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lfunc_lfunctions • Show schema
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{'Lhash': '549734966483432574262239020153', 'a10': [0, 0], 'a2': [1.7320508075688772, -1.0], 'a3': [0.8660254037844386, 0.5], 'a4': [2.0, -3.4641016151377544], 'a5': [0, 0], 'a6': [2.0, 0], 'a7': [-15.588457268119896, 10.0], 'a8': [0, -8.0], 'a9': [-13.0, -22.516660498395403], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.650668502009225, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.7320508075688772, 1.0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [15.588457268119896, -10.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '350.249', 'coefficient_field': 'CDF', 'conductor': 350, 'conductor_radical': 70, 'conjugate': '2193135315122467904553064252309', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7320508075688772, 1.0]], [[1.0, 0], [-0.8660254037844386, -0.5], [13.5, 23.382685902179844]], [[1.0, 0], [0, 0]], [[1.0, 0], [15.588457268119896, -10.0]], [[1.0, 0], [17.5, -30.31088913245535], [-665.5, 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'0.076473597465444365992981007308567918438003631973875572 - 0.997071606701691802338444430606560879755898768845749778*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.23781695437433448', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43366442329176320547944910563', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76202498214661145144693748068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44933552091588508124808041294', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.650668502009225, 'bad_primes': [2, 5, 7], 'central_character': '35.4', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/4/j/d/249/2'], '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': '2-350-35.4-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-350-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.544300661488985, 'root_angle': -0.23781695437433448, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43366442329176320547944910563', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '549734966483432574262239020153', 'Lhash_array': ['549734966483432574262239020153'], 'label': '2-350-35.4-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/4/j/d/249/2'}