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lfunc_lfunctions • Show schema
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{'Lhash': '1407459301931185078195016123689', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.659470158300444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [7, [1, -1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '6720.1', 'coefficient_field': '1.1.1.1', 'conductor': 6720, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, -1], [1, -4, 11], [1, -6, 13], [1, -6, 17], [1, 0, 19], [1, -4, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, -4, 43], [1, 4, 47], [1, -6, 53], [1, -12, 59], [1, -10, 61], [1, -4, 67], [1, 8, 71], [1, 14, 73], [1, 8, 79], [1, 12, 83], [1, 6, 89], [1, 14, 97], [1, 2, 101], [1, 0, 103], [1, 20, 107], [1, -2, 109], [1, 10, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, -4, 11], 1]], [[[1, -6, 13], 1]], [[[1, -6, 17], 1]], [[[1, 0, 19], 1]], [[[1, -4, 23], 1]], [[[1, -6, 29], 1]], [[[1, 0, 31], 1]], [[[1, 2, 37], 1]], [[[1, -2, 41], 1]], [[[1, -4, 43], 1]], [[[1, 4, 47], 1]], [[[1, -6, 53], 1]], [[[1, -12, 59], 1]], [[[1, -10, 61], 1]], [[[1, -4, 67], 1]], [[[1, 8, 71], 1]], [[[1, 14, 73], 1]], [[[1, 8, 79], 1]], [[[1, 12, 83], 1]], [[[1, 6, 89], 1]], [[[1, 14, 97], 1]], [[[1, 2, 101], 1]], [[[1, 0, 103], 1]], [[[1, 20, 107], 1]], [[[1, -2, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-6720-1.1-c1-0-57', 'leading_term': '2.74382281135324022548399894206000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6720/2/a/bg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 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1.2543042486162521, 0.7135239888134988, 0.14074227463775468, -0.4306168069930406, -0.9663418740348725, -1.4336835365138525, -1.8035469371249784, -2.052479273239444, -2.1643154397071283, -2.131365787212775, -1.9550590375644243, -1.6459888036788313, -1.223351631798697, -0.7138054031563373], 'positive_zeros': ['1.11028961898316802987075858482188', '1.34596882192917408053705998907500', '2.78961351737865894884063981659269', '3.73545395675063132271356615123500', '4.31091734830001177834627960397957', '5.41982112131558398553821853222286', '5.74360707289160231244110082463167', '6.60524464671489745849137447262924', '7.02618680094950128125366166463344', '8.091814960945815776456264607969087'], 'prelabel': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1396786929471627832, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11028961898316802987075858482', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.34596882192917408053705998908', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.78961351737865894884063981659', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.659470158300444, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 6720, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 6, 0, -1, 0, 6, 0, 0, 0, -1, 0, 4, 0, 1, 0, -1, 0, 6, 0, 0, 0, -4, 0, 1, 0, -2, 0, -6, 0, 2, 0, 4, 0, 1, 0, -4, 0, 1, 0, -6, 0, 6, 0, 4, 0, 0, 0, 12, 0, 10, 0, 1, 0, 6, 0, 4, 0, -4, 0, -8, 0, -14, 0, -1, 0, 4, 0, -8, 0, 1, 0, -12, 0, 6, 0, -6, 0, -6, 0, 6, 0, 0, 0, 0, 0, -14, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -6, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, 14, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -1, 0], [1, -4, 11], [1, -6, 13], [1, -6, 17], [1, 0, 19], [1, -4, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, -4, 43], [1, 4, 47], [1, -6, 53], [1, -12, 59], [1, -10, 61], [1, -4, 67], [1, 8, 71], [1, 14, 73], [1, 8, 79], [1, 12, 83], [1, 6, 89], [1, 14, 97]], 'index': 57, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6720/bg', 'ModularForm/GL2/Q/holomorphic/6720/2/a/bg/1/1', 'ModularForm/GL2/Q/holomorphic/6720/2/a/bg'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-6720-1.1-c1-0-57', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1396786929471627832, 'z1': {'__RealLiteral__': 0, 'data': '1.11028961898316802987075858482', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21704523
{'Lhash': '1407459301931185078195016123689', 'Lhash_array': ['1407459301931185078195016123689'], 'label': '2-6720-1.1-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/bg'}
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id: 24576352
{'Lhash': '1407459301931185078195016123689', 'Lhash_array': ['1407459301931185078195016123689'], 'label': '2-6720-1.1-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/bg/1/1'}
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id: 102738
{'Lhash': '1396786929471627832', 'Lhash_array': ['1396786929471627832'], 'label': '2-6720-1.1-c1-0-57', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6720/bg'}