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lfunc_lfunctions • Show schema
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{'Lhash': '1747048780446343675280104196291', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 18, 'a6': 0, 'a7': -7, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.824641761928856, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3]], [7, [1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '336.1', 'coefficient_field': '1.1.1.1', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1, -3], [1, -18, 125], [1, 7], [1, -72, 1331], [1, 34, 2197], [1, -6, 4913], [1, 92, 6859], [1, -180, 12167], [1, 114, 24389], [1, 56, 29791], [1, 34, 50653], [1, -6, 68921], [1, 164, 79507], [1, 168, 103823], [1, -654, 148877], [1, -492, 205379], [1, 250, 226981], [1, -124, 300763], [1, 36, 357911], [1, -1010, 389017], [1, 56, 493039], [1, 228, 571787], [1, -390, 704969], [1, 70, 912673], [1, 1350, 1030301], [1, 2000, 1092727], [1, 696, 1225043], [1, 1114, 1295029], [1, 462, 1442897]], 'euler_factors_factorization': [[1], [[[1, -3], 1]], [[[1, -18, 125], 1]], [[[1, 7], 1]], [[[1, -72, 1331], 1]], [[[1, 34, 2197], 1]], [[[1, -6, 4913], 1]], [[[1, 92, 6859], 1]], [[[1, -180, 12167], 1]], [[[1, 114, 24389], 1]], [[[1, 56, 29791], 1]], [[[1, 34, 50653], 1]], [[[1, -6, 68921], 1]], [[[1, 164, 79507], 1]], [[[1, 168, 103823], 1]], [[[1, -654, 148877], 1]], [[[1, -492, 205379], 1]], [[[1, 250, 226981], 1]], [[[1, -124, 300763], 1]], [[[1, 36, 357911], 1]], [[[1, -1010, 389017], 1]], [[[1, 56, 493039], 1]], [[[1, 228, 571787], 1]], [[[1, -390, 704969], 1]], [[[1, 70, 912673], 1]], [[[1, 1350, 1030301], 1]], [[[1, 2000, 1092727], 1]], [[[1, 696, 1225043], 1]], [[[1, 1114, 1295029], 1]], [[[1, 462, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-336-1.1-c3-0-9', 'leading_term': '3.16769073826026314382354490327000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 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'rational': True, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 211249918550843849, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37817848240816738073129413396', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46611696453234412923932194191', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85577483848919244336909269014', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.824641761928856, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, 18, 0, -7, 0, 9, 0, 72, 0, -34, 0, 54, 0, 6, 0, -92, 0, -21, 0, 180, 0, 199, 0, 27, 0, -114, 0, -56, 0, 216, 0, -126, 0, -34, 0, -102, 0, 6, 0, -164, 0, 162, 0, -168, 0, 49, 0, 18, 0, 654, 0, 1296, 0, -276, 0, 492, 0, -250, 0, -63, 0, -612, 0, 124, 0, 540, 0, -36, 0, 1010, 0, 597, 0, -504, 0, -56, 0, 81, 0, -228, 0, 108, 0, -342, 0, 390, 0, 238, 0, -168, 0, -1656, 0, -70, 0, 648, 0], 'euler11': [1, -72, 1331], 'euler13': [1, 34, 2197], 'euler17': [1, -6, 4913], 'euler19': [1, 92, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -180, 12167], 'euler29': [1, 114, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 56, 29791], 'euler37': [1, 34, 50653], 'euler41': [1, -6, 68921], 'euler43': [1, 164, 79507], 'euler47': [1, 168, 103823], 'euler5': [1, -18, 125], 'euler53': [1, -654, 148877], 'euler59': [1, -492, 205379], 'euler61': [1, 250, 226981], 'euler67': [1, -124, 300763], 'euler7': [1, 7, 0], 'euler71': [1, 36, 357911], 'euler73': [1, -1010, 389017], 'euler79': [1, 56, 493039], 'euler83': [1, 228, 571787], 'euler89': [1, -390, 704969], 'euler97': [1, 70, 912673], 'euler_factors': [[1, 0, 0], [1, -3, 0], [1, -18, 125], [1, 7, 0], [1, -72, 1331], [1, 34, 2197], [1, -6, 4913], [1, 92, 6859], [1, -180, 12167], [1, 114, 24389], [1, 56, 29791], [1, 34, 50653], [1, -6, 68921], [1, 164, 79507], [1, 168, 103823], [1, -654, 148877], [1, -492, 205379], [1, 250, 226981], [1, -124, 300763], [1, 36, 357911], [1, -1010, 389017], [1, 56, 493039], [1, 228, 571787], [1, -390, 704969], [1, 70, 912673]], 'index': 9, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/4/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/336/4/a/l'], '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': '2-336-1.1-c3-0-9', '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': '2-336-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 211249918550843849, 'z1': {'__RealLiteral__': 0, 'data': '1.37817848240816738073129413396', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20723519
{'Lhash': '1747048780446343675280104196291', 'Lhash_array': ['1747048780446343675280104196291'], 'factors': ['2-336-1.1-c3-0-9'], 'label': '2-336-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/4/a/l'}
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id: 24557431
{'Lhash': '1747048780446343675280104196291', 'Lhash_array': ['1747048780446343675280104196291'], 'factors': ['2-336-1.1-c3-0-9'], 'label': '2-336-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/4/a/l/1/1'}