back to table · edit · history · where entries came from · files · download
17453 bytes, as of the version from 2026-10-26 13:28 (current). Recorded here, not run.
{
"table": "T516",
"stored": false,
"root_count": {
"excluded_by_value": 206,
"excluded_by_monotonicity": 9,
"root_segments": 12,
"subdivisions": 0,
"left_endpoint": "-227/16"
},
"versions": {
"sage": "10.9",
"mpmath": "1.4.1",
"numberdb": "0.1.10",
"python": "3.12.3"
},
"seconds": 9.97500281687826,
"results": [
{
"n": 1,
"lo": "-3688201661600530173377637553825668104795504087016613742970804892428509073450046145940056689083649686962821739149990413932196900218873836780742111035503389570347/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-3688201661600530173377637553825668104795504087016613742970804892428509073450046145940056689083649686962821739149990413922196900218873836780742111035503389570347/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-0.73764033232010603467552751076513362095910081740332274859416097848570181469000922918801133781672993739256434782999808278543938004377476735615",
"root_200": "-0.7376403323201060346755275107651336209591008174033227485941609784857018146900092291880113378167299373925643478299980827854393800437747673561484222071006779140694275512345412677791237330421462",
"quadrature_left": "[-4.07208050293866733396215300624292256764067804e-121 +/- 5.68e-166]",
"quadrature_right": "[4.072080502938667333962153006242922567640902417e-121 +/- 9.85e-167]",
"series_left_radius": "1.2008184e-210",
"root_relative_bits": 397,
"ode_radius": "6.3101595e-121"
},
{
"n": 2,
"lo": "-1695415754724194149509952366931994260493900818509213786562390864267904221720038672315834547227819743051240389053294951477906641867606883445201879674240540684059/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-1695415754724194149509952366931994260493900818509213786562390864267904221720038672315834547227819743051240389053294951476906641867606883445201879674240540684059/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-3.3908315094483882990199047338639885209878016370184275731247817285358084434400773446316690944556394861024807781065899029548132837352137668904",
"root_200": "-3.390831509448388299019904733863988520987801637018427573124781728535808443440077344631669094455639486102480778106589902954813283735213766890403759348481081368117941984726223467345869826890529",
"quadrature_left": "[7.6626358907003142097776332846868564574535778675357596047445300281235728992465e-121 +/- 6.55e-198]",
"quadrature_right": "[-7.6626358907003142097776332846868564574526887676976618769927206946897834462375e-121 +/- 5.12e-198]",
"series_left_radius": "4.4866898e-209",
"root_relative_bits": 399,
"ode_radius": "3.7226533e-119"
},
{
"n": 3,
"lo": "-2375800395321608920665248802993242380626267759600028291360762123779261208932012889533167613144213622959354350246614818527665005837255695328956275793486857877103/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-2375800395321608920665248802993242380626267759600028291360762123779261208932012889533167613144213622959354350246614818526665005837255695328956275793486857877103/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-4.7516007906432178413304976059864847612525355192000565827215242475585224178640257790663352262884272459187087004932296370543300116745113906579",
"root_200": "-4.751600790643217841330497605986484761252535519200056582721524247558522417864025779066335226288427245918708700493229637054330011674511390657912551586973715754206085848157065313394171439314124",
"quadrature_left": "[-8.11235508112374055233273027278983450698870888647669438971e-121 +/- 6.00e-178]",
"quadrature_right": "[8.11235508112374055233273027278983450699010174794304219783e-121 +/- 5.13e-178]",
"series_left_radius": "7.3964534e-208",
"root_relative_bits": 400,
"ode_radius": "5.1554930e-118"
},
{
"n": 4,
"lo": "-3113535417281305207155643178139105230105143820032526112299313197082532925772147672029475224814858273848562970938931823682707526721221131833986436555684615000239/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-3113535417281305207155643178139105230105143820032526112299313197082532925772147672029475224814858273848562970938931823681707526721221131833986436555684615000239/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-6.227070834562610414311286356278210460210287640065052224598626394165065851544295344058950449629716547697125941877863647364415053442442263668",
"root_200": "-6.227070834562610414311286356278210460210287640065052224598626394165065851544295344058950449629716547697125941877863647364415053442442263667972873111369230000477867674943832319749065693227919",
"quadrature_left": "[8.88423499613841634255095972406130505883340628901351853951e-121 +/- 7.15e-178]",
"quadrature_right": "[-8.88423499613841634255095972406130505883105507522377676655e-121 +/- 7.57e-178]",
"series_left_radius": "2.4841361e-206",
"root_relative_bits": 400,
"ode_radius": "1.5148833e-116"
},
{
"n": 5,
"lo": "-7330170703258512449120389230804608887478109696622147239847546957904095644603685084119273255680849251800701548704093381723480684908737200927177582976619965728799/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-7330170703258512449120389230804608887478109696622147239847546957904095644603685084119273255680849251800701548704093381721480684908737200927177582976619965728799/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-7.3301707032585124491203892308046088874781096966221472398475469579040956446036850841192732556808492518007015487040933817224806849087372009272",
"root_200": "-7.330170703258512449120389230804608887478109696622147239847546957904095644603685084119273255680849251800701548704093381722480684908737200927177582976619965728799125287600851595887713448165681",
"quadrature_left": "[-9.167660484895023570849306504262510920537731788001e-121 +/- 7.77e-170]",
"quadrature_right": "[9.167660484895023570849306504262510920540028976376e-121 +/- 6.28e-170]",
"series_left_radius": "4.7378349e-205",
"root_relative_bits": 400,
"ode_radius": "2.5617333e-115"
},
{
"n": 6,
"lo": "-266582744331726009910247005828369946202463185661669690012065995289484236741688030842837195215860752322997205738352181601899935009292731422447881944775313056943/31250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-266582744331726009910247005828369946202463185661669690012065995289484236741688030842837195215860752322997205738352181601837435009292731422447881944775313056943/31250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-8.5306478186152323171279041865078382784788219411734300803861118492634955757340169869707902469075440743359105836272698112597979202973674055183",
"root_200": "-8.530647818615232317127904186507838278478821941173430080386111849263495575734016986970790246907544074335910583627269811259797920297367405518332222232810017822176231510053532218314777022943722",
"quadrature_left": "[9.61417861403787518398259951184632602219e-121 +/- 1.25e-160]",
"quadrature_right": "[-9.61417861403787518398259951184632602219e-121 +/- 5.70e-160]",
"series_left_radius": "1.5714703e-203",
"root_relative_bits": 401,
"ode_radius": "7.2338225e-114"
},
{
"n": 7,
"lo": "-9504435473068411469490236915270933444297419747185653608121410242329910376541418002735621698064946481482115154714407550465509243961372779490242088953131953201683/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-9504435473068411469490236915270933444297419747185653608121410242329910376541418002735621698064946481482115154714407550463509243961372779490242088953131953201683/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-9.5044354730684114694902369152709334442974197471856536081214102423299103765414180027356216980649464814821151547144075504645092439613727794902",
"root_200": "-9.504435473068411469490236915270933444297419747185653608121410242329910376541418002735621698064946481482115154714407550464509243961372779490242088953131953201682805881924107129744615273495984",
"quadrature_left": "[-9.8272242326755162854999287081601443103449284075809000453997305e-121 +/- 1.34e-183]",
"quadrature_right": "[9.8272242326755162854999287081601443103411131238620705263370818e-121 +/- 2.76e-183]",
"series_left_radius": "3.0551405e-202",
"root_relative_bits": 401,
"ode_radius": "1.3095507e-112"
},
{
"n": 8,
"lo": "-21119135770211366774093181810205132456322020283978729461376694400285962773193872903539738205620618723775380202576087107054061532138521066952294652878117477597/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-21119135770211366774093181810205132456322020283978729461376694400285962773193872903539738205620618723775380202576087107050061532138521066952294652878117477597/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-10.559567885105683387046590905102566228161010141989364730688347200142981386596936451769869102810309361887690101288043553526030766069260533476",
"root_200": "-10.55956788510568338704659090510256622816101014198936473068834720014298138659693645176986910281030936188769010128804355352603076606926053347614732643905873879849566495821021721172798085241376",
"quadrature_left": "[1.01451450314818148127576529713374618916e-120 +/- 3.10e-159]",
"quadrature_right": "[-1.01451450314818148127576529713374618915e-120 +/- 1.90e-159]",
"series_left_radius": "9.1986767e-201",
"root_relative_bits": 401,
"ode_radius": "3.6031079e-111"
},
{
"n": 9,
"lo": "-286254575680401509804543080827767877405841637848618704793745205055485481273018647638114975559162946163731935051158143587296724876783077825473493567857405788411/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-286254575680401509804543080827767877405841637848618704793745205055485481273018647638114975559162946163731935051158143587246724876783077825473493567857405788411/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-11.450183027216060392181723233110715096233665513944748191749808202219419250920745905524599022366517846549277402046325743490868995071323113019",
"root_200": "-11.45018302721606039218172323311071509623366551394474819174980820221941925092074590552459902236651784654927740204632574349086899507132311301893974271429623153644015688239649072194641858772067",
"quadrature_left": "[-1.0318177763554876882415254814374686962811878503130791302379320504634259703806188857108719e-120 +/- 6.22e-209]",
"quadrature_right": "[1.0318177763554876882415254814374686962815115984040718836056166414664840535390418643941505e-120 +/- 3.79e-209]",
"series_left_radius": "1.8708622e-199",
"root_relative_bits": 401,
"ode_radius": "6.7726189e-110"
},
{
"n": 10,
"lo": "-310266317996383331489583401484371053681048489530153929039003155239690206395192956008250891413890895762557373271037580775543311095508697345384824538700746506991/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-310266317996383331489583401484371053681048489530153929039003155239690206395192956008250891413890895762557373271037580775493311095508697345384824538700746506991/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-12.410652719855333259583336059374842147241939581206157161560126209587608255807718240330035656555635830502294930841503231020732443820347893815",
"root_200": "-12.41065271985533325958333605937484214724193958120615716156012620958760825580771824033003565655563583050229493084150323102073244382034789381539298154802986027963566673098697400059563020159674",
"quadrature_left": "[1.0566769206136751957186851558529240680513708567938703562842702900469330723851038601534602e-120 +/- 5.24e-209]",
"quadrature_right": "[-1.0566769206136751957186851558529240680422131260801204110038667761303259427967896694238141e-120 +/- 7.59e-209]",
"series_left_radius": "5.4221885e-198",
"root_relative_bits": 401,
"ode_radius": "1.8304117e-108"
},
{
"n": 11,
"lo": "-662065392315190089528470300417925736350855570228193027984656934809314811370259703604550383719517028164873521941830138941282075078368688813340108076505223981031/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-662065392315190089528470300417925736350855570228193027984656934809314811370259703604550383719517028164873521941830138941182075078368688813340108076505223981031/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-13.241307846303801790569406008358514727017111404563860559693138696186296227405194072091007674390340563297470438836602778824641501567373776267",
"root_200": "-13.24130784630380179056940600835851472701711140456386055969313869618629622740519407209100767439034056329747043883660277882464150156737377626680216153010447962061651201585501800249082744102213",
"quadrature_left": "[-1.071361730535899160481874584062569173920115298306728458645529786600349197779526589e-120 +/- 5.67e-202]",
"quadrature_right": "[1.071361730535899160481874584062569173912641512847429075754824296111495233026165235e-120 +/- 5.92e-202]",
"series_left_radius": "1.1207216e-196",
"root_relative_bits": 401,
"ode_radius": "3.5263277e-107"
},
{
"n": 12,
"lo": "-88333487697346273592897780401994853506241934656566333905248863304226640236871206230070946723577202975430272912049182358889391131372988487117108487804187887017/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"hi": "-88333487697346273592897780401994853506241934656566333905248863304226640236871206230070946723577202975430272912049182358876891131372988487117108487804187887017/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"root_150": "-14.133358031575403774863644864319176560998709545050613424839818128676262437899392996811351475772352476068843665927869177421302581019678157939",
"root_200": "-14.13335803157540377486364486431917656099870954505061342483981812867626243789939299681135147577235247606884366592786917742130258101967815793873735804867006192272301708183992839224870952532277",
"quadrature_left": "[1.091866164627793638643300765941162396062067199289304821938810346705444385e-120 +/- 2.30e-193]",
"quadrature_right": "[-1.091866164627793638643300765941162396068655698443166382870128493609990217e-120 +/- 5.02e-193]",
"series_left_radius": "3.1818600e-195",
"root_relative_bits": 401,
"ode_radius": "9.4053901e-106"
}
]
}