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lfunc_lfunctions • Show schema
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{'Lhash': '1113719128027843216404074354050', 'a10': [3.414213562373095, -5.913591357920932], 'a2': [-1.2071067811865475, 2.0907702751760278], 'a3': [-0.5, 0.8660254037844386], 'a4': [-1.9142135623730951, -3.3155151465676167], 'a5': [-2.8284271247461903, 0.0], 'a6': [-1.2071067811865475, -2.0907702751760278], 'a7': [-1.4142135623730951, -2.449489742783178], 'a8': [4.414213562373095, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.22', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '648482164982561409565701190557', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2071067811865475, -2.0907702751760278], [-1.0, -1.7320508075688772]], [[1.0, 0], [0.5, -0.8660254037844386]], 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'2-507-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.32516952776306657, 'root_number': '0.5220443854178448 - 0.8529183194501714*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.162584763882', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.878569479498000340097638638849', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.68088528151026880490290176226', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33327621237102495705815664279', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '13.9', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/e/d/22/1'], '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': '2-507-13.9-c1-0-4', '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': '2-507-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.16258476388153328, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.878569479498000340097638638849', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1113719128027843216404074354050', 'Lhash_array': ['1113719128027843216404074354050'], 'label': '2-507-13.9-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/e/d/22/1'}