  number: '1.618032970495511780338687616599930589208996178245445628013970733235115263164927424052538696348938110'+  comment: A root of $P_{27}$, with minimal polynomial $x^{27} - x^{26} - x^{24} -+    x^{22} - x^{20} - x^{18} - x^{16} - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} -+    x^{4} - x^{2} - 1$.+- params:+    r: '54'+  number: '1.618032970496944683958594372622324706609889729350103785351949963500471438131217303727853858919894804'+  comment: A root of $Q_{28}$, with minimal polynomial $x^{30} - x^{29} - x^{28} ++    x^{2} - 1$.+- params:+    r: '55'+  number: '1.618033359438026026238901165491703242086464985017968210215095423162683971400228321817036954102863048'+  comment: A root of $P_{28}$, with minimal polynomial $x^{29} - x^{27} - x^{26} -+    x^{25} - x^{24} - x^{23} - x^{22} - x^{21} - x^{20} - x^{19} - x^{18} - x^{17}+    - x^{16} - x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8}+    - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.+- params:+    r: '56'+  number: '1.618033359438573336673250396246203626459581840869958339273054776166026984887408205988724420868884110'+  comment: A root of $Q_{29}$, with minimal polynomial $x^{31} - x^{30} - x^{29} ++    x^{2} - 1$.+- params:+    r: '57'+  number: '1.618033599815336574567100631932552880608568335391982437750809827236041127145973301722064897213120794'+  comment: A root of $P_{29}$, with minimal polynomial $x^{29} - x^{28} - x^{26} -+    x^{24} - x^{22} - x^{20} - x^{18} - x^{16} - x^{14} - x^{12} - x^{10} - x^{8}+    - x^{6} - x^{4} - x^{2} - 1$.+- params:+    r: '58'+  number: '1.618033599815545626086012322254917375874957691369417647049074584787004197809450663427506678804394252'+  comment: A root of $Q_{30}$, with minimal polynomial $x^{32} - x^{31} - x^{30} ++    x^{2} - 1$.+- params:+    r: '59'+  number: '1.618033748375738728063757479429073476875277793245441539038578830560588828285930877271489710587575927'+  comment: A root of $P_{30}$, with minimal polynomial $x^{31} - x^{29} - x^{28} -+    x^{27} - x^{26} - x^{25} - x^{24} - x^{23} - x^{22} - x^{21} - x^{20} - x^{19}+    - x^{18} - x^{17} - x^{16} - x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10}+    - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.+- params:+    r: '60'+  number: '1.618033748375818578034781444715890397100131095987045983757988370269097379795341674587381629088467488'+  comment: A root of $Q_{31}$, with minimal polynomial $x^{33} - x^{32} - x^{31} ++    x^{2} - 1$.+- params:+    r: '61'+  number: '1.618033840190741707941604430175133749350573967093245095758996733010298160727195647031278557280865402'+  comment: A root of $P_{31}$, with minimal polynomial $x^{31} - x^{30} - x^{28} -+    x^{26} - x^{24} - x^{22} - x^{20} - x^{18} - x^{16} - x^{14} - x^{12} - x^{10}+    - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+- params:+    r: '62'+  number: '1.618033840190772207768806359894125977128245225291216184439199781542680087108527631920216250435083937'+  comment: A root of $Q_{32}$, with minimal polynomial $x^{34} - x^{33} - x^{32} ++    x^{2} - 1$.+- params:+    r: '63'+  number: '1.618033896935385806005075010892848497468544878080385320807371408703642480600559510651605294301488646'+  comment: A root of $P_{32}$, with minimal polynomial $x^{33} - x^{31} - x^{30} -+    x^{29} - x^{28} - x^{27} - x^{26} - x^{25} - x^{24} - x^{23} - x^{22} - x^{21}+    - x^{20} - x^{19} - x^{18} - x^{17} - x^{16} - x^{15} - x^{14} - x^{13} - x^{12}+    - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2}+    - x - 1$.+- params:+    r: '64'+  number: '1.618033896935397455866315731334333523030485855870201521350548603175221775481807433193019461838877597'+  comment: A root of $Q_{33}$, with minimal polynomial $x^{35} - x^{34} - x^{33} ++    x^{2} - 1$.+- params:+    r: '65'+  number: '1.618033932005445856718849527159699357061247578236291468094541319022086440629526703792222680229254975'+  comment: A root of $P_{33}$, with minimal polynomial $x^{33} - x^{32} - x^{30} -+    x^{28} - x^{26} - x^{24} - x^{22} - x^{20} - x^{18} - x^{16} - x^{14} - x^{12}+    - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+- params:+    r: '66'+  number: '1.618033932005450306561068039609331972320887882266570704364548928079413753979856803952415697269285063'+  comment: A root of $Q_{34}$, with minimal polynomial $x^{36} - x^{35} - x^{34} ++    x^{2} - 1$.+- params:+    r: '67'+  number: '1.618033953679911781204659054112901327706912927903258572681967179883618897198505908203606095952587995'+  comment: A root of $P_{34}$, with minimal polynomial $x^{35} - x^{33} - x^{32} -+    x^{31} - x^{30} - x^{29} - x^{28} - x^{27} - x^{26} - x^{25} - x^{24} - x^{23}+    - x^{22} - x^{21} - x^{20} - x^{19} - x^{18} - x^{17} - x^{16} - x^{15} - x^{14}+    - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} -+    x^{4} - x^{3} - x^{2} - x - 1$.+- params:+    r: '68'+  number: '1.618033953679913480890993605302364766746072201143781966660388875616136647727956872540428361222662863'+  comment: A root of $Q_{35}$, with minimal polynomial $x^{37} - x^{36} - x^{35} ++    x^{2} - 1$.+- params:+    r: '69'+  number: '1.618033967075459268399127022246199518343981850399448564212910512812007121990987833866902842256579496'+  comment: A root of $P_{35}$, with minimal polynomial $x^{35} - x^{34} - x^{32} -+    x^{30} - x^{28} - x^{26} - x^{24} - x^{22} - x^{20} - x^{18} - x^{16} - x^{14}+    - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+- params:+    r: '70'+  number: '1.618033967075459917621013327690153278861354496592865079073234665376206020469112492741119365891927508'+  comment: A root of $Q_{36}$, with minimal polynomial $x^{38} - x^{37} - x^{36} ++    x^{2} - 1$.+- params:+    r: '71'+  number: '1.618033975354359310516292063083806439836116958073550728097699983857318505921306092060792140507284612'+  comment: A root of $P_{36}$, with minimal polynomial $x^{37} - x^{35} - x^{34} -+    x^{33} - x^{32} - x^{31} - x^{30} - x^{29} - x^{28} - x^{27} - x^{26} - x^{25}+    - x^{24} - x^{23} - x^{22} - x^{21} - x^{20} - x^{19} - x^{18} - x^{17} - x^{16}+    - x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7}+    - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.+- params:+    r: '72'+  number: '1.618033975354359558496859055597654471874124132146971613679444727538843318112721992952031807351259171'+  comment: A root of $Q_{37}$, with minimal polynomial $x^{39} - x^{38} - x^{37} ++    x^{2} - 1$.+- params:+    r: '73'+  number: '1.618033980470999507470063682523934060354736726182357616417617300460265088628911677060779065075629550'+  comment: A root of $P_{37}$, with minimal polynomial $x^{37} - x^{36} - x^{34} -+    x^{32} - x^{30} - x^{28} - x^{26} - x^{24} - x^{22} - x^{20} - x^{18} - x^{16}+    - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+- params:+    r: '74'+  number: '1.618033980470999602190180765712365012153208665287157984545383021640954988152388716701594216151111797'+  comment: A root of $Q_{38}$, with minimal polynomial $x^{40} - x^{39} - x^{38} ++    x^{2} - 1$.+- params:+    r: '75'+  number: '1.618033983633256499378468705112305917526639513398821651309315804743089977306817600610105435980118153'+  comment: A root of $P_{38}$, with minimal polynomial $x^{39} - x^{37} - x^{36} -+    x^{35} - x^{34} - x^{33} - x^{32} - x^{31} - x^{30} - x^{29} - x^{28} - x^{27}+    - x^{26} - x^{25} - x^{24} - x^{23} - x^{22} - x^{21} - x^{20} - x^{19} - x^{18}+    - x^{17} - x^{16} - x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9}+    - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1$.+- params:+    r: '76'+  number: '1.618033983633256535558326492090225455042348556575736721109974400639838819754475866391279579998441504'+  comment: A root of $Q_{39}$, with minimal polynomial $x^{41} - x^{40} - x^{39} ++    x^{2} - 1$.+- params:+    r: '77'+  number: '1.618033985587638582217684769585676076875498487327003805728840284453978706065673687543925706953304938'+  comment: A root of $P_{39}$, with minimal polynomial $x^{39} - x^{38} - x^{36} -+    x^{34} - x^{32} - x^{30} - x^{28} - x^{26} - x^{24} - x^{22} - x^{20} - x^{18}+    - x^{16} - x^{14} - x^{12} - x^{10} - x^{8} - x^{6} - x^{4} - x^{2} - 1$.+- params:+    r: '78'+  number: '1.618033985587638596037158910664826353779888507037442444226853378161231125074096695799307510089400812'+  comment: A root of $Q_{40}$, with minimal polynomial $x^{42} - x^{41} - x^{40} ++    x^{2} - 1$.+- params:+    r: '79'+  number: '1.618033986795513050281884574333095015899117245081282455987875605265561399710086506315603741611847492'+  comment: A root of $P_{40}$, with minimal polynomial $x^{41} - x^{39} - x^{38} -+    x^{37} - x^{36} - x^{35} - x^{34} - x^{33} - x^{32} - x^{31} - x^{30} - x^{29}+    - x^{28} - x^{27} - x^{26} - x^{25} - x^{24} - x^{23} - x^{22} - x^{21} - x^{20}+    - x^{19} - x^{18} - x^{17} - x^{16} - x^{15} - x^{14} - x^{13} - x^{12} - x^{11}+    - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x -+    1$.