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lfunc_lfunctions • Show schema
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{'Lhash': '2299457854503320708601337827306', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.381966011250105, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.427097670511378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '1932.1', 'coefficient_field': 'CDF', 'conductor': 1932, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.381966011250105, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [11.0, 0]], [[1.0, 0], [6.0901699437494745, 0], [13.0, 0]], [[1.0, 0], [5.0, 0], [17.0, 0]], [[1.0, 0], [-5.47213595499958, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.7639320225002102, 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'group': 'GL2', 'index': 18, 'label': '2-1932-1.1-c1-0-18', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1932/2/a/f/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.4724966814704635e-60, 0.16540392199609408, 0.33077407572672907, 0.49603389778305884, 0.6610234745990857, 0.8254632862145698, 0.9889239748328058, 1.1508034329785646, 1.3103120378130193, 1.466466409587007, 1.6180916848749054, 1.7638319909381928, 1.902168589339785, 2.0314450137648863, 2.1498984401303884, 2.2556964757398617, 2.3469785199733706, 2.421900817906382, 2.4786842918027903, 2.5156641901040238, 2.5313405398907385, 2.5244283303194126, 2.493906296595691, 2.4390631229694844, 2.3595398456237286, 2.255367218537199, 2.126996813182276, 1.9753246611560946, 1.8017063213723645, 1.6079623629089481, 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'8.137659041066516298016612437904582', '8.579704083504205905857733171890844'], 'prelabel': '2-1932-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81395240462105523158445141432', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79610498753449416152967632039', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73277189873131724902456897366', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.427097670511378, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 1932, 'conductor_radical': 966, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1932/2/a/f/1/2'], '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': '2-1932-1.1-c1-0-18', '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': '2-1932-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81395240462105523158445141432', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2299457854503320708601337827306', 'Lhash_array': ['2299457854503320708601337827306'], 'label': '2-1932-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1932/2/a/f/1/2'}