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lfunc_lfunctions • Show schema
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{'Lhash': '1600490866378143893961831163021', 'a10': 1, 'a2': 1, 'a3': 1, 'a4': -1, 'a5': 1, 'a6': 1, 'a7': 1, 'a8': -3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.222721433457888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1, -1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '1155.1', 'coefficient_field': '1.1.1.1', 'conductor': 1155, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, -1], [1, -1], [1, -1], [1, 1], [1, -6, 13], [1, -2, 17], [1, -4, 19], [1, 4, 23], [1, 2, 29], [1, -4, 31], [1, 2, 37], [1, -6, 41], [1, -4, 43], [1, -8, 47], [1, 2, 53], [1, 8, 59], [1, -10, 61], [1, 8, 67], [1, 0, 71], [1, 14, 73], [1, 16, 79], [1, 4, 83], [1, 6, 89], [1, -18, 97], [1, -2, 101], [1, 16, 103], [1, 12, 107], [1, -6, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -6, 13], 1]], [[[1, -2, 17], 1]], [[[1, -4, 19], 1]], [[[1, 4, 23], 1]], [[[1, 2, 29], 1]], [[[1, -4, 31], 1]], [[[1, 2, 37], 1]], [[[1, -6, 41], 1]], [[[1, -4, 43], 1]], [[[1, -8, 47], 1]], [[[1, 2, 53], 1]], [[[1, 8, 59], 1]], [[[1, -10, 61], 1]], [[[1, 8, 67], 1]], [[[1, 0, 71], 1]], [[[1, 14, 73], 1]], [[[1, 16, 79], 1]], [[[1, 4, 83], 1]], [[[1, 6, 89], 1]], [[[1, -18, 97], 1]], [[[1, -2, 101], 1]], [[[1, 16, 103], 1]], [[[1, 12, 107], 1]], [[[1, -6, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-1155-1.1-c1-0-19', 'leading_term': '2.82448265823069875832014155609000000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1155/2/a/m', 'plot_delta': {'__RealLiteral__': 0, 'data': 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'z1': {'__RealLiteral__': 0, 'data': '1.26256467364902404033416936943', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75741029317421941120801382240', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68697363374671842050513434949', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.222721433457888, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 1155, 'conductor_radical': 1155, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, -1, 1, 1, 1, -3, 1, 1, -1, -1, 6, 1, 1, -1, 2, 1, 4, -1, 1, -1, -4, -3, 1, 6, 1, -1, -2, 1, 4, 5, -1, 2, 1, -1, -2, 4, 6, -3, 6, 1, 4, 1, 1, -4, 8, -1, 1, 1, 2, -6, -2, 1, -1, -3, 4, -2, -8, -1, 10, 4, 1, 7, 6, -1, -8, -2, -4, 1, 0, -3, -14, -2, 1, -4, -1, 6, -16, -1, 1, 6, -4, -1, 2, 4, -2, 3, -6, 1, 6, 4, 4, 8, 4, 5, 18, 1, -1, -1], 'euler11': [1, 1, 0], 'euler13': [1, -6, 13], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, -1, 2], 'euler23': [1, 4, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, 8, 59], 'euler61': [1, -10, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, 16, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, -1, 2], [1, -1, 0], [1, -1, 0], [1, -1, 0], [1, 1, 0], [1, -6, 13], [1, -2, 17], [1, -4, 19], [1, 4, 23], [1, 2, 29], [1, -4, 31], [1, 2, 37], [1, -6, 41], [1, -4, 43], [1, -8, 47], [1, 2, 53], [1, 8, 59], [1, -10, 61], [1, 8, 67], [1, 0, 71], [1, 14, 73], [1, 16, 79], [1, 4, 83], [1, 6, 89], [1, -18, 97]], 'index': 19, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1155/m', 'ModularForm/GL2/Q/holomorphic/1155/2/a/m/1/1', 'ModularForm/GL2/Q/holomorphic/1155/2/a/m'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1155-1.1-c1-0-19', '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': '2-1155-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1914167561883978118, 'z1': {'__RealLiteral__': 0, 'data': '1.26256467364902404033416936943', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20575466
{'Lhash': '1600490866378143893961831163021', 'Lhash_array': ['1600490866378143893961831163021'], 'label': '2-1155-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/a/m'}
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id: 24552013
{'Lhash': '1600490866378143893961831163021', 'Lhash_array': ['1600490866378143893961831163021'], 'label': '2-1155-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/a/m/1/1'}
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id: 96178
{'Lhash': '1914167561883978118', 'Lhash_array': ['1914167561883978118'], 'label': '2-1155-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1155/m'}