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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '2039278437368751361', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1591.1949311584592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [19, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 19, 23], 'central_character': '199272.1', 'coefficient_field': '1.1.1.1', 'conductor': 199272, 'conductor_radical': 2622, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 0, 5], [1, 2, 7], [1, 0, 11], [1, 2, 13], [1, -8, 17], [1], [1, -1], [1, 2, 29], [1, -4, 31], [1, 6, 37], [1, 10, 41], [1, -6, 43], [1, 0, 47], [1, 12, 53], [1, 4, 59], [1, 10, 61], [1, -6, 67], [1, 0, 71], [1, -2, 73], [1, -6, 79], [1, 0, 83], [1, -12, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-199272-1.1-c1-0-12', 'leading_term': '8.37367949982', '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/199272/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.826597957768619, 2.208728365518547, 0.6122471085676696, -1.769587031823485, -2.678546627705448, -1.1770272937882, 0.8713858861550781, 0.7591871441790915, -1.518080819434427, -3.017160167989273, -1.865794893459862, 0.06146853168602155, 0.201941329494007, -0.4219026523874462, 0.9878348461611363, 3.536130808385309, 3.160033515827674, -0.4742451140289437, -2.341488630718285, 0.09732468909006951, 2.281838906035976, 0.02548373839929016, -3.138788214006104, -2.083104497888383, 0.6879401202172125, -0.4275804137590662, -3.78246947772753, -3.545597396158977, -0.4999056771591204, -0.07450873833960626, 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3.086005559645158, 4.075205785132854, 0.6234404056534297, 0.2787729787243704, 1.881062566454489, -0.5387655305598114, -1.579006126905771, 2.10749552184348, 1.963521102772749, -1.962269070349346, -0.5075279659689031, 2.303707133492685, -0.7703638927018975, -2.356038757987772, 0.7186097110787779, -0.5748331141366025, -4.040636195836551, -0.653995284733582, 3.154565552543727, 0.4850076350769141, -0.9718073276041319, 1.114285185657504, 0.3465391272123415, -0.7037135155553734, 0.8502811630895752, -0.4430761305589238, -2.098239417901684, 1.77321554544835, 3.864973870507985, 0.3686940913240394, -0.257826445308775, 0.1009931865007833, -5.173727610087797, -6.863503534020202, -0.6344093616732358, 1.13814235893545, -1.992460176488231, -0.03747270533486214, 2.034015322099114, -0.7527405119083795, -0.5539946110018005], 'positive_zeros': ['0.8130823468539019', '1.627991839801812', '2.097629686384629', '2.988058263189855', '3.310763871085168', '3.632424321206991', '4.469003894016630', '4.992930382529547', '5.501653024669449', '6.166795526645995', '6.464828983683244', '7.314663377531442', '7.486244624469352', '8.100420508600434', '8.436416508345738', '9.273201630868792', '9.502057045753533', '9.919343118610112', '10.37488408452877', '10.78832173671951', '11.65338407714834', '11.93323996022786', '12.42597982355693', '12.79848184987562', '13.27419626720178', '13.99831169126569', '14.04600297299284', '14.54788369277741', '15.25744217929028', '15.44163562522256', '15.93217824938602', '16.50146491234799', '16.83739163347293', '17.29500825597239', '17.67768683920866', '18.49623148756458', '18.68315842506385', '19.17524953469154', '19.47034449625094', '19.79973996740973'], 'prelabel': '2-199272-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.889784797093846, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2039278437368751361, 'z1': {'__RealLiteral__': 0, 'data': '0.8130823468539019', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.627991839801812', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.097629686384629', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1591.1949311584592, 'bad_primes': [2, 3, 19, 23], 'central_character': '1.1', 'conductor': 199272, 'conductor_radical': 2622, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 8, 0, 0, 0, -2, 0, 1, 0, -5, 0, 1, 0, -2, 0, 4, 0, 0, 0, 0, 0, -6, 0, -2, 0, -10, 0, 6, 0, 0, 0, 0, 0, -3, 0, 8, 0, -12, 0, 0, 0, 0, 0, -4, 0, -10, 0, -2, 0, 0, 0, 6, 0, 1, 0, 0, 0, 2, 0, -5, 0, 0, 0, 6, 0, 1, 0, 0, 0, 0, 0, -2, 0, 12, 0, 4, 0, 4, 0, 0, 0, -6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, -8, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 6, 37], 'euler41': [1, 10, 41], 'euler43': [1, -6, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 5], 'euler53': [1, 12, 53], 'euler59': [1, 4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -6, 67], 'euler7': [1, 2, 7], 'euler71': [1, 0, 71], 'euler73': [1, -2, 73], 'euler79': [1, -6, 79], 'euler83': [1, 0, 83], 'euler89': [1, -12, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 5], [1, 2, 7], [1, 0, 11], [1, 2, 13], [1, -8, 17], [1, 0, 0], [1, -1, 0], [1, 2, 29], [1, -4, 31], [1, 6, 37], [1, 10, 41], [1, -6, 43], [1, 0, 47], [1, 12, 53], [1, 4, 59], [1, 10, 61], [1, -6, 67], [1, 0, 71], [1, -2, 73], [1, -6, 79], [1, 0, 83], [1, -12, 89], [1, 6, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/199272/m'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-199272-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-199272-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.889784797093846, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2039278437368751361, 'z1': {'__RealLiteral__': 0, 'data': '0.8130823468539019', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2039278437368751361', 'Lhash_array': ['2039278437368751361'], 'factors': ['2-199272-1.1-c1-0-12'], 'label': '2-199272-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/199272/m'}