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lfunc_lfunctions • Show schema
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{'Lhash': '2388190894767802900064056811552', 'a10': 4, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 4, 'a6': 0, 'a7': 3, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [37, [1, -1]]], 'bad_primes': [2, 3, 37], 'central_character': '666.1', 'coefficient_field': '1.1.1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -4, 5], [1, -3, 7], [1, 5, 11], [1, -3, 13], [1, 3, 17], [1, 7, 19], [1, 9, 23], [1, 0, 29], [1, 2, 31], [1, -1], [1, 6, 41], [1, -4, 43], [1, -10, 47], [1, 3, 53], [1, -4, 59], [1, 2, 61], [1, -6, 67], [1, -12, 71], [1, -13, 73], [1, 6, 79], [1, 5, 83], [1, 11, 89], [1, -6, 97], [1, 10, 101], [1, 2, 103], [1, -1, 107], [1, 7, 109], [1, -10, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, -4, 5], 1]], [[[1, -3, 7], 1]], [[[1, 5, 11], 1]], [[[1, -3, 13], 1]], [[[1, 3, 17], 1]], [[[1, 7, 19], 1]], [[[1, 9, 23], 1]], [[[1, 0, 29], 1]], [[[1, 2, 31], 1]], [[[1, -1], 1]], [[[1, 6, 41], 1]], [[[1, -4, 43], 1]], [[[1, -10, 47], 1]], [[[1, 3, 53], 1]], [[[1, -4, 59], 1]], [[[1, 2, 61], 1]], [[[1, -6, 67], 1]], [[[1, -12, 71], 1]], [[[1, -13, 73], 1]], [[[1, 6, 79], 1]], [[[1, 5, 83], 1]], [[[1, 11, 89], 1]], [[[1, -6, 97], 1]], [[[1, 10, 101], 1]], [[[1, 2, 103], 1]], [[[1, -1, 107], 1]], [[[1, 7, 109], 1]], [[[1, -10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-666-1.1-c1-0-10', '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/666/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.068028744007609, 3.0693844366475207, 3.0706034605737984, 3.0637140468609387, 3.037148686156273, 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2.130931866956803, 1.0452894847896268, -0.24681251907625873, -1.358232540436702, -1.958293393858769, -1.888649866828509, -1.2185491458490663, -0.2192974415815396, 0.7329973553757043], 'positive_zeros': ['1.88395043108710714192663999988388', '2.40265859153889095661502631676180', '4.18804468941342822592597020970513', '5.19848296413414906626093432671400', '5.83968165780663709630491739946241', '6.61856061275031960976062588392760', '7.989549022432806984304290222280140', '8.668480330778590791299654356015789', '9.914305521533027310416702610709548', '10.66123771129793013895319012928144'], 'prelabel': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 407468219468196264, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88395043108710714192663999988', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40265859153889095661502631676', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18804468941342822592597020971', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 4, 0, 3, 1, 0, 4, -5, 0, 3, 3, 0, 1, -3, 0, -7, 4, 0, -5, -9, 0, 11, 3, 0, 3, 0, 0, -2, 1, 0, -3, 12, 0, 1, -7, 0, 4, -6, 0, 4, -5, 0, -9, 10, 0, 2, 11, 0, 3, -3, 0, -20, 3, 0, 0, 4, 0, -2, -2, 0, 1, 12, 0, 6, -3, 0, 12, 12, 0, 13, 1, 0, -7, -15, 0, -6, 4, 0, -6, -5, 0, -12, 4, 0, -5, -11, 0, 9, -9, 0, 10, -28, 0, 6, 2, 0, 11], 'euler11': [1, 5, 11], 'euler13': [1, -3, 13], 'euler17': [1, 3, 17], 'euler19': [1, 7, 19], 'euler2': [1, -1, 0], 'euler23': [1, 9, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -1, 0], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -10, 47], 'euler5': [1, -4, 5], 'euler53': [1, 3, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -6, 67], 'euler7': [1, -3, 7], 'euler71': [1, -12, 71], 'euler73': [1, -13, 73], 'euler79': [1, 6, 79], 'euler83': [1, 5, 83], 'euler89': [1, 11, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -4, 5], [1, -3, 7], [1, 5, 11], [1, -3, 13], [1, 3, 17], [1, 7, 19], [1, 9, 23], [1, 0, 29], [1, 2, 31], [1, -1, 0], [1, 6, 41], [1, -4, 43], [1, -10, 47], [1, 3, 53], [1, -4, 59], [1, 2, 61], [1, -6, 67], [1, -12, 71], [1, -13, 73], [1, 6, 79], [1, 5, 83], [1, 11, 89], [1, -6, 97]], 'index': 10, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/666/g', 'ModularForm/GL2/Q/holomorphic/666/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/666/2/a/g'], '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': '2-666-1.1-c1-0-10', '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': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 407468219468196264, 'z1': {'__RealLiteral__': 0, 'data': '1.88395043108710714192663999988', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12841331
{'Lhash': '2388190894767802900064056811552', 'Lhash_array': ['2388190894767802900064056811552'], 'label': '2-666-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/g'}
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id: 24550123
{'Lhash': '2388190894767802900064056811552', 'Lhash_array': ['2388190894767802900064056811552'], 'label': '2-666-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/g/1/1'}
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id: 29021
{'Lhash': '407468219468196264', 'Lhash_array': ['407468219468196264'], 'label': '2-666-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/666/g'}