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lfunc_lfunctions • Show schema
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{'Lhash': '2781717273802398972337870016212', 'a10': [3.0, -6.223015277861142e-61], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.5, 2.598076211353316], 'a6': [0.0, 0.0], 'a7': [-0.5, -0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.253', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '3148031125513573942404559604944', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -2.598076211353316], [-2.5, -4.330127018922194]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [3.0, 5.196152422706632], [-5.5, 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-0.591313580177338, -0.6103887653651897, -0.11607284128670697], 'positive_zeros': ['2.19438800668068560131758197913291', '4.40168990874711540339157466810506', '4.86655794452651834681308798852537', '6.22272127375016884944758152832459', '7.37744561624587485312104480999400', '8.172850567326801726922966235812394', '8.943575628321349450974308630358844', '9.833794920243197303086819951412998', '10.82172178761459126534247229491280'], 'prelabel': '2-378-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.8888888888888888, 'root_number': '-0.9396926207859083 - 0.3420201433256689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.444444444444', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19438800668068560131758197913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.40168990874711540339157466811', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86655794452651834681308798853', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '9.4', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/f/a/253/1'], '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': '2-378-9.4-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-378-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.4444444444444444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.19438800668068560131758197913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2781717273802398972337870016212', 'Lhash_array': ['2781717273802398972337870016212'], 'label': '2-378-9.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/f/a/253/1'}