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lfunc_lfunctions • Show schema
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{'Lhash': '1564862793156149919581223647050', 'a10': -20, 'a2': -2, 'a3': 0, 'a4': 4, 'a5': 10, 'a6': 0, 'a7': 7, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 141.2505725537431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [3, [1]], [7, [1, -7]], [19, [1, -19]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1', 'coefficient_field': '1.1.1.1', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[1, 2], [1], [1, -10, 125], [1, -7], [1, 8, 1331], [1, 50, 2197], [1, 114, 4913], [1, -19], [1, -148, 12167], [1, -30, 24389], [1, -304, 29791], [1, 274, 50653], [1, -202, 68921], [1, 116, 79507], [1, -324, 103823], [1, -550, 148877], [1, 628, 205379], [1, 58, 226981], [1, 756, 300763], [1, -216, 357911], [1, 278, 389017], [1, 952, 493039], [1, -1184, 571787], [1, 1542, 704969], [1, 870, 912673], [1, -594, 1030301], [1, 288, 1092727], [1, -276, 1225043], [1, 1714, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 285696684705041662, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23445907955584138301360236049', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26067686156543308061415249168', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82657944644151904778975881842', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 141.2505725537431, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 4, 10, 0, 7, -8, 0, -20, -8, 0, -50, -14, 0, 16, -114, 0, 19, 40, 0, 16, 148, 0, -25, 100, 0, 28, 30, 0, 304, -32, 0, 228, 70, 0, -274, -38, 0, -80, 202, 0, -116, -32, 0, -296, 324, 0, 49, 50, 0, -200, 550, 0, -80, -56, 0, -60, -628, 0, -58, -608, 0, 64, -500, 0, -756, -456, 0, -140, 216, 0, -278, 548, 0, 76, -56, 0, -952, 160, 0, -404, 1184, 0, -1140, 232, 0, 64, -1542, 0, -350, 592, 0, -648, 190, 0, -870, -98, 0, -100], 'euler11': [1, 8, 1331], 'euler13': [1, 50, 2197], 'euler17': [1, 114, 4913], 'euler19': [1, -19, 0], 'euler2': [1, 2, 0], 'euler23': [1, -148, 12167], 'euler29': [1, -30, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -304, 29791], 'euler37': [1, 274, 50653], 'euler41': [1, -202, 68921], 'euler43': [1, 116, 79507], 'euler47': [1, -324, 103823], 'euler5': [1, -10, 125], 'euler53': [1, -550, 148877], 'euler59': [1, 628, 205379], 'euler61': [1, 58, 226981], 'euler67': [1, 756, 300763], 'euler7': [1, -7, 0], 'euler71': [1, -216, 357911], 'euler73': [1, 278, 389017], 'euler79': [1, 952, 493039], 'euler83': [1, -1184, 571787], 'euler89': [1, 1542, 704969], 'euler97': [1, 870, 912673], 'euler_factors': [[1, 2, 0], [1, 0, 0], [1, -10, 125], [1, -7, 0], [1, 8, 1331], [1, 50, 2197], [1, 114, 4913], [1, -19, 0], [1, -148, 12167], [1, -30, 24389], [1, -304, 29791], [1, 274, 50653], [1, -202, 68921], [1, 116, 79507], [1, -324, 103823], [1, -550, 148877], [1, 628, 205379], [1, 58, 226981], [1, 756, 300763], [1, -216, 357911], [1, 278, 389017], [1, 952, 493039], [1, -1184, 571787], [1, 1542, 704969], [1, 870, 912673]], 'index': 97, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/2394/4/a/c'], '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': '2-2394-1.1-c3-0-97', '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': '2-2394-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.884888411497311, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 285696684705041662, 'z1': {'__RealLiteral__': 0, 'data': '1.23445907955584138301360236049', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20982616
{'Lhash': '1564862793156149919581223647050', 'Lhash_array': ['1564862793156149919581223647050'], 'label': '2-2394-1.1-c3-0-97', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/4/a/c'}
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id: 24593491
{'Lhash': '1564862793156149919581223647050', 'Lhash_array': ['1564862793156149919581223647050'], 'label': '2-2394-1.1-c3-0-97', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/4/a/c/1/1'}