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lfunc_lfunctions • Show schema
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{'Lhash': '1662979190001996534915280728697', 'a10': 25, 'a2': -5, 'a3': 0, 'a4': 17, 'a5': -5, 'a6': 0, 'a7': 16, 'a8': -45, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.99749255749154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 5]], [29, [1, 29]]], 'bad_primes': [3, 5, 29], 'central_character': '1305.1', 'coefficient_field': '1.1.1.1', 'conductor': 1305, 'conductor_radical': 435, 'degree': 2, 'euler_factors': [[1, 5, 8], [1], [1, 5], [1, -16, 343], [1, -44, 1331], [1, -78, 2197], [1, 18, 4913], [1, 28, 6859], [1, 184, 12167], [1, 29], [1, 224, 29791], [1, -254, 50653], [1, -78, 68921], [1, 260, 79507], [1, 312, 103823], [1, 574, 148877], [1, 180, 205379], [1, 610, 226981], [1, 340, 300763], [1, 296, 357911], [1, -394, 389017], [1, 960, 493039], [1, -908, 571787], [1, -990, 704969], [1, -1234, 912673], [1, 1022, 1030301], [1, 1248, 1092727], [1, -116, 1225043], [1, 826, 1295029], [1, -2206, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 128325114148810375, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31185926918867997148460769775', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85050503471516195393091753506', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46804834126453856833586438062', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 76.99749255749154, 'bad_primes': [3, 5, 29], 'central_character': '1.1', 'conductor': 1305, 'conductor_radical': 435, 'degree': 2, 'dirichlet_coefficients': [1, -5, 0, 17, -5, 0, 16, -45, 0, 25, 44, 0, 78, -80, 0, 89, -18, 0, -28, -85, 0, -220, -184, 0, 25, -390, 0, 272, -29, 0, -224, -85, 0, 90, -80, 0, 254, 140, 0, 225, 78, 0, -260, 748, 0, 920, -312, 0, -87, -125, 0, 1326, -574, 0, -220, -720, 0, 145, -180, 0, -610, 1120, 0, -287, -390, 0, -340, -306, 0, 400, -296, 0, 394, -1270, 0, -476, 704, 0, -960, -445, 0, -390, 908, 0, 90, 1300, 0, -1980, 990, 0, 1248, -3128, 0, 1560, 140, 0, 1234, 435, 0, 425], 'euler11': [1, -44, 1331], 'euler13': [1, -78, 2197], 'euler17': [1, 18, 4913], 'euler19': [1, 28, 6859], 'euler2': [1, 5, 8], 'euler23': [1, 184, 12167], 'euler29': [1, 29, 0], 'euler3': [1, 0, 0], 'euler31': [1, 224, 29791], 'euler37': [1, -254, 50653], 'euler41': [1, -78, 68921], 'euler43': [1, 260, 79507], 'euler47': [1, 312, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 574, 148877], 'euler59': [1, 180, 205379], 'euler61': [1, 610, 226981], 'euler67': [1, 340, 300763], 'euler7': [1, -16, 343], 'euler71': [1, 296, 357911], 'euler73': [1, -394, 389017], 'euler79': [1, 960, 493039], 'euler83': [1, -908, 571787], 'euler89': [1, -990, 704969], 'euler97': [1, -1234, 912673], 'euler_factors': [[1, 5, 8], [1, 0, 0], [1, 5, 0], [1, -16, 343], [1, -44, 1331], [1, -78, 2197], [1, 18, 4913], [1, 28, 6859], [1, 184, 12167], [1, 29, 0], [1, 224, 29791], [1, -254, 50653], [1, -78, 68921], [1, 260, 79507], [1, 312, 103823], [1, 574, 148877], [1, 180, 205379], [1, 610, 226981], [1, 340, 300763], [1, 296, 357911], [1, -394, 389017], [1, 960, 493039], [1, -908, 571787], [1, -990, 704969], [1, -1234, 912673]], 'index': 110, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1305/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/1305/4/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': '2-1305-1.1-c3-0-110', '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': '2-1305-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.774821511432101, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 128325114148810375, 'z1': {'__RealLiteral__': 0, 'data': '1.31185926918867997148460769775', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21120772
{'Lhash': '1662979190001996534915280728697', 'Lhash_array': ['1662979190001996534915280728697'], 'factors': ['2-1305-1.1-c3-0-110'], 'label': '2-1305-1.1-c3-0-110', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1305/4/a/a'}
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id: 24589499
{'Lhash': '1662979190001996534915280728697', 'Lhash_array': ['1662979190001996534915280728697'], 'factors': ['2-1305-1.1-c3-0-110'], 'label': '2-1305-1.1-c3-0-110', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1305/4/a/a/1/1'}