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  • lfunc_lfunctions • Show schema
    {'Lhash': '568886556593107274878732735804,1057802901973055892536074532727,1145104404260294505161237912897', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 380137.2649529088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -3, 3, -1]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': '1.1.1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'euler_factors': [[1], [1], [1, 1, 11, 9, 55, 25, 125], [1, -3, 3, -1], [1, -2, 8, 15, 88, -242, 1331], [1, -3, 6, -51, 78, -507, 2197], [1, 2, 32, 21, 544, 578, 4913], [1, 3, 33, 35, 627, 1083, 6859], [1, -14, 122, -675, 2806, -7406, 12167], [1, 1, 47, -51, 1363, 841, 24389], [1, -3, 57, -159, 1767, -2883, 29791], [1, 3, 81, 199, 2997, 4107, 50653], [1, 0, 90, -9, 3690, 0, 68921], [1, 3, 33, 539, 1419, 5547, 79507], [1, -21, 261, 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'5.64336960870370262541422985991246', '5.83113604901168522371293506515581', '6.27699519968380166799767301529963', '6.42466648685753167697175721979015', '6.50066208125177032786157463633402', '6.97782190832686351118338297680846', '7.11569329307244015908741327496831', '7.17638321416585559093315536405152', '7.51191016797131226657628929786049', '7.73481455194392707853610726745725', '7.890255605359987409104050115988888'], 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 1681322350237589748, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44877236400210296657002500635', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.834459354795878086136421316391', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '0.903328096917343370678510882771', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 380137.2649529088, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 2, 0, 3, 0, 0, 0, -2, 0, -3, 0, 0, 0, 14, 0, -10, 0, 0, 0, -1, 0, 3, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 21, 0, 6, 0, 0, 0, -6, 0, -2, 0, 0, 0, 31, 0, 6, 0, 0, 0, -3, 0, -6, 0, 0, 0, 17, 0, -3, 0, 0, 0, 6, 0, 9, 0, 0, 0, 20, 0, 2, 0, 0, 0, -12, 0, 9, 0, 0, 0, 3, 0, -9, 0, 0, 0], 'euler11': [1, -2, 8, 15, 88, -242, 1331], 'euler13': [1, -3, 6, -51, 78, -507, 2197], 'euler17': [1, 2, 32, 21, 544, 578, 4913], 'euler19': [1, 3, 33, 35, 627, 1083, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -14, 122, -675, 2806, -7406, 12167], 'euler29': [1, 1, 47, -51, 1363, 841, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, 57, -159, 1767, -2883, 29791], 'euler37': [1, 3, 81, 199, 2997, 4107, 50653], 'euler41': [1, 0, 90, -9, 3690, 0, 68921], 'euler43': [1, 3, 33, 539, 1419, 5547, 79507], 'euler47': [1, -21, 261, -2181, 12267, -46389, 103823], 'euler5': [1, 1, 11, 9, 55, 25, 125], 'euler53': [1, 6, 162, 627, 8586, 16854, 148877], 'euler59': [1, -31, 485, -4647, 28615, -107911, 205379], 'euler61': [1, -6, -12, 357, -732, -22326, 226981], 'euler67': [1, 6, 186, 811, 12462, 26934, 300763], 'euler7': [1, -3, 3, -1, 0, 0, 0], 'euler71': [1, -17, 119, -507, 8449, -85697, 357911], 'euler73': [1, 3, 195, 359, 14235, 15987, 389017], 'euler79': [1, -9, 195, -1053, 15405, -56169, 493039], 'euler83': [1, -20, 362, -3447, 30046, -137780, 571787], 'euler89': [1, 12, 216, 1425, 19224, 95052, 704969], 'euler97': [1, 9, 147, 1673, 14259, 84681, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 1, 11, 9, 55, 25, 125], [1, -3, 3, -1, 0, 0, 0], [1, -2, 8, 15, 88, -242, 1331], [1, -3, 6, -51, 78, -507, 2197], [1, 2, 32, 21, 544, 578, 4913], [1, 3, 33, 35, 627, 1083, 6859], [1, -14, 122, -675, 2806, -7406, 12167], [1, 1, 47, -51, 1363, 841, 24389], [1, -3, 57, -159, 1767, -2883, 29791], [1, 3, 81, 199, 2997, 4107, 50653], [1, 0, 90, -9, 3690, 0, 68921], [1, 3, 33, 539, 1419, 5547, 79507], [1, -21, 261, -2181, 12267, -46389, 103823], [1, 6, 162, 627, 8586, 16854, 148877], [1, -31, 485, -4647, 28615, -107911, 205379], [1, -6, -12, 357, -732, -22326, 226981], [1, 6, 186, 811, 12462, 26934, 300763], [1, -17, 119, -507, 8449, -85697, 357911], [1, 3, 195, 359, 14235, 15987, 389017], [1, -9, 195, -1053, 15405, -56169, 493039], [1, -20, 362, -3447, 30046, -137780, 571787], [1, 12, 216, 1425, 19224, 95052, 704969], [1, 9, 147, 1673, 14259, 84681, 912673]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/bv'], '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': '6-9072e3-1.1-c1e3-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1681322350237589748, 'z1': {'__RealLiteral__': 0, 'data': '0.44877236400210296657002500635', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '568886556593107274878732735804,1057802901973055892536074532727,1145104404260294505161237912897', 'Lhash_array': ['568886556593107274878732735804', '1057802901973055892536074532727', '1145104404260294505161237912897'], 'factors': ['2-9072-1.1-c1-0-15', '2-9072-1.1-c1-0-49', '2-9072-1.1-c1-0-61'], 'label': '6-9072e3-1.1-c1e3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/bv'}