Database - lfunc_search ((description not yet updated on this server))

Formats: - HTML - YAML - JSON - 2026-01-16T13:34:47.029044

Query: /api/lfunc_search/?_offset=0

Column	Type
algebraic	boolean
analytic_conductor	double precision
bad_primes	bigint[]
central_character	text
conductor	numeric
conductor_radical	bigint
degree	smallint
dirichlet_coefficients	numeric[]
euler11	numeric[]
euler13	numeric[]
euler17	numeric[]
euler19	numeric[]
euler2	numeric[]
euler23	numeric[]
euler29	numeric[]
euler3	numeric[]
euler31	numeric[]
euler37	numeric[]
euler41	numeric[]
euler43	numeric[]
euler47	numeric[]
euler5	numeric[]
euler53	numeric[]
euler59	numeric[]
euler61	numeric[]
euler67	numeric[]
euler7	numeric[]
euler71	numeric[]
euler73	numeric[]
euler79	numeric[]
euler83	numeric[]
euler89	numeric[]
euler97	numeric[]
euler_factors	numeric[]
index	smallint
instance_types	text[]
instance_urls	text[]
is_instance_Artin	boolean
is_instance_BMF	boolean
is_instance_CMF	boolean
is_instance_DIR	boolean
is_instance_ECNF	boolean
is_instance_ECQ	boolean
is_instance_G2Q	boolean
is_instance_HMF	boolean
is_instance_MaassGL3	boolean
is_instance_MaassGL4	boolean
is_instance_MaassGSp4	boolean
is_instance_NF	boolean
label	text
motivic_weight	smallint
mu_imag	numeric[]
mu_real	smallint[]
nu_imag	numeric[]
nu_real_doubled	smallint[]
order_of_vanishing	smallint
prelabel	text
primitive	boolean
rational	boolean
root_analytic_conductor	double precision
root_angle	double precision
self_dual	boolean
spectral_label	text
trace_hash	bigint
z1	numeric

{'algebraic': True, 'analytic_conductor': 2418357088276.116, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 7958661109946400884391936, 'conductor_radical': 6, 'degree': 16, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 448, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, -32, 0, 0, 0], 'euler11': [1, 0, 52, 0, -27254, 0, 35152, 0, 643533619, 0, 514660432, 0, -5842136942774, 0, 163198275589492, 0, 45949729863572161], 'euler13': [1, -64, 1938, -43904, 917585, -16846464, 268626994, -4033038784, 55966394628, -681583554496, 7672255575634, -81314664053376, 748502273628785, -6052539226138496, 45151688967368178, -251992088684754496, 665416609183179841], 'euler17': [1, 0, -512, 0, 128638, 0, -58916864, 0, 25894244995, 0, -4920795398144, 0, 897347485695358, 0, -298302585461637632, 0, 48661191875666868481], 'euler19': [1, 112, 7944, 400400, 16089308, 528707760, 14707418296, 348648157648, 7138764394758, 125861984910928, 1916685459753016, 24873522360736560, 273253776704065628, 2454878929623520400, 17582573717061582984, 89488748807683021552, 288441413567621167681], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 1684, 0, 1567210, 0, 1193895376, 0, 737562909139, 0, 334100875915216, 0, 122729759242236010, 0, 36904227543522220564, 0, 6132610415680998648961], 'euler29': [1, 0, 1312, 0, -68879, 0, 492867232, 0, 1487178071104, 0, 348595628716192, 0, -34456472678340719, 0, 464204995565575381792, 0, 250246473680347348787521], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -32, -3204, 53312, 8574986, -87214176, -12763164176, 20448364576, 15388943890707, 19650878357536, -11787050142983696, -77402902235381856, 7313528705582050826, 43696023235520462912, -2523671559258513434244, -24222205927065482250272, 727423121747185263828481], 'euler37': [1, 152, 14148, 1052752, 68338346, 3769954920, 182604066832, 7959720375080, 312882643370547, 10896857193484520, 342229420497927952, 9672672898983482280, 240037036239944354666, 5062246815231635370448, 93135604978624819155588, 1369833316991241261552728, 12337511914217166362274241], 'euler41': [1, 0, 4960, 0, 12861886, 0, 30197432320, 0, 60317717755075, 0, 85330726549995520, 0, 102701198015478182206, 0, 111914911889816282961760, 0, 63759030914653054346432641], 'euler43': [1, 88, -612, -155056, 6344810, 266203080, -20166568208, 132194144104, 71582839745139, 244426972448296, -68945483556078608, 1682766313441990920, 74159410003325600810, -3350990001568602512944, -24455294047924696757412, 6501911446284188331359512, 136614025729312093462315201], 'euler47': [1, 0, 8260, 0, 41411338, 0, 140889994000, 0, 362371697595283, 0, 687498226811914000, 0, 986057240165076446218, 0, 959741650479915256270660, 0, 566977372488557307219621121], 'euler5': [1, 0, 64, 0, 2065, 0, 49984, 0, 1174336, 0, 31240000, 0, 806640625, 0, 15625000000, 0, 152587890625], 'euler53': [1, 0, -6848, 0, 28121284, 0, -110179081280, 0, 376751411527750, 0, -869365947437295680, 0, 1750822435809959507524, 0, -3364140976350060706981568, 0, 3876269050118516845397872321], 'euler59': [1, 0, 1828, 0, -16689686, 0, -7683910256, 0, 213930160568755, 0, -93108714463554416, 0, -2450553898858709733206, 0, 3252372880541865806458468, 0, 21559177407076402401757871041], 'euler61': [1, -52, -13194, 351832, 131454881, -2133191736, -767693888666, 2175520494836, 3512763180412452, 8095111761284756, -10629367519141138106, -109902836822511480696, 25200862016887327178561, 250976863296175311275032, -35021480366882351772887274, -513595291734788540945846932, 36751693856637464631913392961], 'euler67': [1, 40, -15012, -343120, 146205866, 1862629560, -987833506832, -2912835891560, 5195460731156019, -13075720317212840, -19905952524025958672, 168490456577756315640, 59369476451777461456106, -625452107497800388380880, -122838976196348451454149732, 1469289006515875828877373160, 164890958756244164895763202881], 'euler7': [1, -8, 60, 656, -9142, 84264, -22928, -3086840, 44494227, -151255160, -55050128, 9913575336, -52701810742, 185303763344, 830477232060, -5425784582792, 33232930569601], 'euler71': [1, 0, -19304, 0, 191621980, 0, -1440891465176, 0, 8449903601075014, 0, -36615474268675120856, 0, 123740570249304589426780, 0, -316772515625330218135388264, 0, 416997623116370028124580469121], 'euler73': [1, -448, 129468, -26219648, 4214691146, -548015119680, 59898502370032, -5523589779319360, 436661615161596627, -29435209933992869440, 1701012105843239913712, -82933444131446537267520, 3398980208908329560506826, -112682236490535225904487552, 2965082356483000814863200828, -54676166289806471725815543232, 650377879817809571042122834561], 'euler79': [1, -104, -7620, 1016912, 13779338, -111024888, -562743135632, -16933055910680, 7180317096164307, -105679201938553880, -21918890715060386192, -26988757523424006648, 20904755074480252436618, 9628403567736232440863312, -450277314061357048766580420, -38354172516262552690371621224, 2301619141096101839813550846721], 'euler83': [1, 0, 16612, 0, 139485994, 0, 690326743696, 0, 3275935507518835, 0, 32761748197209494416, 0, 314163220778392880091754, 0, 1775656808554638598701594532, 0, 5072820298953863752478356399681], 'euler89': [1, 0, -14912, 0, 265282174, 0, -2499062712320, 0, 25841601881865475, 0, -156796794970495109120, 0, 1044306836520711644004094, 0, -3683120897965189036206105152, 0, 15496731425178936435099327730561], 'euler97': [1, 32, -23172, -593984, 238397450, 2180081760, -3321338271248, 6152381421536, 43362628095714579, 57887756795232224, -294035689111368412688, 1815947074536342995040, 1868424183443801841149450, -43801813258955706787889216, -16077715188986289342836690052, 208907608787394436632833304608, 61425365346268570446197767595521], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 64, 0, 2065, 0, 49984, 0, 1174336, 0, 31240000, 0, 806640625, 0, 15625000000, 0, 152587890625], [1, -8, 60, 656, -9142, 84264, -22928, -3086840, 44494227, -151255160, -55050128, 9913575336, -52701810742, 185303763344, 830477232060, -5425784582792, 33232930569601], [1, 0, 52, 0, -27254, 0, 35152, 0, 643533619, 0, 514660432, 0, -5842136942774, 0, 163198275589492, 0, 45949729863572161], [1, -64, 1938, -43904, 917585, -16846464, 268626994, -4033038784, 55966394628, -681583554496, 7672255575634, -81314664053376, 748502273628785, -6052539226138496, 45151688967368178, -251992088684754496, 665416609183179841], [1, 0, -512, 0, 128638, 0, -58916864, 0, 25894244995, 0, -4920795398144, 0, 897347485695358, 0, -298302585461637632, 0, 48661191875666868481], [1, 112, 7944, 400400, 16089308, 528707760, 14707418296, 348648157648, 7138764394758, 125861984910928, 1916685459753016, 24873522360736560, 273253776704065628, 2454878929623520400, 17582573717061582984, 89488748807683021552, 288441413567621167681], [1, 0, 1684, 0, 1567210, 0, 1193895376, 0, 737562909139, 0, 334100875915216, 0, 122729759242236010, 0, 36904227543522220564, 0, 6132610415680998648961], [1, 0, 1312, 0, -68879, 0, 492867232, 0, 1487178071104, 0, 348595628716192, 0, -34456472678340719, 0, 464204995565575381792, 0, 250246473680347348787521], [1, -32, -3204, 53312, 8574986, -87214176, -12763164176, 20448364576, 15388943890707, 19650878357536, -11787050142983696, -77402902235381856, 7313528705582050826, 43696023235520462912, -2523671559258513434244, -24222205927065482250272, 727423121747185263828481], [1, 152, 14148, 1052752, 68338346, 3769954920, 182604066832, 7959720375080, 312882643370547, 10896857193484520, 342229420497927952, 9672672898983482280, 240037036239944354666, 5062246815231635370448, 93135604978624819155588, 1369833316991241261552728, 12337511914217166362274241], [1, 0, 4960, 0, 12861886, 0, 30197432320, 0, 60317717755075, 0, 85330726549995520, 0, 102701198015478182206, 0, 111914911889816282961760, 0, 63759030914653054346432641], [1, 88, -612, -155056, 6344810, 266203080, -20166568208, 132194144104, 71582839745139, 244426972448296, -68945483556078608, 1682766313441990920, 74159410003325600810, -3350990001568602512944, -24455294047924696757412, 6501911446284188331359512, 136614025729312093462315201], [1, 0, 8260, 0, 41411338, 0, 140889994000, 0, 362371697595283, 0, 687498226811914000, 0, 986057240165076446218, 0, 959741650479915256270660, 0, 566977372488557307219621121], [1, 0, -6848, 0, 28121284, 0, -110179081280, 0, 376751411527750, 0, -869365947437295680, 0, 1750822435809959507524, 0, -3364140976350060706981568, 0, 3876269050118516845397872321], [1, 0, 1828, 0, -16689686, 0, -7683910256, 0, 213930160568755, 0, -93108714463554416, 0, -2450553898858709733206, 0, 3252372880541865806458468, 0, 21559177407076402401757871041], [1, -52, -13194, 351832, 131454881, -2133191736, -767693888666, 2175520494836, 3512763180412452, 8095111761284756, -10629367519141138106, -109902836822511480696, 25200862016887327178561, 250976863296175311275032, -35021480366882351772887274, -513595291734788540945846932, 36751693856637464631913392961], [1, 40, -15012, -343120, 146205866, 1862629560, -987833506832, -2912835891560, 5195460731156019, -13075720317212840, -19905952524025958672, 168490456577756315640, 59369476451777461456106, -625452107497800388380880, -122838976196348451454149732, 1469289006515875828877373160, 164890958756244164895763202881], [1, 0, -19304, 0, 191621980, 0, -1440891465176, 0, 8449903601075014, 0, -36615474268675120856, 0, 123740570249304589426780, 0, -316772515625330218135388264, 0, 416997623116370028124580469121], [1, -448, 129468, -26219648, 4214691146, -548015119680, 59898502370032, -5523589779319360, 436661615161596627, -29435209933992869440, 1701012105843239913712, -82933444131446537267520, 3398980208908329560506826, -112682236490535225904487552, 2965082356483000814863200828, -54676166289806471725815543232, 650377879817809571042122834561], [1, -104, -7620, 1016912, 13779338, -111024888, -562743135632, -16933055910680, 7180317096164307, -105679201938553880, -21918890715060386192, -26988757523424006648, 20904755074480252436618, 9628403567736232440863312, -450277314061357048766580420, -38354172516262552690371621224, 2301619141096101839813550846721], [1, 0, 16612, 0, 139485994, 0, 690326743696, 0, 3275935507518835, 0, 32761748197209494416, 0, 314163220778392880091754, 0, 1775656808554638598701594532, 0, 5072820298953863752478356399681], [1, 0, -14912, 0, 265282174, 0, -2499062712320, 0, 25841601881865475, 0, -156796794970495109120, 0, 1044306836520711644004094, 0, -3683120897965189036206105152, 0, 15496731425178936435099327730561], [1, 32, -23172, -593984, 238397450, 2180081760, -3321338271248, 6152381421536, 43362628095714579, 57887756795232224, -294035689111368412688, 1815947074536342995040, 1868424183443801841149450, -43801813258955706787889216, -16077715188986289342836690052, 208907608787394436632833304608, 61425365346268570446197767595521]], 'id': 24082583, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/3/q/o'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '16-6e32-1.1-c2e8-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2, 2, 2, 2, 2, 2, 2], 'order_of_vanishing': 0, 'prelabel': '16-6e32-1.1-c2e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.942511443917839, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e8-0', 'trace_hash': 1144538024019762091, 'z1': {'__RealLiteral__': 0, 'data': '0.083029602682387342443116617774', 'prec': 107}}