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lfunc_lfunctions • Show schema
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{'Lhash': '928920183678523690162766578987', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': 32, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.64183360551102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 3]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '960.1', 'coefficient_field': '1.1.1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, 3], [1, 5], [1, -32, 343], [1, 64, 1331], [1, -6, 2197], [1, -38, 4913], [1, -116, 6859], [1, 120, 12167], [1, -122, 24389], [1, -164, 29791], [1, 146, 50653], [1, 238, 68921], [1, -148, 79507], [1, 184, 103823], [1, 470, 148877], [1, -216, 205379], [1, 806, 226981], [1, -732, 300763], [1, -264, 357911], [1, 638, 389017], [1, -596, 493039], [1, -884, 571787], [1, -930, 704969], [1, -322, 912673], [1, -946, 1030301], [1, -424, 1092727], [1, -1668, 1225043], [1, -1634, 1295029], [1, -1686, 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3.535677466216516, 2.9918578473854347, 2.3908391434736536, 1.7653137259827667, 1.1493853198832193, 0.5766480370242535, 0.0782719239344553, -0.31879193626757285, -0.5933791531719577, -0.7313569904641557, -0.7264689547325828, -0.5807243899054979, -0.30430511051630293, 0.08501013355719839, 0.562873431543479, 1.0997900650861103, 1.662853183813068, 2.2176886514594494, 2.7304940197775935, 3.1700486532141263, 3.5095725860052154, 3.7283198227219065, 3.8128070991240497, 3.757600751954622, 3.565611042287583, 3.2478734362420028, 2.8228281240556954, 2.31514047666057, 1.7541342123739683], 'positive_zeros': ['0.73278881697470875416392467578975', '1.95337281523667189826740675843131', '3.28116982077714151943725928817736', '4.75224787739857953859482080709502', '5.04201457577229651875157116141098', '6.01825301939854062741964293775020', '7.44788265904948076192256868074151', '7.86563623140392392564374489301849', '8.496526431683263931960041255656622', '9.938460894132747897857396785492181'], 'prelabel': '2-960-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.526076906696543, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 670788351283039995, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73278881697470875416392467579', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95337281523667189826740675843', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28116982077714151943725928818', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.64183360551102, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 0, -5, 0, 32, 0, 9, 0, -64, 0, 6, 0, 15, 0, 38, 0, 116, 0, -96, 0, -120, 0, 25, 0, -27, 0, 122, 0, 164, 0, 192, 0, -160, 0, -146, 0, -18, 0, -238, 0, 148, 0, -45, 0, -184, 0, 681, 0, -114, 0, -470, 0, 320, 0, -348, 0, 216, 0, -806, 0, 288, 0, -30, 0, 732, 0, 360, 0, 264, 0, -638, 0, -75, 0, -2048, 0, 596, 0, 81, 0, 884, 0, -190, 0, -366, 0, 930, 0, 192, 0, -492, 0, -580, 0, 322, 0, -576, 0], 'euler11': [1, 64, 1331], 'euler13': [1, -6, 2197], 'euler17': [1, -38, 4913], 'euler19': [1, -116, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 120, 12167], 'euler29': [1, -122, 24389], 'euler3': [1, 3, 0], 'euler31': [1, -164, 29791], 'euler37': [1, 146, 50653], 'euler41': [1, 238, 68921], 'euler43': [1, -148, 79507], 'euler47': [1, 184, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 470, 148877], 'euler59': [1, -216, 205379], 'euler61': [1, 806, 226981], 'euler67': [1, -732, 300763], 'euler7': [1, -32, 343], 'euler71': [1, -264, 357911], 'euler73': [1, 638, 389017], 'euler79': [1, -596, 493039], 'euler83': [1, -884, 571787], 'euler89': [1, -930, 704969], 'euler97': [1, -322, 912673], 'euler_factors': [[1, 0, 0], [1, 3, 0], [1, 5, 0], [1, -32, 343], [1, 64, 1331], [1, -6, 2197], [1, -38, 4913], [1, -116, 6859], [1, 120, 12167], [1, -122, 24389], [1, -164, 29791], [1, 146, 50653], [1, 238, 68921], [1, -148, 79507], [1, 184, 103823], [1, 470, 148877], [1, -216, 205379], [1, 806, 226981], [1, -732, 300763], [1, -264, 357911], [1, 638, 389017], [1, -596, 493039], [1, -884, 571787], [1, -930, 704969], [1, -322, 912673]], 'index': 8, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/4/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/960/4/a/i'], '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': '2-960-1.1-c3-0-8', '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': '2-960-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.526076906696543, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 670788351283039995, 'z1': {'__RealLiteral__': 0, 'data': '0.73278881697470875416392467579', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20540097
{'Lhash': '928920183678523690162766578987', 'Lhash_array': ['928920183678523690162766578987'], 'factors': ['2-960-1.1-c3-0-8'], 'label': '2-960-1.1-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/a/i'}
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id: 24578085
{'Lhash': '928920183678523690162766578987', 'Lhash_array': ['928920183678523690162766578987'], 'factors': ['2-960-1.1-c3-0-8'], 'label': '2-960-1.1-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/a/i/1/1'}