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lfunc_lfunctions • Show schema
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{'Lhash': '2163969196618725231984889890084', 'a10': [0, -2.7661203788279543], 'a2': [1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [0, -2.7661203788279543], 'a6': [0, 0], 'a7': [-1.0, 0], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116186243894532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.8774472402820013, -3.9338520383915685]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1709', 'coefficient_field': 'CDF', 'conductor': 2394, 'conductor_radical': 798, 'conjugate': '717301788824288416441162987644', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.7661203788279543], [-5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 4.928267923055738], [-11.0, 0]], [[1.0, 0], [0, -2.9394361537273994], [-13.0, 0]], [[1.0, 0], [0, 4.928267923055738], [-17.0, 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'3.36070396690343673486438633902175', '4.43173517490909818712294404443372', '5.21960579078963665109053302489552', '6.30244519511545275812387400937543', '6.75093564321727165859030638451995', '7.44818343732579309677871972673709', '8.218099637314912287704626103039728', '9.430755673601224234405927327169825'], 'prelabel': '2-2394-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': 0.6623478137211181, 'root_number': '-0.4882040389602555788914788919182832793697555700635291560 + 0.87272952072385706186508109611285979568967647801832665323*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.331173906860559', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70707069931503326545000747798', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80256310434919691850517195661', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36070396690343673486438633902', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116186243894532, 'bad_primes': [2, 3, 7, 19], 'central_character': '57.56', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/2/b/j/1709/3'], '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': '2-2394-57.56-c1-0-37', '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': '2-2394-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': 0.33117390686055903, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70707069931503326545000747798', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2163969196618725231984889890084', 'Lhash_array': ['2163969196618725231984889890084'], 'label': '2-2394-57.56-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/b/j/1709/3'}