Formats: - HTML - YAML - JSON - 2026-06-07T01:37:08.097581
Query: /api/lfunc_lfunctions/?_offset=0
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{'A10': -2, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': 2, 'A6': 0, 'A7': 3, 'A8': 3, 'A9': 0, 'Lhash': '1919887120900378809', 'a10': [-0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 476.25175277552285, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [47, [1]]], 'bad_primes': [3, 47], 'central_character': '59643.1', 'coefficient_field': '1.1.1.1', 'conductor': 59643, 'conductor_radical': 141, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1, -2, 5], [1, -3, 7], [1, 2, 11], [1, 2, 13], [1, 4, 17], [1, -3, 19], [1, 0, 23], [1, 0, 29], [1, -8, 31], [1, -2, 37], [1, -4, 41], [1, 4, 43], [1], [1, -10, 53], [1, -8, 59], [1, 13, 61], [1, -7, 67], [1, 8, 71], [1, 7, 73], [1, 1, 79], [1, 16, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'id': 7912417, 'index': 9, 'label': '2-59643-1.1-c1-0-9', 'leading_term': '4.8571646402', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/59643/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.103734190288148, 1.578588617834044, 1.06396824943319, -0.1152110823249942, -0.9317221796059203, -0.5131270344196504, 0.761402003386827, 1.339423606981548, 0.2204768045723147, -1.361231125609971, -0.7216862677280482, 3.101641176999474, 7.333398110414677, 7.783458878275175, 3.610271110595894, -1.271578009957413, -2.563798838989201, -0.6051626731542616, 0.631911874732273, -0.6494196980259732, -1.708026404917636, 0.03552799338856644, 2.289011403192047, 0.8772073063122319, -3.516876314995299, -5.427585976089964, -2.244560370965331, 1.908847772095061, 2.200613151450665, 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2.031277249201392, 0.002580181919669091, -4.25726280959136, -3.174908990277758, 0.5940998011630843, 0.2297392881784691, -0.9929782510180466, 1.825000817655488, 3.310183718034798, -0.1900013055620348, -1.2656132421479, 2.711305220813226, 2.681488663378946, -2.887094120775427, -3.399511302954654, 2.382368217229888, 3.755076880690009, -0.3088541520583003, -0.9863161448725424, 1.022879300695188, -0.9196392266856952, -3.302223274190511, -0.4856657889137918, 2.392730718456552, 0.6081242471353299, -0.8699730805185305, 0.5037710972546909, 0.542694108731649, -0.3121587697048379, 1.349055525814418, 2.324673000836422, 0.06561348611478197, -0.5572237474382686, 1.523587927796151, 1.012212417379057, -0.8705914616507774, 0.4831925301386467, 0.9557869605067917, -2.321447647107272, -1.567257001083349, 4.602181410306272], 'positive_zeros': ['0.9762688980812933', '1.606213298407287', '2.280801730181894', '2.813972811853297', '3.922351922395679', '4.572690909370517', '4.909545354254916', '5.496796140221531', '6.055552462686599', '6.868855666805723', '7.480368847086842', '7.881774437544475', '8.480564820062866', '8.852704303152938', '9.482596564900171', '9.965835939265879', '10.32207965867375', '10.83864673522999', '11.53650027070751', '11.82346083661158', '12.68774289164048', '13.23665451502031', '13.58260972241384', '13.96182043248540', '14.56780207187755', '14.90249309123178', '15.74914008080062', '15.97082020963517', '16.87599719190294', '17.19771311900771', '17.51308667847906', '18.01229760002569', '18.27305553440016', '18.67058806787698', '19.44266609583481', '19.79992018750156'], 'prelabel': '2-59643-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.823193001380957, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1919887120900378809, 'z1': {'__RealLiteral__': 0, 'data': '0.9762688980812933', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.606213298407287', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.280801730181894', 'prec': 57}}