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lfunc_lfunctions • Show schema
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{'Lhash': '1187950717269975559421284418291', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.944775186696442, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.0774219157468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': 'CDF', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.944775186696442, 0], [7.0, 0]], [[1.0, 0], [5.628163685563317, 0], [11.0, 0]], [[1.0, 0], [-4.424011347735828, 0], [13.0, 0]], [[1.0, 0], [-3.414101888011005, 0], [17.0, 0]], [[1.0, 0], [-2.358877074707447, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 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'5.07209862188576399072850917394731', '6.06685960428450268933182335322574', '6.67045380705863239439292027621723', '7.72707615414514505671458753513434', '8.189101527392213688937917858856761'], 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.937127878183543181896950917617', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.91315411310715533294463351270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97150932880094719261851313122', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.0774219157468, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5520/2/a/cc/1/3'], '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': '2-5520-1.1-c1-0-31', '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': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.937127878183543181896950917617', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1187950717269975559421284418291', 'Lhash_array': ['1187950717269975559421284418291'], 'label': '2-5520-1.1-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/cc/1/3'}