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lfunc_lfunctions • Show schema
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{'Lhash': '1967506257519495960662642234543', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.0387109578734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '2760.1', 'coefficient_field': '1.1.1.1', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, -1, 7], [1, 0, 11], [1, 4, 13], [1, 1, 17], [1, 0, 19], [1, -1], [1, 7, 29], [1, 7, 31], [1, 3, 37], [1, 5, 41], [1, -12, 43], [1, 6, 47], [1, -3, 53], [1, -7, 59], [1, -2, 61], [1, 3, 67], [1, 3, 71], [1, 4, 73], [1, 12, 79], [1, -3, 83], [1, 0, 89], [1, 18, 97], [1, 15, 101], [1, -16, 103], [1, -15, 107], [1, -4, 109], [1, -3, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, -1, 7], 1]], [[[1, 0, 11], 1]], [[[1, 4, 13], 1]], [[[1, 1, 17], 1]], [[[1, 0, 19], 1]], [[[1, -1], 1]], [[[1, 7, 29], 1]], [[[1, 7, 31], 1]], [[[1, 3, 37], 1]], [[[1, 5, 41], 1]], [[[1, -12, 43], 1]], [[[1, 6, 47], 1]], [[[1, -3, 53], 1]], [[[1, -7, 59], 1]], [[[1, -2, 61], 1]], [[[1, 3, 67], 1]], [[[1, 3, 71], 1]], [[[1, 4, 73], 1]], [[[1, 12, 79], 1]], [[[1, -3, 83], 1]], [[[1, 0, 89], 1]], [[[1, 18, 97], 1]], [[[1, 15, 101], 1]], [[[1, -16, 103], 1]], [[[1, -15, 107], 1]], [[[1, -4, 109], 1]], [[[1, -3, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-2760-1.1-c1-0-34', '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/2760/2/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1339986824696182e-60, 0.15422643399651292, 0.3080046877333931, 0.4608432786418465, 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0.7716577656073952, 0.38812213767230475, 0.038069689241130134, -0.25480453023424715, -0.46971349193821144, -0.5900215777999327, -0.6042726007838288, -0.5069406633126963], 'positive_zeros': ['1.55208876733483474880543350638248', '2.45678734659435363805920412583638', '3.69174505077139847729500931269982', '4.68768793196728848930348918445629', '5.34768266143787433439439575299617', '5.99550051910892169798928549074416', '7.05459856331129357303821165007905', '7.43528475342911113043891016231993', '8.488446451034819736442803240922345'], 'prelabel': '2-2760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.694540548112605, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 649189564074279171, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55208876733483474880543350638', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45678734659435363805920412584', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69174505077139847729500931270', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.0387109578734, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -4, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, -1, 0, -7, 0, -7, 0, 0, 0, 1, 0, -3, 0, 4, 0, -5, 0, 12, 0, 1, 0, -6, 0, -6, 0, 1, 0, 3, 0, 0, 0, 0, 0, 7, 0, 2, 0, 1, 0, -4, 0, -3, 0, -1, 0, -3, 0, -4, 0, -1, 0, 0, 0, -12, 0, 1, 0, 3, 0, -1, 0, 7, 0, 0, 0, -4, 0, 7, 0, 0, 0, -18, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, 1, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 7, 29], 'euler3': [1, 1, 0], 'euler31': [1, 7, 31], 'euler37': [1, 3, 37], 'euler41': [1, 5, 41], 'euler43': [1, -12, 43], 'euler47': [1, 6, 47], 'euler5': [1, -1, 0], 'euler53': [1, -3, 53], 'euler59': [1, -7, 59], 'euler61': [1, -2, 61], 'euler67': [1, 3, 67], 'euler7': [1, -1, 7], 'euler71': [1, 3, 71], 'euler73': [1, 4, 73], 'euler79': [1, 12, 79], 'euler83': [1, -3, 83], 'euler89': [1, 0, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -1, 7], [1, 0, 11], [1, 4, 13], [1, 1, 17], [1, 0, 19], [1, -1, 0], [1, 7, 29], [1, 7, 31], [1, 3, 37], [1, 5, 41], [1, -12, 43], [1, 6, 47], [1, -3, 53], [1, -7, 59], [1, -2, 61], [1, 3, 67], [1, 3, 71], [1, 4, 73], [1, 12, 79], [1, -3, 83], [1, 0, 89], [1, 18, 97]], 'index': 34, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2760/f', 'ModularForm/GL2/Q/holomorphic/2760/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/2760/2/a/f'], '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': '2-2760-1.1-c1-0-34', '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': '2-2760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.694540548112605, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 649189564074279171, 'z1': {'__RealLiteral__': 0, 'data': '1.55208876733483474880543350638', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20222077
{'Lhash': '1967506257519495960662642234543', 'Lhash_array': ['1967506257519495960662642234543'], 'label': '2-2760-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2760/2/a/f'}
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id: 24558660
{'Lhash': '1967506257519495960662642234543', 'Lhash_array': ['1967506257519495960662642234543'], 'label': '2-2760-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2760/2/a/f/1/1'}
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id: 40703
{'Lhash': '649189564074279171', 'Lhash_array': ['649189564074279171'], 'label': '2-2760-1.1-c1-0-34', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2760/f'}