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lfunc_lfunctions • Show schema
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{'Lhash': '1427728750761352269253652169195', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 30, '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, -30, 343], [1, -50, 1331], [1, 20, 2197], [1, -10, 4913], [1, -44, 6859], [1, -120, 12167], [1, -50, 24389], [1, 108, 29791], [1, 40, 50653], [1, 400, 68921], [1, 280, 79507], [1, 280, 103823], [1, -610, 148877], [1, -50, 205379], [1, 518, 226981], [1, -180, 300763], [1, -700, 357911], [1, 410, 389017], [1, -516, 493039], [1, -660, 571787], [1, -1500, 704969], [1, 1630, 912673], [1, -450, 1030301], [1, 770, 1092727], [1, -660, 1225043], [1, -1754, 1295029], [1, -310, 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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': 1386953931393188486, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12627939473566469899123802418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96944074776692490227011829391', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48110272126592208948751840479', '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, 30, 0, 0, 0, 50, 0, -20, 0, 0, 0, 10, 0, 44, 0, 0, 0, 120, 0, 25, 0, 0, 0, 50, 0, -108, 0, 0, 0, 150, 0, -40, 0, 0, 0, -400, 0, -280, 0, 0, 0, -280, 0, 557, 0, 0, 0, 610, 0, 250, 0, 0, 0, 50, 0, -518, 0, 0, 0, -100, 0, 180, 0, 0, 0, 700, 0, -410, 0, 0, 0, 1500, 0, 516, 0, 0, 0, 660, 0, 50, 0, 0, 0, 1500, 0, -600, 0, 0, 0, 220, 0, -1630, 0, 0, 0], 'euler11': [1, -50, 1331], 'euler13': [1, 20, 2197], 'euler17': [1, -10, 4913], 'euler19': [1, -44, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -120, 12167], 'euler29': [1, -50, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 108, 29791], 'euler37': [1, 40, 50653], 'euler41': [1, 400, 68921], 'euler43': [1, 280, 79507], 'euler47': [1, 280, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -610, 148877], 'euler59': [1, -50, 205379], 'euler61': [1, 518, 226981], 'euler67': [1, -180, 300763], 'euler7': [1, -30, 343], 'euler71': [1, -700, 357911], 'euler73': [1, 410, 389017], 'euler79': [1, -516, 493039], 'euler83': [1, -660, 571787], 'euler89': [1, -1500, 704969], 'euler97': [1, 1630, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -5, 0], [1, -30, 343], [1, -50, 1331], [1, 20, 2197], [1, -10, 4913], [1, -44, 6859], [1, -120, 12167], [1, -50, 24389], [1, 108, 29791], [1, 40, 50653], [1, 400, 68921], [1, 280, 79507], [1, 280, 103823], [1, -610, 148877], [1, -50, 205379], [1, 518, 226981], [1, -180, 300763], [1, -700, 357911], [1, 410, 389017], [1, -516, 493039], [1, -660, 571787], [1, -1500, 704969], [1, 1630, 912673]], 'index': 14, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/bc/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/bc'], '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-c3-0-14', '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': 1386953931393188486, 'z1': {'__RealLiteral__': 0, 'data': '1.12627939473566469899123802418', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20487559
{'Lhash': '1427728750761352269253652169195', 'Lhash_array': ['1427728750761352269253652169195'], 'label': '2-720-1.1-c3-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/bc'}
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id: 24569836
{'Lhash': '1427728750761352269253652169195', 'Lhash_array': ['1427728750761352269253652169195'], 'label': '2-720-1.1-c3-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/bc/1/1'}