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  • lfunc_lfunctions • Show schema
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'4.10840656914172198275122457121595', '4.26667838216577478929509573490838', '4.37295117066608871567554175610372', '4.64863388003871234103167066275623', '4.69648518855496177965789033032653', '5.09825589430655363909642751251370', '5.10963416088376515193759381939387', '5.32014967978384418683299392838219', '5.45116032660235916260362165796020', '5.82520055560519167698584789344176', '6.03835507846753314531492757951509', '6.09183383551575865784281724419672', '6.12595048408386719338227348831981', '6.34782146462985185927274692674245', '6.57472559770087285863394524216622', '6.66916328489374909934527829284069', '6.86974555955036521775890010158039', '7.30154871192107893516637613506834', '7.42892889986029071243694209985200', '7.51826664755648076796812754953757', '7.64422522541150567841712381975032', '7.66031533688569428577097904331786', '7.69066969321607573581739248794840', '7.72915346197858723845644383251353', '8.257065013165311266685521909733312', '8.311455487006037228373533695297242', '8.445268185652624774189794314711237', '8.679654147968431029051762360127222', '8.693304939406647064969092670324458', '9.016582168823071839985359932098535', '9.097331557364757832805985247878492', '9.109959738712378489852191146317451', '9.224179999784616445851081105891836', '9.491403231926375014812525892122809'], 'prelabel': '10-1840e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8330763065605153, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e5-0', 'trace_hash': 1402442851322377352, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32957100908932285842405515070', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.73930114888484845428126629533', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.833169813124345125532751451384', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 684659.5181704174, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 21090608742400000, 'conductor_radical': 230, 'degree': 10, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, 2, 0, -1, 0, 1, 0, 4, 0, 0, 0, 4, 0, -7, 0, 0, 0, 5, 0, 15, 0, -1, 0, 4, 0, -19, 0, 0, 0, -10, 0, 15, 0, 0, 0, 25, 0, 0, 0, 5, 0, 11, 0, -3, 0, 0, 0, 3, 0, -5, 0, 0, 0, 1, 0, -5, 0, -2, 0, -20, 0, -9, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, 0, 2, 0, 5, 0, 45, 0, -20, 0, 0, 0, 6, 0, 8, 0, 0, 0, 35, 0, 25, 0, -1, 0], 'euler11': [1, -1, 20, -16, 227, -174, 2497, -1936, 26620, -14641, 161051], 'euler13': [1, -4, 19, -133, 496, -1606, 6448, -22477, 41743, -114244, 371293], 'euler17': [1, -4, 39, -115, 406, -1566, 6902, -33235, 191607, -334084, 1419857], 'euler19': [1, 7, 54, 352, 1949, 7810, 37031, 127072, 370386, 912247, 2476099], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler29': [1, -4, 104, -500, 4907, 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1, 30, -46, 210, 49, 2401, -4802, 16807], 'euler71': [1, 1, 141, -123, 12967, -23580, 920657, -620043, 50465451, 25411681, 1804229351], 'euler73': [1, 1, 207, 20, 20760, -9066, 1515480, 106580, 80526519, 28398241, 2073071593], 'euler79': [1, -2, 267, -760, 34506, -94092, 2725974, -4743160, 131641413, -77900162, 3077056399], 'euler83': [1, -45, 1199, -21528, 290714, -2994854, 24129262, -148306392, 685572613, -2135624445, 3939040643], 'euler89': [1, -6, 309, -1624, 45458, -202212, 4045762, -12863704, 217835421, -376453446, 5584059449], 'euler97': [1, -25, 446, -5536, 65833, -653150, 6385801, -52088224, 407052158, -2213232025, 8587340257], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, -4, -10, -12, 9, 27, 0, 243], [1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0], [1, -2, 7, 1, 30, -46, 210, 49, 2401, -4802, 16807], [1, -1, 20, -16, 227, -174, 2497, -1936, 26620, -14641, 161051], [1, -4, 19, -133, 496, -1606, 6448, -22477, 41743, -114244, 371293], [1, -4, 39, -115, 406, -1566, 6902, -33235, 191607, -334084, 1419857], [1, 7, 54, 352, 1949, 7810, 37031, 127072, 370386, 912247, 2476099], [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], [1, -4, 104, -500, 4907, -22264, 142303, -420500, 2536456, -2829124, 20511149], [1, 19, 227, 2173, 16253, 98336, 503843, 2088253, 6762557, 17546899, 28629151], [1, -15, 249, -2256, 20618, -125810, 762866, -3088464, 12612597, -28112415, 69343957], [1, -25, 417, -4753, 42913, -303514, 1759433, -7989793, 28740057, -70644025, 115856201], [1, 0, 215, 0, 18490, 0, 795070, 0, 17094005, 0, 147008443], [1, -11, 125, -952, 5780, -41402, 271660, -2102968, 12977875, -53676491, 229345007], [1, -3, 105, -196, 8458, -24194, 448274, -550564, 15632085, -23671443, 418195493], [1, -1, 153, 0, 14236, -6606, 839924, 0, 31422987, -12117361, 714924299], [1, 5, 190, 652, 18257, 49998, 1113677, 2426092, 43126390, 69229205, 844596301], [1, 9, 209, 1980, 24396, 176326, 1634532, 8888220, 62859467, 181360089, 1350125107], [1, 1, 141, -123, 12967, -23580, 920657, -620043, 50465451, 25411681, 1804229351], [1, 1, 207, 20, 20760, -9066, 1515480, 106580, 80526519, 28398241, 2073071593], [1, -2, 267, -760, 34506, -94092, 2725974, -4743160, 131641413, -77900162, 3077056399], [1, -45, 1199, -21528, 290714, -2994854, 24129262, -148306392, 685572613, -2135624445, 3939040643], [1, -6, 309, -1624, 45458, -202212, 4045762, -12863704, 217835421, -376453446, 5584059449], [1, -25, 446, -5536, 65833, -653150, 6385801, -52088224, 407052158, -2213232025, 8587340257]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/a/v'], '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': '10-1840e5-1.1-c1e5-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '10-1840e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8330763065605153, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 1402442851322377352, 'z1': {'__RealLiteral__': 0, 'data': '0.32957100908932285842405515070', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '417780887489903369230089254305,937175545133297732714533819121,1056168213699117820783157040317,1392461830804614939058019203066,1854367528360975354634237862255', 'Lhash_array': ['417780887489903369230089254305', '937175545133297732714533819121', '1056168213699117820783157040317', '1392461830804614939058019203066', '1854367528360975354634237862255'], 'factors': ['2-1840-1.1-c1-0-0', '2-1840-1.1-c1-0-6', '2-1840-1.1-c1-0-9', '2-1840-1.1-c1-0-15', '2-1840-1.1-c1-0-29'], 'label': '10-1840e5-1.1-c1e5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/a/v'}