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lfunc_lfunctions • Show schema
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{'Lhash': '978131209094401059499288914531', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.6927670143944116, 2.931958474307798], 'a4': [0, 0], 'a5': [0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [-2.299189630268435, 0], 'a8': [0, 0], 'a9': [-4.23092033004354, -7.328168974411495], '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], [-2.138999406673937, 3.7979838780922366]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.961', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '516161138004742700467626504549', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.6927670143944116, -2.931958474307798], [-1.5, -2.598076211353316]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [2.299189630268435, 0], [7.0, 0]], [[1.0, 0], 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'7.62480732304010852388693242486839', '8.241799092290988339073772678735976', '9.580186536470709814454089537376720'], 'prelabel': '2-1520-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.07115371096636651, 'root_number': '0.97511969542887739149241855966071112757079179164643629162 - 0.2216790012308188663161227269375296699079166464762256117*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.035576855483183255', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77160947103113199468107845291', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32171944112830156384509171848', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85406982170016119719335575927', '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': '19.11', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/p/961/1'], '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': '2-1520-19.11-c1-0-12', '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': '2-1520-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.035576855483183255, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77160947103113199468107845291', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '978131209094401059499288914531', 'Lhash_array': ['978131209094401059499288914531'], 'label': '2-1520-19.11-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/p/961/1'}