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lfunc_lfunctions • Show schema
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{'Lhash': '2864173792214473378515112933530', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, -1.4142135623730951], 'a4': [0.0, 0.0], 'a5': [0.0, -2.8284271247461903], 'a6': [0.0, 0.0], 'a7': [0.0, -2.8284271247461903], 'a8': [0.0, 0.0], 'a9': [-1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 1.4142135623730951]]]], 'bad_primes': [2, 3], 'central_character': '768.767', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'conjugate': '1197018621811797899180097261098', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 1.4142135623730951]], [[1.0, 0], [0, 2.8284271247461903], [-5.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-17.0, 0]], [[1.0, 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'10.51790162432362088151821340791384'], 'prelabel': '2-768-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 0.6959132760153036, 'root_number': '-0.5773502691896257 + 0.816496580927726*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.347956638008', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25943473043660764430411741962', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07660828285776428562006821508', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00130827318759063374247396910', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/2/c/f/767/1'], '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': '2-768-12.11-c1-0-25', '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': '2-768-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 0.3479566380076518, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25943473043660764430411741962', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2864173792214473378515112933530', 'Lhash_array': ['2864173792214473378515112933530'], 'label': '2-768-12.11-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/c/f/767/1'}