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lfunc_lfunctions • Show schema
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{'Lhash': '1885378691052154158078379133576', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.5, 0.8660254037844386], 'a4': [0, 0], 'a5': [0, -1.0], 'a6': [0, 0], 'a7': [-2.2385785476406874, -1.2924439270824724], 'a8': [0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.456662715319746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [1.8489338012777967, -3.0953907343811116]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.361', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '549229238345708365930479876753', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [2.2385785476406874, 1.2924439270824724], [3.5, 6.06217782649107]], [[1.0, 0], [-2.682638633272148, 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'9.630570921457250444144589297035936'], 'prelabel': '2-1560-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.508807727954818, 'root_number': '-0.0276667626352330815903777304996284002031262167411863543 + 0.9996172018554330933821826213653339365969679172782993120*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25440386397740905', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48730154090780867973546142734', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70122422119727997763589599656', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43648743634715093280408785239', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.456662715319746, 'bad_primes': [2, 3, 5, 13], 'central_character': '13.10', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/2/ec/e/361/2'], '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': '2-1560-13.10-c1-0-24', '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': '2-1560-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.254403863977409, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48730154090780867973546142734', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1885378691052154158078379133576', 'Lhash_array': ['1885378691052154158078379133576'], 'label': '2-1560-13.10-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/2/ec/e/361/2'}