back to table · edit · history · where entries came from · files · download
31105 bytes, as of the version from 2026-11-09 18:56 (current). Recorded here, not run.
{
"Title": "$q$-expansion of the modular discriminant $\\Delta$",
"Definition": "This list contains the coefficients of the modular discrimiant $\\Delta$ CITE{Wiki} in its $q$-expansion, $\\Delta = \\sum_{n=0}^{\\infty} \\tau(n) q^n$. The coefficients are the values of the Ramanujan tau-function.",
"Parameters": {
"n": {
"type": "Z",
"constraints": "$n \\geq 0$"
}
},
"Comments": {
"comment-normalization": "Note that different authors use different normalization factors for $\\Delta$ CITE{Wiki}, CITE{WikiTau}. Here, we use the normalization that makes $\\Delta$ a normalized cusp form (of weight 12 and level 1)."
},
"Formulas": {},
"Programs": {
"program-sage": {
"language": "Sage",
"code": "numbers = {n: delta_qexp(101)[n] for n in [0..100]}"
}
},
"References": {},
"Links": {
"Wiki": {
"title": "Wikipedia: Modular discriminant",
"url": "https://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions#Modular_discriminant"
},
"WikiTau": {
"title": "Wikipedia: Ramanujan tau function",
"url": "https://en.wikipedia.org/wiki/Ramanujan_tau_function"
}
},
"Similar tables": "",
"Keywords": "",
"Tags": [
"Taylor series",
"modular function",
"elliptic curves",
"number theory"
],
"Data properties": {
"type": "Z",
"complete": "no",
"rigour": "exact",
"rigour details": "Exact integer values, without numerical rounding."
},
"Display properties": {
"number-header": "$\\tau(n)$"
},
"Numbers": {
"0": "0",
"1": "1",
"2": "-24",
"3": "252",
"4": "-1472",
"5": "4830",
"6": "-6048",
"7": "-16744",
"8": "84480",
"9": "-113643",
"10": "-115920",
"11": "534612",
"12": "-370944",
"13": "-577738",
"14": "401856",
"15": "1217160",
"16": "987136",
"17": "-6905934",
"18": "2727432",
"19": "10661420",
"20": "-7109760",
"21": "-4219488",
"22": "-12830688",
"23": "18643272",
"24": "21288960",
"25": "-25499225",
"26": "13865712",
"27": "-73279080",
"28": "24647168",
"29": "128406630",
"30": "-29211840",
"31": "-52843168",
"32": "-196706304",
"33": "134722224",
"34": "165742416",
"35": "-80873520",
"36": "167282496",
"37": "-182213314",
"38": "-255874080",
"39": "-145589976",
"40": "408038400",
"41": "308120442",
"42": "101267712",
"43": "-17125708",
"44": "-786948864",
"45": "-548895690",
"46": "-447438528",
"47": "2687348496",
"48": "248758272",
"49": "-1696965207",
"50": "611981400",
"51": "-1740295368",
"52": "850430336",
"53": "-1596055698",
"54": "1758697920",
"55": "2582175960",
"56": "-1414533120",
"57": "2686677840",
"58": "-3081759120",
"59": "-5189203740",
"60": "-1791659520",
"61": "6956478662",
"62": "1268236032",
"63": "1902838392",
"64": "2699296768",
"65": "-2790474540",
"66": "-3233333376",
"67": "-15481826884",
"68": "10165534848",
"69": "4698104544",
"70": "1940964480",
"71": "9791485272",
"72": "-9600560640",
"73": "1463791322",
"74": "4373119536",
"75": "-6425804700",
"76": "-15693610240",
"77": "-8951543328",
"78": "3494159424",
"79": "38116845680",
"80": "4767866880",
"81": "1665188361",
"82": "-7394890608",
"83": "-29335099668",
"84": "6211086336",
"85": "-33355661220",
"86": "411016992",
"87": "32358470760",
"88": "45164021760",
"89": "-24992917110",
"90": "13173496560",
"91": "9673645072",
"92": "-27442896384",
"93": "-13316478336",
"94": "-64496363904",
"95": "51494658600",
"96": "-49569988608",
"97": "75013568546",
"98": "40727164968",
"99": "-60754911516",
"100": "37534859200",
"101": "81742959102",
"102": "41767088832",
"103": "-225755128648",
"104": "-48807306240",
"105": "-20380127040",
"106": "38305336752",
"107": "90241258356",
"108": "107866805760",
"109": "73482676310",
"110": "-61972223040",
"111": "-45917755128",
"112": "-16528605184",
"113": "-85146862638",
"114": "-64480268160",
"115": "90047003760",
"116": "-189014559360",
"117": "65655879534",
"118": "124540889760",
"119": "115632958896",
"120": "102825676800",
"121": "498319933",
"122": "-166955487888",
"123": "77646351384",
"124": "77785143296",
"125": "-359001100500",
"126": "-45668121408",
"127": "-262717201024",
"128": "338071388160",
"129": "-4315678416",
"130": "66971388960",
"131": "631528759932",
"132": "-198311113728",
"133": "-178514816480",
"134": "371563845216",
"135": "-353937956400",
"136": "-583413304320",
"137": "-297198746214",
"138": "-112754509056",
"139": "596793577940",
"140": "119045821440",
"141": "677211820992",
"142": "-234995646528",
"143": "-308865667656",
"144": "-112181096448",
"145": "620204022900",
"146": "-35130991728",
"147": "-427635232164",
"148": "268217998208",
"149": "-1115433620850",
"150": "154219312800",
"151": "-824447297848",
"152": "900676761600",
"153": "784811057562",
"154": "214837039872",
"155": "-255232501440",
"156": "214308444672",
"157": "1315116754406",
"158": "-914804296320",
"159": "-402206035896",
"160": "-950091448320",
"161": "-312162946368",
"162": "-39964520664",
"163": "-357832759588",
"164": "-453553290624",
"165": "650708341920",
"166": "704042392032",
"167": "2754833892216",
"168": "-356462346240",
"169": "-1458379197393",
"170": "800535869280",
"171": "-1211595753060",
"172": "25209042176",
"173": "-950387449578",
"174": "-776603298240",
"175": "426959023400",
"176": "527734751232",
"177": "-1307679342480",
"178": "599830010640",
"179": "1681384224780",
"180": "807974455680",
"181": "-996774496018",
"182": "-232167481728",
"183": "1753032622824",
"184": "1574983618560",
"185": "-880090306620",
"186": "319595480064",
"187": "-3691995187608",
"188": "-3955776986112",
"189": "1226984915520",
"190": "-1235871806400",
"191": "2762403350592",
"192": "680222785536",
"193": "5442387685442",
"194": "-1800325645104",
"195": "-703199584080",
"196": "2497932784704",
"197": "-2876091504354",
"198": "1458117876384",
"199": "728391402200",
"200": "-2154174528000",
"201": "-3901420374768",
"202": "-1961831018448",
"203": "-2150040612720",
"204": "2561714781696",
"205": "1488221734860",
"206": "5418123087552",
"207": "-2118677359896",
"208": "-570305978368",
"209": "5699723069040",
"210": "489123048960",
"211": "-6793168439188",
"212": "2349393987456",
"213": "2467454288544",
"214": "-2165790200544",
"215": "-82717169640",
"216": "-6190616678400",
"217": "884806004992",
"218": "-1763584231440",
"219": "368875413144",
"220": "-3800963013120",
"221": "3989820497292",
"222": "1102026123072",
"223": "7334863021472",
"224": "3293650354176",
"225": "2897808426675",
"226": "2043524703312",
"227": "-1359839565924",
"228": "-3954789780480",
"229": "-11824411223170",
"230": "-2161128090240",
"231": "-2255788918656",
"232": "10847792102400",
"233": "-17563353448518",
"234": "-1575741108816",
"235": "12979893235680",
"236": "7638507905280",
"237": "9605445111360",
"238": "-2775191013504",
"239": "-7139577462960",
"240": "1201502453760",
"241": "-231306909358",
"242": "-11959678392",
"243": "13400796651732",
"244": "-10239936590464",
"245": "-8196341949810",
"246": "-1863512433216",
"247": "-6159507467960",
"248": "-4464190832640",
"249": "-7392445116336",
"250": "8616026412000",
"251": "12983053545252",
"252": "-2800978113024",
"253": "9966916930464",
"254": "6305212824576",
"255": "-8405626627440",
"256": "-13641873096704",
"257": "23961192565506",
"258": "103576281984",
"259": "3050979729616",
"260": "4107578522880",
"261": "-14592514653090",
"262": "-15156690238368",
"263": "-24273728464488",
"264": "11381333483520",
"265": "-7708949021340",
"266": "4284355595520",
"267": "-6298215111720",
"268": "22789249173248",
"269": "25837706543670",
"270": "8494510953600",
"271": "-3767932360528",
"272": "-6817096065024",
"273": "2437758558144",
"274": "7132769909136",
"275": "-13632191675700",
"276": "-6915609888768",
"277": "-16418932005874",
"278": "-14323045870560",
"279": "6005256141024",
"280": "-6832194969600",
"281": "21035722907082",
"282": "-16253083703808",
"283": "16713176326532",
"284": "-14413066320384",
"285": "12976653967200",
"286": "7412776023744",
"287": "-5159168680848",
"288": "22354294505472",
"289": "13420028104723",
"290": "-14884896549600",
"291": "18903419273592",
"292": "-2154700825984",
"293": "-23926858987458",
"294": "10263245571936",
"295": "-25063854064200",
"296": "-15393380766720",
"297": "-39175875516960",
"298": "26770406900400",
"299": "-10770926678736",
"300": "9458784518400",
"301": "286752854752",
"302": "19786735148352",
"303": "20599225693704",
"304": "10524271493120",
"305": "33599791937460",
"306": "-18835465381488",
"307": "15311092828556",
"308": "13176671778816",
"309": "-56890292419296",
"310": "6125580034560",
"311": "49875160575912",
"312": "-12299441172480",
"313": "-99480832756438",
"314": "-31562802105744",
"315": "9190709433360",
"316": "-56107996840960",
"317": "83369248359366",
"318": "9652944861504",
"319": "68647725277560",
"320": "13037603389440",
"321": "22740797105712",
"322": "7491910712832",
"323": "-73627062866280",
"324": "-2451157267392",
"325": "14731871253050",
"326": "8587986230112",
"327": "18517634430120",
"328": "26030014940160",
"329": "-44996963217024",
"330": "-15617000206080",
"331": "-63584021925868",
"332": "43181266711296",
"333": "20707267642902",
"334": "-66116013413184",
"335": "-74777223849720",
"336": "-4165208506368",
"337": "121001428335986",
"338": "35001100737432",
"339": "-21457009384776",
"340": "49099533315840",
"341": "-28250591730816",
"342": "29078298073440",
"343": "61522344410800",
"344": "-1446779811840",
"345": "22691844947520",
"346": "22809298789872",
"347": "-155661561078204",
"348": "-47631668958720",
"349": "-25643022194650",
"350": "-10247016561600",
"351": "42336109121040",
"352": "-105161550594048",
"353": "24909815245602",
"354": "31384304219520",
"355": "47292873863760",
"356": "36789573985920",
"357": "29139505641792",
"358": "-40353221394720",
"359": "157584150853560",
"360": "-46370707891200",
"361": "-2824382481819",
"362": "23922587904432",
"363": "125576623116",
"364": "-14239605545984",
"365": "7070112085260",
"366": "-42072782947776",
"367": "-177901220129584",
"368": "18403444948992",
"369": "-35015731390206",
"370": "21122167358880",
"371": "26724356607312",
"372": "19601856110592",
"373": "-55161734023378",
"374": "88607884502592",
"375": "-90468277326000",
"376": "227027200942080",
"377": "-74185389602940",
"378": "-29447637972480",
"379": "146463116322980",
"380": "-75800137459200",
"381": "-66204734658048",
"382": "-66297680414208",
"383": "231449571733632",
"384": "85193989816320",
"385": "-43235954274240",
"386": "-130617304450608",
"387": "1946216834244",
"388": "-110419972899712",
"389": "-149871571611810",
"390": "16876790017920",
"391": "-128749205976048",
"392": "-143359620687360",
"393": "159145247502864",
"394": "69026196104496",
"395": "184104364634400",
"396": "89431229751552",
"397": "208110680273846",
"398": "-17481393652800",
"399": "-44985733752960",
"400": "-25171202969600",
"401": "-133407937691598",
"402": "93634088994432",
"403": "30529506193984",
"404": "-120325635798144",
"405": "8042859783630",
"406": "51600974705280",
"407": "-97413424224168",
"408": "-147020152688640",
"409": "-206167580638390",
"410": "-35717321636640",
"411": "-74894084045928",
"412": "332311549369856",
"413": "86888027422560",
"414": "50848256637504",
"415": "-141688531396440",
"416": "113644706660352",
"417": "150391981640880",
"418": "-136793353656960",
"419": "73403515193820",
"420": "29999547002880",
"421": "171111932338622",
"422": "163036042540512",
"423": "-305398345130928",
"424": "-134834785367040",
"425": "176095964901150",
"426": "-59218902925056",
"427": "-116479278716528",
"428": "-132835132300032",
"429": "-77834148249312",
"430": "1985212071360",
"431": "-71775829446768",
"432": "-72336417914880",
"433": "99881248225682",
"434": "-21235344119808",
"435": "156291413770800",
"436": "-108166499528320",
"437": "198763752966240",
"438": "-8853009915456",
"439": "-29031220908760",
"440": "218142225100800",
"441": "192848217019101",
"442": "-95755691935008",
"443": "328369848718692",
"444": "67590935548416",
"445": "-120715789641300",
"446": "-176036712515328",
"447": "-281089272454200",
"448": "-45197025083392",
"449": "-612368143631550",
"450": "-69547402240200",
"451": "164724885738504",
"452": "125336181803136",
"453": "-207760719057696",
"454": "32636149582176",
"455": "46723705697760",
"456": "226970543923200",
"457": "303483032911706",
"458": "283785869356080",
"459": "506060490060720",
"460": "-132549189534720",
"461": "-729307946668938",
"462": "54138934047744",
"463": "122188164073712",
"464": "126754807111680",
"465": "-64318590362880",
"466": "421520482764432",
"467": "-617380683662484",
"468": "-96645454674048",
"469": "259227709345696",
"470": "-311517437656320",
"471": "331409422110312",
"472": "-438383931955200",
"473": "-9155609005296",
"474": "-230530682672640",
"475": "-271857947399500",
"476": "-170211715494912",
"477": "181380557687814",
"478": "171349859111040",
"479": "1050837984850080",
"480": "-239423044976640",
"481": "105271555603732",
"482": "5551365824592",
"483": "-78665062484736",
"484": "-733526941376",
"485": "362315536077180",
"486": "-321619119641568",
"487": "-219909971761864",
"488": "587683317365760",
"489": "-90173855416176",
"490": "196712206795440",
"491": "-483863128068108",
"492": "-114295429237248",
"493": "-886767711942420",
"494": "147828179231040",
"495": "-293446222622280",
"496": "-52163393486848",
"497": "-163948629394368",
"498": "177418682792064",
"499": "-108877719272500",
"500": "528449619936000",
"501": "694218140838432",
"502": "-311593285086048",
"503": "506588355787752",
"504": "160751787356160",
"505": "394818492462660",
"506": "-239206006331136",
"507": "-367511557743036",
"508": "386719719907328",
"509": "85753393288710",
"510": "201735039058560",
"511": "-24509721895568",
"512": "-364965248630784",
"513": "-781259049093600",
"514": "-575068621572144",
"515": "-1090397271369840",
"516": "6352678628352",
"517": "1436688754143552",
"518": "-73223513510784",
"519": "-239497637293656",
"520": "-235739289139200",
"521": "927574652509722",
"522": "350220351674160",
"523": "-21818651341228",
"524": "-929610334619904",
"525": "107593673896800",
"526": "582569483147712",
"527": "364931430558912",
"528": "132989157310464",
"529": "-605238167047943",
"530": "185014776512160",
"531": "589716680624820",
"532": "262773809858560",
"533": "-178012887920196",
"534": "151157162681280",
"535": "435865277859480",
"536": "-1307904735160320",
"537": "423708824644560",
"538": "-620104957048080",
"539": "-907217963244684",
"540": "520996671820800",
"541": "-1695266465052058",
"542": "90430376652672",
"543": "-251187172996536",
"544": "1358440752807936",
"545": "354921326577300",
"546": "-58506205395456",
"547": "752144751323996",
"548": "437476554427008",
"549": "-790555104585666",
"550": "327172600216800",
"551": "1368997013214600",
"552": "396895871877120",
"553": "-638228464065920",
"554": "394054368140976",
"555": "-221782757268240",
"556": "-878480146727680",
"557": "187489032934806",
"558": "-144126147384576",
"559": "9894172288504",
"560": "-79833163038720",
"561": "-930382787277216",
"562": "-504857349769968",
"563": "244971285916812",
"564": "-996855800500224",
"565": "-411259346541540",
"566": "-401116231836768",
"567": "-27881913916584",
"568": "827184675778560",
"569": "1352425875836970",
"570": "-311439695212800",
"571": "1432228477996772",
"572": "454650262789632",
"573": "696125644349184",
"574": "123820048340352",
"575": "-475388987464200",
"576": "-306756182605824",
"577": "-877659324192574",
"578": "-322080674513352",
"579": "1371481696731384",
"580": "-912940321708800",
"581": "491186908840992",
"582": "-453682062566208",
"583": "-853270528819176",
"584": "123661090882560",
"585": "317117898149220",
"586": "574244615698992",
"587": "-2434250501782764",
"588": "629479061745408",
"589": "-563383208178560",
"590": "601532497540800",
"591": "-724775059097208",
"592": "-179869321928704",
"593": "-303318212278158",
"594": "940221012407040",
"595": "558507191467680",
"596": "1641918289891200",
"597": "183554633354400",
"598": "258502240289664",
"599": "-1701984261329400",
"600": "-542851981056000",
"601": "2339216023326602",
"602": "-6882068514048",
"603": "1759401252578412",
"604": "1213586422432256",
"605": "2406885276390",
"606": "-494381416648896",
"607": "-2496072486898144",
"608": "-2097168523591680",
"609": "-541810234405440",
"610": "-806395006499040",
"611": "-1552583345382048",
"612": "-1155241876731264",
"613": "2473009012516862",
"614": "-367466227885344",
"615": "375031877184720",
"616": "-756226380349440",
"617": "24336777156666",
"618": "1365367018063104",
"619": "4225450805148020",
"620": "375702242119680",
"621": "-1366161820349760",
"622": "-1197003853821888",
"623": "418481404089840",
"624": "-143717106548736",
"625": "-488895969711875",
"626": "2387539986154512",
"627": "1436330213398080",
"628": "-1935851862485632",
"629": "1258353120405276",
"630": "-220577026400640",
"631": "-4263261111420568",
"632": "3220111123046400",
"633": "-1711878446675376",
"634": "-2000861960624784",
"635": "-1268924080945920",
"636": "592047284838912",
"637": "980401284761766",
"638": "-1647545406661440",
"639": "-1112733760765896",
"640": "1632884804812800",
"641": "1008295928583042",
"642": "-545779130537088",
"643": "303982416160892",
"644": "459503857053696",
"645": "-20844726749280",
"646": "1767049508790720",
"647": "3435828424131096",
"648": "140675112737280",
"649": "-2774210589848880",
"650": "-353564910073200",
"651": "222971113257984",
"652": "526729822113536",
"653": "-1185387156769098",
"654": "-444423226322880",
"655": "3050283910471560",
"656": "304156780634112",
"657": "-166349637206046",
"658": "1079927117208576",
"659": "-2265102374509140",
"660": "-957842679306240",
"661": "-5330121520762738",
"662": "1526016526220832",
"663": "1005434765317584",
"664": "-2478229219952640",
"665": "-862226563598400",
"666": "-496974423429648",
"667": "2393919729693360",
"668": "-4055115489341952",
"669": "1848385481410944",
"670": "1794653372393280",
"671": "3719016970449144",
"672": "829999889252352",
"673": "4741198635421922",
"674": "-2904034280063664",
"675": "1868559748713000",
"676": "2146734178562496",
"677": "-1413071638641474",
"678": "514968225234624",
"679": "-1256027191734224",
"680": "-2817886259865600",
"681": "-342679570612848",
"682": "678014201539584",
"683": "-3031157627077068",
"684": "1783468948504320",
"685": "-1435469944213620",
"686": "-1476536265859200",
"687": "-2979751628238840",
"688": "-16905402892288",
"689": "922102026851124",
"690": "-544604278740480",
"691": "-2747313442193908",
"692": "1398970325778816",
"693": "1017280238423904",
"694": "3735877465876896",
"695": "2882512981450200",
"696": "2733643609804800",
"697": "-2127859436502828",
"698": "615432532671600",
"699": "-4425965069026536",
"700": "-628483682444800",
"701": "5727465442629702",
"702": "-1016066618904960",
"703": "-1942652670145880",
"704": "1443076443734016",
"705": "3270933095391360",
"706": "-597835565894448",
"707": "-1368704107203888",
"708": "1924903992130560",
"709": "698326457818910",
"710": "-1135028972730240",
"711": "-4331712693612240",
"712": "-2111401637452800",
"713": "-985169554365696",
"714": "-699348135403008",
"715": "-1491821174778480",
"716": "-2474997578876160",
"717": "-1799173520665920",
"718": "-3782019620485440",
"719": "9709787093595120",
"720": "-541834695843840",
"721": "3780043874082112",
"722": "67785179563656",
"723": "-58289341158216",
"724": "1467252058138496",
"725": "-3274269549861750",
"726": "-3013838954784",
"727": "2464686886685576",
"728": "817229535682560",
"729": "3082017633650397",
"730": "-169682690046240",
"731": "118269009151272",
"732": "-2580464020796928",
"733": "7912852398754982",
"734": "4269629283110016",
"735": "-2065478171352120",
"736": "-3667249129586688",
"737": "-8276770434109008",
"738": "840377553364944",
"739": "-8406936179151460",
"740": "1295492931344640",
"741": "-1552195881925920",
"742": "-641384558575488",
"743": "1362869794471992",
"744": "-1124976089825280",
"745": "-5387544388705500",
"746": "1323881616561072",
"747": "3333728731570524",
"748": "5434616916158976",
"749": "-1510999629912864",
"750": "2171238655824000",
"751": "6817220120892752",
"752": "2652778444947456",
"753": "3271729493403504",
"754": "1780449350470560",
"755": "-3982080448605840",
"756": "-1806121795645440",
"757": "-667048975014994",
"758": "-3515114791751520",
"759": "2511663066476928",
"760": "4350268758528000",
"761": "-7744079729695638",
"762": "1588913631793152",
"763": "-1230393932134640",
"764": "-4066257732071424",
"765": "3790637408024460",
"766": "-5554789721607168",
"767": "2998000190340120",
"768": "-3437752020369408",
"769": "2524111226919170",
"770": "1037662902581760",
"771": "6038220526507512",
"772": "-8011194672970624",
"773": "-11145268112466978",
"774": "-46709204021856",
"775": "1347459830544800",
"776": "6337146270766080",
"777": "768846891863232",
"778": "3596917718683440",
"779": "3285001442747640",
"780": "1035109787765760",
"781": "5234645524234464",
"782": "3089980943425152",
"783": "-9409519712300400",
"784": "-1675135446577152",
"785": "6352013923780980",
"786": "-3819485940068736",
"787": "13227104255899436",
"788": "4233606694409088",
"789": "-6116979573050976",
"790": "-4418504751225600",
"791": "1425699068010672",
"792": "-5132574924871680",
"793": "-4019022069226556",
"794": "-4994656326572304",
"795": "-1942655153377680",
"796": "-1072192144038400",
"797": "2302477758246246",
"798": "1079657610071040",
"799": "-18558651348375264",
"800": "5015858304614400",
"801": "2840270079131730",
"802": "3201790504598352",
"803": "782560406237064",
"804": "5742890791658496",
"805": "-1507747030957440",
"806": "-732708148655616",
"807": "6511102049004840",
"808": "6905645184936960",
"809": "5604717670694010",
"810": "-193028634807120",
"811": "-5085164185024588",
"812": "3164859781923840",
"813": "-949518954853056",
"814": "2337922181380032",
"815": "-1728332228810040",
"816": "-1717908208386048",
"817": "-182584365785360",
"818": "4948021935321360",
"819": "-1099342046917296",
"820": "-2190662393713920",
"821": "279110773799022",
"822": "1797458017102272",
"823": "-13526517861603928",
"824": "-19071793268183040",
"825": "-3435312302276400",
"826": "-2085312658141440",
"827": "272543929352676",
"828": "3118693073766912",
"829": "18045917610367430",
"830": "3400524753514560",
"831": "-4137570865480248",
"832": "-1559486316150784",
"833": "11719129719838338",
"834": "-3609407559381120",
"835": "13305847699403280",
"836": "-8389992357626880",
"837": "3872298735325440",
"838": "-1761684364651680",
"839": "-7961834707368360",
"840": "-1721713132339200",
"841": "4287752862251071",
"842": "-4106686376126928",
"843": "5301002172584664",
"844": "9999543942484736",
"845": "-7043971523408190",
"846": "7329560283142272",
"847": "-8343868958152",
"848": "-1575524037500928",
"849": "4211720434286064",
"850": "-4226303157627600",
"851": "-3397052374923408",
"852": "-3632092712736768",
"853": "-14982644001390898",
"854": "2795502689196672",
"855": "-5852007487279800",
"856": "7623581505914880",
"857": "-22256130175851894",
"858": "1868019557983488",
"859": "5442366024533060",
"860": "121759673710080",
"861": "-1300110507573696",
"862": "1722619906722432",
"863": "10810987426382112",
"864": "14414456987320320",
"865": "-4590371381461740",
"866": "-2397149957416368",
"867": "3381847082390196",
"868": "-1302434439348224",
"869": "20377723102676160",
"870": "-3750993930499200",
"871": "8944439700308392",
"872": "6207816494668800",
"873": "-8524766970273078",
"874": "-4770330071189760",
"875": "6011114426772000",
"876": "-542984608147968",
"877": "-28102437759471274",
"878": "696749301810240",
"879": "-6029568464839416",
"880": "2548958848450560",
"881": "4222089494633682",
"882": "-4628357208458424",
"883": "516091995437132",
"884": "-5873015772013824",
"885": "-6316091224178400",
"886": "-7880876369248608",
"887": "5719060466578536",
"888": "-3879131953213440",
"889": "4398936813945856",
"890": "2897178951391200",
"891": "890229680050932",
"892": "-10796918367606784",
"893": "28650951002224320",
"894": "6746142538900800",
"895": "8121085805687400",
"896": "-5660667323351040",
"897": "-2714273523041472",
"898": "14696835447157200",
"899": "-6785413121403840",
"900": "-4265574004065600",
"901": "11022255310711932",
"902": "-3953397257724096",
"903": "72261719397504",
"904": "-7193206955658240",
"905": "-4814420815766940",
"906": "4986257257384704",
"907": "-84377784300844",
"908": "2001683841040128",
"909": "-9289515101228586",
"910": "-1121368936746240",
"911": "-11009058285505488",
"912": "2652116416266240",
"913": "-15682896303708816",
"914": "-7283592789880944",
"915": "8467147568239920",
"916": "17405533320506240",
"917": "-10574317556301408",
"918": "-12145451761457280",
"919": "-4863513801242680",
"920": "7607170877644800",
"921": "3858395392796112",
"922": "17503390720054512",
"923": "-5656913118074736",
"924": "3320521288261632",
"925": "4646298291681650",
"926": "-2932515937769088",
"927": "25655490084944664",
"928": "-25258393596395520",
"929": "3575343976258530",
"930": "1543646168709120",
"931": "-18092058797213940",
"932": "25853256276218496",
"933": "12568540465129824",
"934": "14817136407899616",
"935": "-17832336756146640",
"936": "5546608703032320",
"937": "38637331724206586",
"938": "-6221465024296704",
"939": "-25069169854622376",
"940": "-19106402842920960",
"941": "-34899727878407658",
"942": "-7953826130647488",
"943": "5744373208966224",
"944": "-5122449823088640",
"945": "5926337141961600",
"946": "219734616127104",
"947": "-28512291118415604",
"948": "-14139215203921920",
"949": "-845687870789636",
"950": "6524590737588000",
"951": "21009050586560232",
"952": "9768672367534080",
"953": "40033434235820202",
"954": "-4353133384507536",
"955": "13342408183359360",
"956": "10509458025477120",
"957": "17299226769945120",
"958": "-25220111636401920",
"959": "4976295806607216",
"960": "3285476054138880",
"961": "-22616076492128607",
"962": "-2526517334489568",
"963": "-10255287323350908",
"964": "340483770574976",
"965": "26286732520684860",
"966": "1887961499633664",
"967": "18495304308397016",
"968": "42098067939840",
"969": "-18554019842302560",
"970": "-8695572865852320",
"971": "-21487665696030828",
"972": "-19725972671349504",
"973": "-9992711669027360",
"974": "5277839322284736",
"975": "3712431555768600",
"976": "6866990520492032",
"977": "-8738799717564174",
"978": "2164172529988224",
"979": "-13361513402011320",
"980": "12065015350120320",
"981": "-8350791783897330",
"982": "11612715073634592",
"983": "11892426157508232",
"984": "6559563764920320",
"985": "-13891521966029820",
"986": "21282425086618080",
"987": "-11339234730690048",
"988": "9066794992837120",
"989": "-319279232436576",
"990": "7042709342934720",
"991": "23440857788319392",
"992": "10394584268931072",
"993": "-16023173525318736",
"994": "3934767105464832",
"995": "3518130472626000",
"996": "10881679211246592",
"997": "-21400415987399554",
"998": "2613065262540000",
"999": "13352424013671120",
"1000": "-30328412970240000"
}
}