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lfunc_lfunctions • Show schema
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{'Lhash': '1645833238830159147471074796541,1980318954420475299954136122156', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 10, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': -20, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11786.036661172473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -10, 25]], [23, [1, -46, 529]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': '1.1.1.1', 'conductor': 3385600, 'conductor_radical': 230, 'degree': 4, 'euler_factors': [[1], [1, -3, 29, -81, 729], [1, -10, 25], [1, 1, 5, 343, 117649], [1, -27, 2163, -35937, 1771561], [1, 15, 4205, 32955, 4826809], [1, 79, 10051, 388127, 24137569], [1, -71, 10373, -486989, 47045881], [1, -46, 529], [1, 430, 92278, 10487270, 594823321], [1, -305, 74963, -9086255, 887503681], [1, 68, 81098, 3444404, 2565726409], [1, 593, 222457, 40870153, 4750104241], [1, 648, 262246, 51520536, 6321363049], [1, 382, 94906, 39660386, 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'data': '1.29833349862638906188854664506', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56219620301046376305950213672', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.21306781400563819729366918334', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 11786.036661172473, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 3385600, 'conductor_radical': 230, 'degree': 4, 'dirichlet_coefficients': [1, 0, 3, 0, 10, 0, -1, 0, -20, 0, 27, 0, -15, 0, 30, 0, -79, 0, 71, 0, -3, 0, 46, 0, 75, 0, -66, 0, -430, 0, 305, 0, 81, 0, -10, 0, -68, 0, -45, 0, -593, 0, -648, 0, -200, 0, -382, 0, -4, 0, -237, 0, -464, 0, 270, 0, 213, 0, 18, 0, -7, 0, 20, 0, -150, 0, -60, 0, 138, 0, 1029, 0, 74, 0, 225, 0, -27, 0, -692, 0, -104, 0, 1460, 0, -790, 0, -1290, 0, -220, 0, 15, 0, 915, 0, 710, 0, 1339, 0, -540, 0], 'euler11': [1, -27, 2163, -35937, 1771561], 'euler13': [1, 15, 4205, 32955, 4826809], 'euler17': [1, 79, 10051, 388127, 24137569], 'euler19': [1, -71, 10373, -486989, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -46, 529, 0, 0], 'euler29': [1, 430, 92278, 10487270, 594823321], 'euler3': [1, -3, 29, -81, 729], 'euler31': [1, -305, 74963, -9086255, 887503681], 'euler37': [1, 68, 81098, 3444404, 2565726409], 'euler41': [1, 593, 222457, 40870153, 4750104241], 'euler43': [1, 648, 262246, 51520536, 6321363049], 'euler47': [1, 382, 94906, 39660386, 10779215329], 'euler5': [1, -10, 25, 0, 0], 'euler53': [1, 464, 298822, 69078928, 22164361129], 'euler59': [1, -18, 331378, -3696822, 42180533641], 'euler61': [1, 7, 365439, 1588867, 51520374361], 'euler67': [1, 60, 445030, 18045780, 90458382169], 'euler7': [1, 1, 5, 343, 117649], 'euler71': [1, -1029, 724137, -368290419, 128100283921], 'euler73': [1, -74, 674654, -28787258, 151334226289], 'euler79': [1, 692, 299630, 341182988, 243087455521], 'euler83': [1, -1460, 1111418, -834809020, 326940373369], 'euler89': [1, 220, 539138, 155093180, 496981290961], 'euler97': [1, -1339, 1150631, -1222069147, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, -3, 29, -81, 729], [1, -10, 25, 0, 0], [1, 1, 5, 343, 117649], [1, -27, 2163, -35937, 1771561], [1, 15, 4205, 32955, 4826809], [1, 79, 10051, 388127, 24137569], [1, -71, 10373, -486989, 47045881], [1, -46, 529, 0, 0], [1, 430, 92278, 10487270, 594823321], [1, -305, 74963, -9086255, 887503681], [1, 68, 81098, 3444404, 2565726409], [1, 593, 222457, 40870153, 4750104241], [1, 648, 262246, 51520536, 6321363049], [1, 382, 94906, 39660386, 10779215329], [1, 464, 298822, 69078928, 22164361129], [1, -18, 331378, -3696822, 42180533641], [1, 7, 365439, 1588867, 51520374361], [1, 60, 445030, 18045780, 90458382169], [1, -1029, 724137, -368290419, 128100283921], [1, -74, 674654, -28787258, 151334226289], [1, 692, 299630, 341182988, 243087455521], [1, -1460, 1111418, -834809020, 326940373369], [1, 220, 539138, 155093180, 496981290961], [1, -1339, 1150631, -1222069147, 832972004929]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/4/a/h'], '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': '4-1840e2-1.1-c3e2-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-1840e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.41938167122036, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 952089375614075862, 'z1': {'__RealLiteral__': 0, 'data': '1.29833349862638906188854664506', 'prec': 103}}
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{'Lhash': '1645833238830159147471074796541,1980318954420475299954136122156', 'Lhash_array': ['1645833238830159147471074796541', '1980318954420475299954136122156'], 'label': '4-1840e2-1.1-c3e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/4/a/h'}