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lfunc_lfunctions • Show schema
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{'Lhash': '422948620362097746238025412296', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.7320508075688772, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 3.4641016151377544], 'a8': [0.0, 0.0], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.7320508075688772, 0]]]], 'bad_primes': [2, 3], 'central_character': '768.383', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'conjugate': '2128691357808697480490426988231', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.7320508075688772, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-7.0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 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'root_angle': -0.375, 'root_number': '-0.7071067811865475 - 0.7071067811865476*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 20}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33364763152082249397841607729', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86883732524368011485336623159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86836922592150014121603379110', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/2/f/d/383/2'], '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': '2-768-24.11-c1-0-2', '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': '2-768-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': -0.375, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33364763152082249397841607729', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '422948620362097746238025412296', 'Lhash_array': ['422948620362097746238025412296'], 'factors': ['2-768-24.11-c1-0-2'], 'label': '2-768-24.11-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/f/d/383/2'}