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lfunc_lfunctions • Show schema
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{'Lhash': '2488751938437080793322291025062', 'a10': [-4.0, 2.0], 'a2': [-2.0, 0.0], 'a3': [1.0, 0.0], 'a4': [2.0, 0.0], 'a5': [2.0, -1.0], 'a6': [-2.0, 0.0], 'a7': [0.0, -4.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-2.0, 1.0]]], [29, [[1.0, 0], [2.0, -5.0]]]], 'bad_primes': [3, 5, 29], 'central_character': '435.289', 'coefficient_field': 'CDF', 'conductor': 435, 'conductor_radical': 435, 'conjugate': '1058461146011069900055187453696', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.0, 1.0]], [[1.0, 0], [0, 4.0], [-7.0, 0]], [[1.0, 0], [0, 1.0], [-11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [6.0, 0], [17.0, 0]], [[1.0, 0], [0, 4.0], [-19.0, 0]], [[1.0, 0], [0, -9.0], [-23.0, 0]], [[1.0, 0], [2.0, -5.0]], [[1.0, 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'0.08304547985374004 + 0.9965457582448796*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.23676766197', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96327910702602339931425882472', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52509541441722889404633038325', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57114576488874229321384665906', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'bad_primes': [3, 5, 29], 'central_character': '145.144', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/435/2/f/a/289/1'], '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': '2-435-145.144-c1-0-23', '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': '2-435-145.144-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8637307981373539, 'root_angle': 0.23676766197020505, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96327910702602339931425882472', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2488751938437080793322291025062', 'Lhash_array': ['2488751938437080793322291025062'], 'factors': ['2-435-145.144-c1-0-23'], 'label': '2-435-145.144-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/435/2/f/a/289/1'}