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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -2, 'Lhash': '2223464541738339132', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 2488.9050908425024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [11, [1]], [23, [1, 1]]], 'bad_primes': [2, 7, 11, 23], 'central_character': '311696.1', 'coefficient_field': '1.1.1.1', 'conductor': 311696, 'conductor_radical': 3542, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1, -1, 5], [1, -1], [1], [1, -1, 13], [1, -2, 17], [1, 5, 19], [1, 1], [1, -10, 29], [1, -8, 31], [1, 2, 37], [1, 7, 41], [1, 6, 43], [1, 3, 47], [1, 6, 53], [1, 0, 59], [1, 12, 61], [1, 13, 67], [1, -8, 71], [1, -1, 73], [1, 0, 79], [1, 11, 83], [1, 15, 89], [1, 7, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-311696-1.1-c1-0-12', 'leading_term': '1.92139878373', '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': 0, 'origin': 'EllipticCurve/Q/311696/ck', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.921398783734587, 0.7739943642536826, -1.856342927254242, -3.871726242980024, -3.436538359798309, -1.086468720534375, 0.4575275988426335, -0.4458814605715639, -2.036270082189052, -1.607633387882575, 0.3197144336616966, 0.7672667967346987, -0.5982302003972946, -0.5291321463263176, 2.083938672836234, 3.423268167447991, 0.8953454056727068, -1.776943248864132, -0.4823362245477814, 1.8498729905188, 0.2658871161196685, -2.93219004974488, -2.068180456889317, 1.329359984556204, 1.386445794381387, -0.8536501834119847, 0.083384967282512, 2.367521607363858, -0.1494650979178569, 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-0.9028561791165745, 1.038013142746679, 2.359222951869757, -1.011662617253049, -1.744905632164575, 0.6570493729808214, 0.1127054415070186, 0.3530033368700326, 2.293805084195863, -1.976538746283375, -7.140007435679779, -3.04762166849301, 1.371340690798249, -1.267978664740603, -1.428513923098556, 1.062910520923282, -1.907911593841116, -3.005133403973556, 2.619163760482385, 3.556078750558116, -0.9314908007083486, -0.9179400760009865, 0.7003645132319237, -0.02749768084287141, 1.113142255316002, 0.7997007540794414, -3.124225102707428, -2.476426006102015, 0.3377091422369172, -2.380339245437667, -2.948322202875518, 1.091503455114901, -0.8438758672336854, -4.304901520155717, -0.5795480795884568, 1.23711827650783, -0.8463139037504489, 2.269934102279072, 3.843872204364518, -1.638587643444077, -2.655231080650015, 0.6627319665150682], 'positive_zeros': ['0.3310799849105199', '1.381199598387125', '1.681609520548743', '2.454899913573238', '2.897999047330838', '3.315576129126732', '4.062697467041165', '4.541081569228332', '5.018842242069073', '5.643227217285344', '6.140605160913146', '6.492295765813287', '6.992556046281533', '7.796769329129799', '8.188413873301900', '8.427750594232914', '8.811657745710268', '9.525888193449050', '9.853871453454984', '10.39915992858354', '10.67738889700463', '11.38382681872425', '11.75647627259990', '12.17060099298078', '12.60706608480728', '13.27720292348462', '13.73767626965048', '13.90955292079542', '14.26270969217799', '14.90134820023078', '15.24201951310143', '15.55510985765557', '16.14078998411884', '16.73356564427530', '17.08399973480114', '17.37305594203886', '17.93532370210732', '18.15419634367893', '18.88227453534979', '19.18087860425005', '19.61284731589814', '19.91745035359281'], 'prelabel': '2-311696-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 49.88892753750578, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2223464541738339132, 'z1': {'__RealLiteral__': 0, 'data': '0.3310799849105199', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.381199598387125', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.681609520548743', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2488.9050908425024, 'bad_primes': [2, 7, 11, 23], 'central_character': '1.1', 'conductor': 311696, 'conductor_radical': 3542, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 1, 0, -2, 0, 0, 0, 1, 0, 1, 0, 2, 0, -5, 0, 1, 0, -1, 0, -4, 0, -5, 0, 10, 0, 8, 0, 0, 0, 1, 0, -2, 0, 1, 0, -7, 0, -6, 0, -2, 0, -3, 0, 1, 0, 2, 0, -6, 0, 0, 0, -5, 0, 0, 0, -12, 0, -2, 0, 1, 0, -13, 0, -1, 0, 8, 0, 1, 0, -4, 0, 0, 0, 0, 0, 1, 0, -11, 0, 2, 0, 10, 0, -15, 0, 1, 0, 8, 0, -5, 0, -7, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -1, 13], 'euler17': [1, -2, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -10, 29], 'euler3': [1, -1, 3], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 7, 41], 'euler43': [1, 6, 43], 'euler47': [1, 3, 47], 'euler5': [1, -1, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 12, 61], 'euler67': [1, 13, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, -1, 73], 'euler79': [1, 0, 79], 'euler83': [1, 11, 83], 'euler89': [1, 15, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, -1, 5], [1, -1, 0], [1, 0, 0], [1, -1, 13], [1, -2, 17], [1, 5, 19], [1, 1, 0], [1, -10, 29], [1, -8, 31], [1, 2, 37], [1, 7, 41], [1, 6, 43], [1, 3, 47], [1, 6, 53], [1, 0, 59], [1, 12, 61], [1, 13, 67], [1, -8, 71], [1, -1, 73], [1, 0, 79], [1, 11, 83], [1, 15, 89], [1, 7, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/311696/ck'], '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': '2-311696-1.1-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': 0, 'prelabel': '2-311696-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 49.88892753750578, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2223464541738339132, 'z1': {'__RealLiteral__': 0, 'data': '0.3310799849105199', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2223464541738339132', 'Lhash_array': ['2223464541738339132'], 'label': '2-311696-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/311696/ck'}