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lfunc_lfunctions • Show schema
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{'Lhash': '1365143366610097552349813921484', 'a10': -10, 'a2': -2, 'a3': 0, 'a4': 4, 'a5': 5, 'a6': 0, 'a7': 14, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.930515701549973, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [3, [1]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '270.1', 'coefficient_field': '1.1.1.1', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1, 2], [1], [1, -5], [1, -14, 343], [1, -3, 1331], [1, -47, 2197], [1, 39, 4913], [1, -32, 6859], [1, 99, 12167], [1, -51, 24389], [1, -83, 29791], [1, -314, 50653], [1, 108, 68921], [1, -299, 79507], [1, -531, 103823], [1, -564, 148877], [1, -12, 205379], [1, -230, 226981], [1, 268, 300763], [1, -120, 357911], [1, -1106, 389017], [1, 739, 493039], [1, -1086, 571787], [1, 120, 704969], [1, 1642, 912673], [1, -33, 1030301], [1, 1198, 1092727], [1, 1542, 1225043], [1, 556, 1295029], [1, -1605, 1442897]], 'euler_factors_factorization': [[[[1, 2], 1]], [1], [[[1, -5], 1]], [[[1, -14, 343], 1]], [[[1, -3, 1331], 1]], [[[1, -47, 2197], 1]], [[[1, 39, 4913], 1]], [[[1, -32, 6859], 1]], [[[1, 99, 12167], 1]], [[[1, -51, 24389], 1]], [[[1, -83, 29791], 1]], [[[1, -314, 50653], 1]], [[[1, 108, 68921], 1]], [[[1, -299, 79507], 1]], [[[1, -531, 103823], 1]], [[[1, -564, 148877], 1]], [[[1, -12, 205379], 1]], [[[1, -230, 226981], 1]], [[[1, 268, 300763], 1]], [[[1, -120, 357911], 1]], [[[1, -1106, 389017], 1]], [[[1, 739, 493039], 1]], [[[1, -1086, 571787], 1]], [[[1, 120, 704969], 1]], [[[1, 1642, 912673], 1]], [[[1, -33, 1030301], 1]], [[[1, 1198, 1092727], 1]], [[[1, 1542, 1225043], 1]], [[[1, 556, 1295029], 1]], [[[1, -1605, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-270-1.1-c3-0-4', 'leading_term': '1.604830009725089148286892400300000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 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'2-270-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.991305012342451, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 598446409800812048, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07690823194050113738530199769', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39981267230832172461392147635', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11663740448299432732763403080', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.930515701549973, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 4, 5, 0, 14, -8, 0, -10, 3, 0, 47, -28, 0, 16, -39, 0, 32, 20, 0, -6, -99, 0, 25, -94, 0, 56, 51, 0, 83, -32, 0, 78, 70, 0, 314, -64, 0, -40, -108, 0, 299, 12, 0, 198, 531, 0, -147, -50, 0, 188, 564, 0, 15, -112, 0, -102, 12, 0, 230, -166, 0, 64, 235, 0, -268, -156, 0, -140, 120, 0, 1106, -628, 0, 128, 42, 0, -739, 80, 0, 216, 1086, 0, -195, -598, 0, -24, -120, 0, 658, -396, 0, -1062, 160, 0, -1642, 294, 0, 100], 'euler11': [1, -3, 1331], 'euler13': [1, -47, 2197], 'euler17': [1, 39, 4913], 'euler19': [1, -32, 6859], 'euler2': [1, 2, 0], 'euler23': [1, 99, 12167], 'euler29': [1, -51, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -83, 29791], 'euler37': [1, -314, 50653], 'euler41': [1, 108, 68921], 'euler43': [1, -299, 79507], 'euler47': [1, -531, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -564, 148877], 'euler59': [1, -12, 205379], 'euler61': [1, -230, 226981], 'euler67': [1, 268, 300763], 'euler7': [1, -14, 343], 'euler71': [1, -120, 357911], 'euler73': [1, -1106, 389017], 'euler79': [1, 739, 493039], 'euler83': [1, -1086, 571787], 'euler89': [1, 120, 704969], 'euler97': [1, 1642, 912673], 'euler_factors': [[1, 2, 0], [1, 0, 0], [1, -5, 0], [1, -14, 343], [1, -3, 1331], [1, -47, 2197], [1, 39, 4913], [1, -32, 6859], [1, 99, 12167], [1, -51, 24389], [1, -83, 29791], [1, -314, 50653], [1, 108, 68921], [1, -299, 79507], [1, -531, 103823], [1, -564, 148877], [1, -12, 205379], [1, -230, 226981], [1, 268, 300763], [1, -120, 357911], [1, -1106, 389017], [1, 739, 493039], [1, -1086, 571787], [1, 120, 704969], [1, 1642, 912673]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/270/4/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/270/4/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': 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': '2-270-1.1-c3-0-4', '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': '2-270-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.991305012342451, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 598446409800812048, 'z1': {'__RealLiteral__': 0, 'data': '1.07690823194050113738530199769', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20699574
{'Lhash': '1365143366610097552349813921484', 'Lhash_array': ['1365143366610097552349813921484'], 'label': '2-270-1.1-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/4/a/f'}
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id: 24555406
{'Lhash': '1365143366610097552349813921484', 'Lhash_array': ['1365143366610097552349813921484'], 'label': '2-270-1.1-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/4/a/f/1/1'}