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lfunc_lfunctions • Show schema
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{'Lhash': '1896465061402644642060525603146', 'a10': -36, 'a2': -3, 'a3': 4, 'a4': 1, 'a5': 12, 'a6': -12, 'a7': -7, 'a8': 21, 'a9': -11, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.974617774862324, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [1, 7]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.1', 'coefficient_field': '1.1.1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'euler_factors': [[1, 3, 8], [1, -4, 27], [1, -12, 125], [1, 7], [1], [1, 38, 2197], [1, -48, 4913], [1, -70, 6859], [1, -12, 12167], [1, 126, 24389], [1, 70, 29791], [1, 358, 50653], [1, -216, 68921], [1, 344, 79507], [1, -390, 103823], [1, -438, 148877], [1, 552, 205379], [1, 830, 226981], [1, 196, 300763], [1, -648, 357911], [1, -16, 389017], [1, 1352, 493039], [1, 90, 571787], [1, -1146, 704969], [1, 70, 912673], [1, -1254, 1030301], [1, 682, 1092727], [1, -384, 1225043], [1, -646, 1295029], [1, 1314, 1442897]], 'euler_factors_factorization': [[[[1, 3, 8], 1]], [[[1, -4, 27], 1]], [[[1, -12, 125], 1]], [[[1, 7], 1]], [1], [[[1, 38, 2197], 1]], [[[1, -48, 4913], 1]], [[[1, -70, 6859], 1]], [[[1, -12, 12167], 1]], [[[1, 126, 24389], 1]], [[[1, 70, 29791], 1]], [[[1, 358, 50653], 1]], [[[1, -216, 68921], 1]], [[[1, 344, 79507], 1]], [[[1, -390, 103823], 1]], [[[1, -438, 148877], 1]], [[[1, 552, 205379], 1]], [[[1, 830, 226981], 1]], [[[1, 196, 300763], 1]], [[[1, -648, 357911], 1]], [[[1, -16, 389017], 1]], [[[1, 1352, 493039], 1]], [[[1, 90, 571787], 1]], [[[1, -1146, 704969], 1]], [[[1, 70, 912673], 1]], [[[1, -1254, 1030301], 1]], [[[1, 682, 1092727], 1]], [[[1, -384, 1225043], 1]], [[[1, -646, 1295029], 1]], [[[1, 1314, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 115, 'label': '2-847-1.1-c3-0-115', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/847/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.5290143006932258e-60, 0.17844524811844553, 0.35449630563178136, 0.5257777108210328, 0.6899520200753567, 0.8447401789385095, 0.9879434204576785, 1.117467026410959, 1.2313461478793215, 1.3277737191571077, 1.4051303198907854, 1.4620156519114744, 1.4972811070911933, 1.5100627183502113, 1.499813615131282, 1.466334954325546, 1.4098041743606293, 1.3307993298885343, 1.230318212451677, 1.109790953045164, 0.9710848390932036, 0.8165001634498033, 0.648756057908811, 0.47096544839484367, 0.286598502153407, 0.09943421602454204, -0.086499885150729, -0.26699961583593657, -0.43776685612555455, -0.5945020297623039, -0.7330048186181045, -0.8492811954511841, -0.9396544720380473, -1.0008777074254256, -1.0302445155940103, -1.0256950677977745, -0.9859139162555361, -0.9104161856960709, -0.799618698861397, -0.6548927306524153, 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'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1572372418808712650, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49604714505811198885013045503', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47206495890642451598397643915', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58141223781575115856465740341', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.974617774862324, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'dirichlet_coefficients': [1, -3, 4, 1, 12, -12, -7, 21, -11, -36, 0, 4, -38, 21, 48, -71, 48, 33, 70, 12, -28, 0, 12, 84, 19, 114, -152, -7, -126, -144, -70, 45, 0, -144, -84, -11, -358, -210, -152, 252, 216, 84, -344, 0, -132, -36, 390, -284, 49, -57, 192, -38, 438, 456, 0, -147, 280, 378, -552, 48, -830, 210, 77, 433, -456, 0, -196, 48, 48, 252, 648, -231, 16, 1074, 76, 70, 0, 456, -1352, -852, -311, -648, -90, -28, 576, 1032, -504, 0, 1146, 396, 266, 12, -280, -1170, 840, 180, -70, -147, 0, 19], 'euler11': [1, 0, 0], 'euler13': [1, 38, 2197], 'euler17': [1, -48, 4913], 'euler19': [1, -70, 6859], 'euler2': [1, 3, 8], 'euler23': [1, -12, 12167], 'euler29': [1, 126, 24389], 'euler3': [1, -4, 27], 'euler31': [1, 70, 29791], 'euler37': [1, 358, 50653], 'euler41': [1, -216, 68921], 'euler43': [1, 344, 79507], 'euler47': [1, -390, 103823], 'euler5': [1, -12, 125], 'euler53': [1, -438, 148877], 'euler59': [1, 552, 205379], 'euler61': [1, 830, 226981], 'euler67': [1, 196, 300763], 'euler7': [1, 7, 0], 'euler71': [1, -648, 357911], 'euler73': [1, -16, 389017], 'euler79': [1, 1352, 493039], 'euler83': [1, 90, 571787], 'euler89': [1, -1146, 704969], 'euler97': [1, 70, 912673], 'euler_factors': [[1, 3, 8], [1, -4, 27], [1, -12, 125], [1, 7, 0], [1, 0, 0], [1, 38, 2197], [1, -48, 4913], [1, -70, 6859], [1, -12, 12167], [1, 126, 24389], [1, 70, 29791], [1, 358, 50653], [1, -216, 68921], [1, 344, 79507], [1, -390, 103823], [1, -438, 148877], [1, 552, 205379], [1, 830, 226981], [1, 196, 300763], [1, -648, 357911], [1, -16, 389017], [1, 1352, 493039], [1, 90, 571787], [1, -1146, 704969], [1, 70, 912673]], 'index': 115, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/847/4/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': '2-847-1.1-c3-0-115', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-847-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.069272789676624, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1572372418808712650, 'z1': {'__RealLiteral__': 0, 'data': '1.49604714505811198885013045503', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20031097
{'Lhash': '1896465061402644642060525603146', 'Lhash_array': ['1896465061402644642060525603146'], 'label': '2-847-1.1-c3-0-115', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/4/a/a'}
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id: 24574181
{'Lhash': '1896465061402644642060525603146', 'Lhash_array': ['1896465061402644642060525603146'], 'label': '2-847-1.1-c3-0-115', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/4/a/a/1/1'}