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lfunc_lfunctions • Show schema
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{'Lhash': '1131640774458093309429357942442', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [10.392304845413264, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.4641016151377544, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 135.94040065322645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2304.1', 'coefficient_field': 'CDF', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-10.392304845413264, 0], [125.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [343.0, 0]], [[1.0, 0], [0, 0], [1331.0, 0]], [[1.0, 0], [-55.42562584220407, 0], [2197.0, 0]], [[1.0, 0], [-90.0, 0], [4913.0, 0]], [[1.0, 0], [-116.0, 0], [6859.0, 0]], [[1.0, 0], [-103.92304845413264, 0], [12167.0, 0]], [[1.0, 0], [259.8076211353316, 0], 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'7.17679978819873965798763398078337', '7.80417738634900187956603039887752', '8.830744779445334484764803017846250'], 'prelabel': '2-48e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.65934820876478, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.892707165724018343291398271702', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.63879876728257383287394127954', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92925385026552880846325082513', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 135.94040065322645, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'index': 52, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/4/a/bg/1/2'], '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': '2-48e2-1.1-c3-0-52', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-48e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.65934820876478, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.892707165724018343291398271702', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1131640774458093309429357942442', 'Lhash_array': ['1131640774458093309429357942442'], 'label': '2-48e2-1.1-c3-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/4/a/bg/1/2'}