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lfunc_lfunctions • Show schema
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{'Lhash': '3021750735338390740925479414194', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.212', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1676059810722057072941748639249', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 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'positive_zeros': ['2.38374102043130098665145034659026', '3.93805820588745944624488189518877', '5.26080347827440286494183730226889', '6.54316899649752673161633725075074', '7.00229180965700669090160272859792', '8.510731366976896533047150480091424', '9.359248616527200161023906761316925', '10.73729017302974224375945052042912', '11.44025993680020983483871662485085', '12.21478609160988315795871640521945'], 'prelabel': '2-273-273.212-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.3090784774942538, 'root_number': '0.56447545725172972009705262112316 + 0.82544985199614074032936256969098*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1545392387471269', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.38374102043130098665145034659', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93805820588745944624488189519', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.26080347827440286494183730227', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'bad_primes': [3, 7, 13], 'central_character': '273.212', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/1/x/a/212/1'], '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': '2-273-273.212-c0-0-0', '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': '2-273-273.212-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.1545392387471269, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.38374102043130098665145034659', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3021750735338390740925479414194', 'Lhash_array': ['3021750735338390740925479414194'], 'label': '2-273-273.212-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/1/x/a/212/1'}