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lfunc_lfunctions • Show schema
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{'Lhash': '1399758065954142602544596905373', 'a10': [0.0, 0.0], 'a2': [-1.07821664464848, 0.35033382465244767], 'a3': [-1.529876099769747, -2.1056938042840327], 'a4': [-0.5782166446484801, 0.42009898273768415], 'a5': [0.0, 0.0], 'a6': [2.3872336390234277, 1.7344267630355181], 'a7': [0.0, 0.4071615433874513], 'a8': [1.8090169943749475, -2.48989828488278], 'a9': [-1.1663745336286282, 3.589731700329293], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.990650126330026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]]], 'bad_primes': [5], 'central_character': '625.499', 'coefficient_field': 'CDF', 'conductor': 625, 'conductor_radical': 5, 'conjugate': '699335499966984560040587878201', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.07821664464848, -0.35033382465244767], [1.618033988749895, -1.1755705045849463]], [[1.0, 0], [1.529876099769747, 2.1056938042840327], [-0.9270509831248422, 2.853169548885461]], [[1.0, 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'data': '3.24395101422803210159536885261', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48828139473731481697998454802', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.990650126330026, 'bad_primes': [5], 'central_character': '25.19', 'conductor': 625, 'conductor_radical': 5, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/625/2/e/a/499/1'], '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': '2-5e4-25.19-c1-0-13', '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': '2-5e4-25.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.233976303887314, 'root_angle': 0.24000000000000002, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10421441499899767923854050169', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1399758065954142602544596905373', 'Lhash_array': ['1399758065954142602544596905373'], 'label': '2-5e4-25.19-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/625/2/e/a/499/1'}