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lfunc_lfunctions • Show schema
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{'Lhash': '2570374126385128869837331296665', 'a10': -4, 'a2': 2, 'a3': -3, 'a4': 4, 'a5': -2, 'a6': -6, 'a7': 5, 'a8': 8, 'a9': -18, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.942645581940337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '338.1', 'coefficient_field': '1.1.1.1', 'conductor': 338, 'conductor_radical': 26, 'degree': 2, 'euler_factors': [[1, -2], [1, 3, 27], [1, 2, 125], [1, -5, 343], [1, 13, 1331], [1], [1, -27, 4913], [1, 75, 6859], [1, 187, 12167], [1, 13, 24389], [1, -104, 29791], [1, 423, 50653], [1, 195, 68921], [1, -199, 79507], [1, 388, 103823], [1, -618, 148877], [1, 491, 205379], [1, -175, 226981], [1, 817, 300763], [1, 79, 357911], [1, 230, 389017], [1, -764, 493039], [1, -732, 571787], [1, -1041, 704969], [1, -97, 912673], [1, 809, 1030301], [1, -1288, 1092727], [1, -1277, 1225043], [1, 826, 1295029], [1, -947, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [[[1, 3, 27], 1]], [[[1, 2, 125], 1]], [[[1, -5, 343], 1]], [[[1, 13, 1331], 1]], [1], [[[1, -27, 4913], 1]], [[[1, 75, 6859], 1]], [[[1, 187, 12167], 1]], [[[1, 13, 24389], 1]], [[[1, -104, 29791], 1]], [[[1, 423, 50653], 1]], [[[1, 195, 68921], 1]], [[[1, -199, 79507], 1]], [[[1, 388, 103823], 1]], [[[1, -618, 148877], 1]], [[[1, 491, 205379], 1]], [[[1, -175, 226981], 1]], [[[1, 817, 300763], 1]], [[[1, 79, 357911], 1]], [[[1, 230, 389017], 1]], [[[1, -764, 493039], 1]], [[[1, -732, 571787], 1]], [[[1, -1041, 704969], 1]], [[[1, -97, 912673], 1]], [[[1, 809, 1030301], 1]], [[[1, -1288, 1092727], 1]], [[[1, -1277, 1225043], 1]], [[[1, 826, 1295029], 1]], [[[1, -947, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 32, 'label': '2-338-1.1-c3-0-32', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/338/4/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [-2.007894773247384e-60, 0.22798746326741962, 0.45447305097636154, 0.6779482285406704, 0.8968918080241989, 1.109765260971447, 1.3150099371848762, 1.5110467248402353, 1.696278606474335, 1.869096469826965, 2.0278884252961755, 2.171052765981758, 2.2970145849827426, 2.404245940643997, 2.491289336452211, 2.5567841606741557, 2.5994956138329166, 2.6183455418274364, 2.61244449095754, 2.5811242103692336, 2.5239697495854716, 2.4408502360111233, 2.3319473718352683, 2.19778066385805, 2.0392283956536867, 1.857543371215021, 1.6543625046252861, 1.4317094028127597, 1.1919891890070684, 0.9379749434519378, 0.672785294820229, 0.39985287936767516, 0.12288359298021338, -0.15419320922480773, -0.42728316432418967, -0.6921933437235053, -0.9447057606931208, -1.1806567538105317, -1.3960208010429167, -1.586997080016785, -1.7500968759356867, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 524063714575645683, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02766766009684016505747627745', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49121260591226961096832690557', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69063421333706843351600023443', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.942645581940337, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 338, 'conductor_radical': 26, 'degree': 2, 'dirichlet_coefficients': [1, 2, -3, 4, -2, -6, 5, 8, -18, -4, -13, -12, 0, 10, 6, 16, 27, -36, -75, -8, -15, -26, -187, -24, -121, 0, 135, 20, -13, 12, 104, 32, 39, 54, -10, -72, -423, -150, 0, -16, -195, -30, 199, -52, 36, -374, -388, -48, -318, -242, -81, 0, 618, 270, 26, 40, 225, -26, -491, 24, 175, 208, -90, 64, 0, 78, -817, 108, 561, -20, -79, -144, -230, -846, 363, -300, -65, 0, 764, -32, 81, -390, 732, -60, -54, 398, 39, -104, 1041, 72, 0, -748, -312, -776, 150, -96, 97, -636, 234, -484], 'euler11': [1, 13, 1331], 'euler13': [1, 0, 0], 'euler17': [1, -27, 4913], 'euler19': [1, 75, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 187, 12167], 'euler29': [1, 13, 24389], 'euler3': [1, 3, 27], 'euler31': [1, -104, 29791], 'euler37': [1, 423, 50653], 'euler41': [1, 195, 68921], 'euler43': [1, -199, 79507], 'euler47': [1, 388, 103823], 'euler5': [1, 2, 125], 'euler53': [1, -618, 148877], 'euler59': [1, 491, 205379], 'euler61': [1, -175, 226981], 'euler67': [1, 817, 300763], 'euler7': [1, -5, 343], 'euler71': [1, 79, 357911], 'euler73': [1, 230, 389017], 'euler79': [1, -764, 493039], 'euler83': [1, -732, 571787], 'euler89': [1, -1041, 704969], 'euler97': [1, -97, 912673], 'euler_factors': [[1, -2, 0], [1, 3, 27], [1, 2, 125], [1, -5, 343], [1, 13, 1331], [1, 0, 0], [1, -27, 4913], [1, 75, 6859], [1, 187, 12167], [1, 13, 24389], [1, -104, 29791], [1, 423, 50653], [1, 195, 68921], [1, -199, 79507], [1, 388, 103823], [1, -618, 148877], [1, 491, 205379], [1, -175, 226981], [1, 817, 300763], [1, 79, 357911], [1, 230, 389017], [1, -764, 493039], [1, -732, 571787], [1, -1041, 704969], [1, -97, 912673]], 'index': 32, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/338/4/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/338/4/a/d'], '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': '2-338-1.1-c3-0-32', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-338-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.465718932259434, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 524063714575645683, 'z1': {'__RealLiteral__': 0, 'data': '2.02766766009684016505747627745', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20673553
{'Lhash': '2570374126385128869837331296665', 'Lhash_array': ['2570374126385128869837331296665'], 'label': '2-338-1.1-c3-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/338/4/a/d'}
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id: 24557506
{'Lhash': '2570374126385128869837331296665', 'Lhash_array': ['2570374126385128869837331296665'], 'label': '2-338-1.1-c3-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/338/4/a/d/1/1'}