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lfunc_lfunctions • Show schema
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{'Lhash': '666084722141910053030259730317', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': -17, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 127.44412561239979, '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': '2160.1', 'coefficient_field': '1.1.1.1', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, -5], [1, 17, 343], [1, -30, 1331], [1, 61, 2197], [1, 120, 4913], [1, -43, 6859], [1, 90, 12167], [1, 90, 24389], [1, 8, 29791], [1, -317, 50653], [1, 30, 68921], [1, -220, 79507], [1, -180, 103823], [1, 630, 148877], [1, -840, 205379], [1, -599, 226981], [1, 107, 300763], [1, -210, 357911], [1, 421, 389017], [1, 353, 493039], [1, -1350, 571787], [1, -1020, 704969], [1, 997, 912673], [1, 960, 1030301], [1, 1181, 1092727], [1, 330, 1225043], [1, -1454, 1295029], [1, -1230, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, -5], 1]], [[[1, 17, 343], 1]], [[[1, -30, 1331], 1]], [[[1, 61, 2197], 1]], [[[1, 120, 4913], 1]], [[[1, -43, 6859], 1]], [[[1, 90, 12167], 1]], [[[1, 90, 24389], 1]], [[[1, 8, 29791], 1]], [[[1, -317, 50653], 1]], [[[1, 30, 68921], 1]], [[[1, -220, 79507], 1]], [[[1, -180, 103823], 1]], [[[1, 630, 148877], 1]], [[[1, -840, 205379], 1]], [[[1, -599, 226981], 1]], [[[1, 107, 300763], 1]], [[[1, -210, 357911], 1]], [[[1, 421, 389017], 1]], [[[1, 353, 493039], 1]], [[[1, -1350, 571787], 1]], [[[1, -1020, 704969], 1]], [[[1, 997, 912673], 1]], [[[1, 960, 1030301], 1]], [[[1, 1181, 1092727], 1]], [[[1, 330, 1225043], 1]], [[[1, -1454, 1295029], 1]], [[[1, -1230, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-2160-1.1-c3-0-13', 'leading_term': '1.469750079196954907008309036170000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, '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/2160/4/a/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4697500791969549, 1.4542637955086193, 1.408008745934793, 1.3315950214931676, 1.2260350087039258, 1.0927365574624033, 0.9334930595457449, 0.7504701091845566, 0.5461883617976215, 0.32350217822885163, 0.08557364310377653, -0.16415842056881932, -0.4220147518393178, -0.6841174794531432, -0.9464375589993448, -1.20484774450735, -1.4551808387939298, -1.6932927683176464, -1.915129818059731, -2.1167991469447927, -2.2946414919930604, -2.445304767539955, -2.5658170823790774, -2.6536575404099585, -2.7068230668328734, -2.7238894191409777, -2.704064506383122, -2.647232156710948, -2.553984546200296, -2.425641634080015, -2.2642561419659324, -2.0726028669028347, -1.8541514275190196, -1.6130219050059766, -1.3539232495795306, 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'rational': True, 'root_analytic_conductor': 11.289115360044816, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 443229111026444755, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52544819686275328985980179722', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97725404593012011966472774398', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72034048943192975053245375747', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 127.44412561239979, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 5, 0, -17, 0, 0, 0, 30, 0, -61, 0, 0, 0, -120, 0, 43, 0, 0, 0, -90, 0, 25, 0, 0, 0, -90, 0, -8, 0, 0, 0, -85, 0, 317, 0, 0, 0, -30, 0, 220, 0, 0, 0, 180, 0, -54, 0, 0, 0, -630, 0, 150, 0, 0, 0, 840, 0, 599, 0, 0, 0, -305, 0, -107, 0, 0, 0, 210, 0, -421, 0, 0, 0, -510, 0, -353, 0, 0, 0, 1350, 0, -600, 0, 0, 0, 1020, 0, 1037, 0, 0, 0, 215, 0, -997, 0, 0, 0], 'euler11': [1, -30, 1331], 'euler13': [1, 61, 2197], 'euler17': [1, 120, 4913], 'euler19': [1, -43, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 90, 12167], 'euler29': [1, 90, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 8, 29791], 'euler37': [1, -317, 50653], 'euler41': [1, 30, 68921], 'euler43': [1, -220, 79507], 'euler47': [1, -180, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 630, 148877], 'euler59': [1, -840, 205379], 'euler61': [1, -599, 226981], 'euler67': [1, 107, 300763], 'euler7': [1, 17, 343], 'euler71': [1, -210, 357911], 'euler73': [1, 421, 389017], 'euler79': [1, 353, 493039], 'euler83': [1, -1350, 571787], 'euler89': [1, -1020, 704969], 'euler97': [1, 997, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -5, 0], [1, 17, 343], [1, -30, 1331], [1, 61, 2197], [1, 120, 4913], [1, -43, 6859], [1, 90, 12167], [1, 90, 24389], [1, 8, 29791], [1, -317, 50653], [1, 30, 68921], [1, -220, 79507], [1, -180, 103823], [1, 630, 148877], [1, -840, 205379], [1, -599, 226981], [1, 107, 300763], [1, -210, 357911], [1, 421, 389017], [1, 353, 493039], [1, -1350, 571787], [1, -1020, 704969], [1, 997, 912673]], 'index': 13, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2160/4/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/2160/4/a/k'], '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': '2-2160-1.1-c3-0-13', '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': '2-2160-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.289115360044816, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 443229111026444755, 'z1': {'__RealLiteral__': 0, 'data': '0.52544819686275328985980179722', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21229009
{'Lhash': '666084722141910053030259730317', 'Lhash_array': ['666084722141910053030259730317'], 'label': '2-2160-1.1-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/4/a/k'}
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id: 24593018
{'Lhash': '666084722141910053030259730317', 'Lhash_array': ['666084722141910053030259730317'], 'label': '2-2160-1.1-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/4/a/k/1/1'}