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lfunc_lfunctions • Show schema
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{'Lhash': '397394384490502315551377112964', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.5235855629996726, 2.6389276047938655], 'a4': [0, 0], 'a5': [-0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [0.6091753400508947, 0], 'a8': [0, 0], 'a9': [-3.1426259355620583, 5.443187789577162], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [3.6053198420742043, 2.4498303688921066]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.881', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '2799111791532962737984489137818', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5235855629996726, -2.6389276047938655], [-1.5, 2.598076211353316]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.6091753400508947, 0], [7.0, 0]], [[1.0, 0], 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'7.64313229693958104142871155145751', '8.169056033435400965594280203909563', '8.485929060140432133405246738435393'], 'prelabel': '2-1520-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.9243992705553778, 'root_number': '-0.97192761990213015686051708235892785675821591458005268462 + 0.23528004945464544723972947543700548796203666387328035265*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4621996352776889', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31348889387892447092718346522', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93953733543096489774511647582', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61955652257050509348914854238', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '19.7', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/4'], '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': '2-1520-19.7-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': '2-1520-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.4621996352776889, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31348889387892447092718346522', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '397394384490502315551377112964', 'Lhash_array': ['397394384490502315551377112964'], 'label': '2-1520-19.7-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/4'}