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lfunc_lfunctions • Show schema
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{'Lhash': '1975233821635241750937026772745', 'a10': [0.0, 0.0], 'a2': [-0.17364817766693036, 0.984807753012208], 'a3': [0.766044443118978, 0.6427876096865394], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [0.0, 0.0], 'a6': [-0.766044443118978, 0.6427876096865394], 'a7': [0.5, 0.8660254037844386], 'a8': [0.5, -0.8660254037844386], 'a9': [-0.3472963553338607, -1.969615506024416], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.765199025936447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.17364817766693036, -0.984807753012208]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '722.245', 'coefficient_field': 'CDF', 'conductor': 722, 'conductor_radical': 38, 'conjugate': '1261296981330779220105901038806', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.17364817766693036, -0.984807753012208]], [[1.0, 0], [-0.766044443118978, -0.6427876096865394], [0.520944533000791, 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'2.27413665242578004865924568393832', '3.96171804786003108649136739563305', '4.41375252937378254555112539149212', '5.97964615773022321065727361788612', '7.01802220954580161291552755924235', '7.958551488641049551479082112668636', '8.618335687856143581723337852666001', '9.693731900426290115912599349462482', '10.21067785969645760652692510026933'], 'prelabel': '2-722-19.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.401082886102945, 'root_angle': -0.10146446210883864, 'root_number': '0.9496247479997677 - 0.31338927548079515*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0507322310544', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55818474055833538056788055642', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27413665242578004865924568394', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96171804786003108649136739563', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.765199025936447, 'bad_primes': [2, 19], 'central_character': '19.17', 'conductor': 722, 'conductor_radical': 38, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/722/2/e/f/245/1'], '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': '2-722-19.17-c1-0-19', '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': '2-722-19.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.401082886102945, 'root_angle': -0.05073223105441932, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55818474055833538056788055642', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1975233821635241750937026772745', 'Lhash_array': ['1975233821635241750937026772745'], 'label': '2-722-19.17-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/722/2/e/f/245/1'}