Formats: - HTML - YAML - JSON - 2026-10-15T20:00:53.902493
  • lfunc_lfunctions • Show schema
    {'Lhash': '644304334263022231759275526321', 'a10': [2187.0086388124746, 0.0], 'a2': [-10.892443989449804, 0.0], 'a3': [0.0, 0.0], 'a4': [-393.35466393669884, 0.0], 'a5': [-200.78217899773142, 0.0], 'a6': [0.0, 0.0], 'a7': [-2401.0, 0.0], 'a8': [9861.524967517642, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.447257678324014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2401.0, 0]]]], 'bad_primes': [3, 7], 'central_character': '63.1', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [10.892443989449804, 0], [512.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [200.78217899773142, 0], [1953125.0, 0]], [[1.0, 0], [2401.0, 0]], [[1.0, 0], [63864.26870891005, 0], [2357947691.0, 0]], [[1.0, 0], [164678.7470410134, 0], [10604499373.0, 0]], [[1.0, 0], [-362910.17704455386, 0], [118587876497.0, 0]], [[1.0, 0], 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-4.383707418024141, -4.20081317237356, -3.8518559983535514, -3.356557184360957, -2.74438057602878], 'positive_zeros': ['0.50826650036454908993081422118578', '2.53879406179636735069622925640143', '4.32113333999697713709168690980012', '5.55020489777273626156891487215866', '7.45648376424714032787229267113991', '8.293268739667757989138747577093676', '9.811751206294540680825023215048247', '10.27478794030548957643187315349340', '12.07258822678794881184054119853044', '13.02330884061677840197895484485366'], 'prelabel': '2-63-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.696249439615861, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50826650036454908993081422119', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.53879406179636735069622925640', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.32113333999697713709168690980', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 32.447257678324014, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/10/a/d/1/1'], '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': '2-63-1.1-c9-0-2', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-63-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.696249439615861, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50826650036454908993081422119', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '644304334263022231759275526321', 'Lhash_array': ['644304334263022231759275526321'], 'factors': ['2-63-1.1-c9-0-2'], 'label': '2-63-1.1-c9-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/10/a/d/1/1'}