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  • lfunc_lfunctions • Show schema
    {'Lhash': '1527568779085768341470023799057,2754261561590280682249431955053', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -6, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 201.11299652395894, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1, -1, 1]], [37, [1, 10, 37]]], 'bad_primes': [2, 3, 37], 'central_character': '1776.1', 'coefficient_field': '1.1.1.1', 'conductor': 3154176, 'conductor_radical': 222, 'degree': 4, 'euler_factors': [[1], [1, -1, 1], [1, 6, 17, 30, 25], [1, -1, -6, -7, 49], [1, 12, 58, 132, 121], [1, -3, 16, -39, 169], [1, -12, 65, -204, 289], [1, 6, 31, 114, 361], [1, 0, -34, 0, 529], [1, 0, -10, 0, 841], [1, 0, -59, 0, 961], [1, 10, 37], [1, 12, 103, 492, 1681], [1, 0, 61, 0, 1849], [1, 24, 238, 1128, 2209], [1, 6, -17, 318, 2809], [1, -6, 71, -354, 3481], [1, -12, 109, -732, 3721], [1, 5, -42, 335, 4489], [1, 0, -71, 0, 5041], [1, -14, 195, -1022, 5329], 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'root_analytic_conductor': 3.765824132773516, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 446072922767653972, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20503928985695502022872761724', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.17272926869154637850649909301', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.74362771514290852962528570037', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 201.11299652395894, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 3154176, 'conductor_radical': 222, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, -6, 0, 1, 0, 0, 0, -12, 0, 3, 0, -6, 0, 12, 0, -6, 0, 1, 0, 0, 0, 19, 0, -1, 0, 0, 0, 0, 0, -12, 0, -6, 0, -10, 0, 3, 0, -12, 0, 0, 0, 0, 0, -24, 0, 7, 0, 12, 0, -6, 0, 72, 0, -6, 0, 6, 0, 12, 0, 0, 0, -18, 0, -5, 0, 0, 0, 0, 0, 14, 0, 19, 0, -12, 0, -3, 0, -1, 0, 12, 0, -72, 0, 0, 0, 18, 0, 3, 0, 0, 0, 36, 0, 0, 0, 0, 0], 'euler11': [1, 12, 58, 132, 121], 'euler13': [1, -3, 16, -39, 169], 'euler17': [1, -12, 65, -204, 289], 'euler19': [1, 6, 31, 114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -34, 0, 529], 'euler29': [1, 0, -10, 0, 841], 'euler3': [1, -1, 1, 0, 0], 'euler31': [1, 0, -59, 0, 961], 'euler37': [1, 10, 37, 0, 0], 'euler41': [1, 12, 103, 492, 1681], 'euler43': [1, 0, 61, 0, 1849], 'euler47': [1, 24, 238, 1128, 2209], 'euler5': [1, 6, 17, 30, 25], 'euler53': [1, 6, -17, 318, 2809], 'euler59': [1, -6, 71, -354, 3481], 'euler61': [1, -12, 109, -732, 3721], 'euler67': [1, 5, -42, 335, 4489], 'euler7': [1, -1, -6, -7, 49], 'euler71': [1, 0, -71, 0, 5041], 'euler73': [1, -14, 195, -1022, 5329], 'euler79': [1, 3, 82, 237, 6241], 'euler83': [1, -12, 61, -996, 6889], 'euler89': [1, -18, 197, -1602, 7921], 'euler97': [1, 0, -191, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 1, 0, 0], [1, 6, 17, 30, 25], [1, -1, -6, -7, 49], [1, 12, 58, 132, 121], [1, -3, 16, -39, 169], [1, -12, 65, -204, 289], [1, 6, 31, 114, 361], [1, 0, -34, 0, 529], [1, 0, -10, 0, 841], [1, 0, -59, 0, 961], [1, 10, 37, 0, 0], [1, 12, 103, 492, 1681], [1, 0, 61, 0, 1849], [1, 24, 238, 1128, 2209], [1, 6, -17, 318, 2809], [1, -6, 71, -354, 3481], [1, -12, 109, -732, 3721], [1, 5, -42, 335, 4489], [1, 0, -71, 0, 5041], [1, -14, 195, -1022, 5329], [1, 3, 82, 237, 6241], [1, -12, 61, -996, 6889], [1, -18, 197, -1602, 7921], [1, 0, -191, 0, 9409]], 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1776/2/bz/a'], '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': '4-1776e2-1.1-c1e2-0-20', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-1776e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.765824132773516, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 446072922767653972, 'z1': {'__RealLiteral__': 0, 'data': '1.20503928985695502022872761724', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1527568779085768341470023799057,2754261561590280682249431955053', 'Lhash_array': ['1527568779085768341470023799057', '2754261561590280682249431955053'], 'factors': ['2-1776-37.27-c1-0-22', '2-1776-37.11-c1-0-36'], 'label': '4-1776e2-1.1-c1e2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1776/2/bz/a'}