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lfunc_lfunctions • Show schema
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{'Lhash': '828131791453653246505542348294', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 5], [1, 2, 343], [1, 34, 1331], [1, 68, 2197], [1, -38, 4913], [1, 4, 6859], [1, -152, 12167], [1, -46, 24389], [1, -260, 29791], [1, 312, 50653], [1, 48, 68921], [1, -200, 79507], [1, -104, 103823], [1, -414, 148877], [1, 2, 205379], [1, 38, 226981], [1, -244, 300763], [1, -708, 357911], [1, 378, 389017], [1, -852, 493039], [1, -844, 571787], [1, -1380, 704969], [1, -514, 912673], [1, -702, 1030301], [1, 898, 1092727], [1, -876, 1225043], [1, -602, 1295029], [1, 1350, 1442897]], 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[], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/720/4/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.3788359836206272, 1.3648911633374057, 1.3232007020163594, 1.2541976373148398, 1.1586070230879717, 1.0374504355912735, 0.892051344615356, 0.7240404652276758, 0.5353600261981265, 0.32826576149299547, 0.10532535763584965, -0.1305879238186827, -0.3763076812770872, -0.628393988642673, -0.883161145953099, -1.1367142961521475, -1.3849953660250878, -1.623838473742982, -1.8490345954476424, -2.0564049081898097, -2.2418818367369546, -2.4015964387494644, -2.531970378959521, -2.6298103814102958, -2.6924027231935543, -2.7176050573652217, -2.7039326405820105, -2.65063590565687, -2.557766272743627, -2.426227145642789, -2.257807199950781, -2.055193342830454, -1.8219611120953156, -1.5625407832865306, -1.2821580614863846, -0.986748939288658, 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True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 350340054084381892, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65328079464842706794257121661', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39165222229586030186304490517', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31070307408484721161973864201', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, -2, 0, 0, 0, -34, 0, -68, 0, 0, 0, 38, 0, -4, 0, 0, 0, 152, 0, 25, 0, 0, 0, 46, 0, 260, 0, 0, 0, 10, 0, -312, 0, 0, 0, -48, 0, 200, 0, 0, 0, 104, 0, -339, 0, 0, 0, 414, 0, 170, 0, 0, 0, -2, 0, -38, 0, 0, 0, 340, 0, 244, 0, 0, 0, 708, 0, -378, 0, 0, 0, 68, 0, 852, 0, 0, 0, 844, 0, -190, 0, 0, 0, 1380, 0, 136, 0, 0, 0, 20, 0, 514, 0, 0, 0], 'euler11': [1, 34, 1331], 'euler13': [1, 68, 2197], 'euler17': [1, -38, 4913], 'euler19': [1, 4, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -152, 12167], 'euler29': [1, -46, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -260, 29791], 'euler37': [1, 312, 50653], 'euler41': [1, 48, 68921], 'euler43': [1, -200, 79507], 'euler47': [1, -104, 103823], 'euler5': [1, 5, 0], 'euler53': [1, -414, 148877], 'euler59': [1, 2, 205379], 'euler61': [1, 38, 226981], 'euler67': [1, -244, 300763], 'euler7': [1, 2, 343], 'euler71': [1, -708, 357911], 'euler73': [1, 378, 389017], 'euler79': [1, -852, 493039], 'euler83': [1, -844, 571787], 'euler89': [1, -1380, 704969], 'euler97': [1, -514, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, 2, 343], [1, 34, 1331], [1, 68, 2197], [1, -38, 4913], [1, 4, 6859], [1, -152, 12167], [1, -46, 24389], [1, -260, 29791], [1, 312, 50653], [1, 48, 68921], [1, -200, 79507], [1, -104, 103823], [1, -414, 148877], [1, 2, 205379], [1, 38, 226981], [1, -244, 300763], [1, -708, 357911], [1, 378, 389017], [1, -852, 493039], [1, -844, 571787], [1, -1380, 704969], [1, -514, 912673]], 'index': 3, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/g'], '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': '2-720-1.1-c3-0-3', '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': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 350340054084381892, 'z1': {'__RealLiteral__': 0, 'data': '0.65328079464842706794257121661', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20219558
{'Lhash': '828131791453653246505542348294', 'Lhash_array': ['828131791453653246505542348294'], 'label': '2-720-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/g'}
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id: 24569814
{'Lhash': '828131791453653246505542348294', 'Lhash_array': ['828131791453653246505542348294'], 'label': '2-720-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/g/1/1'}