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lfunc_lfunctions • Show schema
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{'Lhash': '1984016192278947804756979969795', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.9574104348217978, -3.390334324376842], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.2568327496616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '5292.881', 'coefficient_field': 'CDF', 'conductor': 5292, 'conductor_radical': 42, 'conjugate': '351282893444439218470203124906', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9574104348217978, 3.390334324376842], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.199582404151623, -1.8472797623313295], [5.5, -9.526279441628825]], [[1.0, 0], [-0.48024166826019865, -0.27726765644610063], [6.5, 11.258330249197702]], [[1.0, 0], [-5.8383167653144685, 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'-0.97913863827477930438847658070170666360958821587988672438 + 0.2031933242934198569913654179814965470907823307727369489*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.46743400451029343', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56511280941431577833002798221', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36235817297237100477092521429', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38980198314570765582694078452', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.2568327496616, 'bad_primes': [2, 3, 7], 'central_character': '63.41', 'conductor': 5292, 'conductor_radical': 42, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5292/2/x/a/881/8'], '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': '2-5292-63.41-c1-0-38', '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': '2-5292-63.41-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.500525574879434, 'root_angle': 0.46743400451029343, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56511280941431577833002798221', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1984016192278947804756979969795', 'Lhash_array': ['1984016192278947804756979969795'], 'label': '2-5292-63.41-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5292/2/x/a/881/8'}