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lfunc_lfunctions • Show schema
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{'Lhash': '2188266282308108832711358206016', 'a10': [0.0, 0.0], 'a2': [-0.8660254037844386, -0.5], 'a3': [-1.0, 0.0], 'a4': [4.582907174078835e-80, 2.6459426906630975e-80], 'a5': [0.0, 0.0], 'a6': [0.8660254037844386, 0.5], 'a7': [0.0, -1.0], 'a8': [-1.3229713452751261e-80, 1.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3458520537546707, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 1.0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '693.571', 'coefficient_field': 'CDF', 'conductor': 693, 'conductor_radical': 231, 'conjugate': '708164163833767583547716315223', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 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[[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-693-693.571-c0-0-1', 'leading_term': '0.32901868107056363389275841969699', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/693/1/bl/a/571/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.32901868107056365, 0.3706526947794426, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72623772032619290438570207430', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.70003429576952060167043918326', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.79662174734155200966589507827', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3458520537546707, 'bad_primes': [3, 7, 11], 'central_character': '693.571', 'conductor': 693, 'conductor_radical': 231, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/693/1/bl/a/571/1', 'ArtinRepresentation/2.693.16t60.a.c'], 'is_instance_Artin': True, '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': '2-693-693.571-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-693-693.571-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5880918752666718, 'root_angle': 0.398975365415862, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72623772032619290438570207430', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603543
{'Lhash': '2188266282308108832711358206016', 'Lhash_array': ['2188266282308108832711358206016'], 'label': '2-693-693.571-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.693.16t60.a.c'}
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id: 19804228
{'Lhash': '2188266282308108832711358206016', 'Lhash_array': ['2188266282308108832711358206016'], 'label': '2-693-693.571-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/693/1/bl/a/571/1'}