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lfunc_lfunctions • Show schema
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{'Lhash': '1656893773634809759256235478241', 'a10': 2, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 2, 'a6': 1, 'a7': 4, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.24561290125763, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [19, [1, 1]], [53, [1, -1]]], 'bad_primes': [2, 3, 19, 53], 'central_character': '6042.1', 'coefficient_field': '1.1.1.1', 'conductor': 6042, 'conductor_radical': 6042, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, -2, 5], [1, -4, 7], [1, 0, 11], [1, -4, 13], [1, 6, 17], [1, 1], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 4, 37], [1, -10, 41], [1, 4, 43], [1, 8, 47], [1, -1], [1, 14, 59], [1, 4, 61], [1, -4, 67], [1, 0, 71], [1, 10, 73], [1, -12, 79], [1, 6, 83], [1, 0, 89], [1, -18, 97], [1, -14, 101], [1, -12, 103], [1, 10, 107], [1, 6, 109], [1, -12, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, -2, 5], 1]], [[[1, -4, 7], 1]], [[[1, 0, 11], 1]], [[[1, -4, 13], 1]], [[[1, 6, 17], 1]], [[[1, 1], 1]], [[[1, 0, 23], 1]], [[[1, -6, 29], 1]], [[[1, -4, 31], 1]], [[[1, 4, 37], 1]], [[[1, -10, 41], 1]], [[[1, 4, 43], 1]], [[[1, 8, 47], 1]], [[[1, -1], 1]], [[[1, 14, 59], 1]], [[[1, 4, 61], 1]], [[[1, -4, 67], 1]], [[[1, 0, 71], 1]], [[[1, 10, 73], 1]], [[[1, -12, 79], 1]], [[[1, 6, 83], 1]], [[[1, 0, 89], 1]], [[[1, -18, 97], 1]], [[[1, -14, 101], 1]], [[[1, -12, 103], 1]], [[[1, 10, 107], 1]], [[[1, 6, 109], 1]], [[[1, -12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 105, 'label': '2-6042-1.1-c1-0-105', 'leading_term': '6.07906131965946438808339265115000000000000000000000000000000000000000000000000000000000000', '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/6042/2/a/m', 'plot_delta': {'__RealLiteral__': 0, 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4.212618774788108, 4.1300962965073715, 3.907108932936843, 3.5593793623328702, 3.109098152344099, 2.583440798557495, 2.0127996756486324, 1.428848463520453, 0.8625667002915829, 0.3423536992370281, -0.10764596806610317, -0.4688984117192502, -0.7294331081992546], 'positive_zeros': ['1.30705872212461425047618725822778', '1.95507177782677035128785949567042', '2.67057526604608401220782403835898', '3.73565787993472093859065600672741', '4.60923037696084761578448190558688', '4.92731636918462634620034174462525', '6.08418025981844902591785628570248', '6.37155307349173285287549425146137', '7.38787382526592493864916637259755', '8.140290228630297279944580099509848'], 'prelabel': '2-6042-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.945906197268837, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1160526036017081099, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30705872212461425047618725823', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95507177782677035128785949567', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67057526604608401220782403836', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.24561290125763, 'bad_primes': [2, 3, 19, 53], 'central_character': '1.1', 'conductor': 6042, 'conductor_radical': 6042, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 2, 1, 4, 1, 1, 2, 0, 1, 4, 4, 2, 1, -6, 1, -1, 2, 4, 0, 0, 1, -1, 4, 1, 4, 6, 2, 4, 1, 0, -6, 8, 1, -4, -1, 4, 2, 10, 4, -4, 0, 2, 0, -8, 1, 9, -1, -6, 4, 1, 1, 0, 4, -1, 6, -14, 2, -4, 4, 4, 1, 8, 0, 4, -6, 0, 8, 0, 1, -10, -4, -1, -1, 0, 4, 12, 2, 1, 10, -6, 4, -12, -4, 6, 0, 0, 2, 16, 0, 4, -8, -2, 1, 18, 9, 0, -1], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 6, 17], 'euler19': [1, 1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 4, 37], 'euler41': [1, -10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, -1, 0], 'euler59': [1, 14, 59], 'euler61': [1, 4, 61], 'euler67': [1, -4, 67], 'euler7': [1, -4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, -12, 79], 'euler83': [1, 6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, -2, 5], [1, -4, 7], [1, 0, 11], [1, -4, 13], [1, 6, 17], [1, 1, 0], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 4, 37], [1, -10, 41], [1, 4, 43], [1, 8, 47], [1, -1, 0], [1, 14, 59], [1, 4, 61], [1, -4, 67], [1, 0, 71], [1, 10, 73], [1, -12, 79], [1, 6, 83], [1, 0, 89], [1, -18, 97]], 'index': 105, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6042/m', 'ModularForm/GL2/Q/holomorphic/6042/2/a/m/1/1', 'ModularForm/GL2/Q/holomorphic/6042/2/a/m'], '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': '2-6042-1.1-c1-0-105', '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': '2-6042-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.945906197268837, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1160526036017081099, 'z1': {'__RealLiteral__': 0, 'data': '1.30705872212461425047618725823', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21728785
{'Lhash': '1656893773634809759256235478241', 'Lhash_array': ['1656893773634809759256235478241'], 'label': '2-6042-1.1-c1-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6042/2/a/m'}
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id: 24573158
{'Lhash': '1656893773634809759256235478241', 'Lhash_array': ['1656893773634809759256235478241'], 'label': '2-6042-1.1-c1-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6042/2/a/m/1/1'}
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id: 26579
{'Lhash': '1160526036017081099', 'Lhash_array': ['1160526036017081099'], 'label': '2-6042-1.1-c1-0-105', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6042/m'}