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lfunc_lfunctions • Show schema
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{'Lhash': '1938695665925580156160860602072', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.6457513110645907, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.97245552025623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '2376.1', 'coefficient_field': 'CDF', 'conductor': 2376, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [2.6457513110645907, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [-0.6457513110645906, 0], [17.0, 0]], [[1.0, 0], [-5.291502622129181, 0], [19.0, 0]], [[1.0, 0], [-2.291502622129181, 0], [23.0, 0]], [[1.0, 0], [1.3542486889354095, 0], [29.0, 0]], 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'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/2376/2/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.0428412321103241e-60, 0.15194534208625662, 0.3035352652784325, 0.45437102289953607, 0.6039697152657639, 0.7517282713653988, 0.8968941774430742, 1.038544417705819, 1.1755735725249525, 1.306691515179907, 1.4304307042595983, 1.545162709578539, 1.6491233394627123, 1.7404455463363044, 1.8171991572746884, 1.8774363859956706, 1.9192420143395945, 1.940787071126194, 1.94038477645815, 1.916547457395958, 1.8680430780325181, 1.7939499679598718, 1.6937082844177915, 1.5671667123777009, 1.414622900845348, 1.2368561596289662, 1.0351510046107977, 0.8113102457808093, 0.5676564640202947, 0.307020921247577, 0.03271919364117566, -0.25148689305348637, -0.5414411178390324, 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'prelabel': '2-2376-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.355738229078537, 'root_angle': 0.5, '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': '1.52936121797010545390920367117', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93875949412210388573819131003', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44180649874906602485806169891', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.97245552025623, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 2376, 'conductor_radical': 66, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2376/2/a/i/1/1'], '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': '2-2376-1.1-c1-0-30', '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': '2-2376-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.355738229078537, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52936121797010545390920367117', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1938695665925580156160860602072', 'Lhash_array': ['1938695665925580156160860602072'], 'factors': ['2-2376-1.1-c1-0-30'], 'label': '2-2376-1.1-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2376/2/a/i/1/1'}