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lfunc_lfunctions • Show schema
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{'Lhash': '2155899747951236760336249843499', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.6016791318831545, 0], 'a4': [0, 0], 'a5': [0, -1.0], 'a6': [0, 0], 'a7': [0, -2.768734305276283], 'a8': [0, 0], 'a9': [3.768734305276283, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.304441810213165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [0.1670551733931289, 3.6016791318831545]]]], 'bad_primes': [2, 5, 13], 'central_character': '1040.961', 'coefficient_field': 'CDF', 'conductor': 1040, 'conductor_radical': 130, 'conjugate': '318912376491701537667979273909', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.6016791318831545, 0], [3.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 2.768734305276283], [-7.0, 0]], [[1.0, 0], [0, 2.1670551733931287], [-11.0, 0]], [[1.0, 0], [0.1670551733931289, 3.6016791318831545]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], 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'4.66066292165129229588555299349667', '5.08490838069994134685934006176482', '6.23052091877607180543411718031569', '6.66293220894506541000174710599472', '7.56473397445938650442714885664978', '8.954323569376293540260334886935835', '9.498784694910238888547798161784031', '10.57555254488736789778563551156358'], 'prelabel': '2-1040-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': 0.9852465398397637, 'root_number': '-0.998926060597949270803022899660267379484404926049750150006 + 0.0463327687308041339350649725345606290691265202696280814*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.49262326991988187', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70070502673456382220951555435', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02915261222446577767822506124', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.66066292165129229588555299350', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.304441810213165, 'bad_primes': [2, 5, 13], 'central_character': '13.12', 'conductor': 1040, 'conductor_radical': 130, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1040/2/k/c/961/1'], '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': '2-1040-13.12-c1-0-20', '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': '2-1040-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': 0.49262326991988187, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70070502673456382220951555435', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2155899747951236760336249843499', 'Lhash_array': ['2155899747951236760336249843499'], 'label': '2-1040-13.12-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1040/2/k/c/961/1'}