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lfunc_lfunctions • Show schema
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{'Lhash': '1120207123138038041832405978288', 'a10': [0.7395143965888079, 1.2808765078204558], 'a2': [0.5, -0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.7395143965888079, 1.2808765078204558], 'a6': [1.0, 3.111507638930571e-61], 'a7': [1.3228756555322954, 2.29128784747792], 'a8': [-1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.713548835255689, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [-1.3228756555322954, -2.29128784747792]]], [23, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.415', 'coefficient_field': 'CDF', 'conductor': 966, 'conductor_radical': 966, 'conjugate': '1934956230057517912978778532339', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-966-7.2-c1-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/966/2/i/n/415/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.9816239287578894, 1.8298012598207545, 1.6483715710616706, 1.4289794838536405, 1.1624449035650353, 0.8415235051735654, 0.4634195555032472, 0.03175098391534252, -0.4421860838880199, -0.9389499989872351, -1.4313716537156993, -1.8859312427243602, -2.2651155857849803, -2.5306842896585153, -2.647647490266265, -2.5886194861245224, -2.3380851146746395, -1.896024958319706, -1.2803157920117636, -0.5273733817034024, 0.3093540816278339, 1.163204692445429, 1.9602976892477666, 2.6272332582446714, 3.099700954423733, 3.3309397001483467, 3.298850304924587, 3.010582806649377, 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'8.761454938454153719590629468395586', '9.855112718819374346270795845026603'], 'prelabel': '2-966-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.777327642763037, 'root_angle': -0.1868396197206128, 'root_number': '0.8326204335587601 - 0.5538440336596778*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0934198098603', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.883687605193698128324155961773', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.45463746133463861279947110657', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95882541029332949109262696145', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.713548835255689, 'bad_primes': [2, 3, 7, 23], 'central_character': '7.2', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/2/i/n/415/2'], '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': '2-966-7.2-c1-0-10', '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': '2-966-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.777327642763037, 'root_angle': -0.0934198098603064, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.883687605193698128324155961773', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1120207123138038041832405978288', 'Lhash_array': ['1120207123138038041832405978288'], 'label': '2-966-7.2-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/2/i/n/415/2'}