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lfunc_lfunctions • Show schema
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{'Lhash': '2813321057698414210455448303301', 'a10': [-1.9320482983837939, -2.226696689361267], 'a2': [0.6592036397692348, -1.1417741966146464], 'a3': [0.0, 0.0], 'a4': [0.13090112262998585, 0.22672739516293963], 'a5': [0.7299351006728015, -2.1135739279253487], 'a6': [0.0, 0.0], 'a7': [-2.12634933305473, -1.5743692431630218], 'a8': [2.9819765450272016, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.515287663670333, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.7299351006728015, 2.1135739279253487]]], [7, [[1.0, 0], [2.12634933305473, 1.5743692431630218]]]], 'bad_primes': [3, 5, 7], 'central_character': '315.89', 'coefficient_field': 'CDF', 'conductor': 315, 'conductor_radical': 105, 'conjugate': '1678417626524896361801113567778', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6592036397692348, 1.1417741966146464], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 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'11.01575356093756174358778654526781', '11.82696542044774384052701244347029'], 'prelabel': '2-315-105.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5859658456821613, 'root_angle': 0.4864840227676681, 'root_number': '0.04244893622181486 + 0.999098637679802*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.243242011384', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21931899625330541728950572378', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.67135556284920355103555665447', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.23152524864495444850102352461', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.515287663670333, 'bad_primes': [3, 5, 7], 'central_character': '105.89', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/2/bb/b/89/8'], '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': '2-315-105.89-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': '2-315-105.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5859658456821613, 'root_angle': 0.24324201138383406, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21931899625330541728950572378', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2813321057698414210455448303301', 'Lhash_array': ['2813321057698414210455448303301'], 'label': '2-315-105.89-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/2/bb/b/89/8'}