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  • lfunc_lfunctions • Show schema
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-1.8413238115492643, -2.3320717348390674, -2.7424945592569756, -3.05353896107018, -3.2508839682607746, -3.3246482632021666, -3.2710328743245305, -3.091415721295252, -2.793542658274644, -2.390012589709208, -1.8988730224491985, -1.3416749938699093, -0.7437106044809134, -0.13140598209167048, 0.46744638134630717, 1.026415418097987], 'positive_zeros': ['0.31068542135626789157765065672942', '1.20447549963689638552495716423285', '1.38824926949537898844379134906594', '2.04072672457927557809682042988663', '2.86879987016955764802847820089465', '3.88761926788114734625837394582438', '4.08442027957201575427829574278854', '4.38853788091406564196720895964876', '5.24290729183518708497856882070554', '6.11879974996111301397018440080155', '6.47733256628916341646336513869695', '7.14237640540903218473166381958829', '7.51898062573216813335713698642623', '8.607713382864770684644181936702806', '8.745507369355611425893436275732622', '9.564958831726811156665950002592059', '9.753766483359357318616796002707319', '10.70206063683238196835383542975205', '10.86711124740368675642674380151684', '12.17353245203254450024984872312435'], 'prelabel': '4-50e2-1.1-c21e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.821111290548409, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21e2-0', 'trace_hash': 2145202568058942348, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31068542135626789157765065673', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.20447549963689638552495716423', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.38824926949537898844379134907', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 19526.896492437263, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 2500, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1048576, 0, 0, 0, 0, 15793573590, 0, 173462359224, 0, 0, 0, 0, 1099511627776, 0, 0, -46064935288840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1468103267042340, 0, -6293328324115136, 0, 0, 0, 0, -16560762220707840, 0, 0, 0, 0, 91429297682952084, 0, 0, -181888466785665024, 0, 0, 0, 0, 389137406452046350, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7560994199956792680, 0, -15239626693659458276, 0, 0, -1152921504606846976, 0, 0, 0, 0, 0, 0, -9052973134907543856, 0, 0, 0, 0, 48302585585430691840, 0, 0, -198672885061850140960, 0, 140017977611233128891, 0, 0, 0, 0, 0, 0, 0, -237605952335473080180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2739590535499259294160, 0], 'euler11': [1, -173462359224, 22322797405405324672966, -1283664814178294943669566679420264, 54763699237492901685126120802225273763666521], 'euler13': [1, 0, 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[1, 46064935288840, 1958913557178000594904649238, 32900014201790287386177137373875569063960, 510095203738582479622335815880298130716653502143703561], [1, 0, -57482173852485474263744529070, 0, 1558005952997140033806173725098810522409738596181909282129], [1, -1468103267042340, 10804517217439463753884463312158, -7535543149390335476284695275869640716225771860, 26346074268992142099064516382762907506814419719803282255713641], [1, 6293328324115136, 51552508135560558055200187373886, 131061749249571898218072521003477165200359914816, 433701716541192355457229753999917360820651622584523552060436161], [1, 0, -1543003328251651193790351597884230, 0, 731934824502651514621160916115101341995441470527191525223322819769], [1, -91429297682952084, 16863587321125983048256808637299446, -675377168292804512472133260422405871921133721806644, 54565982855941191947249368879497196495421462536627690767330656099281], [1, 0, -39587291836490151759737083222910950, 0, 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566044592922467932920289630256783944174352087720184706882390017513705742761841], [1, 0, -2042660489241277980336813015675705157870, 0, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], [1, 198672885061850140960, 24032152627041067302354213983822409865758, 1407043472018306958470687625566142431137685631111548994031840, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], [1, 0, -39955339834227858295563814014879264917110, 0, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], [1, 237605952335473080180, 187183486233083129353779715096137933449878, 20561152566891611105870629431401735190826601214256883229880020, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], [1, 0, -731139692620360939454442675131029829270590, 0, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/22/b/a'], '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': '4-50e2-1.1-c21e2-0-1', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [21, 21], 'order_of_vanishing': 0, 'prelabel': '4-50e2-1.1-c21e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.821111290548409, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21e2-0', 'trace_hash': 2145202568058942348, 'z1': {'__RealLiteral__': 0, 'data': '0.31068542135626789157765065673', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '393840560864433354289035874735,1526854090074908207648114685248', 'Lhash_array': ['393840560864433354289035874735', '1526854090074908207648114685248'], 'factors': ['2-50-5.4-c21-0-8', '2-50-5.4-c21-0-28'], 'label': '4-50e2-1.1-c21e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/22/b/a'}