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lfunc_lfunctions • Show schema
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{'Lhash': '422331407299028870786373544742', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 1.1998008450092592], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.2935231424704, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '6048.2591', 'coefficient_field': 'CDF', 'conductor': 6048, 'conductor_radical': 42, 'conjugate': '1537689622960204293933301680911', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.1998008450092592], [-5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [1.6286262797369309, 0], [11.0, 0]], [[1.0, 0], [2.0963763171773127, 0], [13.0, 0]], [[1.0, 0], [0, 0.585786437626905], [-17.0, 0]], [[1.0, 0], [0, -5.898979485566356], [-19.0, 0]], [[1.0, 0], [-7.0927278948746855, 0], [23.0, 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'4.40764027588677753656834052436486', '4.84595011740279269320612800731070', '5.48391286862503603938263193861111', '6.57956501100216842348765719143252', '7.05340232445177798891165616744471', '7.81826203052803057217035325384386'], 'prelabel': '2-6048-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.949354152903016, 'root_angle': -0.75, 'root_number': '-0.70710678118654752440084436210484903928483593768847403659 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 20}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33316073626517574743890114605', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.32092748651853921460799368334', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.57153215485631563335810402541', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.2935231424704, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 6048, 'conductor_radical': 42, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6048/2/h/g/2591/5'], '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': '2-6048-12.11-c1-0-18', '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': '2-6048-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.949354152903016, 'root_angle': -0.375, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33316073626517574743890114605', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '422331407299028870786373544742', 'Lhash_array': ['422331407299028870786373544742'], 'label': '2-6048-12.11-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6048/2/h/g/2591/5'}