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lfunc_lfunctions • Show schema
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{'Lhash': '1750570275075199490194693925156', 'a10': [-80.20192596812451, -138.91381064166936], 'a2': [1.37409068226173, -2.379994875884299], 'a3': [0.0, 0.0], 'a4': [12.223749593842987, 21.17215535553548], 'a5': [29.183636496287676, -50.547541161191624], 'a6': [0.0, 0.0], 'a7': [-21.436587374826733, 127.85723570342594], 'a8': [155.12796534155174, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [21.436587374826733, -127.85723570342594]]]], 'bad_primes': [3, 7], 'central_character': '63.37', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '2029519291424704479300475146284', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.37409068226173, 2.379994875884299], [-16.0, -27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-29.183636496287676, 50.547541161191624], [-1562.5, 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'6.60440072420327010918554362523399', '7.58263478147098886454878801947333', '9.644740063336668464470147278693151', '10.57791415580590568498951403150473', '11.39999928392880380861640886849217', '13.48963636943716245794381606600958', '13.91921655509214965507532250649812'], 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.032703200915796496, 'root_number': '0.9947268730923662 + 0.10255948492403634*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0163516004579', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38095645184881750988500101384', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51283288971617070275976505547', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.51930212590954880588010106326', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.2', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/e/37/3'], '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': '2-63-7.2-c5-0-9', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.016351600457898248, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38095645184881750988500101384', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1750570275075199490194693925156', 'Lhash_array': ['1750570275075199490194693925156'], 'label': '2-63-7.2-c5-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/e/37/3'}