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lfunc_lfunctions • Show schema
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{'Lhash': '1524708556574275885152997177876', 'a10': [2.41094599724481, 0.0], 'a2': [-0.6158229163717395, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.6207621356714055, 0.0], 'a5': [-3.9149988302634884, 0.0], 'a6': [-0.6158229163717395, 0.0], 'a7': [4.241394686871247, 0.0], 'a8': [2.2297482978775327, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.17172697437388, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [79, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 17, 79], 'central_character': '4029.1', 'coefficient_field': 'CDF', 'conductor': 4029, 'conductor_radical': 4029, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6158229163717395, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.9149988302634884, 0], [5.0, 0]], [[1.0, 0], [-4.241394686871247, 0], [7.0, 0]], [[1.0, 0], [3.4718254537113538, 0], [11.0, 0]], [[1.0, 0], [1.188616408100876, 0], [13.0, 0]], [[1.0, 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'4.88910714524200958390716719167190', '5.50313964776287678236662215973399', '7.40429393107542464014077215614445', '7.53795123203983647719751231200861', '7.960459132389410229637781644794729'], 'prelabel': '2-4029-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6720126035097875, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20278297213740556529666081362', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44996870656012271312450261744', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64521199136164145290750147861', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.17172697437388, 'bad_primes': [3, 17, 79], 'central_character': '1.1', 'conductor': 4029, 'conductor_radical': 4029, 'degree': 2, 'index': 117, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4029/2/a/e/1/9'], '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': '2-4029-1.1-c1-0-117', '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': '2-4029-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6720126035097875, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20278297213740556529666081362', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1524708556574275885152997177876', 'Lhash_array': ['1524708556574275885152997177876'], 'label': '2-4029-1.1-c1-0-117', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4029/2/a/e/1/9'}