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lfunc_lfunctions • Show schema
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{'Lhash': '2854240233715603435374384171024', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.4928571041129442, 1.6604492991131654], 'a4': [0.0, 0.0], 'a5': [-1.8017283915964395, -3.1206851156843873], 'a6': [0.0, 0.0], 'a7': [-1.021326645737861, -2.440674472908227], 'a8': [0.0, 0.0], 'a9': [-2.514183749850805, -1.6367284661745651], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.4928571041129442, -1.6604492991131654]]], [7, [[1.0, 0], [1.021326645737861, 2.440674472908227]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.121', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '773965031060937066479534651214', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.4928571041129442, -1.6604492991131654]], [[1.0, 0], [1.8017283915964395, 3.1206851156843873], [-2.5, 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'10.52618623867818617421035756477794', '11.54415575861382228292832842860842', '12.30207125016125352275672826299381'], 'prelabel': '2-252-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': 0.48180840786051454, 'root_number': '0.0571194665514961 + 0.9983673504982384*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24090420393', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25159853448712322578282531929', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.42795247126110740925294418258', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.29811662324748490775764519898', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'bad_primes': [2, 3, 7], 'central_character': '63.58', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/2/i/b/121/3'], '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': '2-252-63.58-c1-0-5', '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': '2-252-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': 0.24090420393025727, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25159853448712322578282531929', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2854240233715603435374384171024', 'Lhash_array': ['2854240233715603435374384171024'], 'label': '2-252-63.58-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/2/i/b/121/3'}