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  • lfunc_lfunctions • Show schema
    {'Lhash': '2684593076287716549251153945221,3017267796449735804352712866795', 'a10': -2, 'a2': 1, 'a3': 3, 'a4': 2, 'a5': -2, 'a6': 3, 'a7': -3, 'a8': 5, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8644315128125644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -3, 3]], [19, [1, 8, 19]]], 'bad_primes': [3, 19], 'central_character': '171.1', 'coefficient_field': '1.1.1.1', 'conductor': 29241, 'conductor_radical': 57, 'degree': 4, 'euler_factors': [[1, -1, -1, -2, 4], [1, -3, 3], [1, 2, 11, 10, 25], [1, 3, 2, 21, 49], [1, 3, -2, 33, 121], [1, -6, 23, -78, 169], [1, 3, -8, 51, 289], [1, 8, 19], [1, 8, 41, 184, 529], [1, 10, 83, 290, 841], [1, -7, 18, -217, 961], [1, -4, 78, -148, 1369], [1, 2, 83, 82, 1681], [1, 8, 21, 344, 1849], [1, -18, 175, -846, 2209], [1, 3, -44, 159, 2809], [1, -6, 127, -354, 3481], [1, -14, 171, -854, 3721], [1, -4, -51, -268, 4489], [1, -15, 154, -1065, 5041], [1, -5, -48, -365, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 831993316609295999, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11777052431038888001191696307', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38020460520154617673660805410', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72366236420306153594793405401', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.8644315128125644, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 29241, 'conductor_radical': 57, 'degree': 4, 'dirichlet_coefficients': [1, 1, 3, 2, -2, 3, -3, 5, 6, -2, -3, 6, 6, -3, -6, 5, -3, 6, -8, -4, -9, -3, -8, 15, -7, 6, 9, -6, -10, -6, 7, 10, -9, -3, 6, 12, 4, -8, 18, -10, -2, -9, -8, -6, -12, -8, 18, 15, 7, -7, -9, 12, -3, 9, 6, -15, -24, -10, 6, -12, 14, 7, -18, 17, -12, -9, 4, -6, -24, 6, 15, 30, 5, 4, -21, -16, 9, 18, 12, -10, 9, -2, 1, -18, 6, -8, -30, -15, 1, -12, -18, -16, 21, 18, 16, 30, 2, 7, -18, -14], 'euler11': [1, 3, -2, 33, 121], 'euler13': [1, -6, 23, -78, 169], 'euler17': [1, 3, -8, 51, 289], 'euler19': [1, 8, 19, 0, 0], 'euler2': [1, -1, -1, -2, 4], 'euler23': [1, 8, 41, 184, 529], 'euler29': [1, 10, 83, 290, 841], 'euler3': [1, -3, 3, 0, 0], 'euler31': [1, -7, 18, -217, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 2, 83, 82, 1681], 'euler43': [1, 8, 21, 344, 1849], 'euler47': [1, -18, 175, -846, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 3, -44, 159, 2809], 'euler59': [1, -6, 127, -354, 3481], 'euler61': [1, -14, 171, -854, 3721], 'euler67': [1, -4, -51, -268, 4489], 'euler7': [1, 3, 2, 21, 49], 'euler71': [1, -15, 154, -1065, 5041], 'euler73': [1, -5, -48, -365, 5329], 'euler79': [1, -12, 65, -948, 6241], 'euler83': [1, -1, -82, -83, 6889], 'euler89': [1, -1, -88, -89, 7921], 'euler97': [1, -2, -93, -194, 9409], 'euler_factors': [[1, -1, -1, -2, 4], [1, -3, 3, 0, 0], [1, 2, 11, 10, 25], [1, 3, 2, 21, 49], [1, 3, -2, 33, 121], [1, -6, 23, -78, 169], [1, 3, -8, 51, 289], [1, 8, 19, 0, 0], [1, 8, 41, 184, 529], [1, 10, 83, 290, 841], [1, -7, 18, -217, 961], [1, -4, 78, -148, 1369], [1, 2, 83, 82, 1681], [1, 8, 21, 344, 1849], [1, -18, 175, -846, 2209], [1, 3, -44, 159, 2809], [1, -6, 127, -354, 3481], [1, -14, 171, -854, 3721], [1, -4, -51, -268, 4489], [1, -15, 154, -1065, 5041], [1, -5, -48, -365, 5329], [1, -12, 65, -948, 6241], [1, -1, -82, -83, 6889], [1, -1, -88, -89, 7921], [1, -2, -93, -194, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/b'], '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': '4-171e2-1.1-c1e2-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-171e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 831993316609295999, 'z1': {'__RealLiteral__': 0, 'data': '2.11777052431038888001191696307', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2684593076287716549251153945221,3017267796449735804352712866795', 'Lhash_array': ['2684593076287716549251153945221', '3017267796449735804352712866795'], 'factors': ['2-171-171.121-c1-0-11', '2-171-171.106-c1-0-11'], 'label': '4-171e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/b'}