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lfunc_lfunctions • Show schema
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{'Lhash': '1193196908489439961841264847001', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.662554376171684, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '3840.1921', 'coefficient_field': 'CDF', 'conductor': 3840, 'conductor_radical': 30, 'conjugate': '914434760581983472140379978211', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [-6.0, 0], [17.0, 0]], [[1.0, 0], [0, 4.0], [-19.0, 0]], [[1.0, 0], [-8.0, 0], [23.0, 0]], [[1.0, 0], [0, -2.0], [-29.0, 0]], [[1.0, 0], [4.0, 0], [31.0, 0]], [[1.0, 0], [0, -10.0], 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+ 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.941266393337892394198209854188', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.09303570358724683866335201499', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34628195851288466550937329442', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.662554376171684, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 3840, 'conductor_radical': 30, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3840/2/k/s/1921/1'], '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': '2-3840-8.5-c1-0-33', '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': '2-3840-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.537377933297644, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.941266393337892394198209854188', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1193196908489439961841264847001', 'Lhash_array': ['1193196908489439961841264847001'], 'label': '2-3840-8.5-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3840/2/k/s/1921/1'}