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lfunc_lfunctions • Show schema
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{'Lhash': '4793939304239110647467285993478', 'a10': 5, 'a2': 1, 'a3': 3, 'a4': -7, 'a5': 5, 'a6': 3, 'a7': -24, 'a8': -15, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8850286500861096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -3]], [5, [1, -5]]], 'bad_primes': [3, 5], 'central_character': '15.1', 'coefficient_field': '1.1.1.1', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -1, 8], [1, -3], [1, -5], [1, 24, 343], [1, -52, 1331], [1, -22, 2197], [1, 14, 4913], [1, 20, 6859], [1, 168, 12167], [1, -230, 24389], [1, 288, 29791], [1, 34, 50653], [1, -122, 68921], [1, 188, 79507], [1, -256, 103823], [1, 338, 148877], [1, -100, 205379], [1, -742, 226981], [1, 84, 300763], [1, 328, 357911], [1, 38, 389017], [1, 240, 493039], [1, -1212, 571787], [1, -330, 704969], [1, -866, 912673], [1, 1218, 1030301], [1, 88, 1092727], [1, -36, 1225043], [1, 970, 1295029], [1, -1042, 1442897]], 'euler_factors_factorization': [[[[1, -1, 8], 1]], [[[1, -3], 1]], [[[1, -5], 1]], [[[1, 24, 343], 1]], [[[1, -52, 1331], 1]], [[[1, -22, 2197], 1]], [[[1, 14, 4913], 1]], [[[1, 20, 6859], 1]], [[[1, 168, 12167], 1]], [[[1, -230, 24389], 1]], [[[1, 288, 29791], 1]], [[[1, 34, 50653], 1]], [[[1, -122, 68921], 1]], [[[1, 188, 79507], 1]], [[[1, -256, 103823], 1]], [[[1, 338, 148877], 1]], [[[1, -100, 205379], 1]], [[[1, -742, 226981], 1]], [[[1, 84, 300763], 1]], [[[1, 328, 357911], 1]], [[[1, 38, 389017], 1]], [[[1, 240, 493039], 1]], [[[1, -1212, 571787], 1]], [[[1, -330, 704969], 1]], [[[1, -866, 912673], 1]], [[[1, 1218, 1030301], 1]], [[[1, 88, 1092727], 1]], [[[1, -36, 1225043], 1]], [[[1, 970, 1295029], 1]], [[[1, -1042, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-15-1.1-c3-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/15/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.1394334210350683, 1.1436771531798593, 1.1561968242194793, 1.176360127180836, 1.2031197051430664, 1.235019898043879, 1.2702025025033548, 1.3064117144389673, 1.3410013801423148, 1.370950350468404, 1.3928934444475818, 1.4031760943286251, 1.3979402595116976, 1.3732478218069117, 1.3252455168203612, 1.2503725590381733, 1.1456085007136807, 1.0087545764601404, 0.8387369516983469, 0.6359151454934621, 0.402373790253259, 0.14217129695620337, -0.13848450587028824, -0.43116544940842777, -0.7252878584116386, -1.0083405132012473, -1.26629595191296, -1.484214438748635, -1.647035404758402, -1.7405335242872164, -1.7523968052051826, -1.6733636201077935, -1.4983364231033343, -1.2273742757298982, -0.8664567271704773, -0.4279104875431242, 0.0696002217002941, 0.6015973621465196, 1.138870816369043, 1.6491170463461726, 2.0990794720307364, 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True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 2284576682237788672, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.78175129911665234242031093429', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.30445355770960208718872883735', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.847113744022096962511239249312', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8850286500861096, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 1, 3, -7, 5, 3, -24, -15, 9, 5, 52, -21, 22, -24, 15, 41, -14, 9, -20, -35, -72, 52, -168, -45, 25, 22, 27, 168, 230, 15, -288, 161, 156, -14, -120, -63, -34, -20, 66, -75, 122, -72, -188, -364, 45, -168, 256, 123, 233, 25, -42, -154, -338, 27, 260, 360, -60, 230, 100, -105, 742, -288, -216, -167, 110, 156, -84, 98, -504, -120, -328, -135, -38, -34, 75, 140, -1248, 66, -240, 205, 81, 122, 1212, 504, -70, -188, 690, -780, 330, 45, -528, 1176, -864, 256, -100, 483, 866, 233, 468, -175], 'euler11': [1, -52, 1331], 'euler13': [1, -22, 2197], 'euler17': [1, 14, 4913], 'euler19': [1, 20, 6859], 'euler2': [1, -1, 8], 'euler23': [1, 168, 12167], 'euler29': [1, -230, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 288, 29791], 'euler37': [1, 34, 50653], 'euler41': [1, -122, 68921], 'euler43': [1, 188, 79507], 'euler47': [1, -256, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 338, 148877], 'euler59': [1, -100, 205379], 'euler61': [1, -742, 226981], 'euler67': [1, 84, 300763], 'euler7': [1, 24, 343], 'euler71': [1, 328, 357911], 'euler73': [1, 38, 389017], 'euler79': [1, 240, 493039], 'euler83': [1, -1212, 571787], 'euler89': [1, -330, 704969], 'euler97': [1, -866, 912673], 'euler_factors': [[1, -1, 8], [1, -3, 0], [1, -5, 0], [1, 24, 343], [1, -52, 1331], [1, -22, 2197], [1, 14, 4913], [1, 20, 6859], [1, 168, 12167], [1, -230, 24389], [1, 288, 29791], [1, 34, 50653], [1, -122, 68921], [1, 188, 79507], [1, -256, 103823], [1, 338, 148877], [1, -100, 205379], [1, -742, 226981], [1, 84, 300763], [1, 328, 357911], [1, 38, 389017], [1, 240, 493039], [1, -1212, 571787], [1, -330, 704969], [1, -866, 912673]], 'index': 0, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/15/4/a/a'], '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': '2-15-1.1-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9407596133370679, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2284576682237788672, 'z1': {'__RealLiteral__': 0, 'data': '3.78175129911665234242031093429', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9957282
{'Lhash': '4793939304239110647467285993478', 'Lhash_array': ['4793939304239110647467285993478'], 'label': '2-15-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/4/a/a'}
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id: 24546839
{'Lhash': '4793939304239110647467285993478', 'Lhash_array': ['4793939304239110647467285993478'], 'label': '2-15-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/4/a/a/1/1'}