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lfunc_lfunctions • Show schema
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{'Lhash': '638966818812868624359208174763', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': -34, '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, 34, 343], [1, 18, 1331], [1, -12, 2197], [1, 106, 4913], [1, -44, 6859], [1, 56, 12167], [1, -270, 24389], [1, 204, 29791], [1, -120, 50653], [1, -80, 68921], [1, 536, 79507], [1, -536, 103823], [1, -542, 148877], [1, -174, 205379], [1, -186, 226981], [1, 332, 300763], [1, -132, 357911], [1, 602, 389017], [1, -548, 493039], [1, -492, 571787], [1, 1052, 704969], [1, -482, 912673], [1, -1214, 1030301], [1, 898, 1092727], [1, 1364, 1225043], [1, -218, 1295029], [1, -1386, 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'mu_imag': [], 'mu_real': [], '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/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8659203424773279, 0.8518165510801575, 0.8096514922784319, 0.7398651488090787, 0.6431941414708944, 0.5206762235775885, 0.3736556366504314, 0.20378844389820291, 0.013046778505937584, -0.1962791859751935, -0.42158280957774596, -0.6599473844511458, -0.9081585903844155, -1.1627241306291827, -1.419901503264699, -1.6757346402920776, -1.9260998741118542, -2.1667613759041116, -2.393435860829105, -2.6018659802109, -2.7879014313774624, -2.947586423059028, -3.077251750565458, -3.173609373507792, -3.233847063270666, -3.2557204116873404, -3.237639280181885, -3.178745633195574, -3.0789796530761717, -2.9391310861925746, -2.760872930024326, -2.546774843743335, -2.30029405238771, -2.025742015338001, -1.7282257374499785, 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'2-720-1.1-c3-0', 'primitive': 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': 1287953274846581806, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50405594309490977888213094930', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46175904396309083959813148751', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40383944939936800995550728204', '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, -34, 0, 0, 0, -18, 0, 12, 0, 0, 0, -106, 0, 44, 0, 0, 0, -56, 0, 25, 0, 0, 0, 270, 0, -204, 0, 0, 0, 170, 0, 120, 0, 0, 0, 80, 0, -536, 0, 0, 0, 536, 0, 813, 0, 0, 0, 542, 0, 90, 0, 0, 0, 174, 0, 186, 0, 0, 0, -60, 0, -332, 0, 0, 0, 132, 0, -602, 0, 0, 0, 612, 0, 548, 0, 0, 0, 492, 0, 530, 0, 0, 0, -1052, 0, -408, 0, 0, 0, -220, 0, 482, 0, 0, 0], 'euler11': [1, 18, 1331], 'euler13': [1, -12, 2197], 'euler17': [1, 106, 4913], 'euler19': [1, -44, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 56, 12167], 'euler29': [1, -270, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 204, 29791], 'euler37': [1, -120, 50653], 'euler41': [1, -80, 68921], 'euler43': [1, 536, 79507], 'euler47': [1, -536, 103823], 'euler5': [1, 5, 0], 'euler53': [1, -542, 148877], 'euler59': [1, -174, 205379], 'euler61': [1, -186, 226981], 'euler67': [1, 332, 300763], 'euler7': [1, 34, 343], 'euler71': [1, -132, 357911], 'euler73': [1, 602, 389017], 'euler79': [1, -548, 493039], 'euler83': [1, -492, 571787], 'euler89': [1, 1052, 704969], 'euler97': [1, -482, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, 34, 343], [1, 18, 1331], [1, -12, 2197], [1, 106, 4913], [1, -44, 6859], [1, 56, 12167], [1, -270, 24389], [1, 204, 29791], [1, -120, 50653], [1, -80, 68921], [1, 536, 79507], [1, -536, 103823], [1, -542, 148877], [1, -174, 205379], [1, -186, 226981], [1, 332, 300763], [1, -132, 357911], [1, 602, 389017], [1, -548, 493039], [1, -492, 571787], [1, 1052, 704969], [1, -482, 912673]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/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': '2-720-1.1-c3-0-1', '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': 1287953274846581806, 'z1': {'__RealLiteral__': 0, 'data': '0.50405594309490977888213094930', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19979630
{'Lhash': '638966818812868624359208174763', 'Lhash_array': ['638966818812868624359208174763'], 'label': '2-720-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/a'}
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id: 24569808
{'Lhash': '638966818812868624359208174763', 'Lhash_array': ['638966818812868624359208174763'], 'label': '2-720-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/a/1/1'}