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lfunc_lfunctions • Show schema
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{'Lhash': '201863739792326822237409462751', 'a10': [9.524801504349853e-61, -1.1016680873294515], 'a2': [-0.5825598936755856, 0.69426784618918], 'a3': [-1.0697650033805357, -1.3622051378343287], 'a4': [0.20466454280100727, 1.160710300707723], 'a5': [-0.9311757343978333, 0.7813492152944548], 'a6': [1.568937413739302, 0.050862635435537366], 'a7': [-2.067501580381171, -1.6508898252522366], 'a8': [-2.4948348378408594, -1.4403935652110764], 'a9': [-0.7112056750844846, 2.9144787677606474], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0697650033805357, 1.3622051378343287]]], [7, [[1.0, 0], [2.067501580381171, 1.6508898252522366]]]], 'bad_primes': [3, 7], 'central_character': '189.101', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '3445725935697133661685598201693', 'degree': 2, 'euler_factors': [[[1.0, 0], 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{'__RealLiteral__': 0, 'data': '-0.49930931658', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15924241250387371862464249774', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75211182364333206936265779861', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42649331075950972822613175276', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5091725982022, 'bad_primes': [3, 7], 'central_character': '189.101', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/8'], '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': '2-189-189.101-c1-0-0', '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': '2-189-189.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': -0.49930931657973243, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.15924241250387371862464249774', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '201863739792326822237409462751', 'Lhash_array': ['201863739792326822237409462751'], 'factors': ['2-189-189.101-c1-0-0'], 'label': '2-189-189.101-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/8'}