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lfunc_lfunctions • Show schema
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{'Lhash': '2127256839096676802399932885437', 'a10': 1, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': 1, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.417189285300914, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [11, [1, -1]], [19, [1]]], 'bad_primes': [2, 11, 19], 'central_character': '7942.1', 'coefficient_field': '1.1.1.1', 'conductor': 7942, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[1, -1], [1, 0, 3], [1, -1, 5], [1, -1, 7], [1, -1], [1, -2, 13], [1, 0, 17], [1], [1, 6, 23], [1, 8, 29], [1, 10, 31], [1, -3, 37], [1, 2, 41], [1, 8, 43], [1, 0, 47], [1, 9, 53], [1, 14, 59], [1, 0, 61], [1, -12, 67], [1, -6, 71], [1, 0, 73], [1, 11, 79], [1, -7, 83], [1, -14, 89], [1, -5, 97], [1, -10, 101], [1, -6, 103], [1, -17, 107], [1, 10, 109], [1, -2, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 0, 3], 1]], [[[1, -1, 5], 1]], [[[1, -1, 7], 1]], [[[1, -1], 1]], [[[1, -2, 13], 1]], [[[1, 0, 17], 1]], [1], [[[1, 6, 23], 1]], [[[1, 8, 29], 1]], [[[1, 10, 31], 1]], [[[1, -3, 37], 1]], [[[1, 2, 41], 1]], [[[1, 8, 43], 1]], [[[1, 0, 47], 1]], [[[1, 9, 53], 1]], [[[1, 14, 59], 1]], [[[1, 0, 61], 1]], [[[1, -12, 67], 1]], [[[1, -6, 71], 1]], [[[1, 0, 73], 1]], [[[1, 11, 79], 1]], [[[1, -7, 83], 1]], [[[1, -14, 89], 1]], [[[1, -5, 97], 1]], [[[1, -10, 101], 1]], [[[1, -6, 103], 1]], [[[1, -17, 107], 1]], [[[1, 10, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 266, 'label': '2-7942-1.1-c1-0-266', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7942/2/a/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.9538080193675362e-60, 0.3149416860615887, 0.6286598418711166, 0.9398730035533523, 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-1.2229608250892985, -1.216225325532322, -1.1193007102980905, -0.9312015473704001, -0.6567884657048951, -0.30650654321785875, 0.10421047661721723, 0.5558351998614914, 1.025888242842177], 'positive_zeros': ['1.67810975572739271941692074389440', '2.12806283124924986483236126760477', '3.36857783406782692186037950897124', '3.73942835194518482871803641713997', '4.77861108362039441534578245416312', '5.46993281780218697839606870386914', '6.03092320142382643620453181466516', '6.48810927836385473795738443819920', '7.60364628165673185320754092627781'], 'prelabel': '2-7942-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 488434453343869178, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67810975572739271941692074389', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12806283124924986483236126760', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36857783406782692186037950897', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.417189285300914, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 7942, 'conductor_radical': 418, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 1, 1, -3, 1, 1, 0, 2, 1, 0, 1, 0, -3, 0, 1, 0, 1, -6, 0, -4, 2, 0, 1, -8, 0, -10, 1, 0, 0, 1, -3, 3, 0, 0, 1, -2, 0, -8, 1, -3, -6, 0, 0, -6, -4, 0, 2, -9, 0, 1, 1, 0, -8, -14, 0, 0, -10, -3, 1, 2, 0, 12, 0, 0, 1, 6, -3, 0, 3, 0, 0, 1, 0, -11, 1, 9, -2, 7, 0, 0, -8, 0, 1, 14, -3, 2, -6, 0, 0, 0, 0, 5, -6, -3, -4], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 0, 0], 'euler2': [1, -1, 0], 'euler23': [1, 6, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 3], 'euler31': [1, 10, 31], 'euler37': [1, -3, 37], 'euler41': [1, 2, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 5], 'euler53': [1, 9, 53], 'euler59': [1, 14, 59], 'euler61': [1, 0, 61], 'euler67': [1, -12, 67], 'euler7': [1, -1, 7], 'euler71': [1, -6, 71], 'euler73': [1, 0, 73], 'euler79': [1, 11, 79], 'euler83': [1, -7, 83], 'euler89': [1, -14, 89], 'euler97': [1, -5, 97], 'euler_factors': [[1, -1, 0], [1, 0, 3], [1, -1, 5], [1, -1, 7], [1, -1, 0], [1, -2, 13], [1, 0, 17], [1, 0, 0], [1, 6, 23], [1, 8, 29], [1, 10, 31], [1, -3, 37], [1, 2, 41], [1, 8, 43], [1, 0, 47], [1, 9, 53], [1, 14, 59], [1, 0, 61], [1, -12, 67], [1, -6, 71], [1, 0, 73], [1, 11, 79], [1, -7, 83], [1, -14, 89], [1, -5, 97]], 'index': 266, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7942/q', 'ModularForm/GL2/Q/holomorphic/7942/2/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/7942/2/a/q'], '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': '2-7942-1.1-c1-0-266', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7942-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 488434453343869178, 'z1': {'__RealLiteral__': 0, 'data': '1.67810975572739271941692074389', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22099989
{'Lhash': '2127256839096676802399932885437', 'Lhash_array': ['2127256839096676802399932885437'], 'label': '2-7942-1.1-c1-0-266', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7942/2/a/q'}
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id: 24581857
{'Lhash': '2127256839096676802399932885437', 'Lhash_array': ['2127256839096676802399932885437'], 'label': '2-7942-1.1-c1-0-266', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7942/2/a/q/1/1'}
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id: 41137
{'Lhash': '488434453343869178', 'Lhash_array': ['488434453343869178'], 'label': '2-7942-1.1-c1-0-266', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7942/q'}