Database - lfunc_search (L-function search data)

Formats: - HTML - YAML - JSON - 2026-09-20T23:40:38.413948

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': 2226357.2115213773, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 31640625, 'conductor_radical': 15, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 483, 0, 0, 0, 0, -13122, 0, -43024, 0, 0, 0, 0, 171781, 0, 0, 191792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5356424, 0, 21564864, 0, 0, 0, 0, -6337926, 0, 0, 0, 0, 52120744, 0, 0, -20780592, 0, 0, 0, 0, 7424284, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70989328, 0, 682994680, 0, 0, 179877411, 0, 0, 0, 0, 0, 0, 420572128, 0, 0, 0, 0, 92635536, 0, 0, 49510080, 0, 129140163, 0, 0, 0, 0, 0, 0, 0, 855278232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 564560928, 0], 'euler11': [1, 43024, 4044688652, 178502658449680, 16509733561749262486, 420899931328784595688880, 22488134463940355161357853612, 564044390095093004112452271001904, 30912680532870672635673352936887453361], 'euler13': [1, 0, -11151625772, 0, 246868355942517834678, 0, -1254060614366196031063292120588, 0, 12646218552730347184269489080961456410641], 'euler17': [1, 0, -400705004220, 0, 67511869470103011115718, 0, -5635148314712014130248060807057980, 0, 197770344305988984840145602058543169130838081], 'euler19': [1, -191792, 1268962427692, -182695476176498864, 610942436481653327660854, -58953582602032559888768823056, 132133695223172748492251694705832972, -6444329141236166304710360365345204579088, 10842505080063916320800450434338728415281531281], 'euler2': [1, 0, -483, 0, 61508, 0, -126615552, 0, 68719476736], 'euler23': [1, 0, -6185762667356, 0, 15851881101052295455362918, 0, -20067547585699025447829495831091054364, 0, 10524515126174167358877236351104092889324551536161], 'euler29': [1, -5356424, 37968635575820, -160184148995322542168, 866124419995113021056454838, -2323814832495493736916204262943992, 7990775934337940432150846425221552807020, -16353883157265620915855179706613993251228405416, 44292268542362921407825091617016319887724139383235921], 'euler3': [1, 0, 13122, 0, 43046721, 0, 0, 0, 0], 'euler31': [1, -21564864, 254850222557308, -2064497451235571351232, 12347646845481228616684126854, -54584532562336809468073798877796672, 178153970636248442714133883952831390671228, -398577204764553058444094011802885013602612042304, 488675963633769261467693849486036510107332864779998081], 'euler37': [1, 0, -235813135792844, 0, 37371150435232687489468450518, 0, -3982896552778805889176620450235209370692076, 0, 285273917723723876056171083405292782327767461712708093041], 'euler41': [1, -52120744, 2065621356540668, -53195532026610365036632, 1139616718795982383496643641254, -17415256175987605762874011026484579352, 221391088777731614623623502587382300001380028, -1828835898107429636612625582382785539540867589154664, 11487323243342943712727117998313670374759563626306467569441], 'euler43': [1, 0, -1449556389870860, 0, 1016670024360586874658808664598, 0, -366156978058584970764701898239773898139348140, 0, 63806423321775344604618774305037646254726223988233042609201], 'euler47': [1, 0, 233226346198980, 0, 418619072057497767331102830278, 0, 292105040667276510081220373479703295334385220, 0, 1568638556854706336108974223356857608957236560013645822451521], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -13159896059574156, 0, 65072427675497224048098239341718, 0, -143290735515997529396410722100216156507615037484, 0, 118558120445975157028044470669508269904542112710719750776396721], 'euler59': [1, -70989328, 16035884965131212, -1139449896462896576716816, 226506156406626298549248087243094, -9871049688624876212003806199333822754224, 1203453021661553533548351900869055198395650319852, -46152728315235192780172053925507373431719297862567261232, 5632126739027588519658984775872141857619309476789431335641625841], 'euler61': [1, -682994680, 220728044320630156, -43539511830751876444250920, 5710657544716858847883713743624246, -509157412159492913280218952954488546659720, 30185233908369957895122166004068411789025577459436, -1092252044157261372555537222146855565540080983432116024280, 18701397461209715023927088008788055619800417991632621566284510161], 'euler67': [1, 0, -66154849722487660, 0, 2527045331512629901591074648156918, 0, -48967522984454816994135103899827618273036679636940, 0, 547889398733702676213614311297941818478464344374520135510515030481], 'euler7': [1, 0, -7424284, 0, -2147813645596122, 0, -12089805020348979943516, 0, 2651730845859653471779023381601], 'euler71': [1, -420572128, 227319041975789468, -57785730276952203518951776, 16640326266655569406958396273042470, -2649389096118945026142332753441693602929056, 477843952472885551817558167790438788351413699862748, -40533667750552423294362961149354095398390600564779616041248, 4418761423445010359012517479030513507821439762288727229544623559521], 'euler73': [1, 0, -206940304125633116, 0, 17597742390708973668609061878850278, 0, -717226892595370854711194543260340788034284763743004, 0, 12012211336350227316446820100278887925603925639507433655692782073761], 'euler79': [1, -49510080, 86794200964738876, -8067285836171064224026560, 30732511063671069753869766173367366, -966877082713073587327941062617217798552640, 1246747059480165396455078392971892137510701217544636, -85236398847178930452899197156367101069654907205533336550720, 206336132715709669990485567530001552309415935666586885734738159549121], 'euler83': [1, 0, -621372529743013292, 0, 162462101194788535173454682320806198, 0, -21714893933436412477191642048339091243008430439820428, 0, 1221268978022589508833760255513684608154133797863046939086649799003281], 'euler89': [1, -855278232, 1586931818873564732, -900081731054504366840214504, 866485961269122574969667875121239014, -315349398335064058526107841735230939967271336, 194795261258449516102649135164900736738339676031418492, -36782191250578301274131213705909156475708187610598596446826328, 15067466661578195724088403821109198918255739721817916514744422568289761], 'euler97': [1, 0, -1275322199616361340, 0, 1254577702924112297485729333539372678, 0, -737074075417444168539769500519938421926009040760539260, 0, 334027661875095082935878165689897695724025886105865253311336914562753921], 'euler_factors': [[1, 0, -483, 0, 61508, 0, -126615552, 0, 68719476736], [1, 0, 13122, 0, 43046721, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -7424284, 0, -2147813645596122, 0, -12089805020348979943516, 0, 2651730845859653471779023381601], [1, 43024, 4044688652, 178502658449680, 16509733561749262486, 420899931328784595688880, 22488134463940355161357853612, 564044390095093004112452271001904, 30912680532870672635673352936887453361], [1, 0, -11151625772, 0, 246868355942517834678, 0, -1254060614366196031063292120588, 0, 12646218552730347184269489080961456410641], [1, 0, -400705004220, 0, 67511869470103011115718, 0, -5635148314712014130248060807057980, 0, 197770344305988984840145602058543169130838081], [1, -191792, 1268962427692, -182695476176498864, 610942436481653327660854, -58953582602032559888768823056, 132133695223172748492251694705832972, -6444329141236166304710360365345204579088, 10842505080063916320800450434338728415281531281], [1, 0, -6185762667356, 0, 15851881101052295455362918, 0, -20067547585699025447829495831091054364, 0, 10524515126174167358877236351104092889324551536161], [1, -5356424, 37968635575820, -160184148995322542168, 866124419995113021056454838, -2323814832495493736916204262943992, 7990775934337940432150846425221552807020, -16353883157265620915855179706613993251228405416, 44292268542362921407825091617016319887724139383235921], [1, -21564864, 254850222557308, -2064497451235571351232, 12347646845481228616684126854, -54584532562336809468073798877796672, 178153970636248442714133883952831390671228, -398577204764553058444094011802885013602612042304, 488675963633769261467693849486036510107332864779998081], [1, 0, -235813135792844, 0, 37371150435232687489468450518, 0, -3982896552778805889176620450235209370692076, 0, 285273917723723876056171083405292782327767461712708093041], [1, -52120744, 2065621356540668, -53195532026610365036632, 1139616718795982383496643641254, -17415256175987605762874011026484579352, 221391088777731614623623502587382300001380028, -1828835898107429636612625582382785539540867589154664, 11487323243342943712727117998313670374759563626306467569441], [1, 0, -1449556389870860, 0, 1016670024360586874658808664598, 0, -366156978058584970764701898239773898139348140, 0, 63806423321775344604618774305037646254726223988233042609201], [1, 0, 233226346198980, 0, 418619072057497767331102830278, 0, 292105040667276510081220373479703295334385220, 0, 1568638556854706336108974223356857608957236560013645822451521], [1, 0, -13159896059574156, 0, 65072427675497224048098239341718, 0, -143290735515997529396410722100216156507615037484, 0, 118558120445975157028044470669508269904542112710719750776396721], [1, -70989328, 16035884965131212, -1139449896462896576716816, 226506156406626298549248087243094, -9871049688624876212003806199333822754224, 1203453021661553533548351900869055198395650319852, -46152728315235192780172053925507373431719297862567261232, 5632126739027588519658984775872141857619309476789431335641625841], [1, -682994680, 220728044320630156, -43539511830751876444250920, 5710657544716858847883713743624246, -509157412159492913280218952954488546659720, 30185233908369957895122166004068411789025577459436, -1092252044157261372555537222146855565540080983432116024280, 18701397461209715023927088008788055619800417991632621566284510161], [1, 0, -66154849722487660, 0, 2527045331512629901591074648156918, 0, -48967522984454816994135103899827618273036679636940, 0, 547889398733702676213614311297941818478464344374520135510515030481], [1, -420572128, 227319041975789468, -57785730276952203518951776, 16640326266655569406958396273042470, -2649389096118945026142332753441693602929056, 477843952472885551817558167790438788351413699862748, -40533667750552423294362961149354095398390600564779616041248, 4418761423445010359012517479030513507821439762288727229544623559521], [1, 0, -206940304125633116, 0, 17597742390708973668609061878850278, 0, -717226892595370854711194543260340788034284763743004, 0, 12012211336350227316446820100278887925603925639507433655692782073761], [1, -49510080, 86794200964738876, -8067285836171064224026560, 30732511063671069753869766173367366, -966877082713073587327941062617217798552640, 1246747059480165396455078392971892137510701217544636, -85236398847178930452899197156367101069654907205533336550720, 206336132715709669990485567530001552309415935666586885734738159549121], [1, 0, -621372529743013292, 0, 162462101194788535173454682320806198, 0, -21714893933436412477191642048339091243008430439820428, 0, 1221268978022589508833760255513684608154133797863046939086649799003281], [1, -855278232, 1586931818873564732, -900081731054504366840214504, 866485961269122574969667875121239014, -315349398335064058526107841735230939967271336, 194795261258449516102649135164900736738339676031418492, -36782191250578301274131213705909156475708187610598596446826328, 15067466661578195724088403821109198918255739721817916514744422568289761], [1, 0, -1275322199616361340, 0, 1254577702924112297485729333539372678, 0, -737074075417444168539769500519938421926009040760539260, 0, 334027661875095082935878165689897695724025886105865253311336914562753921]], 'id': 22904355, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/10/b/f'], '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': '8-75e4-1.1-c9e4-0-4', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [9, 9, 9, 9], 'order_of_vanishing': 0, 'prelabel': '8-75e4-1.1-c9e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.215117674854636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9e4-0', 'trace_hash': 1855143199109001184, 'z1': {'__RealLiteral__': 0, 'data': '0.34921553033541188286077896033554', 'prec': 107}}