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lfunc_lfunctions • Show schema
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{'Lhash': '1211945851575562179834688825290', 'a10': 0, 'a2': 5, 'a3': 0, 'a4': 17, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': 45, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 146.02972726420808, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1, -11]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1', 'coefficient_field': '1.1.1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, -5, 8], [1], [1], [1, 3, 343], [1, -11], [1, 32, 2197], [1, -33, 4913], [1, -47, 6859], [1, -113, 12167], [1, -54, 24389], [1, -178, 29791], [1, 19, 50653], [1, 139, 68921], [1, -308, 79507], [1, -195, 103823], [1, -152, 148877], [1, -625, 205379], [1, -320, 226981], [1, 200, 300763], [1, -947, 357911], [1, -448, 389017], [1, 721, 493039], [1, -142, 571787], [1, 404, 704969], [1, 79, 912673], [1, -545, 1030301], [1, -1306, 1092727], [1, -1938, 1225043], [1, 576, 1295029], [1, 1104, 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'primitive': True, 'rational': True, 'root_analytic_conductor': 12.084276033929715, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 668011609730556056, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.956056701552747997786135195036', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.26540546028668896082198846582', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03251736270985456306182652396', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 146.02972726420808, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, 5, 0, 17, 0, 0, -3, 45, 0, 0, 11, 0, -32, -15, 0, 89, 33, 0, 47, 0, 0, 55, 113, 0, 0, -160, 0, -51, 54, 0, 178, 85, 0, 165, 0, 0, -19, 235, 0, 0, -139, 0, 308, 187, 0, 565, 195, 0, -334, 0, 0, -544, 152, 0, 0, -135, 0, 270, 625, 0, 320, 890, 0, -287, 0, 0, -200, 561, 0, 0, 947, 0, 448, -95, 0, 799, -33, 0, -721, 0, 0, -695, 142, 0, 0, 1540, 0, 495, -404, 0, 96, 1921, 0, 975, 0, 0, -79, -1670, 0, 0], 'euler11': [1, -11, 0], 'euler13': [1, 32, 2197], 'euler17': [1, -33, 4913], 'euler19': [1, -47, 6859], 'euler2': [1, -5, 8], 'euler23': [1, -113, 12167], 'euler29': [1, -54, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -178, 29791], 'euler37': [1, 19, 50653], 'euler41': [1, 139, 68921], 'euler43': [1, -308, 79507], 'euler47': [1, -195, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -152, 148877], 'euler59': [1, -625, 205379], 'euler61': [1, -320, 226981], 'euler67': [1, 200, 300763], 'euler7': [1, 3, 343], 'euler71': [1, -947, 357911], 'euler73': [1, -448, 389017], 'euler79': [1, 721, 493039], 'euler83': [1, -142, 571787], 'euler89': [1, 404, 704969], 'euler97': [1, 79, 912673], 'euler_factors': [[1, -5, 8], [1, 0, 0], [1, 0, 0], [1, 3, 343], [1, -11, 0], [1, 32, 2197], [1, -33, 4913], [1, -47, 6859], [1, -113, 12167], [1, -54, 24389], [1, -178, 29791], [1, 19, 50653], [1, 139, 68921], [1, -308, 79507], [1, -195, 103823], [1, -152, 148877], [1, -625, 205379], [1, -320, 226981], [1, 200, 300763], [1, -947, 357911], [1, -448, 389017], [1, 721, 493039], [1, -142, 571787], [1, 404, 704969], [1, 79, 912673]], 'index': 127, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/4/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/2475/4/a/k'], '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': '2-2475-1.1-c3-0-127', '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': '2-2475-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.084276033929715, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 668011609730556056, 'z1': {'__RealLiteral__': 0, 'data': '0.956056701552747997786135195036', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21207115
{'Lhash': '1211945851575562179834688825290', 'Lhash_array': ['1211945851575562179834688825290'], 'label': '2-2475-1.1-c3-0-127', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/4/a/k'}
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id: 24593675
{'Lhash': '1211945851575562179834688825290', 'Lhash_array': ['1211945851575562179834688825290'], 'label': '2-2475-1.1-c3-0-127', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/4/a/k/1/1'}